What Makes Good Problem Solving. PREP Workshop, July 2003 Maria G. Fung. George Polya’s Framework. Understanding the problem Designing a plan (strategy) Carrying out the plan Looking back. Understanding the Problem. Get Familiar with Common Paradigms Ratios, percents

Download Presentation

What Makes Good Problem Solving

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

Draw a logic matrix (objects vs properties so we can identify/exclude possibilities)

Guess and check

Solve algebraic equation

Work backwards

Designing a Plan (Strategy)

More common strategies

Venn diagram

Finite differences

Change perspective

Sub-problems

Solve an easier related problem

Change focus

Carrying Out the Plan

Homework Problems

Peer review grading

In-class discussions and presentations

Problems of the Week

Written and graded using Oregon Scoring Guide rubric

Scoring Practice with Oregon children’s work using the Guide

Carrying Out the Plan

Portfolio Problems

Have students write summaries of problem-solving exploration activities (with open-ended problems)

As with weightlifting, this skill is developed by consistent practice (not by watching)

Oregon Scoring Guide Rubric

Rubric for assessing problem solving (scale of 1-6)

Conceptual Understanding

Processes and Strategies

Verification

Communication

Accuracy (scale of 1, 2, or 5)

Teaching and learning tool

Proficiency in scoring children's work

Portfolio Problems

Problems that the students write using a particular strategy and then solve

Assessment of Portfolio Problems:

10 points per problem

6 points for writing the problem

4 points for writing an appropriate mathematically interesting problem, following the correct strategy

2 points for clarity and good use of language

4 points for solving the problem correctly, with complete explanations

Example of a Portfolio Problem

Lucky Lollipops (Original Version)

Logan the Leprechaun loves Lucky Lollipops.

He decides to increase his luck by eating one lucky lollipop every day for 12 days, and also by giving away 1 lollipop on the first day and, for the other days, by giving away as many lollipops as he had given on all the previous days plus one more. How many lollipops total did Logan give away? Extra question: If he started giving away lollipops on a Tuesday, how many had he given away at the end of the day Sunday?

Math Forum Version of Portfolio Problem in the Pre-Algebra POW

Lucky Lollipops - posted March 10, 2003

Logan the Leprechaun loves Lucky Lollipops. He decides that he is going to give away his lollipops, and to increase his luck he's thought of the following routine:

I'll give away one lollipop on the first day and, for the other days, I'll give away as many lollipops as I've given on all the previous days plus one more.

How many lollipops did Logan give away on the 12th day? on the 24th day?

Extra: Write an expression to generalize Logan's routine. How many lollipops did Logan give away on the nth day?

Problem Writing Unit

Students pick their best portfolio problems and one other problem they love

Groups discuss how to improve each problem

Change context to a more interesting one for children

Discuss how to modify problem to make it simpler or more complex depending on level

What would happen if

Class presentations of “best” problems

Resources for finding good word problems

What Makes a Good Problem

More than one step

More than one method to solve

Possibly more than one answer

Clear language with no redundant information

Fun and relevant to children’s lives

Develops, illustrates, or enhances an important mathematical idea

Some Student-Generated Responses to Getting Stuck

Consider another strategy

Put problem aside for a while and come back

Try to explain the problem to a caring ear

Build a model or draw a diagram or picture

Solve an easier related problem or consider a sub-case

Online Math Mentoring Project

Opportunity to act as mentors to children in Fundamental (3-6) and Pre-algebra (5-8) Problems at www.mathforum.org/pow

Each student is assigned from 6-20 different replies to mentor

Great experience in reading and evaluating real solutions

Practice at giving feedback and good hints to children