Methodology

Teaching Through Problem-solving (TTP) Methodology

Overview

Teaching Through Problem-solving (TTP) is a teaching methodology that has evolved over decades in Japan, uniquely integrating problem-solving into every part of the math lesson, unlike typical curricula that treat it as a concluding activity. This method ensures that problem-solving is a continuous focus, not just a lesson finale. Moreover, the learning process extends beyond finding solutions; it involves in-depth discussions among students to explore and evaluate various solution strategies. This approach not only broadens students' understanding but also caters to diverse learning styles by demonstrating multiple ways to approach a problem.

Typical Lesson Flow

While each lesson has it's own distinct lesson segments, the typical flow of a TTP lesson contains the following phases:

1. Review Activities: Reflecting on what was previously learned.

2. Posing the Task: Help students understand the mathematical challenge behind the problem.

3. Solving the Problem/Investigation: Monitor students’ independent work to take note of different approaches being used to solve the problem.

4. Comparing and Discussing: Help students compare and discuss their solutions and thinking.

5. Summary and Reflection: Lead students to look back on what they have learned.

Neriage

A distinctive feature of Teaching Through Problem-solving (TTP) that differentiates it from conventional math education methods is the practice of Neriage. This term, originating from Japanese, means "kneading" and is akin to a pottery technique where different clays are blended to create something new. In the context of TTP, Neriage refers to the collaborative classroom discussions that synthesize diverse student ideas into a comprehensive understanding. This process not only enhances learning by considering multiple perspectives but also mirrors the collaborative nature of real-world problem solving.

Conducting Neriage

The following is a set of best practices to conduct Neriage in your classroom:

1. Anticipate how students may attempt to solve the given problem.

2. Monitor student’s work during class.

3. Selecting students’ work for class discussion.

4. Sequence selected student’s work to engage in rich discussion that will accomplish the goals of the lesson.

5. Convene the class to discuss shared knowledge and understanding of mathematic concepts.

Essential Learning Techniques

The LoiLo TTP Math curriculum is designed to foster independent thinking by encouraging students to find their own solutions to mathematical problems using creative strategies. Each new math concept is introduced by presenting challenges that students may not immediately know how to solve, prompting them to draw upon previous knowledge to forge new understandings. This process of discovery is crucial to the learning model.

The curriculum further solidifies these concepts during Neriage, a critical phase where students discuss and share their approaches and solutions. This interactive session allows students to learn from each other's perspectives and mistakes, enhancing their understanding through collaborative discourse. The ultimate goal of the curriculum is to cultivate a deep comprehension of mathematical concepts through student-driven creativity, active participation, and reflective discussion.

Lesson Types

4 Core Lesson Types:

LoiLo TTP Math curriculum is structured in four types of lessons for optimal understanding of concepts.

Students use previously learned knowledge and skills to investigate a problem and overcome a new mathematical challenge.

Based on the discussion in the previous lesson, students solidify a shared understanding of new mathematical ideas and procedures.

Students apply mathematical ideas and procedures to solve problems that exted the mathematics.

Students develop accuracy, flexibility, and efficency in using the math they learned.

Additional Lesson Type:

Students attack non-routine problems to extend their understanding and capacity to solve problems.