Incorporating RTI and the Mastery Model into Mathematics Tutoring Sessions

Abstract: 

Through my tutoring project and additional research, I have determined multiple ways to assess students on their math skills and improve their comprehension. During each tutoring session, I chose eight third-grade students to test and tutor on different math concepts. I believed the students’ test scores would improve after the tutoring sessions. Each session was structured using the Mastery Model, which incorporated the use of manipulatives as well as guided and independent practice. The Mastery Model allowed me to create a more authentic and organized Response to Intervention (RTI) program that met each student’s need. Incorporating RTI into the process was imperative because it enabled me to analyze the students’ learning as well as assess my own teaching. The post-test results regarding the students’ math skills and comprehension did not show a significant change from the pre-test; however, my observations of the students in the tutoring sessions showed how hands-on activities allow students to view abstract concepts in a more concrete way.

Table of Contents: 

    Introduction

    As I began the first semester of my student teaching I was overwhelmed by the thought of teaching math. My lack of confidence prevented me from having a positive outlook. After previous struggles with mathematics, I worried not only that I would not be able to teach, but also that I would not be able to help children who fear math like I do. I was eager to learn how to boost my confidence in teaching math and the students’ confidence in learning math. This question coincides with the purpose of this paper, which is to present a case study of a tutoring project in which I participated as a math tutor. The case study involved the analysis of Response to Intervention (RTI) notes from the project. There was no research question or hypothesis associated with the study; rather, it only involved descriptive responses that examine the tutoring process and learning.

    Tutoring Procedure

    Diagnostic

    The initial step in the tutoring process was to have the students take a pretest, which allowed me to determine the basic skill levels of the students, as well as which portions of the Texas Essential Knowledge and Skills (TEKS) curricula were problematic for them. The diagnostics showed me that on the 100-point scale the highest score was a 65, and the lowest score was a 25. Although the results included a wide range of scores, I noticed that the students struggled with many of the same portions of the TEKS curricula. These portions included:

    • 2.1(A) use concrete models of hundreds, tens, and ones to represent a given whole number (up to 999) in various ways;
    • 2.1(C), use place value to compare and order whole numbers to 999 and record the comparisons using numbers and symbols (<, =, >);
    • 2.4(A), model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined;
    • 2.3(D), determine the value of a collection of coins up to one dollar; and 2.5 (B), use patterns in place value to compare and order whole numbers through 999.

    After observing the diagnostic results, I decided to group all of the students together for the tutoring sessions. The portions of the TEKS curricula that they had not yet mastered included those with a focus on place value, which is essential to performing addition, subtraction, multiplication, and division. That the students did not understand place value could also explain why they missed most of the questions involving money. I believed that the students struggled with questions that asked them to use patterns in place value to compare and order whole numbers through 999 because they had not mastered place value, and also, because the concept involved algebraic thinking, which might have been too difficult for the students to understand at this stage. After making these determinations from the first sessions, I created my first intervention that involved the Mastery Model.

    Instructional Model

    The Mastery Model consists of different steps that incorporate a variety of teaching strategies. The first step is the orientation, during which the teacher introduces the concept through a song, piece of art, or a story. This process enables students to activate their prior knowledge either from other subjects or from previous math lessons. It also engages the students and attracts the interest of students who are more visual, auditory, or kinesthetic learners. I spoke to the students for only a short period of time. The instruction part of the model was a recap of the orientation in order to ensure that all of the students understood what we would be learning.

    Another strategy that I used involved incorporating structured, guided, and independent practice during the tutoring sessions. During structured and guided practice the students practiced the concept through activities that included the whole class or partners. Independent practice enabled both the students and me to determine what the students knew and how they could apply it. During this practice, the students usually answered math problems that I could score and review. The last step of the mastery model was the assessment, which usually consisted of a game. This game could be played with partners, the whole class, or even independently. I tried to make the games interactive so that the students could work on their communication skills and could learn from one another. This not only helps the students with their math skills, but also assists students in other subject areas because student communication is very important. Communication helps the students organize their thoughts and also enables them to feel comfortable asking questions to clarify and increase their knowledge.

    Throughout these sessions I incorporated the use of manipulatives, which allowed the work to be more hands on and comprehensive. The manipulatives that I used most often were base ten blocks. Base ten blocks are made up of individual units that represent the ones place, rods or groups of ten that represent the tens place, and flats or groups of hundreds that represent the hundreds place. These base ten blocks were applied to many different concepts, rather than to solely place value. The blocks ultimately allowed the students to continue to build on the concept of place value.

    Response to Intervention

    Response to Intervention was another method that I used during the tutoring sessions. “Response to Intervention (RTI) integrates assessment and intervention within a school-wide, multi-level prevention system to maximize student achievement and reduce behavior problems” (National Center on Response to Intervention, 2011). This systematic process was conducted through the tutoring sessions, assessments, and weekly narrative responses. Although this project was not as formal as RTI it had the same intent and goals.

    The RTI system is separated into three tiers. In Tier 1, class instruction is differentiated for various types of learners. In Tier 2, some students are pulled out to work together under the guidance and instruction of a teacher or specialist. Tier 3 is implemented when the student or students show little success with Tier 1 or 2. This type of instruction is more explicit and in depth, and it can either be provided to individual students or to small groups of students. The tutoring sessions were most similar to Tier 2 because the students were organized into small groups who were assessed and tutored over a period of time. RTI was incorporated into the tutoring process through weekly responses in which I reflected on the students’ learning, my learning and the effectiveness of the plan. These responses allowed me to understand that it is imperative to consistently assess and improve the students’ learning as well as my own teaching.

    Weekly Responses (RTI): Week 3

    Descriptions of Learning Among the Children

    At the beginning of the lesson I instructed the students on how to use the “greater than” and “less than” symbols. I had the students use manipulatives, such as base ten blocks, for comparisons so that they could actually see how one shape was greater than the other, rather than just using numbers. I had the students create rows of marks representing each number. This enabled them to use one-on-one correspondence and also provided them with a visual of “greater than/less than.” I believe that the approach I used in teaching the concept of “greater than” and “less than” was a different perspective for the students, because they. They all discussed how they had learned this concept with the alligator representation, where the greater than/less than symbols are seen as the opened mouths of alligators (> or <). Overall, this activity helped show the students how the “greater than” and “less than” symbol can be created and understood in a different manner.

    Specific Details of Student Learning

    Students demonstrated their learning through the practice activities. First, I noticed that they had a good understanding of how to use the base ten blocks, because they counted the different amounts that I gave them and separated the blocks into ones, tens, and hundreds. Then, the students ordered themselves from least to greatest. At first they struggled because they were not looking at everyone’s numbers, but they were able to readjust themselves by figuring out which numbers were greater and which numbers were lesser in value. By observing the thinking processes of the students I was able to assess their knowledge. The students also learned when they had to apply their knowledge to real life examples, because they thought about how “greater than” or “less than” situations would occur in their own lives.

    How the Intervention Plan Facilitated Student Learning

    I believe that the learning was facilitated by my use of various approaches to teach the concept of “greater than” and “less than.” The students demonstrated that they understood “greater than” or “less than” in both a concrete and abstract way, which is important because it shows that the students truly understand the concept. In addition, I believe using manipulatives, visuals, and real life examples enabled the students to better understand their learning process.

    Description of the Learning that Occurred for Me

    I learned that it was important to allow the students to converse during the lesson, talking as much, or even more, than I was. This allowed me to understand how the students were thinking, in addition to observing whether they were or were not engaged in the lesson. I also learned that it is beneficial to continue to incorporate specific learning strategies such as the base ten blocks. As the students continued to practice with the base ten blocks their understanding of the concept improved, and they became more comfortable using them. It was important to incorporate a variety of techniques, so that the students could learn in a variety of ways.

    Specific Details of My Learning

    I observed the learning occurring among my students as they reacted to my teaching. In the past few tutoring sessions, I realized that each one is a learning experience, because you never know what the students are going to understand or how they are going to react. During a particular session I saw the importance of having the students engage in discussion, because, as they would call out answers, I would ask them why they thought their answer was correct, rather than simply responding “good job,” “that’s correct,” or “try again.” This forced the students to explain why or how they got their answer, which allowed me to observe their learning and thinking processes. It was important to be consistent when using manipulatives and to use a variety of techniques. My use of the base ten blocks made the blocks seem less foreign to the students, and thus allowed them to continue to use them.

    How the Intervention Plan Facilitated My Learning

    I believe my learning was facilitated because the intervention plan was student-centered. I did less talking and allowed the students to figure out questions on their own. I also learned by simply asking the students questions about what they know and what they would like to work on. This strategy helped me develop my next intervention plan, because it allowed me to learn more about the students’ strengths and weaknesses.

    Reflection on the Plan—What Worked? Why?

    The parts of my project that did work included the students’ use of manipulatives, the creation of a group discussion, and allowing the students to move around during the activity. Using the manipulatives allowed the students to continue to see the concepts in both a concrete and abstract way. It also made them more comfortable using the manipulatives, which might have encouraged them to use the manipulatives in class. Our discussion of the concepts during the lesson allowed the students to take ownership of their learning, and also allowed me to facilitate the students’ learning. Allowing the students to move around during one of the activities enabled them to get their energy out as they created a visual image of least to greatest.

    What Did Not Work? Why?

    First, I believe I should not have had the students work in the conference room. They got so excited to be in a new and different place that I found it hard to keep them focused on the task at hand. I also think that I should not have had all six children together, because it made it more difficult to work with each student individually. That being said, there was no alternative that would have made this possible, because the students were not in school on Monday. I also found it difficult to get the students to create their own word problems. Most of the students simply sat there and said that they could not think of anything, or they created a problem that did not make sense. As a result, I worked with the students, and together we created a problem on the board. Having the students work with partners during the game also did not work, because the students were very particular about their partner and they complained if they had to be partners with somebody that they did not like. These distractions prevented them from staying on task, and they did not put very much effort into the game they were playing.

    What Would Have Made It Work Even Better? Why?

    I believe that the intervention plan would have worked better if the students had been divided into two groups of three. That would have allowed me to work with more of the students individually and to better understand their learning. The next time I teach these concepts I will take one group of students on Monday and another group of students on Tuesday. Another way I could have improved my tutoring session would have been to have the students continue the activities or the game the following week rather than trying to get everything done during one session. I believe that this session was rushed, and I want the students to have enough time during each activity to really grasp the concept. The last way that I could have further improved my session would have been to have the game include the whole group instead of just one partner. With a group game, I believe the students would not complain so much about their partner and would instead focus on their learning and the application of their knowledge.

    Weekly Responses (RTI): Week 6

    Description of the Student Learning

    During Week 6 we finished the intervention plan from the previous week, which focused on double digit subtraction. The students completed a worksheet and played BINGO. The students were very excited to play BINGO, which seemed to make them put extra effort into their work. They are continuing to become more proficient in subtraction with regrouping, because they are applying their knowledge to the games and math problems. The students are also continuing to use their manipulatives as aids, which shows that the manipulatives really are beneficial for them.

    Specific details of students’ learning

    I could tell that learning occurred by observing the students work on their problems. They were showing improvement by showing they knew how to work problems, and by answering most of the problems correctly. They verbalized their understanding and also showed their work on paper. I felt it important that the students continue to use the base ten blocks, because they indicated that they better understood the concept having material in their hands. Although they did not use the base ten blocks during BINGO, I thought it was important that they were able to complete the problems without the blocks, because. I knew that they understood the concept and believed they should not use the blocks every time.

    How the Intervention Plan Facilitated this Learning

    I believe the intervention plan enabled the students to apply their knowledge in a fun and engaging way. All of the students loved playing BINGO, which was both an encouragement for them to do their work and a way for me to further assess their understanding of concepts. I believe having them complete a worksheet with word problems that included subtraction and regrouping proved helpful, because it allowed the students to practice questions that they might see on future standardized tests.

    Description of the Learning that Occurred for Me

    I learned that it is important to make sure that every student is on track. During the BINGO game I decided to work with one of the students individually, because I knew that the two other students were able to do the problems. This student needed extra help, so I took the opportunity to support him as he played the BINGO game. I noticed this was beneficial, because he got more of the work finished than he usually did during the tutoring sessions. After this experience, I understood that it is important to take every opportunity to help the children take control of their learning. Seeing the students so excited about the BINGO game taught me that I should incorporate fun and enjoyable activities for them so that they would become more engaged and be more able to apply their knowledge.

    Specific Details of My Learning

    I knew that learning occurred when the students demonstrated their comprehension, but they also felt a sense of accomplishment when they completed their work. This taught me that it is important for teachers to make sure their students not only understand the concept, but also that they and are proud of themselves. If students have drive and confidence they will perform to the best of their abilities.

    How the Intervention Plan Facilitated My Learning

    I think that I had more time during the intervention plan to work with the students individually, which enabled me to learn more about the students’ learning. This also let me assess the students more thoroughly, because they were completing individualized activities where they had to apply their own knowledge. This knowledge helped with assessment of the students’ progress in their learning. Another aspect of the intervention plan that was helpful was that we were continuing the previous lesson. This allowed me to see what the students remembered, and it also gave the students more time to talk and complete their activities. In other words, the plan was centered more around the students than previously.

    Reflection on the Plan

    What Worked? Why?

    I believe that both of the activities worked because students were allowed to continue to practice single subtraction and regrouping subtraction. The worksheets had the students apply their knowledge and use their higher order thinking skills to solve word problems. Although they struggled more with the word problems, I believe this was important for me to know in order to determine what else the students needed to work on. The students also continued to practice using the base ten blocks as they completed the worksheet, which was another reason the BINGO game was successful.

    What Did Not Work? Why?

    I found it difficult to get the students to do the worksheet at the beginning. They are not used to coming in and having to get right to work. I think I should have started off with an orientation or opening activity to get the students more engaged and also to help recap what we learned the previous week. One issue with the BINGO game was that I did not have a prize for the winner. The students seemed to expect it, so they were disappointed when they did not receive anything.

    What Would Have Made It Work Even Better? Why?

    I believe the plan would have worked better if I had incorporated a “warm-up” at the beginning to get the students thinking and to activate their prior knowledge from the previous session. Another way that I could have improved the plan would have been to have the students play a game where they had to interact more with each other. This would have allowed me to see how the students communicated and voiced their understanding, and it would also have allowed the students to learn from one another.

    Summary

    Although the pre-test and post-test served as formal assessments, I believe that the formative assessments of the tutoring sessions allowed me to get a more accurate perspective of the students’ successes, both because. I was able to work with each student individually and because I was able to reflect on each session. These reflections taught me that RTI allows teachers to analyze the students learning, as well as assess their own teaching strategies. I believe that RTI is a very important and helpful tool, and all teachers should implement it in their classroom. Typing up responses and figuring out what worked and what did not work helped me improve my sessions from week to week.

    Learning from the Process of RTI

    Implementing RTI throughout the tutoring process was extremely beneficial and had a positive impact on the overall process. A common misunderstanding is that RTI should be used only for students who have learning disabilities, but Douglass and Horstman found that “many researchers affirm that there is evidence to support RTI as a means of monitoring the progress of students with or without disabilities” (Douglass & Horstman, 2011, p. 24). Determining which strategies were the most effective and how the students responded to them helped me with the RTI part of the tutoring project. I constantly made changes to my lesson so that the students could better grasp the concepts. I was able to think on my feet and create modifications during the sessions. I believe that every teacher should incorporate RTI into their classroom based on the three tiers. This strategy will help improve the learning of all students.

    I noticed that most of the students I tutored had the greatest difficulty with word problems. They might have been able to do the mathematical procedures just fine, but when they had to start applying them to different scenarios it seemed to get really confusing for them. I believe that there are two reasons for this. First, they do not know where to begin when they are answering a word problem, and second, they simply have not had enough practice. In order to help the students effectively practice answering word problems, I believe that the teacher has to model the process and break it up into steps rather than long explanations. The article The Problem with Word Problems argues that “[t]urning these lists into simple graphic organizers allows students to approach problems in a step-by-step fashion” (Forsten, 2004, p. 23). Throughout the tutoring sessions, the information was organized through the Mastery Model. The Mastery Model incorporates different types of instruction and practice in order to make the learning successful. The students must understand why they are taking these steps and how each step affects the solution, so they can apply it to everyday situations and incorporate it into their mathematical thinking. I also believe that this will continue to help students and teachers assess and understand the students’ ongoing learning and thinking.

    The main focus of the article, Using Manipulatives to Teach Elementary Mathematics, is that “educational research indicated that the most valuable learning occurs when students actively construct their own mathematical understanding, which is often accomplished through the use of manipulatives” (Boggan, Harper, & Whitmire, 2010, p. 2). Other benefits of using manipulatives include improvement of students’ short-term and long-term memory of math, as well as the opportunity to reflect on one’s accomplishments and the prevention of math anxiety.

    Theorist James Zull conducted many studies on the brain, discussing the central nervous system and the complicated process of neurons reacting to certain experiences and behaviors. “The more brain areas we use, the more neurons fire and the more neural networks change–and thus the more learning occurs” (Zull, 2004, p. 72). This reaction enables students to better understand and retain information, showing the importance of limiting anxiety by creating new dendrites in order to build a bridge between fear and pleasure. “Research also indicates that using manipulatives is especially useful for teaching low achievers, students with learning disabilities, and English language learners” (Boggan, et al., 2010, p. 5). It is crucial for teachers to implement manipulatives in the classroom, because students’ learning styles and backgrounds are so diverse.

    One potential problem with manipulatives is that they can be used without being internalized. Students might enjoy using the manipulative and might seem more engaged, but that does not necessarily mean that they understand the concept they are learning. In the article Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer, we find that, “We hypothesize that it is not only the content of the learning materials (concrete versus abstract) but also how those materials are used that is critical to learning complex cognitive skills such as those taught in mathematics and science” (Belenky & Nokes, 2009, p. 103). In this article, I learned the importance of not only incorporating hands on activities with students, but also of making sure that students are thinking metacognitively as they learn. After working with a group of students, the article concluded that their “research suggests that pairing concrete materials with metacognitive prompts should facilitate procedural fluency as well as conceptual understanding and transfer” (p. 108). I believe that students have to make the connection to what they are learning and how it relates to their prior knowledge. In order to facilitate this connection the students must be provided with these opportunities.

    The basic goal of the tutoring sessions was to clearly determine what the students knew or had not yet learned, and then to help them with their understanding. I used manipulatives, RTI, the Mastery Model, and different assessments to determine the students’ comprehension. However, what helped me the most was feedback from the students. I know that the techniques I used to help teach the students do have an effect on how they learn the concepts, but the most crucial part of the learning process is to make sure that the students have used their mathematical thinking to help them realize how they figured out a problem. According to Kostos and Shin, “It is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos and Shin, 2010, p. 223). This article, entitled “Using Math Journals to Enhance Second Graders’ Communication of Mathematical Thinking,” discusses an action research study involving math journals. The journalist’s process of working with the students and using manipulatives seems very similar to my tutoring project, but her approach also included documentation of the students’ mathematical thinking. This is extremely important, because it helps the students show their mathematical thinking as they solve a problem, rather than by simply memorizing the method they use to solve a problem. If students just memorize ways to figure out the answer, then they will not truly understand why they used that method and how it relates to the overall math concept.

    Learning subtraction with regrouping is a difficult task for students to grasp conceptually. If each student is given base 10 blocks, we can use the units, rods, and flats to demonstrate how ten units in the ones place can be regrouped into a rod that moves to the tens place. Manipulatives are much easier for students to understand than the abstract concept of crossing out numbers and changing them. Some might be able to memorize this method and determine the correct answers, but it will not help them think mathematically. If children are not thinking mathematically, then they will continue to have difficulty with math concepts that are even more abstract.

    Personal Reflection

    During each tutoring session, I would either come across a challenge and try to overcome it, or I would be working on a challenge I already had from the previous sessions. Some of the more challenging situations I encountered were those that I could not control, such as only having a limited amount of time to tutor the students. In these situations, I thought about what was best for the students rather than focusing on finishing the intervention plan. If the students did not complete everything I had planned for them, I would make sure to continue the lesson during the next session. I believe that it is more important for the students to really understand the concept and to be able to show their teacher that understanding, than it is for students to be able to show the teacher that they can rush through an activity. I observed some of the students taking their time to really apply their knowledge and understanding when they used their base ten blocks to determine the answer and even to check their answer. This showed me that the students have really taken ownership of their learning.

    Some of the tutoring sessions did not go exactly as planned, but this gave me the opportunity to figure out how to make the next tutoring session better. I view these types of experiences as changes that I made in order to improve the students’ learning, rather than as challenges. During the first tutoring session, I had all six students attend at the same time. I decided to change it to two sessions of three students for the next time because of the results from the first tutoring session. There were too many students in that first session, so they were getting distracted, and I was not given the opportunity to work with each student individually. I also noticed that the students were on different levels both academically and behaviorally. One of the students I worked with had a very difficult time listening and making the right choices. I did not give up on him even though this was frustrating and disrupting to the other students. During the next tutoring sessions I worked with him, rather than for him, and was able to observe where he was getting confused. In order to help break down the concept and look at it in a more comprehensible way, I had him work with the base ten blocks and use them to complete each problem. I believe that this really did work, because he asked for the base ten blocks during the rest of the sessions. Although this might not have solved all of his problems it was beneficial, because it enabled him to stay on the right track rather than falling even further behind.

    After experiencing the tutoring sessions and the challenges that went along with them, I learned that it is important for teachers to help the students take ownership of their learning. I witnessed the students taking charge by following directions, staying on task, asking questions, and even helping their peers. The students should not come into the tutoring sessions thinking that they are there to simply get lectured or to play pointless games; they should realize that they are receiving help that will allow them to be able to do the math problems or figure out the concepts on their own. Tutoring is also not for the teacher to just tell students the answers or to make the information any easier. As a tutor, I made sure to have the same expectations I would with any other student. I just approached the content in a different way and provided the students with more one-on-one time so I could understand their thinking process. This enabled me to determine both their strengths and weaknesses, so I could work with both.

    I have also learned how essential it is to include different strategies and techniques during the tutoring sessions. My use of the Mastery Model enabled me to make sure that all of the students were provided with hands-on and engaging activities that helped the students better understand the math concepts. During these activities the students also interacted with each other and worked with base ten blocks. This allowed them to understand the abstract material in a more concrete way. Overall, this model taught me that it is important to structure learning environments in this way, whether it is for a small group tutoring session or for a large group and classroom setting. The Mastery Model also helped me to create a more authentic and organized RTI that met each student’s needs. Another positive experience that I gained from the tutoring project was learning how to communicate with the students on a more personal level. When teaching an entire classroom in the future, I may find it difficult to make sure that everyone understands the concept and is on track. The tutoring sessions helped me to practice this skill and helped me prepare for working with individual students in a classroom setting.

    I have learned that it is crucial for teachers to provide the students with opportunities to activate prior knowledge and connect their learning to real life situations. This will help the students see how math can be applied every day. If I asked a student what 22 minus 12 was, then most likely they would be able to find the correct answer. However, if I gave them a word problem where they had to figure out how to use subtraction to get the right answer, most students seemed to get confused. I noticed this difficulty with word problems throughout the tutoring process, and it reminded me of what I should not do. Some teachers have the students remember certain words that could help them figure out if they should add or subtract such as “sum,” “difference,” “how many more,” and so on. However, having the students memorize these words will not help their mathematical thinking—where they really understand why they are adding or subtracting. This is why I always made sure that the students used manipulatives when they were trying to determine an answer to a word problem. They also benefitted from acting out the scenario so they could make a better connection. Not only would I have the students act out the scenario, use the manipulatives, and find the answer, but I would also have them tell me why they added or subtracted. Overall, this method seemed to help the students reflect on their own thinking and to practice using their mathematical thinking rather than memorization.

    The tutoring project was very rewarding, because it allowed me to gain experience working with and assessing diverse learners. Having the opportunity to work with students also showed me the differing perspectives students have of the concepts. As a tutor and pre-service teacher, I believe that it was my duty to help the students believe in themselves by showing them that they have the capability to learn and understand math.

    Recommendations

    During each tutoring session, I discovered new things about myself and the students. I enjoyed the fact that it was a learning experience in both situations, and that I was able to reflect on myself as a tutor and a pre-service teacher. Although none of the sessions were perfect and none went exactly the way I planned, they all gave me the opportunity to think on my feet and implement modifications that would best meet the needs of the students. I believe that this is an important skill to develop, because I will experience situations such as those during the tutoring sessions when I have a classroom of my own.

    In order to help a student solve a problem, teachers cannot simply demonstrate their mathematical thinking; they have to make sure the students provide evidence of their mathematical thinking as well. Using math journals could be beneficial for future tutoring projects or even for math lessons in the classroom. Not only will math journals allow the students to reflect on their understanding, but it will also allow teachers to better understand the learning process and to reflect on how their students were able to understand the concepts. I would consider the weekly responses as a sort of journal I kept throughout the process. These reflections helped me immensely; therefore, I would assume that the students would benefit from writing responses each week as well.

    My final recommendation is to provide students with a survey that asks them questions about their overall experience. If I had used the survey in this project I could have used the student responses to help me to better reflect on my experiences. I could have asked students to fill out surveys after each session, because I might have gotten a more honest response on paper than by asking them in person. Also, I think it would have been beneficial to have had tutoring sessions with each student individually both at the beginning and at the end of the tutoring project. This would have given me a better understanding of each student’s prior knowledge and of their personal growth. As for future tutoring projects, I would recommend that more time be given to work with the students and that teachers be given fewer students to tutor. Extra time and fewer students would enable tutors to get to know the students better, so that the intervention plans could be individualized to fit the needs of each student and, therefore, be more effective.  

    References

    • Belenky, D. M., & Nokes, T. J. (2009). Examining the role of manipulatives and metacognition on engagement, learning, and transfer. Journal of Problem Solving, 2(2), 102-129. Retrieved from http://docs.lib.purdue.edu/jps/  
    • Boggan, M., Harper, S., & Whitmire, A. (2010). Using manipulatives to teach elementary mathematics. Journal of Instructional Pedagogies, 3, 31-6. Retrieved from http://www.aabri.com/jip.html
    • Douglass, L., & Horstman, A. (2011). Integrating response to intervention in an inquiry based math classroom. Ohio Journal of School Mathematics, (64), 23-30. Retrieved from http://www.ohioctm.org/ojsm.htm 
    • Forsten, C. (2004). The problem with word problems. Principal, 84(2), 20-23. Retrieved from http://naesp.org/  
    • Kostos, K., & Shin, E. (2010). Using math journals to enhance second graders' communication of mathematical thinking. Early Childhood Education Journal, 38(3), 223-231. doi:10.1007/s10643-010-0390-4
    • National Center on Response to Intervention. RTI4SUCCESS.org. Retrieved from http://www.rti4success.org
    • Zull, J. E. (2004). The art of changing the brain. Educational Leadership, 62(1), 68-72. Retrieved from http://www.ascd.org/Default.aspx