NCTM: Think! Communicate! Justify!

Think! Communicate! Justify!
Presenter: Mickey Jo Sobierajski, Fulton County Schools

This session focused on ideas and activities to empower primary students to become confident problem solvers, good questioners, and critical thinkers.

Ms. Sobierajski opened her session with the following clip:

One of the most important things we need to do is to teach our children how to think. For example, in the clip, the operator did not just answer the little girl’s question, but asked her how much she thought it was. He was attempting to get her to think about it.

The session gave several different calculator game examples for primary students to build critical thinking skills. The games begin easy and build on each other. There is a strategy to each game and each strategy is a little different. In each game, students work in pairs to get the final sum on their calculators. A final sum is given to students as well as a set of rules for each game. Students must take turns until one student reaches the final sum and wins the game.
1. Target Number: 7. Students must start with a 0. They can take turns adding only a 1 or a 2 to reach the target number. (Sample strategy: You would want to get a four so that the next time it is your turn, you can win the game by adding a 1 or a 2.)
2. Target Number 10. Students must start with a 0. They take turns adding 1, 2, or 3 to the number to reach the target number.
3. Target Number: 21. Students must start with a 0. They take turns adding 1, 2, 3, or 4 to the number to reach the target number.
4. This is the hardest because it has special conditions and students will have to really think about each number before entering it. Target Number: 25. Students must start with 0. They take turns adding 1, 2, 3, 4, or 5 to the number only if that number or the sum of its digits is not on the screen. (For example, I put in 5. My partner may not add 5 because it is on the screen, so instead she adds 4. I add 3. Now we are on 12. My partner may not add a 1 or 2 because they are on the screen. She may also not add a 3 because the sum of the digits are 3. My partner may only add a 4 or a 5.

To become good problem solvers, students need time to struggle with the problem for teachers to see what they are thinking. Here is a sample problem:

Lauren has 84 identical cubes, each with 2 cm edges. She glues them together to form a rectangular prism. The perimeter of the base is 28 cm. Find the height of the rectangular prism in cm.
What do you know by reading the problem? What do you have to find out? To understand the math, you need to be able to talk the math.
A good problem for students to solve involves interrelated concepts and is at a high level.

Question: When there are 52 green doors, how many blocks will I need all together? Allow students the use of manipulatives to model problems like this if they would like to use them. (Some students will create a number string to solve instead.) If you give students manipulatives, give K students too many and give 2nd grade students not enough to allow them to think critically about it.

Make sure not to use key words when working with a story problem. In all does not always mean to add. If you teach students to look for key words, you are teaching them not to be critical thinkers, but rather to read only the parts of the problem that you need, then solve.
For example: Brian rode 12 rides at the carnival. In all, he spent $9 for rides and $3.50 on snacks. How much did each ride cost? What is this problem really asking us?

Beware of the vocabulary you use. Are you using vocabulary that may cause a misconception? Do you tell students “I’ll be there in a second” and take longer than a second? This does not help them develop an accurate understanding of one second.

Word Walls can also be used to promote critical thinking in the math classroom. For example, use circles to help sort rules.
Which word does not belong and why? (There could be more than one answer.)
Choose a number that has something in common with the empty circle. (Allow students to figure out what the numbers have in common.)

Another way to promote critical thinking is to give students a scenario and a solution and have them determine the question to be asked.

For example: There are 2 fish tanks in my room. One has 8 guppies and 11 goldfish. The other has 24 fish with an equal number of guppies and goldfish. What question could I ask that would give me a solution of 43? Of 12? Of 23?