Building Understanding: Using Math Journals to Increase Learning in an Intermediate Classroom

Abstract

Purpose As an elementary school teacher I have watched my students struggle with new mathematical concepts: word problems, fractions, and increasingly difficult types of division have totally baffled many of my students. For the first several months of the school year most of my students did very well in math class, but they struggled with increasing difficulty as the concepts became more abstract. I have struggled to figure out ways to help them better understand. This project has grown out of our struggles with teaching, learning, understanding, and the working together to improve them all. I entered into this research with several guiding questions. Can the use of mathematics journals help students better understand word problems and other mathematical concepts? Are students able to learn by teaching themselves through writing and use writing as a tool for learning? Are mathematics journals useful as an evaluative tool? Methods I utilized math journals in this project as a tool to assist my students in constructing mathematical meaning and believed that this method of construction would lead them to a greater conceptual understanding of mathematics and give them greater confidence in their problem solving abilities. I also planned to use the journals as an ongoing assessment tool, which would serve as a window into the students' confusion as well as their understanding, and thus be a guide for my daily teaching. This paper discusses how my students and I entered into this project together. It outlines our discussions leading up to the actual starting date, how the journals were set up, and how they were implemented. It also discusses the mandated curriculum, as well as student demographics, and finally will present the problems used in this project and the dates on which they were assigned. At the end of the project time frame, I read each of the journals several times in order to immerse myself in the data and let the thematic elements jump out at me. As I began reading the journals I wanted to see what the students were thinking and if there were any particular foci that repeated themselves in multiple journals. As I read each journal I wrote on post-it notes about what I saw in each, whether they were engaged or not, if they were writing good detailed explanations of their strategies, what strategies they used, and, whether they were actually able to solve the problems or not. I also made notes about particular problems that I thought might make good material for writing about in the analyses. Ultimately, I chose the three journals which I analyzed because I thought that they would provide the broadest look at the different levels of learning and understanding within the class. Results The main focus of my analyses was on how the children think mathematically, and especially what counts as a reasonable mathematical explanation. These analyses are rich and full of detailed investigations into these three children’s mathematical thinking. Although this project did not produce the results I had expected, nonetheless, I did learn a great deal and would like to share some of those lessons with you. The first guiding question of this project was: Can the use of math journals help students better understand word problems and other mathematical concepts? I would have to say that after ten weeks this was not especially evident, but the research did take place during the last quarter of the school year, and that ten weeks may not really have been a sufficient period of time for this to develop. If the journals were implemented at the beginning of the school year and used regularly, I believe that the students would have, over time, started to construct deeper conceptual understandings, better problem solving skills and a more fully developed sense of mathematical reasoning, and thus the ability to justify their answers. A second guiding question was: Are students able to learn by teaching themselves through writing and use writing as a tool for learning? This was also not as evident as I had hoped it would be. These journals have shown me a lot about how children think mathematically and the processes they go through in order to problem solve, but at this point I have not seen a lot of support for their mathematical thinking in these journals. Again, I do believe that this is something which would develop over time and I would like to see the results of a full year’s immersion in writing about mathematics