Step 2

SolvingProblem

“ A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations, he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.”-George Polya

George Polya the father of problem solving in mathematics education.1887–1985

Impact of Instructional Approaches•Key words •Every problem has a given strategy•There is one way to solve a given problem•Teacher’s Way or the Highway•Problem Solving should be nice and neat and quick• If you can’t remember the formula there is no hope of solving the problem

The Poster MethodMario has a wall in his room that measures 13 ft long and 8 ft high. He wants to hang ½his favorite posters on the wall. Each poster measures 3 ft by 2 ft. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap?

Poster

ActivityMethod

What is a Good Problem-Solving Task?

• Non-routine• No prescribed method or memorized rules • No perception by students that there is a specific correct solution method.

Selecting the Problem Solving Task•Does it relate to current instructional focus?•Does it match students’ current instructional level?• Is it relevant and engaging to students?•Does it require students to “stretch” their mathematical reasoning abilities?• Involve more than one strand or standard of mathematics?• Is there more than one way to solve the problem?

Common Core Math Practices• Solve Problems and persevere in solving them•Reason abstractly and quantitatively•Construct viable arguments•Model with mathematics•Use tools strategically•Attend to precision

•Emphasize mathematical reasoning and verification and use of math vocabulary •Believe that students have the capacity to problem solve•Don’t “save” students•Train components of the process•Build student capacity to problem solve

Teacher’s Role

Promoting and Implementing Effective DiscourseClarify students’ ideas in a variety of waysrestate students ideas as questionshave students restate others ideasEmphasize Reasoningask follow up questions whether the answer is right or wrongteacher’s role is to understand student’s thinkingEncourage Student Dialogprovide opportunity to share in small group or with peer

Guiding Questions •What are you doing?•Why are you doing it?•How does that help you?•What did you do that helped you understand?•Did you find the information that you didn’t need?•How did you decide what to do?•How did you decide your answer was correct?

Sequence to Build CapacityPoster MethodPoster Method with a Write-UpAlternative MethodPoster Method– 2x’s Month

Rationale “Writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas—all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content they’re learning.” Source: Marilyn Burns, “Writing in Math,” Education Leadership, 62(2) (October 2004), p. 30.

Alternative Method

Set up• Problem• Review Rubric• Small Groups• Data sheet

Independent Work and Recording

(5 Minutes)

“Hint” Process(Throughout work time.)

Initial Group Workand Recording

(10-12 Minutes)

1st RotationContinued Group Work

and Recording(10-12 Minutes)

Answer & Verification(10-12 Minutes)

Create Final Product

Independently

Process the Solution(Next class period,

30 minutes)

Self-Assessment(Based on the rubric,

How did I do?)

2nd RotationContinued Group Work

and Recording(10-12 Minutes)

Language Frames for Math Discourse

“Listen to understandnot speak to be understood”

Find or create a word problem that meets the criteria discussed .