1.3.2 During Phase

Teacher Actions in the During Phase
Once you are comfortable that students are ready to work on the task, it is time to let go. You must demostrate confidence and respect for your students’ abilities. Your role now shifts to that facilitator and active listener. You might sit down with a group, listen for a while, have the students explain what they are doing, or just take note.

Provide Hints and Suggestions

How much help to give students is always going to be an issue. Should you let them stumble down the wrong path? How much direction should you provide? Do you correct errors you see?

In Kelebek’s Furniture Store, Kelebek has priced all of her furniture at 20 percent over wholesale. In preparation for a sale, Kelebek decides to cut all prices by 10 percent. Will Kelebek be making 10 percent profit, less than 10 percent, or more than 10 percent profit? Explain your answer.

For this problem, consider the following hints:
Try drawing a picture or a diagram of something that shows what 10 percent off means. Try drawing a picture or diagram that shows what 20 percent more means.

Encourage Testing of Ideas

Students will look to you for approval of their results or ideas. Avoid being the source of “truth” or of right and wrong. When asked if a result or method is correct ask, “how can you decide?” or “why do you think that might be right?” or “I see what you have done. How can you check that somehow?” reminds students that answers without reasons are not acceptable.

Suggest Extensions or Generalizations

Lots of good problems are simple on the surface. It is the extensions that are excellent.

The area and perimeter task is a case in point. Many students will quickly come up with one or two solutions. “I see you found one way to this. Are there any other solutions? Are any of the solutions different or more interesting than others?

What can you find out about that? This general question is at the very heart of mathematics as a science of pattern and order. It asks students to look for something interesting, to generalize.

Questions that begin “what if you tried...?” or “would that same idea work for...” are also ways to suggest different extensions.

Find a Second Method

The value of students’ solving a problem in more than one way cannot be overestimated. It shifts the value system in the classroom from answers to processes and thinking. It is a good way for students to make new and different connections.

Consider this sixth-grade problem
The dress was originally priced at 1000 TL. If the sale price is 25 percent off, how much will it cost on sale?

This is an example of straightforward problem with a single answer. Many students will solve it by multiplying by 0.25 and subtracting the result from 1000 TL. The suggestion to find another way may be all that is neccassary. Others may require specific directions: “How would you do it with fractions instead of decimals?” Draw me a diagram that explains what you did?”

  1.3.3 After Phase

Teacher Actions in the After Phase
Be certain to plan ample time for this portion. Often this is when the best learning will take place. This is not a time to check answers but for the class to share ideas. You must teach your students about your expectations for this time and how to interact with their peers.

Engage the Class in Discussion

Your function is to make sure that all students participate, that all listen, and that all understand what is being said.

Who has an idea about this?.... Yesim, I have noticed that you got a different answer than Ali. What do you think of his explanation? (Open the discussion to the class)

Encouarge students to ask questions
Veli, did you understand how they did that? Do you want to ask Jale a question?

Identify Rules, Hypotheses, and Future Problems

When you are satisfied the discussion around the answer and the solution, summarize the main points of the discussion, and make sure that all students understand what has been agreed on.

Use Praise Cautiously

Be attentive listener to both good and so good ideas. Support and praise effort and risk taking, but expect students to do good work.

In place of praise that is judgmental, comments of interest and extension can be suggested:
I wonder what would happen if you tried .....
Please tell me how you figured that out.

Engage all Class Members

The needs and abilities of children are different, and it requires skill and practice to conduct a large group discussion that is balanced and includes all children.

The discussion is more important than hearing an answer.

Begin discussions by calling first on the children who tend to be shy or lack the ability to express themselves well. Try to support children’s thinking without evaluating responses.

There will, of course, be times when a response is simply not forthcoming. When this occurs, you might suggest taking some time to get thoughts together or to work out the idea with some materials. Promise to return to the child later, and then be certain to return to hear what was figured out.