#9 Blog of 2017
Math journals allow students to record mathematical ideas, improve communication skills and build upon previous learning. They serve as a repository for task-based lessons and key math knowledge learned, and they promote varied entry points and encourage multiple solution paths. My use of math journals has evolved during an incredible journey with colleagues and students. Inspired by the Japanese format for math journals, my students deepen their mathematical understanding while using this powerful tool.
My journey with journals began soon after taking the AFT’s Thinking Mathematics course. I quickly saw the power of using a single task as a means to build students’ knowledge and deepen their conceptual understanding. It was then that I knew the traditional worksheets weren’t going to be the tool to move students forward. One of Thinking Mathematics’ 10 principles is to base instruction on situational story problems to provide context and keep students interested. Using student names and real-world (their world) experiences only increases engagement. So, if I’m ditching workbooks and worksheets for these situational tasks, how can I share them with students? This challenge prompted my use of journals.
At first, students just used their journals as workspaces to jot down their strategies and solutions. It was after continued work and study with our Japanese colleagues that the true power of math journals became apparent. My teaching partner at the time, Heather Williams, had spent time visiting schools in Japan and was our local lesson study expert. She shared the basic structure she saw used in classrooms, and I knew I had to step up my game. More than just a place to show work or take notes, the math journals she had seen and started to use with students became an essential tool in the classroom. Check out this CPALMS video highlighting the techniques she uses with students: http://www.cpalms.org/beyond_standards/grade_3-5_v5.aspx.
Math journal format and template:
In my classes, my students use grid-paper composition books. They are sturdy, survive the entire school year and provide students with an inherent tool: graph paper. Charts, diagrams, arrays and tables are much easier to construct with grid paper. I also print our task for the day on address labels so students can add them to their journals.
When I present students with a task, I give them some independent time to think about what we already know and what we’ll need to find out. Once they make sense of the problem I pose (part of Common Core State Standards’ Math Practice 1), they consider how they plan to attack it and record their thinking, reasoning quantitatively and abstractly (Math Practice 2).
Having students first wrestle with the task and then record their thoughts is also in line with the National Council of Teachers of Mathematics’ eight Effective Mathematics Teaching Practices. It recommends to “support productive struggle in learning mathematics” as students engage with tasks without being told how to solve them, and to “elicit and use evidence of student thinking,” which journals accomplish by capturing student thinking.
This independent time also gives me an opportunity to circulate around the room and get a sense of students’ initial understanding, misconceptions, struggles and varying degrees of sophistication of solution strategies.
Math journals also provide a framework to help meet the NCTM’s practice of facilitating “meaningful mathematical discourse,” as students share solutions, critique others, and record models, strategies and concepts. As students report out (selecting purposefully to show a progression of more concrete to more abstract or efficient strategies), students record their classmates’ ideas. This prompts rich discourse as students explain their own strategies and discuss how strategies are similar or different (Math Practice 3).
I have used a variety of ways for students to share their strategies. At times, teams of students will share strategies together and come to a consensus to record one solution on chart paper (a bit old school but still one of the best ways to capture student thinking and see multiple strategies at once). Other times, I will have individual students bring their journals to our document camera for classroom discussion. I’ve also used Padlet so that students can upload images of their journal pages and then receive feedback from others. Here’s one example: https://padlet.com/auspies/HeathersPunch.
One of the best takeaways from the Japanese journals was their use of student summaries. These summaries are not just a retelling of what students did in math. Instead, students generate a learning objective at the end of each lesson signifying the key math knowledge they are taking away from the day. While it takes some modeling and practice, after a few weeks students eagerly and articulately generate summary statements that clearly express the goal of the lesson. And they are always written in red so they stand out for students, allowing them to quickly refer to previous lessons. Teacher Becky Pittard illustrates the summaries beautifully in her “A Passion for Fractions” video below
Another essential journal element is the reflection section, providing space for students to discuss what surprised or confused them. They can ask questions, make connections to previous work or share their aha moment. Student reflections are an invaluable formative tool for me. I get a better gauge of where students are and how to hook them the following day. It is incredibly powerful for students to see their question become the focus of the next day’s lesson. The reflections also serve as a powerful review to read the following day at the start of class.
Sample pages from a teacher’s journal during a Thinking Mathematics course:
Student Sample 1
Student Sample 2
The use of math journals allows all students the opportunity to engage in rich math tasks and mathematical discourse. While entry points may vary, by the conclusion of the lesson, all students will be exposed to a continuum of strategies while solidifying the key math content of the lesson. Journals can also be adapted and differentiated to meet the individual needs of students. Using math journals helps ensure all students are afforded high-quality, research-based math instruction. With each new school year, I eagerly plan how to make better use of math journals, learning from the prior classes. This year’s journey should prove to be even more exciting than the last!