Getting Students to Work Together in Cooperative Groups

One of my colleagues completed a Leadership Project with her ten students that I want to share with you. She had two similar 100 piece puzzles. (The puzzles are fairly inexpensive at Walmart or Dollar General.) Kay took these two similar puzzles which had alike colors/pictures on them and mixed them up. She then separated them into two baggies, and put each baggie in one of the original two boxes.

The class numbered off, 1-2-1-2...and so on, and then separated into two groups. At first, the students thought this was going to be a race to see which group could complete their puzzle first; however, each group started at the same time, writing the starting time on the board. After that, Kay didn’t say a word, and answered no questions! She simply observed the students. The students tried asking her, "Hey we don’t have all the edges; these pieces don’t match; are these the right puzzles?" Something is wrong; what's up?"

Kay waited to see who would take the lead to combine the groups, and how they joined. She wondered, "Would they join peacefully? Would they gather and form one group; two new groups; work together, or divide again?"  As she continued to observe, she began to write names on the board of those who were positive and took leadership. She then wrote the time on the board when they commenced to form one group.

When they finished, she held a Socratic Seminar (an Avid strategy) about how they felt concerning the activity. One student, who did not want to join a group in the beginning, became so involved during the project that he actually was the leader in getting the groups together.  It was one of those fantastic teacher moments!

Kay's students learned quite a bit from the activity since in reality, this is how life, social, and work environments are. She pointed out that they may not have a project that is going well, but by joining together with another group, you can problem solve, gain assistance, and acquire more pieces to your puzzle to accomplish your project.

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Since working together doesn't seem to be a skill that comes naturally, I use this activity with my college freshman as they begin their final group projects. Plus, as you think about your class and are puzzled about how you can get your students to work well in cooperative groups, keep this activity in mind.  It might just put the pieces together for you.

If your class enjoys cooperative learning, try this rubric for grading co-op groups.

More Math Patterns to Analyze!

Some people say mathematics is the science of patterns which I think is a pretty accurate description. Not only do patterns take on many forms, but they occur in every part of mathematics. But then again patterns occur in other disciplines as well. They can be sequential, spatial, temporal, and even linguistic.

Recognizing number patterns is an important problem-solving skill. If you recognize a pattern when looking systematically at specific examples, that pattern can then be used to make things easier when needing a solution to a problem.

Mathematics is especially useful when it helps you to predict or make educated guesses, thus we are able to make many common assumptions based on reoccurring patterns. Let’s look at our first pattern below to see what we can discover.

What can you say about the multiplicand? (the number that is or is to be multiplied by another. In the problem 8 × 32, the multiplicand is 32.) Did you notice it is multiples of 9? What number is missing in the multiplier?

 
Now look at the product or answer. That’s an easy pattern to see! Use a calculator to find out what would happen if you multiplied 12,345,679 by 90, by 99 or by 108? Does another pattern develop or does the pattern end?

 
Here is a similar pattern that uses the multiples of 9. How is the multiplier in this pattern different from the ones in the problems above? Look at the first digit of each answer (it is highlighted). Notice how it increases by 1 each time. Now, observe the last digit of each answer. What pattern do you see there? Using a calculator, determine if the pattern continues or ends.

Recognizing, deciphering and understanding patterns are essential for several reasons. First, it aids in the development of problem solving skills. Secondly, patterns provide a clear understanding of mathematical relationships. Next, the knowledge of patterns is very helpful when transferred into other fields of study such as science or predicting the weather. But more importantly, understanding patterns provides the basis for comprehending Algebra since a major component of solving algebraic problems

is data analysis which, in turn, is related to the understanding of patterns. Without being able to recognize the development of patterns, the ability to be proficient in Algebra will be limited.

So everywhere you go today, look for patterns. Then think about how that pattern is related to mathematics. Better yet, share the pattern you see by making a comment on this blog posting.

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Check out the resource Pattern Sticks. It might be something you will want to use in your classroom.