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i Utah Valley University Interactive Math Strategy Teaching Guide A project submitted in partial satisfaction of the requirements for the degree of Master of Education In English as a Second Language by Linda Warnick 2013 ii Utah Valley University Graduate Committee Approval of a project submitted by Linda Warnick This project has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. ________________ ______________________________________ Date Dr. Maureen Andrade, Chair ________________ ______________________________________ Date Dr. Mary Sowder, Committee Member ! iii Acknowledgements I would like to give a huge thanks to my six wonderful children for all the support and encouragement they have given me for the past two years. Becky, Ben, Krista, Thomas, Rachael and Sarah have constantly been there for me and gently urged me to keep going, even when I was so overwhelmed and wanted to put it aside. Also, I would like to give a big thank you, to Dr. Maureen Andrade for her countless hours of reading and rereading my project and encouraging me to keep going. Thank you to Dr. Mary Sowder for her support and encouragement. Thank you to all who have helped and supported me on this journey. iv Abstract With the minority student population growing, the need for teachers’ aides to help with tutoring and helping language learners is also growing. Students need a foundation of language before they can understand concepts being taught in other curricula. As students are identified as needing extra support, they are referred to a tutoring program entitled Double Dosing. The aides teaching the Double Dosing program are not in the same room as the teacher and do not have the teacher support for their instruction. The purpose of this project was to create a resource booklet of lesson examples using five specific mathteaching strategies for the aides to use as a guide when teaching math concepts. The strategies are ToWithBy, Think/Pair/Share, Games, Realia, and Total Physical Response. Each of the lessons in the booklet will have one or more of these strategies implemented into the instruction. The lessons are created using the fourth grade fraction concepts. The research will show the benefits of using these strategies in teaching. It will review research on Double Dosing and the effects on student learning. It will explore the effectiveness and define how best to implement these strategies into small group instruction for ELL students. v Table of Contents !"#$%&'()(************************************************************************************************************************************************(+! ,./0&(,123456(7#%"89&#:234(;3%&'<&3%23(='4'#>(********************************************************************(?! @%#%&>&3%(A(%"&(='/0&>(**************************************************************************************************************************(B! @%#%&>&3%(A(%"&(=.'$1&(**************************************************************************************************************************()B! ,&A232%23(A(C&'>1(*************************************************************************************************************************************())! 9&1&#'D"(E.&1%23(**************************************************************************************************************************************()F! 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Chapter 1 Introduction It is important to understand that math is a language all its own. Phillips (2009) states that individuals need to understand that math symbols represent math concepts just as a reader needs to understand that letters represent sounds. Understanding that the letter sounds put together create words is like understanding that numbers and symbols create math problems. “It is a myth that mathematics is a universal language. For English Language Learners (ELLs), operational mathematics is performed differently around the world” (Gottlieb, 2006, p.66). According to Tomlinson (2003) “The number of English language learners in classrooms across the country is increasing, even in localities where there were virtually no such students just a few years ago.” Due to the increasing volume of ELL students, lessons for preteaching and reteaching math concepts are needed to support the growing diverse population. Math teaching strategies enhance the ability of ELLs to learn math concepts and “make connections between mathematics and other subjects” (Tiedt & Tiedt,1990, p.226). Students also need to understand the connections of math to other subjects and life applications to recognize that math ideas are not just disconnected facts. Helping students understand math and its application can be accomplished by applying strategies and methods that teach students to “question, analyze, evaluate and reflect” the reasons of math language and concepts (Tiedt & Tiedt,1990, p.334). Teachers must find ways to help students actively employ these strategies. 8 The Utah Professional Teacher Standards clearly identify the responsibilities of teachers to ensure students’ academic success. Standard 2 states: “Promoting student learning and enhancing professional practice are the focuses of Utah Professional Teacher Standards.” (see Appendix A). Standard 2 states that teachers need to be “planning curriculum and designing instruction to enhance student learning.” Standard 3 explains the importance of “engaging and supporting all students in learning” (see Appendix A). The purpose of this project is to develop a booklet of teaching strategies and guidelines for the teacher aides to use, which supports these three standards as suggested. Double DosingA Math/Reading Intervention Program A school district in the Western United States has implemented a Double Dosing program as a Response to Intervention (RTI), to address the needs of struggling students, particularly ELL students in its elementary schools. Double Dosing is the name of the program in this particular district. Other names for similar programs are Flex Time or Regrouping. RTI is an intervention process of three tiers of instruction that increasingly intensifies in the instruction level depending on the intervention needs of the student and varies in duration, time and frequency of intervention. Tier 1 is the daily instruction given as whole class instruction. A Tier 2 intervention is given after determining the students that are struggling and reteaching in small groups such as tutoring. The Tier 3 intervention is more intense instruction such as specific teaching through resource classes or special education. Through the Double Dosing program, a Tier 2 intervention is applied as a tutoring session. For this specific intervention, the teaching of math concepts 9 and vocabulary for ELL students in small groups will help enable them to perform at higher levels of proficiency. Most of the elementary students in the district are set up on an A Track or B Track time schedule. Half of the students in each class are the A track students who arrive at 8:00 and leave at 2:15. The remaining half, are on the B Track and arrive at 9:15 and leave at 3:30. These scheduling differences, allow the teacher to have one hour and fifteen minutes of small group time with each track of students. This can be used for language arts, reading and on occasion some math instruction. The Double Dosing program provides identified students with an extra session of learning within a small group setting, by coming early or staying late. The students on the A Track stay after school to attend the 2:153:30 p.m. Double Dosing session. The B Track students participate in the Double Dosing session from 8:009:15 a.m. The Double Dosing sessions run on an every other week schedule (see Appendix C for Time Chart). Grades three and four share teaching aides; therefore the students in grade three attend every day for one week, and then the students in grade four attend daily for the next week. The sessions consist of a week of math instruction followed by a week off, and then a week with reading/language arts instruction. The Double Dosing program preteaches and reteaches math and reading/language arts to struggling students, which includes ELL students. Students are identified as a need for extra instruction and invited by their teachers to attend the program with the permission of their parents. These students are determined as the teachers review through common assessments, the progress and understanding of each student, and then determine which concepts that students may need 10 to be retaught. At the end of each week the teachers determine what concept needs more explanation and which students would best benefit from the extra tutoring sessions. Statement of the Problem Within a classroom, a percentage of ELL students need extra support to understand math and reading concepts. Therefore, teachers must find students’ level of understanding, and differentiate their teaching methods and the amount of support to provide those students. Being aware of the students’ needs and abilities and what they understand is the beginning to effective differentiation (Tomlinson, 2003). Scaffolding the lessons to reach the needs of all learners will also help create an atmosphere of confident learning. The challenge is in creating innovative and engaging lessons that will be effective for ELL students and determining the most effective strategies to enhance that learning. To enhance the students learning can be accomplished by modifying and enhancing instruction, which will give ELL students the basic tools to become successful learners (RichardAmato, 2010). Statement of the Purpose The purpose of this project is to create a booklet with lesson guides, consisting of five math teaching strategies. This booklet will guide the teachers’ aides, who instruct the students participating in the Double Dosing program, how to implement the five math strategies into their teaching styles which will help enhance student learning. The lesson guides will include definitions and stepbystep instructions to show the process of application for each strategy or method use. The five teaching strategies to be applied in 11 the lessons include: ToWithBy (TWB), Think Pair Share (TPS), Games, Total Physical Response (TPR), Realia/Manipulatives. Definition of Terms For the purpose of this study the following terms and definitions will be applied: • Double Dosing: The name of the tutoring intervention program described in this project. • ELL: English Language Learners refers to students who are learning English along with the curriculum. • ESL: English as a Second Language refers to students’ for whom English is a second language. • RTI: Response to Intervention is an approach that aims to reduce the number of children being referred to special education through intensive instruction. The teacher becomes aware of a need to intervene with instruction to help that student understand the concepts before the student gets too far behind. • TWB: ToWithBy is a process of scaffolding, where the teacher instructs the student through direct instruction and modeling and the student watches and listens. Then the teacher works alongside the student and helps. The final step is that the teacher releases the student to work independently to show mastery of the concept. • TPS: Think/Pair/Share is a process where the students think about the question or problem, and then pairs up with a partner to work and then shares their ideas or discovery with the class. 12 • Tier Interventions is a 3 level intervention system. Tier 1 is the daily instruction given as whole class instruction. A Tier 2 intervention is instruction given after determining the students that are struggling and then reteaching these students in small groups, such as tutoring. The Tier 3 intervention is more intense instruction such as specific teaching through resource classes or special education Research Question The question guiding this creative project is: “What different mathematic teaching strategies and methods might be used in the Double Dosing program to enhance student learning?” Overview of Methodology Five math strategies or methods will be implemented into ten lessons to be used as guides for teachers’ aides when helping students’ master math concepts. These lesson guides will be formatted into a booklet form and available as a resource to all aides, especially those in the Double Dosing program, but not exclusively. Chapter 2 Literature Review This literature review will review research on Double Dosing programs and their effects on student learning. It will explore the effectiveness of these types of interventions and define how to best implement math teaching strategies in small group lessons for ELL students. It will also define the five math teaching strategies and ways to implement them through ten sample math lessons. Response to Intervention FaggellaLudy and Wardwell (2011) defined RTI as a response to intervention that occurs through a multitier model of instruction created to focus on the specific needs of an “academically diverse group of students” (p. 34). The most notable characteristics of an RTI are • evidence based instructional practices • progress monitoring to establish rate and level of student learning • assessment of fidelity of implementation; and • universal screening To implement instructional practices that are researchedbased, FaggellaLudy and Wardwell (2011) suggested that RTI “requires substantial instructional intensity to improve outcomes for struggling students” (p. 34). They use a pyramid to provide a visual of how this method can be constructed. An example of this can be found in Appendix B. Although this example was created for reading interventions, the format could also apply for math interventions. 14 Teachers need to create tasks that “involve the introduction or the use of models, representations, tools, or explanations that elaborate or exemplify the mathematics” (Clark & Sanders, 2006, p. 10). Such tasks are associated with good traditional mathematics teaching (Watson & Mason, 2007). Differentiated instruction is responsive instruction. It occurs as teachers become increasingly proficient in understanding their students as individuals, increasingly comfortable with the meaning and structure of the disciplines they teach, and increasingly expert at teaching flexibly in order to match instruction to student needs with the goal of “maximizing the potential of each learner in a given area.” (Tomlinson, 2003, p. 2) Mary Howard (2009) states that if Tier 2 instruction (small group) is given in a classroom, this specific student instruction needs to be provided separately from the general instruction. She also mentions implementing specific times worked into the day and designating those times as Tier 2 interventions by grade level. She further suggests using assistants for small group instruction or the use of support staff such as aides to help monitor and reteach the students. Double Dosing fits this description. The RTI is set up in three tiers of intervention. The purpose of the intervention levels, Tier 2 and Tier 3, are to address the students’ needs and increase the instruction to meet students’ diverse needs. The length of time and frequency of instruction varies accordingly. With the extended day schedule, the schools are already set up for a Tier 2 intervention. The extended day schedule creates an atmosphere conducive to allowing some small group instruction, which is a Tier 2 intervention. Double Dosing will give the students a Tier 2 intervention, which is more intense. The more interventions ELL and other struggling students have, the more opportunities they have to learn and understand the concepts. 15 Strategies/Methods This section will focus on the five math teaching strategies and learning methods for this project. ToWithBy. ToWithBy is a scaffolding strategy, also known as direct instruction, which the teacher shows the students, then guides the students, and then gradually releases students to work on their own as they learn new concepts. Echevarria et al. (2013) described scaffolding as the “gradual release of responsibility” (p. 120). The purpose of this strategy is to provide substantial support in the beginning and then gradually let the student work through a problem independently. The strategy is designed to explicitly teach a concept in stages. In the first stage, the teacher gives all the instruction by talking through each step of the math problem (to). In the next stage, the teacher walks through the problem again, but asks for help from the students (with). This stage is referred to as “with the students.” If the students are successful, they can begin working with other students then gradually work on their own (by). Some students may need to be retaught and start again with the first stage until the concept is understood. The goal is for all students to be independent in their math work (Echevarria, et al., 2013). Think/Pair/Share. The Think/Pair/Share strategy gives students the opportunity to discuss a concept with peers. The strategy is implemented through a question being presented to the students, and then five minutes of think time is allowed for processing and formulating ideas. After the initial five or so minutes of think time, the students are then asked to turn and talk with a partner about their ideas. Speaking and listening skills are great for ELLs. This allows students to verbalize their ideas with another peer before 16 sharing with the class. All the students will have the opportunity to share their ideas with the class and respond with understanding to the teachers’ questions (Echevarria, et al., 2013). Herrell and Jordan (2012) suggest that sharing with peers is a way for language learners to share in a less stressful or inhibited environment (p. 192). “Giving students opportunities to voice their ideas and explain them to others helps extend and cement their learning” (Burns, 2007). Games. Peregoy and Boyle (2008) reiterate that using games in lessons will improve the learning and the attitude of the student. “Games create experiences with language and ideas, and experience is the glue that makes learning stick” (Peregoy & Boyle, 2008, p. 134). As students play games, the level of anxiety with language lessons and more language usage occurs. Games also help students practice, in an innovative way, what they have been taught. Burns (2007) explains that games are an “effective way to stimulate” students practice of the learned skills (p. 6). The word fun is associated with games and catches the interest of students and engages them. “Games can lower anxiety and thus can make acquisition more likely” (RichardAmato, 2010 p. 294). Realia. “Current mathematics pedagogy emphasizes extensive use of manipulatives (realia) to promote discovery of basic mathematics concepts, in a sequence that goes from concrete to pictorial to abstract” (Peregoy & Boyle, 2008). Making math meaningful through real life situations creates greater math understanding (p. 134). Because students are physically manipulating objects, this reduces the language load of an activity. The student can still participate in the activity, even if the language is limited, and demonstrate understanding. Students can master the concept more easily when allowed to use multiple opportunities to practice with handson materials called 17 manipulatives or realia (Echevarria et all, 2012, p. 175). It also helps understanding in connection with the abstract concepts. Total Physical Response (TPR). Asher (1977) is the founder of Total Physical Response, and he compared using TPR to directing a play. “The instructor is the director of a stage play in which the students are the actors” (Brown, 2007). Total Physical Response is an active learning approach. “In TPR, the teacher gradually introduces commands acting them out as she or he says them. Students respond by performing the actions” (Herrell & Jordan, 2012). Peregoy and Boyle (2008) describe TPR as a teaching strategy that combines the action with words as they are being said. As ELL students learn language, they begin first by listening. They verbalize when they are ready and then begin to act out the language and be more involved (RichardAmato, 2010, p. 217). The use of TPR can be very effective when teaching vocabulary associated with a content area (Herrell & Jordan, 2012). Students can use all their senses with TPR. Echevarria et al. (2012) states that through TPR students need to “see, hear, feel, perform, create, and participate in order to make connections” (p. 39). 18 Advantages of Using a Variety of Teaching Strategies Well structured and organized knowledge allows people to solve novel problems and to remember more information than do memorized facts or procedures. Such wellstructured knowledge requires that people integrate their contextual, conceptual and procedural knowledge in a domain (RittleJohnson & Koedinger, 2005, p. 313). Creating lessons that ELL students can apply will create a base knowledge and build their understanding through contextual, conceptual and procedural processes by “targeting their weakness in student learning” (Lewis, 2002). Handson activities and interactive stories use more senses for deeper learning. Lewis (2002) talks about two of the five strategies that enhance student learning which are: • Realia: Giving hands on experiences and aiding children’s understanding. The use of real objects and tools help with the explanation and gives students the opportunity to experiment with practical materials for better understanding. • Think/Pair/Share: Learning from peers through sharing, discussion and working together. Teaching others enhances students’ own understanding through verbalization and explaining their understanding. Having a handson and logical approach to teaching math gives students a tool to assist their understanding of why and how the concepts apply. This approach to teaching is useful for visual learners (Clarke & Sanders, 2006). By intervening and supporting struggling students early, we can get most students to grade level within the regular classroom. More intense instruction is given to those 19 who need second and third tier interventions to accelerate their learning (Howard, 2009, p. 3) Tomlinson (2003) reminds teachers that we “want students in our classrooms to experience affirmation, contribution, power, purpose, and challenge” (p. 11). She also explained that the “premise of differentiation is that while students have the same basic needs, those needs will manifest themselves in different ways, depending on student gender, culture, general life experience, talents, interests, [and] learning preference” (p. 12). Using a variety of methods and materials to “support different learning styles and multiple intelligences” (Echevarria et al. 2013) helps students make connections through feeling, hearing, seeing and doing. “Howard Gardner’s work around multiple intelligences has had a profound impact on thinking and practice in education” (Smith, 2002, 2008). Palmer (2001) mentioned several reasons teachers agree with Gardner’s theories The theory validates educator’s everyday experience: students think and learn in many different ways. It also provides educators with a conceptual framework for organizing and reflecting on curriculum assessment and pedagogical practices. In turn this reflection has led many educators to develop new approaches that might better meet the needs of the range of learners in their classrooms (p. 213). Challenges Some of the challenges for tiered instruction are related to the time it takes to create and put in the extra work for the lessons (Clarke & Sanders, 2003). Clarke and 20 Sanders listed the following challenges and reasons for teachers not implementing these math strategies: • Organization and provision of all materials • The time taken to plan and organize a good lesson • Finding appropriate activities • Clarity of the model and extending the model into a lesson with meaningful independent/group work. Another challenge would be the lack of experience of an aid teaching the materials. Aides are usually parents that would like to be involved in the school where their children attend and want some part time work. With this inexperience, comes the task of training these aids on the skills needed to help students who are struggling. This project will help eliminate some of these challenges. Each of the aides will be trained to apply the strategies and methods into their teaching styles. The booklet will be a guide for them to use as they implement the strategies into their teaching. It will also have clear definitions of each strategy and examples lessons for them to follow. The organization of the materials will be prepared and given to the aides, so they will not need to gather them nor will they need to search for appropriate activities. The activities and materials for the lessons, that the aides will be teaching, will be provided by the teachers’ from the third and fourth grade teams. 21 Chapter 3 Methodology This chapter is an overview of the methods to be used for creating the booklet with the strategies and learning methods. It will address who will be using the booklet, what is the purpose of the booklet and the availability of the booklet. Project Design This study is a creative project designed as a tool to support aides in incorporating five specific teaching strategies or methods into their lessons to enhance student learning. The following strategies and methods have been identified: ToWithBy, ThinkPair Share, Games, Realia or Manipulatives, Total Physical Response (TPR). Each lesson will consist of one or more of these specific strategies. The purpose, use and benefits for teaching each of these strategies and learning methods were described in the literature review. Each of these strategies and learning methods were defined and will be implemented into lesson guides, which will be developed into a booklet form to show how each of the strategies or learning methods can be taught and applied to math concepts. The purpose is to help aids understand how to replicate each strategy for teaching any math standard or concept. By creating this booklet, the aids will have a guide for examining the steps for teaching different math concepts and the application as to how the strategy may be implemented. Each lesson guide will have stepbystep instructions to guide the aid through an entire lesson, using that specific strategy. The booklet will be available in 22 each classroom along with the teaching tools where each of these aids will be teaching. The guides will be available for all aids to use. Context The context of this study is directed to aides working with elementary age students. The student ages range from eight to tenyearsold. The class sizes are small, with five to ten students at a time. This allows small group instruction and individualized help. The population of this school is approximately 1,000 students with the majority being Caucasian, which creates a low population of ELL students. The languages represented within the school are English, Tagalog and Spanish. Because of the low ethnic differences and language variance, aides will have struggling students who are native speakers of English as well as ELL students. The aides assigned to work in the school are determined as to the needs of the students. The needs are determined through the students with IEP assessments. Some of these may be medical needs, behavioral help, students with autism and other various challenges that require a little support in the class or to work directly with the student. Therefore the aides may differ from year to year. There is no specific qualification such as a degree or experience. The applicants are usually parents of students of the school, but if they have worked at the school in previous years they are usually hired again. The experience level of the aides varies, with some having teaching degrees and others with no previous experience or degree. The district determines according to student needs, 23 how many aides the school qualifies for. These aides are then asked to teach the Double Dosing sessions and help tutor the students. The classroom for the aides is a separate room from the classroom for the core teachers. The aides are alone teaching these students, thus the need for this booklet to give them some assistance and examples. The small group aides will be trained as to how to teach, how to use the guidebook and the use of the tools and materials in the guidebook. ! ! 24 Chapter 4 Unit Design Double Dosing is an intervention program designed by the district to tutor ELL and struggling students. The instructors for this program are aides that work at the school. Some have little or no background in teaching. The following booklet is designed to support the aides by giving them a guide of teaching strategies. The lessons examples in this booklet are designed using fractions as the unit of study. The strategies are listed at the beginning of the booklet and also suggested in the objective for each lesson. Upon completion of the Double Dosing Instruction Booklet: Teaching Strategies for Aides, the aides should feel empowered to create lessons of their own and have the tools to tutor the students in their class. Unit Content This next section is an explanation of the lessons plans within the Double Dosing Instruction Booklet: Teaching Strategies for Aides. Lesson 1: Fraction Vocabulary. The objective of this lesson is for the aides to understand the procedures and purpose of using the ToWithBy strategy of instruction. This strategy is used throughout most of the lessons. The aides are to instruct by example, watch for understanding, then work together with the students and gradually release the students to work on their own. It is important to start with vocabulary when instructing language learners. Teaching and understanding the terms is important to build a base knowledge for the students to understand the unit. 25 Lesson 2: Creating Fractions. The objective for this lesson is to teach the aides the purpose and procedures for implementing the Think/Pair/Share strategy along with the Total Physical Response method of learning. The Think/Pair/Share portion of this lesson is designed for the students to first think about whole items that are easily divided into fractions, and then discuss together in small groups about how the whole items that can be divided into fractions. After discussing with partners and creating a list of ideas, they are to share with the class. The students will be paired with a different partner and will then create a list of ways fractions are used in everyday life. For the Total Physical Response portion of the lesson the students will create pairs and they will then pantomime to the class who will try to guess what the situation is the students are acting. Lesson 3: Creating Fraction Sets. The objective for the aides in this lesson will be incorporating Realia, ToWithBy and the Think/Pair/Share methods into their teaching. The Realia are objects that come in sets and are items the students would recognize and use in their daily lives. The ToWithBy is the instruction given by the aides, during the introduction of the lesson, using examples of what fraction sets are. The Think/Pair/Share strategy has the students working together discovering the fractional parts of the sets. The students will be introduced to sets through objects that come in sets, such as eggs, crayons, table settings, ball teams or any other sets determined. The students will then be divided into small groups and given one set of items to be divided among the group. The instruction for how to create a fraction will be given at the beginning of the activity through the use of Realia, such as a set of blocks or buttons or other items, then 26 show the students how to create a fraction by knowing the whole number of the set and what the fraction of the set is after being divided. Lesson 3 includes two activities that incorporate Realia. These two activities include first using pictures to create pizzas and second dividing graham crackers into fractions. Lesson 4: Review of Fractions. To help students review fractions, the aides will implement Total Physical Response into their teaching. The students will go outside or into a gym where there is a line of numbered squares on the ground. An explanation of how to prepare these squares has been included in the lesson format. The students will be asked to stand in these square boxes, as they students listen to specific commands. In this lesson the teacher commands might instruct students who are blonde, or a girl or on an even number. If the command applies to them, they are to step out of the box. The students will calculate the fraction of students standing outside the boxes and those standing in the boxes. Lesson 5: Benchmark Fractions. This lesson the aides will be using ToWith By, Think/Pair/Share and Realia as methods of instruction. The aides will read the book Fraction Fun by David A. Adler. Within the Fraction Fun book there are activities to do using paper plates, rulers and crayons to create fractions. The students will also be learning a new vocabulary word. As part of the Think/Pair/Share the students will discuss with a partner what their idea of what a “benchmark” fraction might be. A fraction such as onehalf would be the benchmark to use for comparing fractions to determine if the fraction is less than or greater than the onehalf benchmark. After sharing and some discussion, the aide will give the original 27 definition and then observe to see if the students understand how to do the vocabulary page on their own. The aides may assist as needed. The use of the plastic fraction plates will be an activity to show their understanding of 1/2, 1/3, 1/4, 2/3 and 3/4 fractions. This activity enforces the understanding through Realia. Lesson 6: Line Plot Fractions. Realia, ToWithBy and Think/Pair/Share are again implemented into this lesson. For the Realia portion of this lesson, the students are given a bag of buttons. They must measure the width of each button and record the measurements on a line plot from smallest to largest. Think/Pair/Share will be demonstrated in the beginning of the lesson as the students share with a partner ways they used fractions during the week. They are encouraged to use the vocabulary words they have been learning. They will then share their experiences with the class. The ToWith By method is demonstrated as the aide launches into the activity by showing the students how to measure, then practice with them, then the aide will watch to see if all the students understand and support those students that need extra support. Lesson 7: Comparing and Ordering Fractions. The aides will be implementing Games along with Think/Pair/Share and Realia in this lesson. A new vocabulary word is introduced and the students will think about the meaning of what an equivalent fraction might be and follow with a discussion with a partner, after which they will share in a class discussion the final definition. The students will create another vocabulary page for this new term after the class discussion. The class will then be given paper fraction “tiles” which they will cut out and use to find equivalent fractions. As the students launch into this activity, the aide may show 28 them a simple example such as two halves make one whole. The aide will then encourage the students to find as many fraction equivalents as they can on their own. Lesson 8: Comparing and Ordering Fractions. This lesson will be implemented through a board game. The aide will give the directions for the game and a quick example and then allow time questions for greater understanding. The students will then be divided into groups of four. The students will roll a set of die. The greater number on the dice is the denominator and the lesser number on the dice is the numerator. The purpose of this game is to help the students understand the value of the fraction by determining if the created fraction is greater or less than the benchmark fraction. Each group will play their game about 2030 minutes, then the students will be regrouped and play again with another group of students. The aide will rotate through the groups to help and assess the understanding of comparing and ordering fractions. Lesson 9: Fraction Review. The games in this lesson are used as a review to show understanding and application of the fraction concepts. There will be three different games and the aide will give the directions fore each game and a quick example of each and then allow questions from students for understanding. The students will then be divided into groups of four. Each group will play their game about 1520 minutes. They will then rotate to another game. This gives the students the opportunity to play all three games and reinforce the concepts through three different games. The aide is also free to walk around and observe to see who understands the fraction concepts and assist those who need help Lesson 10: Fraction Situations. Within this lesson the aides will be using Realia and Total Physical Response in their instruction. The lesson will start with the students 29 all having a set of tiles and some graph paper. The aide will read the book Spaghetti and Meatballs for All! written by Marilyn Burns. In the story, as different guests come, the tables are rearranged to accommodate the new guests. With each new arrangement the dinner plans become frustrated. As the story is being read, the students are to arrange the tiles as Mrs. Comfort arranges and rearranges the tables in the story. After the story, the students are to create and perform a story or scenario about fractions. The aide will have props available for them to use. This allows the students to use language skills, vocabulary and give some life examples of how fractions are used in everyday lives. ! ! 30 Chapter 5 Discussion Double Dosing Instruction Booklet: Teaching Strategies for Aides is a guide, intended to be used by the aides within their tutoring times to help improve their teaching strategies. The researcher is a teacher who was given the responsibility to create lessons for the aides to teach the 4th grade Double Dosing students (students that have been identified as needing learning interventions for math). The inability of the researcher to be in the classroom to help the aides has prompted the design of this project. The purpose is to give the aides a set of teaching strategies to guide them in their instruction. This booklet will be available to all aides for instruction and guidance. The aides change from year to year, so with this booklet, the aides will feel better equipped to teach the students. The Double Dosing Booklet: Teaching Strategies for Aides will empower them to use various instructional methods within lessons. Implementation The booklet will be provided to all aides, during the 20132014 school year, as guides for their instruction methods. The aides will have a meeting at the beginning of the school year with instructions for the use of the booklet. The booklet provides lessons with examples of how to implement the five teaching strategies, ToWithBy, Think/Pair/Share, Games, Realia/Manipulatives and Total Physical Response, within the aides teaching style. The booklet is designed with the fourth grade math curriculum in mind and is designed to teach the beginning of the fraction unit. 31 Limitations This booklet was created after the school year finished; therefore the ability to instruct and practice with an aide was impossible. The implementation of this booklet is crucial for the researcher to know if there are areas that need clarification or changes that need to be made. The implementation of this booklet would have be more ideally introduced before school dissembled for the summer break to have given the aides the ability to come into the new year better prepared. With the new Core Standards being set, students that were struggling to keep up may now be a little further behind. The need for the aides to be familiar with the teaching strategies is important to better enhance student learning. Further Research This booklet is focused on the math portion of instruction. The researcher would like to create a similar booklet with strategies for implementing reading instruction. Within the Double Dosing program students are tutored both reading and math; therefore, a reading strategy guide would have been beneficial. Conclusion Parents, teachers and aides have the same goal for the students, which is to help all students feel successful. Creating an atmosphere of learning in all circumstances is important for the student. The goal of this booklet is to train and support the aides to create the best learning environment for each of the students that come through the Double Dosing program. References Burns, M. (2007). Nine ways to catch kids up. Educational Leadership, 65(3), 1621. Cavanagh, S. (2006). Students doubledosing on reading and math. Retrieved from http://www.Edweek.org Chassels, C., & Melville, W. (2009). Collaborative, reflective, and iterative Japanese lesson study in an initial teacher education program: Benefits and challenges. Canadian Journal of Education 32(4), 734761. Clark, B., & Sanders, P. (2009). Making the mathematics explicit as we build tasks into lessons. Australian Primary Mathematics Classroom, 14(2),1014. Echevarria, E., Vogt, M.E., & Short, D. J. (2013). Making content comprehensible for English Learners: The SIOP model (4th ed.). Boston, N.Y: Pearson. FaggellaLuby, M., & Wardwell, M. (2011). RTI in a middle school: findings and practical implications of a tier 2 reading comprehension study. Learning Disability Quarterly, 34, 3549. Fox, L., Carta, J., Strain, P., Dunlap, G., & Hemmeter, M. L. (2009). Response to intervention and the pyramid model. (pp. 110). Tampa, FL. Retrieved from http://www.challengingbehavior.org/do/resources/documents/rti_pyramid_web Gottlieb, M. (2006). Assessing English language learners: Bridges from language proficiency to academic achievement. Thousand Oaks, CA: Corwin Press. Herrell, A. L., & Jordan, M. (2012). 50 strategies for teaching English language learners. (4th ed.) Boston, MA: Pearson. 33 Howard, M. (2009). RTI from all sides: What every teacher needs to know. Portsmouth, NH: Heineman. Retrieved from http://pzweb.harvard.edu/Research/SUMIT.htm Lewis, C. (2002). Does lesson study have a future in the United States? Nagoya Journal of Education and Human Development, 1(123)1. Palmer, J., (2001). Fifty modern thinkers on education. From Piaget to the present. London: Routledge. Peregoy, S. F., & Boyle, O. F. (2008). Reading, writing, and learning in ESL. Boston, Boston, MA: Pearson. Phillips, D. C. K., Bardsley, M. E., Bach, T., & GibbBrown, K. (2009). “But I teach math!” The journey of middle school mathematics teachers and literacy coaches learning to integrate literacy strategies into the math instruction. Education, 129(3), 467472. RichardAmato, P. A. (2010). Making it happen. From interactive to participatory language teaching: Evolving theory and practice. (4th ed.). White Plains, NY: Pearson. RittleJohnson, B., & Koediner, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23(3), 313349. Smith, M. K. (2002). Howard Gardner and multiple intelligences: The encyclopedia of informal education. Retrieved from http://www.infed.org/thinkers/gardner.htm Tiedt, P. L., & Tiedt, I. M. (1990). Multicultural teaching: A handbook of activities, information, and resources. (3rd ed.). Needham Heights, MA: Allyn and Bacon. 34 Tomlinson, C. A. (2003). Fulfilling the promise of the differentiated classroom. Alexandria, VA: Association for Supervision and Curriculum Development. Watson,A., & Mason, J. (2007). Takenasshared: A review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education, 10(46), 205215. 35 Appendix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ppendix B ! 37 Appendix C Double Dosing takes place during each track time. The B Track students will arrive for Double Dosing during the A Track arrival time as if they are attending a before school Tutoring session. They are not taught in the regular classroom, but are in a different class with an aide. The A Track students will be attending at the end of their school day as if it is an after school Tutoring program. ! ! "!#$%&'!()*+,).! "$$/0,!12334(5%66! 7$8*9!:.)$*&)/8! 1233;<2=>?! @!#$%&'!()*+,).! "$$/0,!<2=>!4A8$,! #,%&B/C!D/)B!"66! ()*+,).! <2=>;E2=>?! "!#$%&'!F/.5/..%6! E2=>!4(5%66!7$8*9! :.)$*&)/8! E2=>;G2G3?!! 38 Appendix D (The strategies booklet and lesson guides.) ! ! 39 Created by Linda Warnick 40 Teaching Strategies ToWithBy: ToWithBy is a scaffolding strategy, also known as direct instruction, that shows and guides the students, and then gradually releases students to work on their own as they learn new concepts. The TO portion is your instruction to the students. The WITH portion is you and the students do the problem/activity together and the BY portion is the students are working on their own. If the student struggles during the BY, then stop and go back to the WITH and support them till they can work on their own. Think/Pair/Share. This strategy gives students the opportunity to discuss a concept with peers. The strategy is implemented through a question being presented to the students, and then 5 minutes of think time is allowed for processing and formulating ideas. After the five or so minutes of think time, the students are then asked to turn and talk with a partner (pair) about their ideas. After a short discussion the pair will then Share with the class. Games: These are specific games or activities that are guided and specific to the lessons being taught. The games are math specific. Realia: This task activity is the use of manipulatives to promote discovery of basic mathematics concepts, in a sequence that goes from concrete to abstract. This is the use of real life situations and objects to create life application. Total Physical Response (TPR): This is an active learning response; this teaching strategy involves combining actions with the words being said. Students are able to use all their senses by preforming, creating and participating in order to make connections. 41 Fraction Unit Lesson 1: Fraction Vocabulary I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the To WithBy method of instruction through creating the vocabulary pages using the vocabulary terms needed for the Fraction Math Unit. II. Preparation and Materials needed: ! The book Full House: An Invitation to Fractions by Dayle Ann Dodds. ! Definition of each of the words available at the end of the lesson unit. ! Vocabulary word strips, provided at the end of this lesson, should be printed and ready to use as a visual for the students to view as they write the words. ! Vocabulary pages, provided also at the end of this lesson, should be printed and ready for use for this lesson. There should be one page per term, for each student. Also extra pages for example use. (It would be good to create an individual vocabulary booklet for each student to use throughout the entire year for math.) III. Technology Use: ! No technology is required. If a document camera were available, this lesson would be better understood if the aide showed the 42 students how to create the Vocabulary Page on the actual artifact. If there is none available, quickly creating a draft on the board will work also. IV. Instructional Procedures: ! Place all vocabulary word strips on the board where all students are able to see them easily. ! Begin by reading Full House: An Invitation to Fractions by Dayle Ann Dodds. ! If a document camera is available, show the Math Vocabulary page on the board and proceed to show the students how to fill in the page. If there is not a document camera, draw the page on the board as an example. ! This is the “TO” section of the ToWithBy strategy. Write the word “fraction” in the Vocabulary Word box saying the word out loud and spelling fraction out loud as your write. Without asking for students’ response, think out loud about the definition of the word fraction, using the story as your background knowledge. Relate story examples to show the relationship to the fraction. Now in the Describe box, tell what you think the meaning of the word fraction might be according to the story. In the Example box, write an example of a fraction from the story. As you are writing, keep thinking out loud as an example for the students to think and create. In the Draw a Picture box, draw a 43 simple picture of a fraction talked about in the book to represent the fraction. Using the definition from the end of the lesson resource, state the technical definition and say it again as you write the words in the Definition box on the Vocabulary page. ! The “With”. Hand each student a Math Vocabulary page (or booklet if created). Step by step have them do the same as you did by writing the word fraction in the Vocabulary Box, saying the word as they write. Then have them discuss their understanding of a good description of the word “fraction”. Help them phrase and write it on their paper. Let each student share a fraction from the story and write them on the board. After the discussion, have them write one of them in the Example box then give them time to Draw a picture of that example. When this is finished have them read the definition aloud together and then have them write it on their paper. Then read the word “fraction” and the definition together again as a group. ! Repeat the “with” portion of this activity with the term denominator. Help students as needed. ! The “by” part of this strategy is when the student is able to do the Math Vocabulary pages on their own. Introduce numerator and have students start on their own to see if they can do “by” with out support. If the student seems confused, go to the “with” again and work towards the “by”. 44 ! As you incorporate each of the vocabulary words into the following lessons, have the students start with a review of previous vocabulary words, then create the next page with the new word. 45 Fraction Unit Vocabulary Words and Definitions Fraction: represents the equal parts of a whole (Lesson 1) Numerator: The numerator is the top part of a fraction. The numerator represents how many parts of the whole or a part of a group are being considered. (Lesson 1) Denominator: The denominator is the bottom part of a fraction. The denominator represents the total number of parts of the whole or in a group. (Lesson 1) Benchmark: A size or amount you already know that you can compare and understand a different size or amount. Equivalent Fraction: Fractions that name the same amount are called equivalent fractions. Common Denominator: When two or more fractions have the same denominator. The denominator must be the same before adding or subtracting fractions. Simplest Form: When the fraction is divided down and has only 1 as a common factor. Mixed Number: When the amount given has a whole number and a fraction. 46 Fraction Denominator 47 Numerator Benchmark 48 Equivalent Fraction 49 Math Vocabulary Vocabulary Word Describe Definition Example Draw a Picture 50 Fraction Unit Lesson 2: Creating Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Think/Pair/Share and Total Physical Response as strategies of instruction through this fraction lesson. The sharing helps language learners say the words and understand meaning and the Physical helps the students become actively engage in the lesson. II. Preparation and Materials needed: ! The book Fraction Action by Loreen Leedy ! Word strips from Lesson 1. ! Three white sheets of paper per student. ! Colored pencils or crayons. ! Fraction Cards: 1/2, 1/4, 3/4, 1/3, 1 III. Technology Use: ! No Technology needed in this lesson. IV. Instructional Procedures ! Begin by placing the word strips from Lesson 1 on the board. Have the students read them together, then review the definitions again. ! Read page 4 of Fraction Action without showing the picture. Repeat the activity on the board for the class doing the same as “Miss Prime” from the story. Before telling the students what 51 fraction you have divided the whole circle into, ask the students if they know what the two equal parts of the whole are called. ! Read page 5 to the class and show the pictures. Then read page 6 and show pictures. ! Hand out the papers and pencils or crayons. Have the class turn and talk with their neighbors about things that they can divide in half. Have them list and draw them on one sheet of paper. ! Read pages 710. Discuss the equal parts with the class and talk about which fraction is the largest and which fraction is the smallest. ! Have the students form small groups of 34 and Think/Pair/Share by turning and talking in these groups about whole items that can be divided into fractions of 1/2,1/3, and 1/4. Have them create a list together and create pictures of these items. ! Pair the students up with different partners and have them turn and talk/discuss ways to use fractions every day life. On the third piece of paper have them list and draw examples of these every day situations when fractions are used. ! When the students have a list of ideas of everyday fraction use, have them individually come to the front of the class and act out one of the situations on their list. They are just miming the action and no words. The class is to try to guess what is the fraction action. 52 ! After several have shared, have the whole class get in a circle with plenty of movement room. If the gym were available, that would be a good place to do this activity. You could also go outside if the weather permits. ! Explain to the students that you are going to show them a fraction card. When they see and or hear what the card says, they are to jump in a circle that the fraction represents. ! Demonstrate or have a student demonstrate by saying the fraction is 1/2 and now the student will jump half way around in a circle. ! You will need to say the fraction card as you show the card because sometimes the students will be backwards to the card. Saying the words and fractions also helps language learners. 53 Fraction Unit Lesson 3: Creating Fraction Sets I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for incorporating Realia, ToWithBy and Think/Pair/Share methods in teaching math concepts for student’s greater understanding while teaching this math lesson. II. Preparation and Materials needed: ! The book Fraction Action by Loreen Leedy from Lesson 2. ! Fraction word strips from Lesson1 ! Items that are in sets such as plastic eggs in a carton, box of crayons, measuring cups or spoons, table settings, pictures of sports teams. These are just a few examples. ! Items that can be divided into sets such as; marbles, colored tiles, coins, buttons etc. ! Pizza templates and condiments printed for each student. These are found at the end of the lesson. ! Paper and pencil for each student. ! Alternative activity: Graham Crackers, 34 different decorative candies (small), small bowls for candies, plastic spoons for scooping candy, frosting in bowls, plastic knives. III. Technology Use: ! No Technology needed for this lesson. 54 IV. Instructional Procedures: ! Review the vocabulary words from Lesson 1. ! Review the previous lesson about the creating of fractions by breaking something apart. Explain that some things come in sets and give the students a few minutes to “Think/Pair/Share for some set suggestions. Have them turn and discuss with a partner about different sets and write them down. Have these partners share with the class their list of sets and as they share, write them on the board. ! Read Fraction Action pages 1115 titled Get Ready, Get Set. After reading these pages show some “sets” of items. Discuss the fractional part if you take one away or two away. Review: the “whole” is the total of the set pieces and the fraction is what is left or taken away of the whole when the set is broken apart. ! Have students create another vocabulary page using the vocabulary words of fraction of a Whole piece and fraction of a Set. Have them use their definitions and pictures to show the difference. ! Divide the students into groups of 34. Give each group of students one of the sets of collected objects. Have them count out the whole set to find the total amount within the set. Then divide the set pieces among the group giving each member of the group an equal amount. ! Have students write the fraction of their portion of the set. 55 ! Share the different sets around the class so all students have several opportunities to practice this activity. ! Give each student the Pizza Page. They may color it to create a pizza with sauce. ! Have students talk with each other discussing by creating scenarios about how many pizza pieces each ate and what fraction of the pizza that would be. ! Give each student the Pepperoni/Mushroom/Olive page. Instruct the students they are now going to create their own pizzas. They must cut out the food items and place them on their pizza. They must have equal amounts on each piece, but not all food items must be equal amounts. For example, put six mushrooms on each slice of pizza and four pepperoni pieces on each slice and five olives per slice. ! After all the students have designed their pizzas, have them write the total set of olives, mushrooms and pepperonis per pizza. After this is done, they will find a partner and ask for X amount of pizza from the partner’s pizza. That person must then create the fraction of how many mushrooms from the whole set were eaten and how many are left of the set. They will do the same for all the food items on their pizza. ! The students will share with each other for about 15 min. then have them share with the class what they have learned. 56 ! An alternate investigative Realia activity to supplement this lesson: give each student a graham cracker. Have them examine the “breaking” apart sections of the crackers. Ask how many equal parts can these crackers be broken into? ! Have the students frost their crackers. All sections. ! Let the students decorate each of their crackers using the candy decorations. Each candy must have the same amount per cracker section, but each candy may have different amounts from each other. For example, there might be 6 silver candies on each cracker section and 3 flower candies per section and 10 red hearts per cracker section. ! Once these are done, the students will write down the total amount of candies used for their own cracker. ! Students will find partners and show their cracker to this partner. They will take turns asking questions about each other’s crackers such as: if I ate two pieces of my cracker, what fraction of my cracker is left, and what is the fraction of silver candy is left and what fraction of red hearts did I eat. Questions such as these. 57 Create Your Pizza 58 Fraction Unit Lesson 4: Review of Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Total Physical Response method of instruction for creating this activity to review fraction understanding. II. Preparation and Materials Needed: ! Sidewalk chalk if going outdoors or blue painters’ tape if indoors. ! Create large boxes on the ground or floor and number them inside the box. The boxes need to be made large enough for a student to stand inside. One box per student. ! The boxes should be in a straight line with connecting sides. 1 2 3 4 5 6 7 ! Something like this III. Technology Use: ! No Technology required for this lesson. IV. Instructional Procedures: ! Take students to where the boxes are located, either indoors or outside. ! Have students select their own box and go stand in the box. ! Remind the class this is a quiet activity. Instruct the students that you will be calling out some commands and they need to listen 59 carefully so they will know if they are the ones to “step outside the box” or not. ! Ask all of the even numbers to step out of the box. Then call on a student to tell you what fraction is outside the box. Ask another student what fraction is inside the box. ! Repeat with other questions such as: step out of the box if you Have brown hair Have blue eyes Have shorts on Are on a number that is a multiply of 5, 3, 4 Was born in Jan., Feb., March or any other month. ! Create any commands of your own that will work with this activity. ! Continue asking questions for fractions with each command. Observe to see which students understand the fraction concept and which students still needs some extra work. 60 Fraction Unit Lesson 5: Benchmark Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the teaching methods ToWithBy, Think/Pair/Share and using Realia as methods of instruction II. Preparation and Materials needed: ! The book Fraction Fun by David A. Adler. ! Paper plates, 3 plates per student (plates need to all be the same size) ! Pencils, rulers, crayons. The story suggests red, green and blue. ! Vocabulary page. ! Vocabulary word strip—Benchmark ! Plastic Plate fraction plates. One for each student (example for making these are at the end of the lesson) III. Technology Use: ! If a document camera is available, this would be a great activity to show the book as you read. If there is not one available just show the book as you read. IV. Instructional Procedures: ! Read the book Fraction Fun to the class to the Pizza Math page. ! Have students get out the next vocabulary page. 61 ! Put the Benchmark word strip on the board. Have the students write the word on their vocabulary page. ! Have students think about what a good definition for a Benchmark Fraction might be. Have them turn and discuss with a partner then share with the class what they decided a good definition might be. ! Give the students the definition (to) of a Benchmark fraction and have them write this on the vocabulary page. Have them finish the page (by). ! Handout the paper plates and rulers and crayons to the students. ! Read the rest of the Fraction Fun with the class. Have them do the activities as you read the story. ! Discuss what a good benchmark fraction might be that is easy to recognize. ! Give students the Fraction Plates. The plates are two different colors; let the students know which color is representing the fraction you are giving them. ! Have them show you the fraction 1/2. Look to see that all students have the same fraction. ! Have students show you 1/4 fraction using the plates, again observe for understanding. ! Now have the students show you 1/3 fraction of the plate. ! Discuss how these fractions could be great benchmark fractions. 62 How to make Fraction Plates Purchase two different colored disposable Plastic Plates. They don’t need to be the large dinner plates, just the desert size. Cut each plate from the edge to the center. Then slide the plates together on the slits. The plates will turn over each other creating the fraction of the plate showing. Cutting to the center of the plates. Sliding plates together at the slits. Showing 1/2 fraction. Showing 1/3 fraction. Turn the plates to create the fractions. 63 Fraction Unit Lesson 6: Line Plot Fractions I. Lesson Objective Goals: ! Aids will understand the purpose and procedure for using To WithBy, Think/Pair/Share and Realia as methods of instruction for teaching fraction values through line plots. II. Preparation and Materials needed: ! A small handful of Buttons for each student. (buttons can be purchased through Oriental Trading at $6.00 per package of 800) ! Line plot handout for each student. You will find this at the end of the lesson. ! Ruler for each student. III. Technology Use: ! No Technology needed. IV. Instructional Procedures: ! Review all vocabulary words as a class. ! Have students share one with a partner a way they used fractions this past week. Encourage them to use vocabulary words to describe their fraction experience. ! Give students a few minutes to share their experiences with the class. ! Hand rulers to all the students. Review the fractions of an inch. 64 ! Encourage the students to share a Benchmark fraction that is easy to notice. ! Hand out the buttons and the Button Plot sheet. ! Choose one button to show the class how to do this activity. Then give the students about 30 minutes to work on these themselves. ! Monitor the students and help (with) the students that are struggling with the measurements. ! Watch for students’ creative ways of plotting their measurements. Ask a few to share with their peers, at the end of class, how they recorded their data. 65 Name________________________________________ Date____________________ BUTTON, BUTTON, LET’S MEASURE THE BUTTON Task: You are to measure each of your buttons. Create a line plot to show the sizes of your buttons. Tell what you notice about your data. Include your smallest and largest button sizes. 01inch 66 Fraction Unit Lesson 7: Comparing and Ordering Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using Realia, Think/Pair/Share and Games within the lesson instruction for understanding Equivalent Fractions. II. Preparation and Materials needed: ! Equivalent Fraction word strip. ! Prepare Labeled Fraction Tile page for each student, which is provided at the end of this lesson. ! Fraction Equivalency page can be found at the end of the lesson. ! Scissors for each student. III. Technology Use: ! If a document camera is available, have students share their fraction Equivalents, using their tiles, with the class by projecting them for all to see. IV. Instructional Procedures: ! Review with the class about the Button activity. Discuss which fractions were greater than 1/2 and which fractions were less than 1/2. ! Show the word strip Equivalent fraction and have the students discuss with a partner what they think the meaning of Equivalent fraction means to them. ! Share with the class and give examples of an Equivalent Fraction. 67 ! Have students add Equivalent fraction to their Vocabulary booklet or page. Give them a textbook definition and then have then write it in their own words. ! Give each student the labeled Fraction Tiles handout. ! Instruct the class to carefully cut the tiles out. ! When all the tiles are cut out, let the students work with the tiles and try to find as many Fraction Equivalents as they can. ! Hand out the Equivalency Fraction page. ! Have students find a partner and compare what fractions they have the same and see if there are any differences. ! Have the students list all the fraction equivalents that they find on the Equivalency page. ! Have students share some fractions with the class using the document camera if available. If no camera is available, list the fractions on the board. 68 Labled Fraction Strips 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/7 1/7 1/7 1/7 1/7 1/7 1/7 1/6 1/6 1/6 1/6 1/6 1/6 1/5 1/5 1/5 1/5 1/5 1/4 1/4 1/4 1/4 1/3 1/3 1/3 1/2 1/2 1 69 Fraction Strips 70 Fraction Strips 71 Labled Fraction Strips 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/7 1/7 1/7 1/7 1/7 1/7 1/7 1/6 1/6 1/6 1/6 1/6 1/6 1/5 1/5 1/5 1/5 1/5 1/4 1/4 1/4 1/4 1/3 1/3 1/3 1/2 1/2 1 72 Fraction Equivalent _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ 73 Fraction Unit Lesson 8: Comparing and Ordering Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using Games for understanding in the instruction Ordering and Comparing Fractions. II. Preparation and Materials needed: ! Prepare game board at the end of the lesson. One for each group of four students. ! Prepare instructions for each game board. ! 2 dice for each game board. ! A game piece for each student. Different colored tiles or disks work great. ! A page of unlabeled fraction tiles for each student. III. Technology Use: ! No technology is required. IV. Instructional Procedures: ! Review fraction vocabulary. ! Review fraction benchmarks and equivalency. ! Give each student a set of the unlabeled fraction tiles. ! Give the class a few minutes to label their tiles, but do not cut them out. 74 ! Divide students into groups of four. ! Give each group a game board, instructions, 2 dice and a game piece for each student. ! Review the instructions for playing the game. Roll the dice and show the class how the game is played. ! Explain to the class that the fraction tile page is for them to look at and see if the fraction they roll is greater or less than 1/2. This is a comparison chart for them. 75 Game Rules 1 Roll each die one time. 2 Choose the greatest number to be the Denominator. 3 Choose the least number to be the Numerator. 4 Decide if the fraction is greater than, less than or equal to the benchmark fraction of 1/2. 5 If the fraction is greater than 1/2, you move ahead 2 spaces. 6 If the fraction is less than 1/2 you move back 1 space. 7 If the fraction is equal to 1/2 you move ahead 1 space and roll again. 8 The first person to the end is the winner. 76 77 78 Fraction Unit Lesson 9: Fraction Review I. Lesson Objective: ! Aides will understand the purpose and procedure for instructing and using games as a tool for understanding fractions. II. Preparation and Materials needed: ! Print and cut out the Fraction Cards. Enough for each team ! Best printed on colored cardstock so numbers and printing do not show through. ! Print game instructions for each team III. Technology Use: ! No technology needed for this activity. IV. Instructional Procedures: ! Divide the students into groups of 4. ! Explain to the class that there will be 3 different games going on at the same time. Everyone will have the opportunity to play each. ! Review the rules of the games, showing quick examples of each game. ! Ask for questions and clarification. 79 Concentration Rules 1. Shuffle cards really well. 2. Lay all cards face down on the table or floor. 3. One person starts by turning over 2 cards. 4. If they match, that person gets to keep the pair and will then turn over 2 more cards. 5. If there is not a match, the cards are turned back over, face down. 6. It is now the person to the left to take their turn. 7. Repeat this activity till all cards are gathered. 8. The winner is the one with the most pairs. 80 Do You Have? 1. Shuffle the cards really well. 2. Deal 5 of the cards to each player. 3. The remaining cards are placed face down in the middle of the players. 4. Everyone picks up their set of cards and holds them so only they can see their own cards and their opponents do not know what they have. 5. The object of the game is to get as many matching pairs of fraction cards as possible. 6. The person to the left of the dealer starts the game. 7. First look to see if you have any pairs, if so lay them down in front of you. 8. This person may ask anyone in the circle for a fraction card that might match one they have in their hand. 9. If that person has that fraction they must give it to the person requesting the card. 10. The person giving up their card must now pick up a card from the face down pile. 11. The person asking must now place that match down in front of them and draws another card from the face down pile. 12. Repeat till all cards are paired. Count up pairs to find the winner. 81 Fraction War 1. The players sit in a circle. 2. Shuffle the cards really well. 3. Choose the objective of this game before you start. a. The winner gets all the cards. b. The winner is the one who gets rid of their cards first. 4. The dealer passes all the cards out face down to all the players. 5. The players keep their cards facedown in front of them. 6. When the dealer says go, each person takes the card from the top of their pile and lays it down in the center of the group. 7. The person with the highest fraction on their card takes all the cards in the center. 8. Repeat steps 5 and 6. 9. When your facedown pile is gone, shuffle the cards you take from the center and place them facedown to create a new pile to draw from. 82 Fraction Cards 1 1/2 1/3 2/3 1/4 2/4 83 3/4 1/5 2/5 3/5 4/5 1/6 2/6 84 3/6 4/6 5/6 1/7 2/7 3/7 4/7 85 5/7 6/7 1/8 2/8 3/8 4/8 86 5/8 6/8 7/8 87 1/9 2/9 3/9 4/9 5/9 6/9 88 7/9 8/9 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 89 90 Fraction Unit Lesson10: Fraction Situations I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Total Physical Response method of instruction for the student learning in this fraction lesson. II. Preparation and Materials needed: ! Book Spaghetti and Meatballs for All! By Marilyn Burns. ! Paper and pencil for each student. ! Scenarios for each group. ! Props for students to use. ! Math tiles. III. Technology Use: ! Technology is not needed for this lesson. IV. Instructional Procedures: ! Give each students paper and pencil. ! Explain that as you read this story, they are to listen and create the table placements as Mrs. Comfort creates her placements in the story. ! Explain that they will be creating several different setting designs, so draw small and not take up the whole page on the first setting. ! Tell them to do simple drawings and not take a long time or detail. *Another option for this story is to give the students tiles and graph paper and they can move the tiles around on the paper. ! Read to the class the book Spaghetti and Meatballs for All! ! As you read each situation, give time for the class to recreate their table placements on the paper. ! When the book is finished ask for discussion about the story and how many ways did the family rearrange the tables. ! Divide the class into 2 or 3 groups. 91 ! Explain that they are going to create a skit to perform for the class. ! They can use one of the fraction books we have read to perform or they can create a scenario to act out or they can choose one of the teachers’ situations to present.
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Title  Interactive Math Strategy Teaching Guide 
Author  Warnick, Linda 
Abstract  This thesis looks at a supplemental tutoring program for elementary grades math education called Double Dosing, which is conducted separately from the regular classroom and teacher, and for which the teaching aides do not have a teacher's support materials. The purpose of this project was to create a resource booklet of lesson examples using five specific mathteaching strategies for the aides to use as a guide when teaching math concepts. The research will explore the effectiveness of using these strategies and define how best to implement these strategies into small group instruction for ELL students. 
Edition  Electronic reproduction 
Date Original  201308 
Publisher Digital  Published digitally by Utah Valley University Library 
Date Digital  20131023 
Physical Description  91 pages; 22 cm.; 
Owning Institution  Utah Valley University 
Subject 
Education, Elementary English languageStudy and teaching MathematicsStudy and teaching 
Local Subjects  Education; 
Language  eng 
Collection Name  Utah Valley University Theses Collection 
Rights  The author retains all copyright ownership. The right to download or print any of the pages of these theses is granted by the copyright owner only for personal or classroom use. The author retains all proprietary rights, including copyright ownership. Any reproduction or editing by any means mechanical or electronic without the express written permission of the copyright owner is strictly prohibited. 
Copyright Status/Owner  Copyright 2013 by the author. 
Type  Text 
Format  application/pdf 
Contributor Metadata  McIntyre, Catherine 
Metadata Entry Date  20131023 
Metadata Entry Tool  CONTENTdm version 6.4 
Full Text  i Utah Valley University Interactive Math Strategy Teaching Guide A project submitted in partial satisfaction of the requirements for the degree of Master of Education In English as a Second Language by Linda Warnick 2013 ii Utah Valley University Graduate Committee Approval of a project submitted by Linda Warnick This project has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. ________________ ______________________________________ Date Dr. Maureen Andrade, Chair ________________ ______________________________________ Date Dr. Mary Sowder, Committee Member ! iii Acknowledgements I would like to give a huge thanks to my six wonderful children for all the support and encouragement they have given me for the past two years. Becky, Ben, Krista, Thomas, Rachael and Sarah have constantly been there for me and gently urged me to keep going, even when I was so overwhelmed and wanted to put it aside. Also, I would like to give a big thank you, to Dr. Maureen Andrade for her countless hours of reading and rereading my project and encouraging me to keep going. Thank you to Dr. Mary Sowder for her support and encouragement. Thank you to all who have helped and supported me on this journey. iv Abstract With the minority student population growing, the need for teachers’ aides to help with tutoring and helping language learners is also growing. Students need a foundation of language before they can understand concepts being taught in other curricula. As students are identified as needing extra support, they are referred to a tutoring program entitled Double Dosing. The aides teaching the Double Dosing program are not in the same room as the teacher and do not have the teacher support for their instruction. The purpose of this project was to create a resource booklet of lesson examples using five specific mathteaching strategies for the aides to use as a guide when teaching math concepts. The strategies are ToWithBy, Think/Pair/Share, Games, Realia, and Total Physical Response. Each of the lessons in the booklet will have one or more of these strategies implemented into the instruction. The lessons are created using the fourth grade fraction concepts. The research will show the benefits of using these strategies in teaching. It will review research on Double Dosing and the effects on student learning. It will explore the effectiveness and define how best to implement these strategies into small group instruction for ELL students. v Table of Contents !"#$%&'()(************************************************************************************************************************************************(+! ,./0&(,123456(7#%"89&#:234(;3%&'<&3%23(='4'#>(********************************************************************(?! @%#%&>&3%(A(%"&(='/0&>(**************************************************************************************************************************(B! @%#%&>&3%(A(%"&(=.'$1&(**************************************************************************************************************************()B! ,&A232%23(A(C&'>1(*************************************************************************************************************************************())! 9&1&#'D"(E.&1%23(**************************************************************************************************************************************()F! 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Chapter 1 Introduction It is important to understand that math is a language all its own. Phillips (2009) states that individuals need to understand that math symbols represent math concepts just as a reader needs to understand that letters represent sounds. Understanding that the letter sounds put together create words is like understanding that numbers and symbols create math problems. “It is a myth that mathematics is a universal language. For English Language Learners (ELLs), operational mathematics is performed differently around the world” (Gottlieb, 2006, p.66). According to Tomlinson (2003) “The number of English language learners in classrooms across the country is increasing, even in localities where there were virtually no such students just a few years ago.” Due to the increasing volume of ELL students, lessons for preteaching and reteaching math concepts are needed to support the growing diverse population. Math teaching strategies enhance the ability of ELLs to learn math concepts and “make connections between mathematics and other subjects” (Tiedt & Tiedt,1990, p.226). Students also need to understand the connections of math to other subjects and life applications to recognize that math ideas are not just disconnected facts. Helping students understand math and its application can be accomplished by applying strategies and methods that teach students to “question, analyze, evaluate and reflect” the reasons of math language and concepts (Tiedt & Tiedt,1990, p.334). Teachers must find ways to help students actively employ these strategies. 8 The Utah Professional Teacher Standards clearly identify the responsibilities of teachers to ensure students’ academic success. Standard 2 states: “Promoting student learning and enhancing professional practice are the focuses of Utah Professional Teacher Standards.” (see Appendix A). Standard 2 states that teachers need to be “planning curriculum and designing instruction to enhance student learning.” Standard 3 explains the importance of “engaging and supporting all students in learning” (see Appendix A). The purpose of this project is to develop a booklet of teaching strategies and guidelines for the teacher aides to use, which supports these three standards as suggested. Double DosingA Math/Reading Intervention Program A school district in the Western United States has implemented a Double Dosing program as a Response to Intervention (RTI), to address the needs of struggling students, particularly ELL students in its elementary schools. Double Dosing is the name of the program in this particular district. Other names for similar programs are Flex Time or Regrouping. RTI is an intervention process of three tiers of instruction that increasingly intensifies in the instruction level depending on the intervention needs of the student and varies in duration, time and frequency of intervention. Tier 1 is the daily instruction given as whole class instruction. A Tier 2 intervention is given after determining the students that are struggling and reteaching in small groups such as tutoring. The Tier 3 intervention is more intense instruction such as specific teaching through resource classes or special education. Through the Double Dosing program, a Tier 2 intervention is applied as a tutoring session. For this specific intervention, the teaching of math concepts 9 and vocabulary for ELL students in small groups will help enable them to perform at higher levels of proficiency. Most of the elementary students in the district are set up on an A Track or B Track time schedule. Half of the students in each class are the A track students who arrive at 8:00 and leave at 2:15. The remaining half, are on the B Track and arrive at 9:15 and leave at 3:30. These scheduling differences, allow the teacher to have one hour and fifteen minutes of small group time with each track of students. This can be used for language arts, reading and on occasion some math instruction. The Double Dosing program provides identified students with an extra session of learning within a small group setting, by coming early or staying late. The students on the A Track stay after school to attend the 2:153:30 p.m. Double Dosing session. The B Track students participate in the Double Dosing session from 8:009:15 a.m. The Double Dosing sessions run on an every other week schedule (see Appendix C for Time Chart). Grades three and four share teaching aides; therefore the students in grade three attend every day for one week, and then the students in grade four attend daily for the next week. The sessions consist of a week of math instruction followed by a week off, and then a week with reading/language arts instruction. The Double Dosing program preteaches and reteaches math and reading/language arts to struggling students, which includes ELL students. Students are identified as a need for extra instruction and invited by their teachers to attend the program with the permission of their parents. These students are determined as the teachers review through common assessments, the progress and understanding of each student, and then determine which concepts that students may need 10 to be retaught. At the end of each week the teachers determine what concept needs more explanation and which students would best benefit from the extra tutoring sessions. Statement of the Problem Within a classroom, a percentage of ELL students need extra support to understand math and reading concepts. Therefore, teachers must find students’ level of understanding, and differentiate their teaching methods and the amount of support to provide those students. Being aware of the students’ needs and abilities and what they understand is the beginning to effective differentiation (Tomlinson, 2003). Scaffolding the lessons to reach the needs of all learners will also help create an atmosphere of confident learning. The challenge is in creating innovative and engaging lessons that will be effective for ELL students and determining the most effective strategies to enhance that learning. To enhance the students learning can be accomplished by modifying and enhancing instruction, which will give ELL students the basic tools to become successful learners (RichardAmato, 2010). Statement of the Purpose The purpose of this project is to create a booklet with lesson guides, consisting of five math teaching strategies. This booklet will guide the teachers’ aides, who instruct the students participating in the Double Dosing program, how to implement the five math strategies into their teaching styles which will help enhance student learning. The lesson guides will include definitions and stepbystep instructions to show the process of application for each strategy or method use. The five teaching strategies to be applied in 11 the lessons include: ToWithBy (TWB), Think Pair Share (TPS), Games, Total Physical Response (TPR), Realia/Manipulatives. Definition of Terms For the purpose of this study the following terms and definitions will be applied: • Double Dosing: The name of the tutoring intervention program described in this project. • ELL: English Language Learners refers to students who are learning English along with the curriculum. • ESL: English as a Second Language refers to students’ for whom English is a second language. • RTI: Response to Intervention is an approach that aims to reduce the number of children being referred to special education through intensive instruction. The teacher becomes aware of a need to intervene with instruction to help that student understand the concepts before the student gets too far behind. • TWB: ToWithBy is a process of scaffolding, where the teacher instructs the student through direct instruction and modeling and the student watches and listens. Then the teacher works alongside the student and helps. The final step is that the teacher releases the student to work independently to show mastery of the concept. • TPS: Think/Pair/Share is a process where the students think about the question or problem, and then pairs up with a partner to work and then shares their ideas or discovery with the class. 12 • Tier Interventions is a 3 level intervention system. Tier 1 is the daily instruction given as whole class instruction. A Tier 2 intervention is instruction given after determining the students that are struggling and then reteaching these students in small groups, such as tutoring. The Tier 3 intervention is more intense instruction such as specific teaching through resource classes or special education Research Question The question guiding this creative project is: “What different mathematic teaching strategies and methods might be used in the Double Dosing program to enhance student learning?” Overview of Methodology Five math strategies or methods will be implemented into ten lessons to be used as guides for teachers’ aides when helping students’ master math concepts. These lesson guides will be formatted into a booklet form and available as a resource to all aides, especially those in the Double Dosing program, but not exclusively. Chapter 2 Literature Review This literature review will review research on Double Dosing programs and their effects on student learning. It will explore the effectiveness of these types of interventions and define how to best implement math teaching strategies in small group lessons for ELL students. It will also define the five math teaching strategies and ways to implement them through ten sample math lessons. Response to Intervention FaggellaLudy and Wardwell (2011) defined RTI as a response to intervention that occurs through a multitier model of instruction created to focus on the specific needs of an “academically diverse group of students” (p. 34). The most notable characteristics of an RTI are • evidence based instructional practices • progress monitoring to establish rate and level of student learning • assessment of fidelity of implementation; and • universal screening To implement instructional practices that are researchedbased, FaggellaLudy and Wardwell (2011) suggested that RTI “requires substantial instructional intensity to improve outcomes for struggling students” (p. 34). They use a pyramid to provide a visual of how this method can be constructed. An example of this can be found in Appendix B. Although this example was created for reading interventions, the format could also apply for math interventions. 14 Teachers need to create tasks that “involve the introduction or the use of models, representations, tools, or explanations that elaborate or exemplify the mathematics” (Clark & Sanders, 2006, p. 10). Such tasks are associated with good traditional mathematics teaching (Watson & Mason, 2007). Differentiated instruction is responsive instruction. It occurs as teachers become increasingly proficient in understanding their students as individuals, increasingly comfortable with the meaning and structure of the disciplines they teach, and increasingly expert at teaching flexibly in order to match instruction to student needs with the goal of “maximizing the potential of each learner in a given area.” (Tomlinson, 2003, p. 2) Mary Howard (2009) states that if Tier 2 instruction (small group) is given in a classroom, this specific student instruction needs to be provided separately from the general instruction. She also mentions implementing specific times worked into the day and designating those times as Tier 2 interventions by grade level. She further suggests using assistants for small group instruction or the use of support staff such as aides to help monitor and reteach the students. Double Dosing fits this description. The RTI is set up in three tiers of intervention. The purpose of the intervention levels, Tier 2 and Tier 3, are to address the students’ needs and increase the instruction to meet students’ diverse needs. The length of time and frequency of instruction varies accordingly. With the extended day schedule, the schools are already set up for a Tier 2 intervention. The extended day schedule creates an atmosphere conducive to allowing some small group instruction, which is a Tier 2 intervention. Double Dosing will give the students a Tier 2 intervention, which is more intense. The more interventions ELL and other struggling students have, the more opportunities they have to learn and understand the concepts. 15 Strategies/Methods This section will focus on the five math teaching strategies and learning methods for this project. ToWithBy. ToWithBy is a scaffolding strategy, also known as direct instruction, which the teacher shows the students, then guides the students, and then gradually releases students to work on their own as they learn new concepts. Echevarria et al. (2013) described scaffolding as the “gradual release of responsibility” (p. 120). The purpose of this strategy is to provide substantial support in the beginning and then gradually let the student work through a problem independently. The strategy is designed to explicitly teach a concept in stages. In the first stage, the teacher gives all the instruction by talking through each step of the math problem (to). In the next stage, the teacher walks through the problem again, but asks for help from the students (with). This stage is referred to as “with the students.” If the students are successful, they can begin working with other students then gradually work on their own (by). Some students may need to be retaught and start again with the first stage until the concept is understood. The goal is for all students to be independent in their math work (Echevarria, et al., 2013). Think/Pair/Share. The Think/Pair/Share strategy gives students the opportunity to discuss a concept with peers. The strategy is implemented through a question being presented to the students, and then five minutes of think time is allowed for processing and formulating ideas. After the initial five or so minutes of think time, the students are then asked to turn and talk with a partner about their ideas. Speaking and listening skills are great for ELLs. This allows students to verbalize their ideas with another peer before 16 sharing with the class. All the students will have the opportunity to share their ideas with the class and respond with understanding to the teachers’ questions (Echevarria, et al., 2013). Herrell and Jordan (2012) suggest that sharing with peers is a way for language learners to share in a less stressful or inhibited environment (p. 192). “Giving students opportunities to voice their ideas and explain them to others helps extend and cement their learning” (Burns, 2007). Games. Peregoy and Boyle (2008) reiterate that using games in lessons will improve the learning and the attitude of the student. “Games create experiences with language and ideas, and experience is the glue that makes learning stick” (Peregoy & Boyle, 2008, p. 134). As students play games, the level of anxiety with language lessons and more language usage occurs. Games also help students practice, in an innovative way, what they have been taught. Burns (2007) explains that games are an “effective way to stimulate” students practice of the learned skills (p. 6). The word fun is associated with games and catches the interest of students and engages them. “Games can lower anxiety and thus can make acquisition more likely” (RichardAmato, 2010 p. 294). Realia. “Current mathematics pedagogy emphasizes extensive use of manipulatives (realia) to promote discovery of basic mathematics concepts, in a sequence that goes from concrete to pictorial to abstract” (Peregoy & Boyle, 2008). Making math meaningful through real life situations creates greater math understanding (p. 134). Because students are physically manipulating objects, this reduces the language load of an activity. The student can still participate in the activity, even if the language is limited, and demonstrate understanding. Students can master the concept more easily when allowed to use multiple opportunities to practice with handson materials called 17 manipulatives or realia (Echevarria et all, 2012, p. 175). It also helps understanding in connection with the abstract concepts. Total Physical Response (TPR). Asher (1977) is the founder of Total Physical Response, and he compared using TPR to directing a play. “The instructor is the director of a stage play in which the students are the actors” (Brown, 2007). Total Physical Response is an active learning approach. “In TPR, the teacher gradually introduces commands acting them out as she or he says them. Students respond by performing the actions” (Herrell & Jordan, 2012). Peregoy and Boyle (2008) describe TPR as a teaching strategy that combines the action with words as they are being said. As ELL students learn language, they begin first by listening. They verbalize when they are ready and then begin to act out the language and be more involved (RichardAmato, 2010, p. 217). The use of TPR can be very effective when teaching vocabulary associated with a content area (Herrell & Jordan, 2012). Students can use all their senses with TPR. Echevarria et al. (2012) states that through TPR students need to “see, hear, feel, perform, create, and participate in order to make connections” (p. 39). 18 Advantages of Using a Variety of Teaching Strategies Well structured and organized knowledge allows people to solve novel problems and to remember more information than do memorized facts or procedures. Such wellstructured knowledge requires that people integrate their contextual, conceptual and procedural knowledge in a domain (RittleJohnson & Koedinger, 2005, p. 313). Creating lessons that ELL students can apply will create a base knowledge and build their understanding through contextual, conceptual and procedural processes by “targeting their weakness in student learning” (Lewis, 2002). Handson activities and interactive stories use more senses for deeper learning. Lewis (2002) talks about two of the five strategies that enhance student learning which are: • Realia: Giving hands on experiences and aiding children’s understanding. The use of real objects and tools help with the explanation and gives students the opportunity to experiment with practical materials for better understanding. • Think/Pair/Share: Learning from peers through sharing, discussion and working together. Teaching others enhances students’ own understanding through verbalization and explaining their understanding. Having a handson and logical approach to teaching math gives students a tool to assist their understanding of why and how the concepts apply. This approach to teaching is useful for visual learners (Clarke & Sanders, 2006). By intervening and supporting struggling students early, we can get most students to grade level within the regular classroom. More intense instruction is given to those 19 who need second and third tier interventions to accelerate their learning (Howard, 2009, p. 3) Tomlinson (2003) reminds teachers that we “want students in our classrooms to experience affirmation, contribution, power, purpose, and challenge” (p. 11). She also explained that the “premise of differentiation is that while students have the same basic needs, those needs will manifest themselves in different ways, depending on student gender, culture, general life experience, talents, interests, [and] learning preference” (p. 12). Using a variety of methods and materials to “support different learning styles and multiple intelligences” (Echevarria et al. 2013) helps students make connections through feeling, hearing, seeing and doing. “Howard Gardner’s work around multiple intelligences has had a profound impact on thinking and practice in education” (Smith, 2002, 2008). Palmer (2001) mentioned several reasons teachers agree with Gardner’s theories The theory validates educator’s everyday experience: students think and learn in many different ways. It also provides educators with a conceptual framework for organizing and reflecting on curriculum assessment and pedagogical practices. In turn this reflection has led many educators to develop new approaches that might better meet the needs of the range of learners in their classrooms (p. 213). Challenges Some of the challenges for tiered instruction are related to the time it takes to create and put in the extra work for the lessons (Clarke & Sanders, 2003). Clarke and 20 Sanders listed the following challenges and reasons for teachers not implementing these math strategies: • Organization and provision of all materials • The time taken to plan and organize a good lesson • Finding appropriate activities • Clarity of the model and extending the model into a lesson with meaningful independent/group work. Another challenge would be the lack of experience of an aid teaching the materials. Aides are usually parents that would like to be involved in the school where their children attend and want some part time work. With this inexperience, comes the task of training these aids on the skills needed to help students who are struggling. This project will help eliminate some of these challenges. Each of the aides will be trained to apply the strategies and methods into their teaching styles. The booklet will be a guide for them to use as they implement the strategies into their teaching. It will also have clear definitions of each strategy and examples lessons for them to follow. The organization of the materials will be prepared and given to the aides, so they will not need to gather them nor will they need to search for appropriate activities. The activities and materials for the lessons, that the aides will be teaching, will be provided by the teachers’ from the third and fourth grade teams. 21 Chapter 3 Methodology This chapter is an overview of the methods to be used for creating the booklet with the strategies and learning methods. It will address who will be using the booklet, what is the purpose of the booklet and the availability of the booklet. Project Design This study is a creative project designed as a tool to support aides in incorporating five specific teaching strategies or methods into their lessons to enhance student learning. The following strategies and methods have been identified: ToWithBy, ThinkPair Share, Games, Realia or Manipulatives, Total Physical Response (TPR). Each lesson will consist of one or more of these specific strategies. The purpose, use and benefits for teaching each of these strategies and learning methods were described in the literature review. Each of these strategies and learning methods were defined and will be implemented into lesson guides, which will be developed into a booklet form to show how each of the strategies or learning methods can be taught and applied to math concepts. The purpose is to help aids understand how to replicate each strategy for teaching any math standard or concept. By creating this booklet, the aids will have a guide for examining the steps for teaching different math concepts and the application as to how the strategy may be implemented. Each lesson guide will have stepbystep instructions to guide the aid through an entire lesson, using that specific strategy. The booklet will be available in 22 each classroom along with the teaching tools where each of these aids will be teaching. The guides will be available for all aids to use. Context The context of this study is directed to aides working with elementary age students. The student ages range from eight to tenyearsold. The class sizes are small, with five to ten students at a time. This allows small group instruction and individualized help. The population of this school is approximately 1,000 students with the majority being Caucasian, which creates a low population of ELL students. The languages represented within the school are English, Tagalog and Spanish. Because of the low ethnic differences and language variance, aides will have struggling students who are native speakers of English as well as ELL students. The aides assigned to work in the school are determined as to the needs of the students. The needs are determined through the students with IEP assessments. Some of these may be medical needs, behavioral help, students with autism and other various challenges that require a little support in the class or to work directly with the student. Therefore the aides may differ from year to year. There is no specific qualification such as a degree or experience. The applicants are usually parents of students of the school, but if they have worked at the school in previous years they are usually hired again. The experience level of the aides varies, with some having teaching degrees and others with no previous experience or degree. The district determines according to student needs, 23 how many aides the school qualifies for. These aides are then asked to teach the Double Dosing sessions and help tutor the students. The classroom for the aides is a separate room from the classroom for the core teachers. The aides are alone teaching these students, thus the need for this booklet to give them some assistance and examples. The small group aides will be trained as to how to teach, how to use the guidebook and the use of the tools and materials in the guidebook. ! ! 24 Chapter 4 Unit Design Double Dosing is an intervention program designed by the district to tutor ELL and struggling students. The instructors for this program are aides that work at the school. Some have little or no background in teaching. The following booklet is designed to support the aides by giving them a guide of teaching strategies. The lessons examples in this booklet are designed using fractions as the unit of study. The strategies are listed at the beginning of the booklet and also suggested in the objective for each lesson. Upon completion of the Double Dosing Instruction Booklet: Teaching Strategies for Aides, the aides should feel empowered to create lessons of their own and have the tools to tutor the students in their class. Unit Content This next section is an explanation of the lessons plans within the Double Dosing Instruction Booklet: Teaching Strategies for Aides. Lesson 1: Fraction Vocabulary. The objective of this lesson is for the aides to understand the procedures and purpose of using the ToWithBy strategy of instruction. This strategy is used throughout most of the lessons. The aides are to instruct by example, watch for understanding, then work together with the students and gradually release the students to work on their own. It is important to start with vocabulary when instructing language learners. Teaching and understanding the terms is important to build a base knowledge for the students to understand the unit. 25 Lesson 2: Creating Fractions. The objective for this lesson is to teach the aides the purpose and procedures for implementing the Think/Pair/Share strategy along with the Total Physical Response method of learning. The Think/Pair/Share portion of this lesson is designed for the students to first think about whole items that are easily divided into fractions, and then discuss together in small groups about how the whole items that can be divided into fractions. After discussing with partners and creating a list of ideas, they are to share with the class. The students will be paired with a different partner and will then create a list of ways fractions are used in everyday life. For the Total Physical Response portion of the lesson the students will create pairs and they will then pantomime to the class who will try to guess what the situation is the students are acting. Lesson 3: Creating Fraction Sets. The objective for the aides in this lesson will be incorporating Realia, ToWithBy and the Think/Pair/Share methods into their teaching. The Realia are objects that come in sets and are items the students would recognize and use in their daily lives. The ToWithBy is the instruction given by the aides, during the introduction of the lesson, using examples of what fraction sets are. The Think/Pair/Share strategy has the students working together discovering the fractional parts of the sets. The students will be introduced to sets through objects that come in sets, such as eggs, crayons, table settings, ball teams or any other sets determined. The students will then be divided into small groups and given one set of items to be divided among the group. The instruction for how to create a fraction will be given at the beginning of the activity through the use of Realia, such as a set of blocks or buttons or other items, then 26 show the students how to create a fraction by knowing the whole number of the set and what the fraction of the set is after being divided. Lesson 3 includes two activities that incorporate Realia. These two activities include first using pictures to create pizzas and second dividing graham crackers into fractions. Lesson 4: Review of Fractions. To help students review fractions, the aides will implement Total Physical Response into their teaching. The students will go outside or into a gym where there is a line of numbered squares on the ground. An explanation of how to prepare these squares has been included in the lesson format. The students will be asked to stand in these square boxes, as they students listen to specific commands. In this lesson the teacher commands might instruct students who are blonde, or a girl or on an even number. If the command applies to them, they are to step out of the box. The students will calculate the fraction of students standing outside the boxes and those standing in the boxes. Lesson 5: Benchmark Fractions. This lesson the aides will be using ToWith By, Think/Pair/Share and Realia as methods of instruction. The aides will read the book Fraction Fun by David A. Adler. Within the Fraction Fun book there are activities to do using paper plates, rulers and crayons to create fractions. The students will also be learning a new vocabulary word. As part of the Think/Pair/Share the students will discuss with a partner what their idea of what a “benchmark” fraction might be. A fraction such as onehalf would be the benchmark to use for comparing fractions to determine if the fraction is less than or greater than the onehalf benchmark. After sharing and some discussion, the aide will give the original 27 definition and then observe to see if the students understand how to do the vocabulary page on their own. The aides may assist as needed. The use of the plastic fraction plates will be an activity to show their understanding of 1/2, 1/3, 1/4, 2/3 and 3/4 fractions. This activity enforces the understanding through Realia. Lesson 6: Line Plot Fractions. Realia, ToWithBy and Think/Pair/Share are again implemented into this lesson. For the Realia portion of this lesson, the students are given a bag of buttons. They must measure the width of each button and record the measurements on a line plot from smallest to largest. Think/Pair/Share will be demonstrated in the beginning of the lesson as the students share with a partner ways they used fractions during the week. They are encouraged to use the vocabulary words they have been learning. They will then share their experiences with the class. The ToWith By method is demonstrated as the aide launches into the activity by showing the students how to measure, then practice with them, then the aide will watch to see if all the students understand and support those students that need extra support. Lesson 7: Comparing and Ordering Fractions. The aides will be implementing Games along with Think/Pair/Share and Realia in this lesson. A new vocabulary word is introduced and the students will think about the meaning of what an equivalent fraction might be and follow with a discussion with a partner, after which they will share in a class discussion the final definition. The students will create another vocabulary page for this new term after the class discussion. The class will then be given paper fraction “tiles” which they will cut out and use to find equivalent fractions. As the students launch into this activity, the aide may show 28 them a simple example such as two halves make one whole. The aide will then encourage the students to find as many fraction equivalents as they can on their own. Lesson 8: Comparing and Ordering Fractions. This lesson will be implemented through a board game. The aide will give the directions for the game and a quick example and then allow time questions for greater understanding. The students will then be divided into groups of four. The students will roll a set of die. The greater number on the dice is the denominator and the lesser number on the dice is the numerator. The purpose of this game is to help the students understand the value of the fraction by determining if the created fraction is greater or less than the benchmark fraction. Each group will play their game about 2030 minutes, then the students will be regrouped and play again with another group of students. The aide will rotate through the groups to help and assess the understanding of comparing and ordering fractions. Lesson 9: Fraction Review. The games in this lesson are used as a review to show understanding and application of the fraction concepts. There will be three different games and the aide will give the directions fore each game and a quick example of each and then allow questions from students for understanding. The students will then be divided into groups of four. Each group will play their game about 1520 minutes. They will then rotate to another game. This gives the students the opportunity to play all three games and reinforce the concepts through three different games. The aide is also free to walk around and observe to see who understands the fraction concepts and assist those who need help Lesson 10: Fraction Situations. Within this lesson the aides will be using Realia and Total Physical Response in their instruction. The lesson will start with the students 29 all having a set of tiles and some graph paper. The aide will read the book Spaghetti and Meatballs for All! written by Marilyn Burns. In the story, as different guests come, the tables are rearranged to accommodate the new guests. With each new arrangement the dinner plans become frustrated. As the story is being read, the students are to arrange the tiles as Mrs. Comfort arranges and rearranges the tables in the story. After the story, the students are to create and perform a story or scenario about fractions. The aide will have props available for them to use. This allows the students to use language skills, vocabulary and give some life examples of how fractions are used in everyday lives. ! ! 30 Chapter 5 Discussion Double Dosing Instruction Booklet: Teaching Strategies for Aides is a guide, intended to be used by the aides within their tutoring times to help improve their teaching strategies. The researcher is a teacher who was given the responsibility to create lessons for the aides to teach the 4th grade Double Dosing students (students that have been identified as needing learning interventions for math). The inability of the researcher to be in the classroom to help the aides has prompted the design of this project. The purpose is to give the aides a set of teaching strategies to guide them in their instruction. This booklet will be available to all aides for instruction and guidance. The aides change from year to year, so with this booklet, the aides will feel better equipped to teach the students. The Double Dosing Booklet: Teaching Strategies for Aides will empower them to use various instructional methods within lessons. Implementation The booklet will be provided to all aides, during the 20132014 school year, as guides for their instruction methods. The aides will have a meeting at the beginning of the school year with instructions for the use of the booklet. The booklet provides lessons with examples of how to implement the five teaching strategies, ToWithBy, Think/Pair/Share, Games, Realia/Manipulatives and Total Physical Response, within the aides teaching style. The booklet is designed with the fourth grade math curriculum in mind and is designed to teach the beginning of the fraction unit. 31 Limitations This booklet was created after the school year finished; therefore the ability to instruct and practice with an aide was impossible. The implementation of this booklet is crucial for the researcher to know if there are areas that need clarification or changes that need to be made. The implementation of this booklet would have be more ideally introduced before school dissembled for the summer break to have given the aides the ability to come into the new year better prepared. With the new Core Standards being set, students that were struggling to keep up may now be a little further behind. The need for the aides to be familiar with the teaching strategies is important to better enhance student learning. Further Research This booklet is focused on the math portion of instruction. The researcher would like to create a similar booklet with strategies for implementing reading instruction. Within the Double Dosing program students are tutored both reading and math; therefore, a reading strategy guide would have been beneficial. Conclusion Parents, teachers and aides have the same goal for the students, which is to help all students feel successful. Creating an atmosphere of learning in all circumstances is important for the student. The goal of this booklet is to train and support the aides to create the best learning environment for each of the students that come through the Double Dosing program. References Burns, M. (2007). Nine ways to catch kids up. Educational Leadership, 65(3), 1621. Cavanagh, S. (2006). Students doubledosing on reading and math. Retrieved from http://www.Edweek.org Chassels, C., & Melville, W. (2009). Collaborative, reflective, and iterative Japanese lesson study in an initial teacher education program: Benefits and challenges. Canadian Journal of Education 32(4), 734761. Clark, B., & Sanders, P. (2009). Making the mathematics explicit as we build tasks into lessons. Australian Primary Mathematics Classroom, 14(2),1014. Echevarria, E., Vogt, M.E., & Short, D. J. (2013). Making content comprehensible for English Learners: The SIOP model (4th ed.). Boston, N.Y: Pearson. FaggellaLuby, M., & Wardwell, M. (2011). RTI in a middle school: findings and practical implications of a tier 2 reading comprehension study. Learning Disability Quarterly, 34, 3549. Fox, L., Carta, J., Strain, P., Dunlap, G., & Hemmeter, M. L. (2009). Response to intervention and the pyramid model. (pp. 110). Tampa, FL. Retrieved from http://www.challengingbehavior.org/do/resources/documents/rti_pyramid_web Gottlieb, M. (2006). Assessing English language learners: Bridges from language proficiency to academic achievement. Thousand Oaks, CA: Corwin Press. Herrell, A. L., & Jordan, M. (2012). 50 strategies for teaching English language learners. (4th ed.) Boston, MA: Pearson. 33 Howard, M. (2009). RTI from all sides: What every teacher needs to know. Portsmouth, NH: Heineman. Retrieved from http://pzweb.harvard.edu/Research/SUMIT.htm Lewis, C. (2002). Does lesson study have a future in the United States? Nagoya Journal of Education and Human Development, 1(123)1. Palmer, J., (2001). Fifty modern thinkers on education. From Piaget to the present. London: Routledge. Peregoy, S. F., & Boyle, O. F. (2008). Reading, writing, and learning in ESL. Boston, Boston, MA: Pearson. Phillips, D. C. K., Bardsley, M. E., Bach, T., & GibbBrown, K. (2009). “But I teach math!” The journey of middle school mathematics teachers and literacy coaches learning to integrate literacy strategies into the math instruction. Education, 129(3), 467472. RichardAmato, P. A. (2010). Making it happen. From interactive to participatory language teaching: Evolving theory and practice. (4th ed.). White Plains, NY: Pearson. RittleJohnson, B., & Koediner, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23(3), 313349. Smith, M. K. (2002). Howard Gardner and multiple intelligences: The encyclopedia of informal education. Retrieved from http://www.infed.org/thinkers/gardner.htm Tiedt, P. L., & Tiedt, I. M. (1990). Multicultural teaching: A handbook of activities, information, and resources. (3rd ed.). Needham Heights, MA: Allyn and Bacon. 34 Tomlinson, C. A. (2003). Fulfilling the promise of the differentiated classroom. Alexandria, VA: Association for Supervision and Curriculum Development. Watson,A., & Mason, J. (2007). Takenasshared: A review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education, 10(46), 205215. 35 Appendix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ppendix B ! 37 Appendix C Double Dosing takes place during each track time. The B Track students will arrive for Double Dosing during the A Track arrival time as if they are attending a before school Tutoring session. They are not taught in the regular classroom, but are in a different class with an aide. The A Track students will be attending at the end of their school day as if it is an after school Tutoring program. ! ! "!#$%&'!()*+,).! "$$/0,!12334(5%66! 7$8*9!:.)$*&)/8! 1233;<2=>?! @!#$%&'!()*+,).! "$$/0,!<2=>!4A8$,! #,%&B/C!D/)B!"66! ()*+,).! <2=>;E2=>?! "!#$%&'!F/.5/..%6! E2=>!4(5%66!7$8*9! :.)$*&)/8! E2=>;G2G3?!! 38 Appendix D (The strategies booklet and lesson guides.) ! ! 39 Created by Linda Warnick 40 Teaching Strategies ToWithBy: ToWithBy is a scaffolding strategy, also known as direct instruction, that shows and guides the students, and then gradually releases students to work on their own as they learn new concepts. The TO portion is your instruction to the students. The WITH portion is you and the students do the problem/activity together and the BY portion is the students are working on their own. If the student struggles during the BY, then stop and go back to the WITH and support them till they can work on their own. Think/Pair/Share. This strategy gives students the opportunity to discuss a concept with peers. The strategy is implemented through a question being presented to the students, and then 5 minutes of think time is allowed for processing and formulating ideas. After the five or so minutes of think time, the students are then asked to turn and talk with a partner (pair) about their ideas. After a short discussion the pair will then Share with the class. Games: These are specific games or activities that are guided and specific to the lessons being taught. The games are math specific. Realia: This task activity is the use of manipulatives to promote discovery of basic mathematics concepts, in a sequence that goes from concrete to abstract. This is the use of real life situations and objects to create life application. Total Physical Response (TPR): This is an active learning response; this teaching strategy involves combining actions with the words being said. Students are able to use all their senses by preforming, creating and participating in order to make connections. 41 Fraction Unit Lesson 1: Fraction Vocabulary I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the To WithBy method of instruction through creating the vocabulary pages using the vocabulary terms needed for the Fraction Math Unit. II. Preparation and Materials needed: ! The book Full House: An Invitation to Fractions by Dayle Ann Dodds. ! Definition of each of the words available at the end of the lesson unit. ! Vocabulary word strips, provided at the end of this lesson, should be printed and ready to use as a visual for the students to view as they write the words. ! Vocabulary pages, provided also at the end of this lesson, should be printed and ready for use for this lesson. There should be one page per term, for each student. Also extra pages for example use. (It would be good to create an individual vocabulary booklet for each student to use throughout the entire year for math.) III. Technology Use: ! No technology is required. If a document camera were available, this lesson would be better understood if the aide showed the 42 students how to create the Vocabulary Page on the actual artifact. If there is none available, quickly creating a draft on the board will work also. IV. Instructional Procedures: ! Place all vocabulary word strips on the board where all students are able to see them easily. ! Begin by reading Full House: An Invitation to Fractions by Dayle Ann Dodds. ! If a document camera is available, show the Math Vocabulary page on the board and proceed to show the students how to fill in the page. If there is not a document camera, draw the page on the board as an example. ! This is the “TO” section of the ToWithBy strategy. Write the word “fraction” in the Vocabulary Word box saying the word out loud and spelling fraction out loud as your write. Without asking for students’ response, think out loud about the definition of the word fraction, using the story as your background knowledge. Relate story examples to show the relationship to the fraction. Now in the Describe box, tell what you think the meaning of the word fraction might be according to the story. In the Example box, write an example of a fraction from the story. As you are writing, keep thinking out loud as an example for the students to think and create. In the Draw a Picture box, draw a 43 simple picture of a fraction talked about in the book to represent the fraction. Using the definition from the end of the lesson resource, state the technical definition and say it again as you write the words in the Definition box on the Vocabulary page. ! The “With”. Hand each student a Math Vocabulary page (or booklet if created). Step by step have them do the same as you did by writing the word fraction in the Vocabulary Box, saying the word as they write. Then have them discuss their understanding of a good description of the word “fraction”. Help them phrase and write it on their paper. Let each student share a fraction from the story and write them on the board. After the discussion, have them write one of them in the Example box then give them time to Draw a picture of that example. When this is finished have them read the definition aloud together and then have them write it on their paper. Then read the word “fraction” and the definition together again as a group. ! Repeat the “with” portion of this activity with the term denominator. Help students as needed. ! The “by” part of this strategy is when the student is able to do the Math Vocabulary pages on their own. Introduce numerator and have students start on their own to see if they can do “by” with out support. If the student seems confused, go to the “with” again and work towards the “by”. 44 ! As you incorporate each of the vocabulary words into the following lessons, have the students start with a review of previous vocabulary words, then create the next page with the new word. 45 Fraction Unit Vocabulary Words and Definitions Fraction: represents the equal parts of a whole (Lesson 1) Numerator: The numerator is the top part of a fraction. The numerator represents how many parts of the whole or a part of a group are being considered. (Lesson 1) Denominator: The denominator is the bottom part of a fraction. The denominator represents the total number of parts of the whole or in a group. (Lesson 1) Benchmark: A size or amount you already know that you can compare and understand a different size or amount. Equivalent Fraction: Fractions that name the same amount are called equivalent fractions. Common Denominator: When two or more fractions have the same denominator. The denominator must be the same before adding or subtracting fractions. Simplest Form: When the fraction is divided down and has only 1 as a common factor. Mixed Number: When the amount given has a whole number and a fraction. 46 Fraction Denominator 47 Numerator Benchmark 48 Equivalent Fraction 49 Math Vocabulary Vocabulary Word Describe Definition Example Draw a Picture 50 Fraction Unit Lesson 2: Creating Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Think/Pair/Share and Total Physical Response as strategies of instruction through this fraction lesson. The sharing helps language learners say the words and understand meaning and the Physical helps the students become actively engage in the lesson. II. Preparation and Materials needed: ! The book Fraction Action by Loreen Leedy ! Word strips from Lesson 1. ! Three white sheets of paper per student. ! Colored pencils or crayons. ! Fraction Cards: 1/2, 1/4, 3/4, 1/3, 1 III. Technology Use: ! No Technology needed in this lesson. IV. Instructional Procedures ! Begin by placing the word strips from Lesson 1 on the board. Have the students read them together, then review the definitions again. ! Read page 4 of Fraction Action without showing the picture. Repeat the activity on the board for the class doing the same as “Miss Prime” from the story. Before telling the students what 51 fraction you have divided the whole circle into, ask the students if they know what the two equal parts of the whole are called. ! Read page 5 to the class and show the pictures. Then read page 6 and show pictures. ! Hand out the papers and pencils or crayons. Have the class turn and talk with their neighbors about things that they can divide in half. Have them list and draw them on one sheet of paper. ! Read pages 710. Discuss the equal parts with the class and talk about which fraction is the largest and which fraction is the smallest. ! Have the students form small groups of 34 and Think/Pair/Share by turning and talking in these groups about whole items that can be divided into fractions of 1/2,1/3, and 1/4. Have them create a list together and create pictures of these items. ! Pair the students up with different partners and have them turn and talk/discuss ways to use fractions every day life. On the third piece of paper have them list and draw examples of these every day situations when fractions are used. ! When the students have a list of ideas of everyday fraction use, have them individually come to the front of the class and act out one of the situations on their list. They are just miming the action and no words. The class is to try to guess what is the fraction action. 52 ! After several have shared, have the whole class get in a circle with plenty of movement room. If the gym were available, that would be a good place to do this activity. You could also go outside if the weather permits. ! Explain to the students that you are going to show them a fraction card. When they see and or hear what the card says, they are to jump in a circle that the fraction represents. ! Demonstrate or have a student demonstrate by saying the fraction is 1/2 and now the student will jump half way around in a circle. ! You will need to say the fraction card as you show the card because sometimes the students will be backwards to the card. Saying the words and fractions also helps language learners. 53 Fraction Unit Lesson 3: Creating Fraction Sets I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for incorporating Realia, ToWithBy and Think/Pair/Share methods in teaching math concepts for student’s greater understanding while teaching this math lesson. II. Preparation and Materials needed: ! The book Fraction Action by Loreen Leedy from Lesson 2. ! Fraction word strips from Lesson1 ! Items that are in sets such as plastic eggs in a carton, box of crayons, measuring cups or spoons, table settings, pictures of sports teams. These are just a few examples. ! Items that can be divided into sets such as; marbles, colored tiles, coins, buttons etc. ! Pizza templates and condiments printed for each student. These are found at the end of the lesson. ! Paper and pencil for each student. ! Alternative activity: Graham Crackers, 34 different decorative candies (small), small bowls for candies, plastic spoons for scooping candy, frosting in bowls, plastic knives. III. Technology Use: ! No Technology needed for this lesson. 54 IV. Instructional Procedures: ! Review the vocabulary words from Lesson 1. ! Review the previous lesson about the creating of fractions by breaking something apart. Explain that some things come in sets and give the students a few minutes to “Think/Pair/Share for some set suggestions. Have them turn and discuss with a partner about different sets and write them down. Have these partners share with the class their list of sets and as they share, write them on the board. ! Read Fraction Action pages 1115 titled Get Ready, Get Set. After reading these pages show some “sets” of items. Discuss the fractional part if you take one away or two away. Review: the “whole” is the total of the set pieces and the fraction is what is left or taken away of the whole when the set is broken apart. ! Have students create another vocabulary page using the vocabulary words of fraction of a Whole piece and fraction of a Set. Have them use their definitions and pictures to show the difference. ! Divide the students into groups of 34. Give each group of students one of the sets of collected objects. Have them count out the whole set to find the total amount within the set. Then divide the set pieces among the group giving each member of the group an equal amount. ! Have students write the fraction of their portion of the set. 55 ! Share the different sets around the class so all students have several opportunities to practice this activity. ! Give each student the Pizza Page. They may color it to create a pizza with sauce. ! Have students talk with each other discussing by creating scenarios about how many pizza pieces each ate and what fraction of the pizza that would be. ! Give each student the Pepperoni/Mushroom/Olive page. Instruct the students they are now going to create their own pizzas. They must cut out the food items and place them on their pizza. They must have equal amounts on each piece, but not all food items must be equal amounts. For example, put six mushrooms on each slice of pizza and four pepperoni pieces on each slice and five olives per slice. ! After all the students have designed their pizzas, have them write the total set of olives, mushrooms and pepperonis per pizza. After this is done, they will find a partner and ask for X amount of pizza from the partner’s pizza. That person must then create the fraction of how many mushrooms from the whole set were eaten and how many are left of the set. They will do the same for all the food items on their pizza. ! The students will share with each other for about 15 min. then have them share with the class what they have learned. 56 ! An alternate investigative Realia activity to supplement this lesson: give each student a graham cracker. Have them examine the “breaking” apart sections of the crackers. Ask how many equal parts can these crackers be broken into? ! Have the students frost their crackers. All sections. ! Let the students decorate each of their crackers using the candy decorations. Each candy must have the same amount per cracker section, but each candy may have different amounts from each other. For example, there might be 6 silver candies on each cracker section and 3 flower candies per section and 10 red hearts per cracker section. ! Once these are done, the students will write down the total amount of candies used for their own cracker. ! Students will find partners and show their cracker to this partner. They will take turns asking questions about each other’s crackers such as: if I ate two pieces of my cracker, what fraction of my cracker is left, and what is the fraction of silver candy is left and what fraction of red hearts did I eat. Questions such as these. 57 Create Your Pizza 58 Fraction Unit Lesson 4: Review of Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Total Physical Response method of instruction for creating this activity to review fraction understanding. II. Preparation and Materials Needed: ! Sidewalk chalk if going outdoors or blue painters’ tape if indoors. ! Create large boxes on the ground or floor and number them inside the box. The boxes need to be made large enough for a student to stand inside. One box per student. ! The boxes should be in a straight line with connecting sides. 1 2 3 4 5 6 7 ! Something like this III. Technology Use: ! No Technology required for this lesson. IV. Instructional Procedures: ! Take students to where the boxes are located, either indoors or outside. ! Have students select their own box and go stand in the box. ! Remind the class this is a quiet activity. Instruct the students that you will be calling out some commands and they need to listen 59 carefully so they will know if they are the ones to “step outside the box” or not. ! Ask all of the even numbers to step out of the box. Then call on a student to tell you what fraction is outside the box. Ask another student what fraction is inside the box. ! Repeat with other questions such as: step out of the box if you Have brown hair Have blue eyes Have shorts on Are on a number that is a multiply of 5, 3, 4 Was born in Jan., Feb., March or any other month. ! Create any commands of your own that will work with this activity. ! Continue asking questions for fractions with each command. Observe to see which students understand the fraction concept and which students still needs some extra work. 60 Fraction Unit Lesson 5: Benchmark Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the teaching methods ToWithBy, Think/Pair/Share and using Realia as methods of instruction II. Preparation and Materials needed: ! The book Fraction Fun by David A. Adler. ! Paper plates, 3 plates per student (plates need to all be the same size) ! Pencils, rulers, crayons. The story suggests red, green and blue. ! Vocabulary page. ! Vocabulary word strip—Benchmark ! Plastic Plate fraction plates. One for each student (example for making these are at the end of the lesson) III. Technology Use: ! If a document camera is available, this would be a great activity to show the book as you read. If there is not one available just show the book as you read. IV. Instructional Procedures: ! Read the book Fraction Fun to the class to the Pizza Math page. ! Have students get out the next vocabulary page. 61 ! Put the Benchmark word strip on the board. Have the students write the word on their vocabulary page. ! Have students think about what a good definition for a Benchmark Fraction might be. Have them turn and discuss with a partner then share with the class what they decided a good definition might be. ! Give the students the definition (to) of a Benchmark fraction and have them write this on the vocabulary page. Have them finish the page (by). ! Handout the paper plates and rulers and crayons to the students. ! Read the rest of the Fraction Fun with the class. Have them do the activities as you read the story. ! Discuss what a good benchmark fraction might be that is easy to recognize. ! Give students the Fraction Plates. The plates are two different colors; let the students know which color is representing the fraction you are giving them. ! Have them show you the fraction 1/2. Look to see that all students have the same fraction. ! Have students show you 1/4 fraction using the plates, again observe for understanding. ! Now have the students show you 1/3 fraction of the plate. ! Discuss how these fractions could be great benchmark fractions. 62 How to make Fraction Plates Purchase two different colored disposable Plastic Plates. They don’t need to be the large dinner plates, just the desert size. Cut each plate from the edge to the center. Then slide the plates together on the slits. The plates will turn over each other creating the fraction of the plate showing. Cutting to the center of the plates. Sliding plates together at the slits. Showing 1/2 fraction. Showing 1/3 fraction. Turn the plates to create the fractions. 63 Fraction Unit Lesson 6: Line Plot Fractions I. Lesson Objective Goals: ! Aids will understand the purpose and procedure for using To WithBy, Think/Pair/Share and Realia as methods of instruction for teaching fraction values through line plots. II. Preparation and Materials needed: ! A small handful of Buttons for each student. (buttons can be purchased through Oriental Trading at $6.00 per package of 800) ! Line plot handout for each student. You will find this at the end of the lesson. ! Ruler for each student. III. Technology Use: ! No Technology needed. IV. Instructional Procedures: ! Review all vocabulary words as a class. ! Have students share one with a partner a way they used fractions this past week. Encourage them to use vocabulary words to describe their fraction experience. ! Give students a few minutes to share their experiences with the class. ! Hand rulers to all the students. Review the fractions of an inch. 64 ! Encourage the students to share a Benchmark fraction that is easy to notice. ! Hand out the buttons and the Button Plot sheet. ! Choose one button to show the class how to do this activity. Then give the students about 30 minutes to work on these themselves. ! Monitor the students and help (with) the students that are struggling with the measurements. ! Watch for students’ creative ways of plotting their measurements. Ask a few to share with their peers, at the end of class, how they recorded their data. 65 Name________________________________________ Date____________________ BUTTON, BUTTON, LET’S MEASURE THE BUTTON Task: You are to measure each of your buttons. Create a line plot to show the sizes of your buttons. Tell what you notice about your data. Include your smallest and largest button sizes. 01inch 66 Fraction Unit Lesson 7: Comparing and Ordering Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using Realia, Think/Pair/Share and Games within the lesson instruction for understanding Equivalent Fractions. II. Preparation and Materials needed: ! Equivalent Fraction word strip. ! Prepare Labeled Fraction Tile page for each student, which is provided at the end of this lesson. ! Fraction Equivalency page can be found at the end of the lesson. ! Scissors for each student. III. Technology Use: ! If a document camera is available, have students share their fraction Equivalents, using their tiles, with the class by projecting them for all to see. IV. Instructional Procedures: ! Review with the class about the Button activity. Discuss which fractions were greater than 1/2 and which fractions were less than 1/2. ! Show the word strip Equivalent fraction and have the students discuss with a partner what they think the meaning of Equivalent fraction means to them. ! Share with the class and give examples of an Equivalent Fraction. 67 ! Have students add Equivalent fraction to their Vocabulary booklet or page. Give them a textbook definition and then have then write it in their own words. ! Give each student the labeled Fraction Tiles handout. ! Instruct the class to carefully cut the tiles out. ! When all the tiles are cut out, let the students work with the tiles and try to find as many Fraction Equivalents as they can. ! Hand out the Equivalency Fraction page. ! Have students find a partner and compare what fractions they have the same and see if there are any differences. ! Have the students list all the fraction equivalents that they find on the Equivalency page. ! Have students share some fractions with the class using the document camera if available. If no camera is available, list the fractions on the board. 68 Labled Fraction Strips 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/7 1/7 1/7 1/7 1/7 1/7 1/7 1/6 1/6 1/6 1/6 1/6 1/6 1/5 1/5 1/5 1/5 1/5 1/4 1/4 1/4 1/4 1/3 1/3 1/3 1/2 1/2 1 69 Fraction Strips 70 Fraction Strips 71 Labled Fraction Strips 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/7 1/7 1/7 1/7 1/7 1/7 1/7 1/6 1/6 1/6 1/6 1/6 1/6 1/5 1/5 1/5 1/5 1/5 1/4 1/4 1/4 1/4 1/3 1/3 1/3 1/2 1/2 1 72 Fraction Equivalent _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ _____________ + _____________ = ____________ 73 Fraction Unit Lesson 8: Comparing and Ordering Fractions I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using Games for understanding in the instruction Ordering and Comparing Fractions. II. Preparation and Materials needed: ! Prepare game board at the end of the lesson. One for each group of four students. ! Prepare instructions for each game board. ! 2 dice for each game board. ! A game piece for each student. Different colored tiles or disks work great. ! A page of unlabeled fraction tiles for each student. III. Technology Use: ! No technology is required. IV. Instructional Procedures: ! Review fraction vocabulary. ! Review fraction benchmarks and equivalency. ! Give each student a set of the unlabeled fraction tiles. ! Give the class a few minutes to label their tiles, but do not cut them out. 74 ! Divide students into groups of four. ! Give each group a game board, instructions, 2 dice and a game piece for each student. ! Review the instructions for playing the game. Roll the dice and show the class how the game is played. ! Explain to the class that the fraction tile page is for them to look at and see if the fraction they roll is greater or less than 1/2. This is a comparison chart for them. 75 Game Rules 1 Roll each die one time. 2 Choose the greatest number to be the Denominator. 3 Choose the least number to be the Numerator. 4 Decide if the fraction is greater than, less than or equal to the benchmark fraction of 1/2. 5 If the fraction is greater than 1/2, you move ahead 2 spaces. 6 If the fraction is less than 1/2 you move back 1 space. 7 If the fraction is equal to 1/2 you move ahead 1 space and roll again. 8 The first person to the end is the winner. 76 77 78 Fraction Unit Lesson 9: Fraction Review I. Lesson Objective: ! Aides will understand the purpose and procedure for instructing and using games as a tool for understanding fractions. II. Preparation and Materials needed: ! Print and cut out the Fraction Cards. Enough for each team ! Best printed on colored cardstock so numbers and printing do not show through. ! Print game instructions for each team III. Technology Use: ! No technology needed for this activity. IV. Instructional Procedures: ! Divide the students into groups of 4. ! Explain to the class that there will be 3 different games going on at the same time. Everyone will have the opportunity to play each. ! Review the rules of the games, showing quick examples of each game. ! Ask for questions and clarification. 79 Concentration Rules 1. Shuffle cards really well. 2. Lay all cards face down on the table or floor. 3. One person starts by turning over 2 cards. 4. If they match, that person gets to keep the pair and will then turn over 2 more cards. 5. If there is not a match, the cards are turned back over, face down. 6. It is now the person to the left to take their turn. 7. Repeat this activity till all cards are gathered. 8. The winner is the one with the most pairs. 80 Do You Have? 1. Shuffle the cards really well. 2. Deal 5 of the cards to each player. 3. The remaining cards are placed face down in the middle of the players. 4. Everyone picks up their set of cards and holds them so only they can see their own cards and their opponents do not know what they have. 5. The object of the game is to get as many matching pairs of fraction cards as possible. 6. The person to the left of the dealer starts the game. 7. First look to see if you have any pairs, if so lay them down in front of you. 8. This person may ask anyone in the circle for a fraction card that might match one they have in their hand. 9. If that person has that fraction they must give it to the person requesting the card. 10. The person giving up their card must now pick up a card from the face down pile. 11. The person asking must now place that match down in front of them and draws another card from the face down pile. 12. Repeat till all cards are paired. Count up pairs to find the winner. 81 Fraction War 1. The players sit in a circle. 2. Shuffle the cards really well. 3. Choose the objective of this game before you start. a. The winner gets all the cards. b. The winner is the one who gets rid of their cards first. 4. The dealer passes all the cards out face down to all the players. 5. The players keep their cards facedown in front of them. 6. When the dealer says go, each person takes the card from the top of their pile and lays it down in the center of the group. 7. The person with the highest fraction on their card takes all the cards in the center. 8. Repeat steps 5 and 6. 9. When your facedown pile is gone, shuffle the cards you take from the center and place them facedown to create a new pile to draw from. 82 Fraction Cards 1 1/2 1/3 2/3 1/4 2/4 83 3/4 1/5 2/5 3/5 4/5 1/6 2/6 84 3/6 4/6 5/6 1/7 2/7 3/7 4/7 85 5/7 6/7 1/8 2/8 3/8 4/8 86 5/8 6/8 7/8 87 1/9 2/9 3/9 4/9 5/9 6/9 88 7/9 8/9 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 89 90 Fraction Unit Lesson10: Fraction Situations I. Lesson Objective Goal: ! Aides will understand the purpose and procedure for using the Total Physical Response method of instruction for the student learning in this fraction lesson. II. Preparation and Materials needed: ! Book Spaghetti and Meatballs for All! By Marilyn Burns. ! Paper and pencil for each student. ! Scenarios for each group. ! Props for students to use. ! Math tiles. III. Technology Use: ! Technology is not needed for this lesson. IV. Instructional Procedures: ! Give each students paper and pencil. ! Explain that as you read this story, they are to listen and create the table placements as Mrs. Comfort creates her placements in the story. ! Explain that they will be creating several different setting designs, so draw small and not take up the whole page on the first setting. ! Tell them to do simple drawings and not take a long time or detail. *Another option for this story is to give the students tiles and graph paper and they can move the tiles around on the paper. ! Read to the class the book Spaghetti and Meatballs for All! ! As you read each situation, give time for the class to recreate their table placements on the paper. ! When the book is finished ask for discussion about the story and how many ways did the family rearrange the tables. ! Divide the class into 2 or 3 groups. 91 ! Explain that they are going to create a skit to perform for the class. ! They can use one of the fraction books we have read to perform or they can create a scenario to act out or they can choose one of the teachers’ situations to present. 
Publication Type  Thesis 
Degree  Master of Education in English as a Second Language 
Department  Department of Education 
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Degree Granting Institution  Utah Valley University 
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