Chapter 3 Teaching Through Problem Solving Copyright © Allyn and Bacon 2010 This multimedia product and its contents are protected under copyright law. The following are prohibited by law: any public performance or display, including transmission of any image over a network preparation of any derivative work, including the extraction, in whole or in part, of any images any rental, lease, or lending of the program

Teaching Through Problem Solving Most, if not all, important mathematics concepts and procedures can best be taught through problem solving Copyright © Allyn and Bacon 2010

Problems and Tasks for Learning Mathematics Begin where the students are The problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn Require justifications and explanations for answers and methods Copyright © Allyn and Bacon 2010

A Shift in the Role of Problems Away from: Explain, practice, then story problems One way (the teacher’s way) Show and tell approach with the student as a passive learner Problem-solving problems as a separate activity Expecting explicit directions for how to solve problems Copyright © Allyn and Bacon 2010

The Value of Teaching Through Problem Solving The focus of the students’ attention on ideas and sense making Develops the belief in students that they are capable of doing mathematics and that mathematics makes sense! Provides a context to help students build meaning for the concept Allows an entry point for a wide range of students Copyright © Allyn and Bacon 2010

The Value of Teaching Through Problem Solving (Continued) Provides ongoing assessment data that can be used to make instructional decisions, help students succeed, and inform parents Allows for extensions and elaborations Engages students so that there are fewer classroom discipline problems Develops “mathematical power” It is a lot of fun! Copyright © Allyn and Bacon 2010

Examples of Problem-Based Tasks Procedures and Processes Students develop procedures via a problem-solving approach. They are engaged in the process of figuring out mathematics, not just accepting procedures blindly. Copyright © Allyn and Bacon 2010

Selecting or Designing Problem-Based Tasks Multiple Entry Points Provides the opportunity for students to work on the problem using their own ideas at their own level Allows for more than one correct way to work the problem Copyright © Allyn and Bacon 2010

How to Find Quality Tasks and Problem-Based Lessons A Task Selection Guide How is the activity done? What is the purpose of the activity? Can the activity accomplish your learning goals? What must you do? Good tasks: check out http://illuminations.nctm.org Copyright © Allyn and Bacon 2010

How to Find Quality Tasks and Problem-Based Lessons (Continued) A standards-based curriculum provides an increased emphasis on learning through problem solving Traditional textbooks can be used to adapt a non-problem-based lesson by using the best lessons or using the main ideas of the chapter Copyright © Allyn and Bacon 2010

Four-Step Problem-Solving Process Understanding the problem Developing a plan Carrying out the plan Looking back Copyright © Allyn and Bacon 2010

Teaching in a Problem-Based Classroom Let students do the talking How much to tell and not to tell The importance of student writing Metacognition Disposition Additional goals Copyright © Allyn and Bacon 2010

Teaching in the Problem-Based Classroom How much to tell Mathematical conventions Carefully suggest alternative methods Clarification of students’ methods And not to tell Establish teacher- preferred methods Teacher thinking Copyright © Allyn and Bacon 2010

Teaching in the Problem-Based Classroom Importance of student writing — a reflective process — can be a rehearsal for the discussion period — can serve as a written record that remains long after the lesson. Tools for writing — text editing — wikis — blogging tools Copyright © Allyn and Bacon 2010

Teaching in the Problem-Based Classroom Metacognition—being aware of how and why you are doing something Disposition—attitudes and beliefs about (in this case) mathematics Attitudinal goals for student — gaining confidence — taking risks — enjoying doing math Attitudinal goals for teacher — build in success — praise effort and risk taking — listen to all students Copyright © Allyn and Bacon 2010

A Three-Part Lesson Format Before: Getting Ready Activate useful prior knowledge. Be certain the problem is understood. Establish clear expectations. During: Students Work Let go! Avoid stepping in front of the struggle. Listen carefully. Provide appropriate hints. Observe and assess. After: Class Discussion Encourage a community of learners. Listen! Accept student solutions without evaluation. Summarize main ideas and identify future problems. Copyright © Allyn and Bacon 2010

A Closer Look at Text Books Examine a chapter of the book. Determine grade level. Find the standards that correspond. Compare the intent of the standard (Objectives) with the lessons. What modifications could you incorporate? (See pgs. 39-42 of Van De Walle book) Copyright © Allyn and Bacon 2010