{"id":3144,"date":"2025-09-16T09:07:52","date_gmt":"2025-09-16T16:07:52","guid":{"rendered":"https:\/\/theothermath.com\/?p=3144"},"modified":"2025-10-29T11:26:11","modified_gmt":"2025-10-29T18:26:11","slug":"give-teaching-through-problem-solving-a-try","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2025\/09\/16\/give-teaching-through-problem-solving-a-try\/","title":{"rendered":"Give Teaching Through Problem Solving a Try"},"content":{"rendered":"

A fundamental goal of mathematics education is to develop students\u2019 ability to engage in mathematical problem solving. Despite our textbooks supposedly including problems labeled as “problem solving”, many teachers are uncertain how to establish a classroom environment in which students\u2019 natural problem solving inclinations can occur.<\/span><\/p>\n

There is consensus in the mathematics education community that problem solving should not be taught as an isolated topic focused solely on developing problem solving skills and strategies or presented as an end-of-chapter activity. Instead, problem solving should be integrated throughout virtually every lesson as a fundamental part of mathematics teaching and learning.<\/span><\/p>\n

If the goal of math instruction is to foster students’ problem solving skills and problem solving should be included in every lesson, why isn’t it happening in our classrooms? I think this is because teachers, when they were students themselves, experienced a math that focused merely on answer getting. Problem solving was only introduced, if at all, at the end of the lesson or the chapter after the “real” math instruction\u2013 focused exclusively on algorithms \u2013was completed. I am NOT blaming teachers for the reason for the lack of problem solving in the classroom, but I am saying teachers are the solution.<\/span><\/p>\n

It is essential that every teacher learns the \u2018Teaching Through Problem Solving\u2019 (TTP) approach, a problem solving style of instruction that treats problem solving as a core practice rather than an \u2018add-on\u2019 to mathematics instruction.<\/span><\/p>\n

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What is Teaching Through Problem Solving (TTP)<\/span><\/h2>\n

Teaching Through Problem Solving originated in Japan. TTP is a powerful instructional technique that promotes mathematical understanding as a by-product of solving problems, where the teacher presents students with a strategically selected problem that targets certain mathematics content. The lesson implementation does not start with the teacher showing students how to solve the problem. Rather, the lesson starts with the teacher presenting the problem and ensuring that students understand the context of the problem and what they are trying to solve. Students then work on the problem either individually or in groups, inventing their own approaches. At this stage, the teacher does not model or suggest a solution procedure. Instead, they take on the role of facilitator, providing support to students only at the right time. As students solve the problem, the teacher circulates, observes the range of student strategies, and identifies work that illustrates desired features. However, the problem solving lesson does not end when the students find a solution. The subsequent sharing phase, Japanese teachers call this\u00a0Neriage<\/span><\/em> (polishing ideas), is considered by Japanese teachers to be the heart of the lesson rather than its culmination. During Neriage, the teacher guides the class through a whole class discussion by purposefully selecting students to share their strategies, comparing various approaches, and introducing increasingly sophisticated solution methods. Effective questioning is central to this process, alongside careful recording of the multiple solutions on the board. The teacher concludes the lesson by formalizing and consolidating the lesson\u2019s main points. This process promotes learning for all students.<\/span><\/p>\n

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The new demands on the teacher<\/span><\/h2>\n

Adopting a TTP approach challenges the common pre-existing belief that students must be shown how to solve a problem before they can learn how to do it themselves. We call this belief “I do, We do, You do” in which the teacher demonstrates a skills first, then the whole class does some problems together, before students finally practice individually.<\/span><\/p>\n

TTP also requires teachers to adopt a more expansive view of mathematics that is more than just a rule-based endeavor focused on answer getting.<\/span><\/p>\n

In addition to changing teachers’ beliefs about what math instruction should look like, TTP also requires teachers to develop their own deep understanding of problem solving and to understand the various stages problem solvers go through. George P\u00f3lya was a master at this and had plenty to say on problem solving.<\/span><\/p>\n

Despite the acknowledged benefits of TTP for students, I have observed teachers skeptical or reluctant to try TTP, citing a variety of reasons:<\/span><\/p>\n