Helping Your Students Connect the Dots!

Helping Your Students Connect the Dots!

Toni PouttuMansfield ISD

Michael StephensFort Worth ISD

CAMT 2010

Special Thanks• Teacher Quality Project grant

through the Mathematics Department at the University of

Texas at Arlington under the supervision of

• Dr. Theresa Jorgenson• Dr. Christopher Kribs-Zaleta

Chickens and Rabbits Problem

• In the barnyard there are some chickens and rabbits. There are 50 heads and 120 legs on the chickens and rabbits. How many chickens and how many rabbits are in the barnyard?

How Did You Solve It?• What helped you?• What did you do when/if you got

stuck?• What do you notice about the

strategies from your group members?

What is Problem Solving?

• Problem solving means engaging in a task for which the solution method is not known in advance. (Principles and Standards for School Mathematics, National Council for the Teachers of Mathematics)

• A problem is defined as any task or activity for which the students have no prescribed or memorized rules of methods, nor is there a perception by students that there is a specific “correct” solution method. (Hiebert et al., 1997).

Creating a Problem-Based Classroom

• Encourage more than one strategy

• Avoid stepping in front of the struggle, Let Go!

• Listen carefully, observe and assess

• Provide appropriate hints

• Accept student solutions without evaluation

• Celebrate student interaction with one another/Let them talk!– ( Van de Walle, John. Elementary and Middle School Mathematics: Teaching

Developmentally, 6th Edition. 2007.)

Creating a Problem-Based Activity

• “Flip It” Approach– Begin with a clear, understandable problem– Let students apply their own thinking first– Allow students to share their solutions

without your help– Encourage students to challenge one

another’s ideas– Teacher then steps in for refinement of

solutions at an appropriate time

Pizza PartyEmily and Elijah are having a party. They have 2 ½ pizzas. How many friends can they invite if each person will have ¾ of a pizza?

Broken Calculator

• Find a way to solve 36 x 9 if the “9” key is broken.

Creating Definitions

• After working in groups to sort a variety of polygons, write a group definition to describe all of the shapes in each pile.

Area and Perimeter

• Mr. Wonka needs your help in determining which chocolate bar would would cost him the least amount of money to make but gives his customer the most choclate.

Constructing Knowledge

• And once I had a teacher who understood. He brought with him the beauty of mathematics. He

made me create it for myself. He gave me nothing, and it was more than any other teacher has ever

dared to give me.-Cochran (1991, pp.213-214)

Resources• Burns, Marilyn. 2007. About Teaching

Mathematics: A K-8 Resource. Sausalito,CA: Math Solutions.

• Van de Walle, John A. and LouAnn H. Lovin. 2006. Teaching Student-Centered Mathematics: Grades 3-5. New York. Pearson Education, Inc.

• Van de Walle, John A. 2007. Elementary and Middle School Mathematics: Teaching Developmentally. New York. Pearson Education, Inc.

• NCTM. Teaching Mathematics through Problem Solving . 2003.