Bansho: Visually Arranging Mathematical Ideas

Hello Everyone and welcome to my final blog of this semester.

                In todays class we learned the last strategy to use in our classrooms. As a recap, we have used a Gallery Walk and a Math Congress which were mentioned in my previous blogs. The focus of this blog is going to be unfolding the strategy called “Japanese Bansho.” Eloise et al., (2018) describe this method as an organizational strategy to facilitate multiple problem representations and better classroom communication. The term Bansho refers to the intentional use of board space for facilitating student learning, and everything written on the board is meaningful and significant (Eloise et al., 2018). Once the students have shared their ideas on the board you then can sort and classify the solutions according to similar methods used and in order of complexity.  This method is used for feedback to the students as there is no grading or scoring to groups answers. In class today, we used this method to solve the following problem:

“There are 36 children in Mrs Smith’s Class. There are 8 more boys than girls. How many boys? How many girls?

Photos, D. (2018). Trabajo en equipo y el concepto de éxito. [online] Depositphotos. Available at: https://sp.depositphotos.com/80206616/stock-photo-teamwork-and-succes-concept.html [Accessed 23 Oct. 2018]

          Every group thought of about 2-4 ways to answer the problem. Below are the classmates work posted on the board in order of complexity and categorized. Prior to the solutions being organized we had a class discussion on where we thought each solution should be on the board and defended our work in terms of why we believe it should be organized in this manner. We then wrote beside each idea by summarizing the method used and ordered them in terms of complexity. 1 being a more concrete idea, and 3 being the most complex. This strategy was helpful for us as teachers also as we got to discuss where the levels of learning were. For example, using the table of differences is grade 8-9 level of learning where the system of equations is grade 10. Therefore, we can also use this strategy to gauge an understanding of where our students are at in terms of their level of learning.

           I found this method extremely useful as it allowed us to systematically display various solutions and engage in conversation and then discuss and extend our knowledge on a problem.  This method also allowed the teacher to act as a facilitator by activating our prior knowledge and wanted us to unfold our understanding of one problem. Eloise et al., (2018) believes Bansho offers a structure for sequencing mathematics visually on the board and is best suited for problems allowing multiple solutions or representations which then fosters mathematical communication amongst your peers.

          On a side note, something I am struggling with in this class is moving from traditional style lesson planning which involves demonstrating a fixed procedure, assigning similar problems then assigning more similar problems for homework. This is the way that I was taught throughout my whole mathematical educational journey. However, this class is unfolding many new strategies that will be an excellent tool to use in my future. Math lessons should involve presenting a problem to students without demonstrating how to do it, have students work in groups to develop communication, critical thinking and collaboration skills. Then consolidate these ideas as a group by comparing and discussing many ways of solving one problem by summarizing, reflecting and connecting the classes ideas. Therefore, I am beginning to understand new ways to approach problem solving, which is something I did struggle with in high school. I believe if I got to use these strategies, gallery walk, math congress and Japanese Bansho, I would have gauged a better understanding of problem solving and wouldn’t be scared of word problems. Conversely, as a future educator these methods can be used in other classrooms also, like chemistry or physics, where we need to move from traditional style teaching to more of a student-centered space that focuses on students collaborating and engaging in solving problems together with the teacher acting as a facilitator. This way of learning will benefit the student greatly as they will be more focused and willing to learn in class by increasing their creativity and critical thinking when learning through dialogue.

References

Eloise R. A. Kuehnert, Colleen M. Eddy, Daphyne Miller, Sarah S. Pratt, & Chanika Senawongsa. (2018). Bansho: Visually Sequencing Mathematical Ideas. Teaching Children Mathematics, 24(6), 362-369