I often share with my students my own experience learning math. It was not good. I hated math, and I didn't think I was any good at it. I remember watching the teacher work out problems, and they made sense. I could understand what she was doing. Then, when I tried to complete problems on my own, nothing made any sense. I felt like I was given problems from a different section of the book.
I didn't understand how ideas connected and were built upon each other. Every day was a new random experience. Luckily, things started to come together in high school, but I still saw math as a set of definitions and formulas to memorize.
I even taught math this way.
It wasn't until I had the time to study the Engage New York curriculum from first grade to fifth grade in depth that I began to see the brilliant way math could be taught as problem solving.
I always believed that "math is real life," but I didn't fully understand what that could mean for teaching math concepts.
At the very end of the school year last year, I happened to read an article about the way some Japanese teachers teach math. They would put one problem on the board. The entire class would then work independently to solve it. The problem would be based on ideas the students had familiarity with, but would be a stretch from what they had already done.
As students thought they had solved the problem, they would bring their work to the teacher. The teacher would ask questions about the work to help the students uncover misconceptions or mistakes. The student would then return to his seat to try again. This process would be repeated as necessary. At the end of the session, the students would come together in a group to share their ideas.
I loved this strategy because it fit so well with the very popular idea of a growth mindset. Kids could see right at that moment that they would make mistakes and overcome them to learn something new.
I also liked the challenge aspect of the process. This wasn't math that required memorization, but instead used understanding, common sense, and ingenuity. Sure, the typically "high" math kids could have an advantage because of their strong math skills, but they weren't just repeating what the teacher did anymore. They had to think just as much as the kids who struggled with math.
Finally, I liked that we only worked on one or two problems. This meant I didn't have to find resources with dozens of problems, I didn't have to manage the kids that finished too early or took too long, and I didn't end up with a basket of papers to grade. Now, if doing worksheets would help my students learn better, I would do these things. I just felt like I was doing a ton of of work, and it wasn't paying off the way I hoped. With this new strategy, the kids were doing the work, and they were learning.
I have been thinking a lot about the last couple of weeks of school recently, especially our math classes. The kids loved them and I loved them. I wanted to find a way to bring that experience to other classrooms and teachers.
I also wanted to follow up on what I had read to learn more about this style of teaching. I found some interesting information.
First of all, this style of teaching didn't come from Japan. It came from the United States. It was called the "Problem-Solving Approach" and it started in the United States in the 1980s. It didn't catch on in the United States, but Japanese teachers embraced it.
In the 1970s and 1980s Japan began to focus on the student-centered classroom. They wanted classrooms where students were the "active constructors of knowledge" instead of passive recipients. A teacher was seen as a facilitator instead of a lecturer. Structured problem-solving was seen as a way to accomplish this goal in math.
There are other cultural norms that have influenced the way math is taught in Japan as well. First, the teachers are seen as the best source of information on education. This bottom-up approach is the exact opposite of the top-down method currently employed by the United States. Also, Japanese teachers spend fewer hours teaching, so they have time to work together in teams to build the best lessons.
Japanese teachers engage in Jugyokenkyu or "lesson study". The teachers come together and look at a concept students are struggling with at school. They then look at relevant literature or lessons by other teachers. Once they have a firm understanding of what they want to accomplish, they begin lesson planning together. Finally, after months of work, one teacher from the group will teach the lesson to her class. The rest of the group and other teachers will watch the lesson, but they won't watch the teacher. Instead, they watch the kids. They ask questions to help understand the children's thinking in order to determine in their lesson was successful. If it was, the rest of the teachers will teach it. If not, they will revise the lesson and try again.
This process takes months of work. It can't be accomplished in the 30 minute weekly PLC meetings.
While U.S. teachers don't currently have the environment that Japanese teachers do for lesson development, they can still utilize the principles of the "Problem-Solving Approach." Think about what your students really need to know about a topic. For example, they might need to know how to find the area of a rectangle. Then, give the students the tools that they can use to solve this problem without teaching them a step-by-step process to follow. They would need to know that area and arrays are related and how to tile a rectangle. Then, give them a problem and ask them to solve it. If students can discover for themselves that they can multiply to find the area of a rectangle, they will be much more likely to remember it than if you tell them and have them do ten problems repeating the steps.
To help teachers with implementing this new way of teaching math I have created two sets of differentiated question sets. These are individual pages that you can give to students instead of writing the same problem on the board for the entire class. I have found this very helpful in dealing with the need for differentiation. Plus, if a student completes his or her page, you can give her another page that is even more challenging.
More of these are coming soon. I think that this is a revolutionary way to teach math, and I think it has the power to change students' ideas about math.
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