Chapter 4

A Three-Phase Lesson Format: 

Learning Outcome 4.1: Explain the Features of a Three-Phase Lesson Format for Problem-Based Lessons

In Chapter 4 of "Elementary and Middle School Mathematics: Teaching Developmentally," the three-phase lesson format for problem-based lessons is a central concept. This format is designed to engage students in mathematical thinking and problem-solving. The three phases are:

1. Before (Launching the Task):

   • Purpose: Prepare students for the problem-solving task.

   • Teacher's Role:

     • Introduce the task and ensure students understand the problem without giving away the solution.

     • Connect the task to prior knowledge and experiences.

     • Establish expectations for the task.

   • Student's Role:

     • Listen and engage with the task's introduction.

     • Ask clarifying questions to understand the problem.

2. During (Engaging in the Task):

   • Purpose: Students actively work on the problem, developing their understanding and strategies.

   • Teacher's Role:

     • Observe and listen to students’ discussions and problem-solving processes.

     • Ask probing questions to guide thinking without providing answers.

     • Encourage multiple strategies and representations.

   • Student's Role:

     • Collaborate with peers to explore and solve the problem.

     • Use various strategies and tools to approach the task.

     • Communicate their thinking and reasoning.

3. After (Discussing the Task):

   • Purpose: Reflect on the problem-solving process and solutions to deepen understanding.

   • Teacher's Role:

     • Facilitate a discussion where students share their strategies and solutions.

     • Highlight and compare different approaches and solutions.

     • Connect the task to broader mathematical concepts and future learning.

   • Student's Role:

     • Share and explain their problem-solving process and solutions.

     • Listen to and consider peers' strategies and reasoning.

     • Reflect on their own understanding and learning.

This three-phase format ensures that students are actively involved in their learning, encourages the development of critical thinking and problem-solving skills, and allows for meaningful mathematical discourse.