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The Effect of Mathematics Journaling on Mathematics Problem-Solving Skills of Second Graders An Action Research Project Submitted in Partial Fulfillment of the Requirements of the Master of Education Degree Melissa Sneed and Kelly Williams July, 2009 Bagwell College of Education Department of Elementary and Early Childhood Education Kennesaw State University Kennesaw, Georgia David J. Martin, Ph.D., Advisor Kelly Williams and Melissa Sneed ECE 7550 July 14, 2009 Abstract The purpose of this research was to determine the effect of mathematics journaling on mathematic problem-solving skills of second graders. There has been a decrease in math problem-solving skills within our school. Journaling is a strategy that could aid in improving these weaknesses. The significance of this study to this school is to improve mathematical problem-solving skills. The theoretical basis is to show whether journaling is an effective strategy to improve these areas in mathematics. This study was implemented to explore the benefits of math journaling for second grade students and to discover if math journaling improves and enhances the understanding of mathematical problem-solving skills. The word problems were selected from the county’s math inventory dealing with the topic that we were teaching and were applied as the pre-test and post-test for the phase without journaling (wording and numbers was changed to minimize the Test-Retest Effect). A different word problem was selected from the county’s math inventory dealing with the topic that we were teaching for the phase with math journaling. Wording and numbers were changed to minimize the Test-Retest Effect. Before the study began, a series of problem solving strategies were taught to all of the students. For Week 1-3, there was an application and practice time without journaling. The students were given a pre-test at the start of Week 1. They were given a post-test at the end of Week 3. For Week 4-6, the journaling process was implemented. Week 4 began with a pre-test and Week 6 concluded with a post-test. We compared Weeks 1-3 results to Weeks 4-6 results to see if math journaling was beneficial in improving mathematical problem solving skills. The students had math problems that are similar in difficulty for both phases. The problems that were used during the application process came from the county inventory as well as a math word problem resource book. We examined descriptive statistics to make the determination of the effect of journal writing on math problem-solving. The significance of any changes that occurred between studying mathematics problem solving skills without the use of journals and studying math problem solving skills with the use of journaling was calculated using a t-test to compare the pre-post test gains in weeks 1-3 with the pre-post test gains of weeks 4-6. This research project was six weeks long and included 32 students. Of these students, there were 24 regular education students, 5 Special Education/ESOL students, and 3 gifted students. The study was quantitative. The data was analyzed by comparing the pre/post gains of each phase of the study. Each pre- and post- test in both phases was scored by percentage correct out of 100. All data from each test was inputted into a spreadsheet into Microsoft Excel. A t-test of Two Sample Assuming Unequal Variances showed that this project was statistically significant. This t-test illustrates that math journaling had a positive effect on the students in this study. In order to establish statistical significance, the t-test needs to be <.05. Our t-test demonstrates a value of .045, which achieves statistical significance. It is not a large significance, but it still shows that math journaling is beneficial. In addition, this study found that it was more significant for students in regular education, but was not significant for students in special education, including ESOL and gifted students. We can hypothesize that because the sample size of this sub-group was small that we could not achieve the desired results. However, if the sample size was larger the treatment may have yielded more significant results. We will continue to implement this practice because it was beneficial to most of the students. The Effect of Mathematics Journaling on Mathematic Problem-Solving Skills of Second Graders Kelly Williams and Melissa Sneed Kennesaw State University Dr. David J. Martin Effects of Math Journaling 2 Abstract The purpose of this research was to determine the effect of mathematics journaling on mathematic problem-solving skills of second graders. There has been a decrease in math problem-solving skills within our school. Journaling is a strategy that could aid in improving these weaknesses. The significance of this study to this school is to improve mathematical problem-solving skills. The theoretical basis is to show whether journaling is an effective strategy to improve these areas in mathematics and written expression. This study is being implemented to explore the benefits of math journaling for second grade students and to discover if math journaling improves and enhances the understanding of mathematical problem solving skills. Introduction Background This study took place at an elementary school in a suburb of a southeastern metropolitan city. Our school serves students from a variety of economic and cultural backgrounds. This includes middle-class neighborhoods, apartment complexes, and some mobile home communities. The school population consists of 964 students, 461 females and 503 males. Of these students, 115 are on free/reduced lunch. Our school faces the challenges of a growing ESOL population, including a rising number of students that speak languages other than Spanish, and an increase in the percentage of EIP students. Of the entire student population, 1.6% of the students are considered gifted. The staff members at our school provide a nurturing environment to develop responsible citizens. Effects of Math Journaling 3 It is a collaborative effort of the students, staff, parents, and the community to create the best learning environment. Our students are provided with opportunities for an authentic and challenging education. Students learn best when they are actively engaged in meaningful work. The teachers at our school collaboratively use data to identify and improve instructional practices. All of the characteristics of our school aided in the decision to complete our research on the benefit of math journaling for mathematic problem-solving in second graders. Statement of the Problem/Purpose The purpose of this study was to explore the benefits of mathematics journaling in mathematical problem-solving skills in second graders. To find this out, we used a pre- and post- test assessment for each of two phases of the study. The questions on these tests were taken from the County School District Constructed Response questions. The first phase involved math problem-solving without the use of a journal. The second phase of this research was with the use of a math journal. Our expectation for this project was that journaling would improve mathematical problem-solving skills by setting up certain steps to complete math word problems. At the same time, the journaling would aide in improving writing skills as well as mathematical problem-solving skills. Research Question What is the effect of math journaling on mathematical problem-solving skills of second graders? Effects of Math Journaling 4 Literature Review The purpose of this literature review is to examine the benefits of math journaling to improve problem-solving skills in students. Studies have found that math journaling is a great way for students to explain their thoughts when solving word problems. Math journaling is an additional tool that should be used along side a mathematics curriculum adopted by the school. A famous mathematician, George Polya, said, “Solving problems is a practical art, like swimming or skiing or playing the piano: you can do it by imitation and practice… if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems” ( Math Gym, p. 1). For the purpose of this research, the literature review will discuss the many approaches to journaling, investigate if there is a relation between math journaling and problem solving and examine the effectiveness of math journaling to improve a student’s problem solving skills. Math journaling is a way that teachers use to get their students to write about a math problem by picking out key information, illustrating the information and then using the information to solve a math problem. The National Council of Teachers of Mathematics emphasizes that mathematical communication organizes and consolidates mathematical thinking (NCTM, 2004). Burns stated in 2004 that “writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas-all useful processes for making sense of mathematics” (p. 31). Burns wanted to test the hypothesis that writing helped make sense of mathematics. According to Flores and Brittain (2003) it was discovered through their research that process writing helped students learn mathematics and create a personal connection to new concepts. Process Effects of Math Journaling 5 writing is a model used in writing instruction that sees writing as an evolving process. Students follow a given set of procedures for planning, drafting, revising, editing (proofreading and correcting), and publishing (sharing by some means) their writing. Gurule stated (2007), “When you begin focusing more on student reflections in mathematics, students became more engaged in building a deeper understanding of mathematics. Students could understand their goals, where they were according to the learning goals, and what they needed to do to achieve those goals” (p. 3). Gurule wanted to show that with a deeper understanding of mathematic concepts, students would improve and become more engages in mathematical concepts. Harmon (1995) discusses how using background knowledge and strategies that have been implemented help children to become effective problem- solvers. Some of Harmon’s findings suggest that, “the most effective problem solvers were those who had sufficient domain-specific knowledge of mathematics to solve the problem, and who also engaged in the sophisticated monitoring strategies required for goal attainment. The research findings indicate that successful problem solvers engage in sophisticated monitoring strategies and are aided by sufficient domain-specific knowledge. Children, as they grow older, gain more knowledge and become more efficient in the strategies they employ. Another key finding lies in the importance of metacognitive skill. This is reflected in more efficient problem solving and in better choice of appropriate strategies even when knowledge alone is not the critical factor” (p.580). As presented by Benko, Loaiza, Long, Sacharski, and Winkler (1999) many educators today put emphasis on using metacognitive skills and recommend methods of developing these skills. Also reported in this article by Benko, Loaiza, Long, Sacharski, and Winkler Effects of Math Journaling 6 (1999), Howell and Barnhart (1992) discovered that students can learn to think about math concepts successfully by using a three- step process. First, the students are introduced to concrete, hands- on experience. Second, teachers begin teaching the students to use symbols and drawings to represent information from the problem. Lastly, teachers teach the concepts through an abstract create of the equation. Educators seem to be skipping the first two steps frequently. According to Sezer (2008), by improving critical thinking skills, students will be able to understand mathematical concepts better and positive effects would be seen in problem solving as well. Sezer showed that positive effects would happen if students had a deeper understanding of mathematical concepts. A study conducted by Kelly (2006) stated that problem solving across all areas normally involves some sort of tool or manipulative, and if manipulatives help to make mathematics “come to life,” teachers should be encouraged to use them in an effort to improve problem solving skills. Kelly (2006) suggests that when teaching problem solving skills the problems should be related to real- life experiences. Kelly showed that using manipulatives in problem solving would be beneficial at all times, including assessments. Caracelo stated in 2008, “… the use of math journaling does in fact impact a students’ ability to apply math problem solving strategies taught in class. Through the data analysis it is noted that the experimental group did score higher on the post-test and exhibited greater gains as compared to those members of the control group. This study supports that more research should be done on the use of math journaling and its effectiveness on the development on problem solving skills” (p.14). Effects of Math Journaling 7 Though much of the research found supports math journaling as a tool to enhance a students’ problem solving skills, there has been some research that found some deficiencies with math journaling. Educators know that using math journaling as the only tool used for teaching mathematics concepts will not help children understand all math concepts. According to Pugalee (1997), although mathematics teachers are being encouraged to implement various activities into their instruction, there is insufficient research to provide a basis that these practices are occurring regularly. Writing in mathematics is beneficial when implemented. Pugalee (1997) hypothesized that writing is only helpful when being taught in the classroom. A study by Whitin & Whitin (2002) stated that writing challenges children to make their own understanding of the ideas being discussed. This study wanted to figure out if writing enhanced understanding of a specific topic. Stonewater (2002) reports the NCTM built a strong case for including writing in mathematics. The results indicate that “successful” writers are more likely than “unsuccessful” writers to use appropriate mathematical language (Stonewater, 2002). The students who lack the necessary writing skills may not have the same results as a student who is a proficient writer. Stonewater’s findings were as follows: when students exhibit difficulties with the writing process they are also challenged to effectively communicate their reflections in math. In addition when using math journals appropriately it is important that the teacher give feedback to the students, because students stop seeing journals as purposeful if there is no feedback from the teacher (Manning 1999). In a study that Pugalee (2001) conducted, he investigated whether students’ writing about how they solved math problems demonstrated a metacognitive arrangement. Effects of Math Journaling 8 Pugalee’s findings “indicated the presence of a metacognitive framework. Metacognition, or the monitoring of one's mental activities, is essential to employing the appropriate information and strategies during problem solving” (p.236). As stated in Pugalee’s article, “The term is used to encompass the awareness of the student in such mental processes as planning, monitoring, and evaluating” (Fortunato, Hecht, Tittle & Alvarez, 1991). Math journaling is an outlet for students to write their plans, evaluate and solve problems. . From the literature that we have read, we have realized that math journaling in second grade could be very beneficial to improve problem-solving skills. Math journals are a great tool for teachers to use as an assessment to evaluate a student’s comprehension of a standard. They could also provide insight for the teacher if re- teaching is necessary for the student or if the teacher should be challenging the student. Math journals provide documentation of the student’s knowledge of the math concepts taught. This study will examine the benefits of math journaling in improving mathematical problem-solving skills in second grade students. Methodology Participants A total of 32 students (two second grade classes) participated in this research project. There were 16 boys and 16 girls. Of these students, 24 were regular education, 5 were special education/ESOL, and 3 were gifted students. The participants consisted of 17 Caucasian students, 2 Asian students, 6 African- American students, 3 multi-racial students, 3 Hispanic students and 1 Arab student. All students were eligible for this study. At this point, please describe how you each have your own classroom, and how Effects of Math Journaling 9 close they are to each, and how you continually talked with each other to ensure that the teaching was as close to identical as possible. Research Design/Procedure of Study The purpose of this study was to examine the benefits of math journaling on mathematical problem-solving in second grade students. Word problems were selected from the county’s math inventory dealing with the topic that we were teaching and were applied as the pre-test and post-test for the phase without journaling. Wording and numbers were changed to minimize the Test-Retest Effect. The same type of word problems were used for Phase 2, with math journaling. Wording and numbers were changed to minimize the Test-Retest Effect (see Appendix A). Each pre- and post- test in both phases was scored by percentage correct out of 100. All data from each test was inputted into a spreadsheet into Microsoft Excel. Appendix B shows the scores and gains of the entire sample size. Before the study began, a series of problem-solving strategies were taught to all of the students. For Week 1-3, there was an application and practice time without journaling. The students were given a pre-test at the start of Week 1. They were given a post-test at the end of Week 3. For Week 4-6, the journaling process was implemented. Week 4 began with a pre-test and Week 6 concluded with a post-test. The math problems that were used during application and practice times were collected from a math resource book along with county math inventory problems. We compared Weeks 1-3 results to Weeks 4-6 results to see if math journaling was beneficial in improving mathematical problem solving skills. The students had math problems that were similar in difficulty for both phases. We examined descriptive statistics to make the determination of the effect of Effects of Math Journaling 10 journal writing on math problem-solving skills. The significance of any changes that occurred between studying mathematics problem solving skills without the use of journals and studying math problem solving skills with the use of journaling was calculated using a t-test to compare the pre-post test gain in weeks 1-3 with the pre-post test gains of weeks 4-6. Definition of Terms Math Journaling is a way for students to record their thoughts, understandings, and explanations about mathematical ideas or concepts. The purpose is for students to keep track of their thought process and concepts that they are learning. Problem solving is an approach that involves identifying the causes of a problem and proposing potential, often creative, solutions to the problem, which will be agreeable to multiple parties or individuals. Instruments The same types of problem-solving questions were used to measure the growth in each part of the study. We compared Weeks 1-3 results to Weeks 4-6 results to see if math journaling was beneficial in improving mathematical problem solving skills. We used Microsoft Excel to assess the results of both phases of the research. Results Figure 1 is a table that we created to show the mean and standard deviation from this study and the participant’s pre-test/post-test gains. This table consists of whole group data. For the first phase pre-test, without math journaling, the mean was 0.093. The post- test in phase 1 had a mean of 0.254. The pre/post test gain in phase 1 was 0.161. For the Effects of Math Journaling 11 second phase pre-test, with math journaling, the mean was 0.312. The post-test in phase 2 had a mean of 0.556. The pre/post test gain in phase 2 was 0.244. This data shows that the whole group gained more in the treatment phase than without the treatment. Figure 1 Whole Pre-test 1 Post-test 1 Pre/Post Gain Pre-test 2 Post-test 2 Pre/Post Group Gain Mean 0.093 0.254 0.161 0.312 0.556 0.244 Standard 0.157 0.219 0.196 0.226 0.249 0.179 Deviation A Two Sample Assuming Unequal Variances t-test was conducted and showed that the result of the treatment was statistically significant. Figure 2 shows the results from the t-test. This t-test illustrates that math journaling had a positive effect on the students in this study. In order to establish statistical significance, the t-test needs to be <.05. Our t-test demonstrates a value of .045, which achieves statistical significance. It is not a large significance, but it still shows that math journaling is beneficial. Effects of Math Journaling 12 Figure 2 t-Test: Two-Sample Assuming Unequal Pre/Post Variances Gains Without With 0.666 0.5 Mean 0.145065 0.236548 Variance 0.031056 0.031091 Observations 31 31 Hypothesized Mean Difference 0 Df 60 t Stat -2.04321 P(T<=t) one-tail 0.022715 t Critical one-tail 1.670649 P(T<=t) two-tail 0.04543 t Critical two-tail 2.000298 Figure 3 shows a graph of pre/post test gains of Phase 1 and 2 of all subjects of the study. According to this graph, the majority of the students improved in Phase 2 from math journaling. Figure 3 Pre/Post Gains for Phase 1 and 2 80% 70% 60% 50% 40% 30% Pre/Post Gain 1 Pre/Post Gain 2 20% 10% 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 -10% -20% -30% Effects of Math Journaling 13 Figure 4 is a table that consists of regular education students in this study. For the first phase pre-test, without math journaling, the mean was 0.069. The post-test in phase 1 had a mean of 0.228. The pre/post test gain in phase 1 was 0.159. For the second phase pre-test, with math journaling, the mean was 0.284. The post-test in phase 2 had a mean of 0.555. The pre/post test gain in phase 2 was 0.270. This data shows that the regular education participants gained more in the treatment phase than without the treatment. Figure 4 Regular Pre-test 1 Post-test 1 Pre/Post Gain Pre-test 2 Post-test 2 Pre/Post Education Gain Mean 0.069 0.228 0.159 0.284 0.555 0.270 Standard 0.146 0.201 0.166 0.222 0.272 0.182 Deviation According to this study, math journals are more beneficial for regular education students. This t-test (Figure 5) illustrates that math journaling had a positive effect on the regular education students in this study. In order to establish statistical significance, the t- test needs to be <.05. Our t-test demonstrates a value of .032, which achieves statistical significance. This shows that compared to the whole group of students, this study was more statistically significant for regular education students than for the general population. Effects of Math Journaling 14 Figure 5 t-Test: Two-Sample Assuming Unequal Regular Variances Education Variable Variable 1 2 Mean 0.159708 0.270708 Variance 0.027704 0.03341 Observations 24 24 Hypothesized Mean Difference 0 Df 46 t Stat -2.19966 P(T<=t) one-tail 0.016447 t Critical one-tail 1.67866 P(T<=t) two-tail 0.032894 t Critical two-tail 2.012896 Figure 6 shows a graph of the pre/post test gains of Phase 1 and 2 of regular education students only. According to this graph, 14 of the 24 regular education students improved their score with math journaling. Figure 6 Pre/Post Gains 1 and 2 in Regular Education Students 70% 60% 50% 40% Pre/Post Gain 1 Pre/Post Gain 2 30% 20% 10% 0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Figure 7 is a table that consists of special education students in this study. For the first phase pre-test, without math journaling, the mean was 0.166. The post-test in phase 1 Effects of Math Journaling 15 had a mean of 0.332. The pre/post test gain in phase 1 was 0.166. For the second phase pre-test, with math journaling, the mean was 0.395. The post-test in phase 2 had a mean of 0.562. The pre/post test gain in phase 2 was 0.167. This data shows that the special education participants gained a small amount in the treatment phase, but it was not significant. Figure 7 Special Pre-test 1 Post-test 1 Pre/Post Gain Pre-test 2 Post-test 2 Pre/Post Education Gain Mean 0.166 0.332 0.166 0.395 0.562 0.167 Standard 0.178 0.267 0.282 0.234 0.176 0.154 Deviation This t-test (Figure 8) illustrates that math journaling did not have a positive effect on the special education students in this study. Our t-test demonstrates a value of .994, which does not achieve statistical significance. This group of students included Special Education, gifted, and ESOL students. Effects of Math Journaling 16 Figure 8 t-Test: Two-Sample Assuming Unequal Special Variances Education Variable Variable 1 2 Mean 0.16625 0.167 Variance 0.079589 0.023858 Observations 8 8 Hypothesized Mean Difference 0 Df 11 t Stat -0.0066 P(T<=t) one-tail 0.497428 t Critical one-tail 1.795885 P(T<=t) two-tail 0.994856 t Critical two-tail 2.200985 Figure 9 shows a graph of the pre/post test gains of Phase 1 and 2 of special education students, which includes ESOL and gifted students. It illustrates that 4 of the 8 students did not improve their score with math journaling. This was a small sample size, so we can not conclude that it is not beneficial for all students in these sub-groups. This data only shows that math journaling did not prove to be beneficial for special education students in this particular study. Effects of Math Journaling 17 Figure 9 Pre/Post Gains 1 and 2 in Special Education Students 60% 50% 40% 30% 20% Series1 Series2 10% 0% 1 2 3 4 5 6 7 8 -10% -20% -30% Conclusions Discussion According to the research and our results, math journaling is beneficial to improving mathematical problem-solving skills in second grade students – especially with regular education students. Math journaling is also a great teaching tool for educators. It allows educators to view the journals and see if a student has mastered the concept or if the concept needs to be re-taught. Students were given a pre-test and a post- test for each phase of the project to determine if the treatment was effective for improving mathematical problem- solving skills in second grade students. The student’s problem- solving skills did have a significant improvement after the treatment phase was Effects of Math Journaling 18 completed. We looked at the results of the pre/post test gains. It is evident that the strategies implemented helped the students become successful math problem solvers. We have determined that the use of math journaling is an effective tool to use in the classroom. It provides students with tools for success when solving mathematical problems. In addition, to improving their mathematical problem solving skills it helped the students communicate their answers through writing. The data suggests that further implementation would produce greater results. Through journal writing the student’s confidence with solving math word problems increased. Overall, the research shows that math journaling did improve the problem-solving skills in second grade students. Limitations Limitations of this study were the length of the project, types of math word problems, sample size, and time constraints during the school day. Other limitations were participant’s absences, different makeup of classes, and the difference in teachers. This research was conducted over six weeks. We know that math journaling will be even more beneficial if used throughout the school year. Teachers need more time to teach the variety of mathematical problem-solving strategies effectively. The same type of math word problems were used throughout the study. This could contribute to the Test/Retest Effect. Even though we changed the numbers and information in the math problems, they were still the same type of problems every time. If teachers used journals throughout the school year, then more types of problems will be addressed. Even though we were able to combine two classrooms of second graders, it would be more beneficial if the sample size was larger. One limitation that we noticed was students tend to write at extremely different paces. The opportunity of having extra time to finish was not always evident. Effects of Math Journaling 19 The school day is full of many other activities. Another limitation was student absences. Absences definitely had an impact on the student’s individual results, especially if it was in Phase 1 where all of the problem-solving strategies were taught. Since this study was conducted with two different second-grade classrooms, the class makeup of the two classes was a limitation. Also, there were two different teachers involved in this study. Implications for Further Research and Classroom Practice The results of this study have shown that math journaling is a beneficial method of improving mathematical problem-solving skills. We would like to see other teachers use this method also. It would be helpful to see if a larger group of students have the same success with math journaling as our group did. When we use the research next year we will provide a list of problem solving strategies posted for student’s who have trouble remembering all of the problem-solving steps. They will be provided their own copy of problem- solving strategies to refer to in their math journal. This project has made us realize that journaling would be beneficial in all areas of education. Journals are a great tool for teachers to use as an assessment to evaluate a student’s comprehension of a standard. It will also provide insight for the teacher if re- teaching is necessary for the student or if the teacher should be challenging the student. Journals provide a documentation of the student’s knowledge of the concepts taught. We will continue to use math journals next year, as well as in other subject areas. Effects of Math Journaling 20 References Benko, A.; Loazia,R; Long,R; Sachrarski,M; Winkler, J.(1999) Math Word Problem Remediation with Elementary Students. Saint Xaiver University. Burns, M. (2004). Writing in Math. Educational Leadership. V. 62, no. 2, 30-33. Caracelo, S. (2008). Effects of Math Journaling on Third Grade Students, p.14. Flores, A. & Brittain, C. (2003). Writing to reflect in a methods course. Teaching Children Mathematics, 10, 112-118. Fortunato, I., Hecht, D. Tittle, C. K., & Alvarez, L. (1991). Metacognition and problem solving. Arithmetic Teacher, 39(4), 38-40. Gurule, K. (2007, November). Problem Solving Time. Educational Leadership Making Math Count, v.65(3). Harmon, M. & Morse, L. Strategies and Knowledge in Problem Solving: Results and Implication for Education. 1995, V.115. Issue 4. ,p.580. Howell & Barnhart. Teaching Exceptional Children, Winter 1992, V.24, n2 p44-46. Kelly, Catherine A. Using Manipulatives in Mathematical Problem Solving: A Performance-Based Analysis. Montana Mathematics Enthusiast. 2006, V. 3 Issue 2, p184-193. Manning, M. (1999). Too many journals. Teaching Pre K-8, 30. Math Gym , (2006). Math Gym notes: George Polya Retrieved June 24, 2009, from http://www.ccs.neu.edu/home/lieber/courses/materials/Polya_Father_of_Problem Solving.pdf. (p.1-2). Effects of Math Journaling 21 National Council of Teachers of Mathematics.(2004). Retrieved July 20, 2008 from http://standards.nctm.org Pugalee, D. (1997). Connecting writing to the mathematics curriculum. Mathematics Teacher, 90, 308-310. Puglee, D. Writing, Mathematics, and Metacognition: Looking for Connections through Students' Work in Mathematical Problem Solving. School Science and Mathematics., 2001, V.101. Issue: 5, p. 236. Sezer, Renan. . Integration of Critical Thinking Skill into Elementary School Teacher Education Courses in Mathematics. Education. Spring2008, V. 128 Issue 3, p349- 362. Stonewater, J. (2002) The Mathematics Writer’s Checklist: The Development of a Preliminary Assessment Tool for Writing in Mathematics. School Science Mathematics, 102 Retrieved June 15, 2009 from http://www.questia.com/PM.qst?a=o&d=5002503854 Whitin, D. J. & Whitin, P. (2002). Promoting communication in the mathematics classroom. Teaching Children Mathematics, 9, 205. Effects of Math Journaling 22 Appendix A Effects of Math Journaling 23 Effects of Math Journaling 24 Effects of Math Journaling 25 Effects of Math Journaling 26 Effects of Math Journaling 27 Effects of Math Journaling 28 Effects of Math Journaling 29 Effects of Math Journaling 30 Effects of Math Journaling 31 Effects of Math Journaling 32 Effects of Math Journaling 33 Effects of Math Journaling 34 Effects of Math Journaling 35 Effects of Math Journaling 36 Effects of Math Journaling 37 Effects of Math Journaling 38 Effects of Math Journaling 39 Appendix B Pre/Post Gain Pre/Post Gain Student Pre 1 Post 1 1 Pre 2 Post 2 2 1 0% 67% 67% 33% 83% 50% 2 0% 17% 17% 33% 33% 0% 3 17% 67% 50% 67% 83% 17% 4 33% 33% 0% 50% 67% 17% 5 33% 67% 33% 50% 67% 17% 6 0% 17% 17% 50% 67% 17% 7 0% 17% 17% 0% 17% 17% 8 0% 0% 0% 33% 33% 0% 9 0% 0% 0% 0% 0% 0% 10 0% 33% 33% 17% 67% 50% 11 0% 17% 17% 17% 17% 0% 12 0% 0% 0% 0% 50% 50% 13 0% 50% 50% 67% 100% 33% 14 0% 0% 0% 0% 17% 17% 15 0% 17% 17% 0% 50% 50% 16 0% 17% 17% 33% 67% 33% 17 0% 17% 17% 33% 67% 33% 18 0% 0% 0% 50% 67% 17% 19 0% 33% 33% 50% 67% 17% 20 17% 17% 0% 33% 50% 17% 1a 0% 0% 0% 17% 33% 17% 2a 33% 50% 17% 50% 100% 50% 3a 50% 33% -17% 67% 50% -17% 4a 0% 17% 17% 17% 67% 50% 5a 0% 17% 17% 0% 50% 50% 6a 50% 50% 0% 67% 100% 33% 7a 33% 50% 17% 50% 67% 17% 8a 0% 50% 50% 0% 33% 33% 9a 0% 0% 0% 17% 33% 17% 10a 17% 50% 33% 50% 67% 17% 11a 0% 17% 17% 17% 50% 33% 12a 17% 0% -17% 33% 67% 34%