The Japanese Bansho Strategy & Assessment In Mathematics
Hi everyone!
I was introduced to a new concept which is another form of problem-solving strategy, known as the Japanese Bansho strategy. This was my favorite part of the lesson, and this lecture in particular I found to be particular important, especially for enhancing problem-solving capacities in students. Although I connected the Japanese Bansho strategy to some of the structured and non-structured problem-solving strategies we have learned in previous classes, I realized that there are some distinctive features with the Japanese Bansho strategy. Features such as discussing all parts of the problems through collaboration, arranging various solutions based on complexity, and the extensive need of justification in this strategy is what makes this technique distinguished.
We were then split into groups to answer the following question: "There are 36 children in Mrs. Smith's class. There are 8 more boys than girls. How many boys? How many girls?". Below are the following strategies to solve this problem, which are grouped and ordered from least complex to most complex solutions.
Ordering these solutions based on their complexity really allowed me to connect to the Ontario curriculum. I noticed that the solutions that are 'least' complex are expectations that you would see in a grade 6 math classroom, particularly in the numeracy and/or patterning strands. The next set of solutions are at a grade 7/8 level, since we are asking to use very basic algebraic techniques such as trial and error, which is seen in the numeracy strand of the curriculum. And the more abstract solutions are directly related to grade 9 and 10 math skills in the linear relations strand. This helped me visual the spiral curriculum in Ontario, and that all solutions are somehow interconnected between grades.
I also had an 'ah-ha' moment when I realized that this activity directly reinforced the idea of low floor-high ceiling problems. In previous classes, I had a hard time conceptualizing low floor high ceiling problems, but now seeing that solutions can 'grow' to become very abstract in nature shows how some problems can really have a large quantity of solutions, and gives students a lot of space to problem-solve. Another aspect of the learning process that I realized I am improving on is being able to make other solutions other than algebraic solutions. I have been talking in my blog about my struggle with giving various solutions to one question, but I can tell through this activity that I have made improvement.
We also briefly discussed differently types of comprehensive assessment strategies that are used in mathematics classroom, and can be implemented into our lesson plans for this class. We discussed the differences between ongoing tasks (diagnostic/formative) versus snapshot tasks (summative, sometimes formative). What I noticed in the class is that ongoing assessment tasks are imperative in order to maximize success in snapshot tasks. When I implement my lesson plans in the future, I will definitely ensure that there are a wide variety of ongoing assessment tasks that allow for differentiated instruction opportunities, student-directed learning and inclusive education. A lingering question I still have is how do I implement holistic-based rubrics, in something like a mathematics classroom? I hope this is a topic we can touch on in future classes. Another question I have is what journal prompts can we use, and how do we know if the prompts are actually being beneficial to our students' learning?
Here is the Japanese Bansho strategy coming to life in an actual primary level mathematics classroom:
For future classes, I am going to continue to challenge my problem-solving skills. Because if I can become a good problem-solver, then that will make my future students better problem-solvers!
References
Wendler, M. (2012). Bansho (The Three Part Math Lesson). Retrieved from https://www.youtube.com/watch?v=qCf_tVf_CSM&t=392s
I was introduced to a new concept which is another form of problem-solving strategy, known as the Japanese Bansho strategy. This was my favorite part of the lesson, and this lecture in particular I found to be particular important, especially for enhancing problem-solving capacities in students. Although I connected the Japanese Bansho strategy to some of the structured and non-structured problem-solving strategies we have learned in previous classes, I realized that there are some distinctive features with the Japanese Bansho strategy. Features such as discussing all parts of the problems through collaboration, arranging various solutions based on complexity, and the extensive need of justification in this strategy is what makes this technique distinguished.
We were then split into groups to answer the following question: "There are 36 children in Mrs. Smith's class. There are 8 more boys than girls. How many boys? How many girls?". Below are the following strategies to solve this problem, which are grouped and ordered from least complex to most complex solutions.
I also had an 'ah-ha' moment when I realized that this activity directly reinforced the idea of low floor-high ceiling problems. In previous classes, I had a hard time conceptualizing low floor high ceiling problems, but now seeing that solutions can 'grow' to become very abstract in nature shows how some problems can really have a large quantity of solutions, and gives students a lot of space to problem-solve. Another aspect of the learning process that I realized I am improving on is being able to make other solutions other than algebraic solutions. I have been talking in my blog about my struggle with giving various solutions to one question, but I can tell through this activity that I have made improvement.
We also briefly discussed differently types of comprehensive assessment strategies that are used in mathematics classroom, and can be implemented into our lesson plans for this class. We discussed the differences between ongoing tasks (diagnostic/formative) versus snapshot tasks (summative, sometimes formative). What I noticed in the class is that ongoing assessment tasks are imperative in order to maximize success in snapshot tasks. When I implement my lesson plans in the future, I will definitely ensure that there are a wide variety of ongoing assessment tasks that allow for differentiated instruction opportunities, student-directed learning and inclusive education. A lingering question I still have is how do I implement holistic-based rubrics, in something like a mathematics classroom? I hope this is a topic we can touch on in future classes. Another question I have is what journal prompts can we use, and how do we know if the prompts are actually being beneficial to our students' learning?
Here is the Japanese Bansho strategy coming to life in an actual primary level mathematics classroom:
For future classes, I am going to continue to challenge my problem-solving skills. Because if I can become a good problem-solver, then that will make my future students better problem-solvers!
References
Wendler, M. (2012). Bansho (The Three Part Math Lesson). Retrieved from https://www.youtube.com/watch?v=qCf_tVf_CSM&t=392s
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