chapter 3 teaching through problem solving copyright © allyn and bacon 2010 this multimedia product...

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


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


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


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


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!

The Value of Teaching Through Problem Solving

(Continued)


Examples of Problem-Based TasksProcedures 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.


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


How to Find Quality Tasks and Problem-Based Lessons

A Task Selection Guide1. How is the activity done?2. What is the purpose of the activity?3. Can the activity accomplish your

learning goals?4. What must you do?

Good tasks: check out http://illuminations.nctm.org


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


Four-Step Problem-Solving Process

1. Understanding the problem2. Developing a plan3. Carrying out the plan4. Looking back


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


How much to tell Mathematical

conventions Carefully suggest

alternative methods

Clarification of students’ methods

And not to tell Establish

teacher- preferred methods

Teacher thinking

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


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


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.


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)

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