Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Reasoning and ProofSession 04 Overviewtab atab btab cTab dtab eReference
Part D

Applying Reasoning and Proof
  Introduction | Using Venn Diagrams | Classroom Practice | Reasoning and Proof in Action | Classroom Checklist | Your Journal


Reflect on each of the following questions about the button activity you observed in Ms. Gayles's class, and then select "Show Answer" to reveal our commentary.

Question: How does this problem help students extend their understanding of classification?

Show Answer
Our Answer:
This simple sorting task gives young students the opportunity to decide on one physical characteristic of the buttons, such as color, and then sort the buttons according to that characteristic. Recording their results on graph paper gives students the opportunity to organize their information and, later, to make inferences from the data or information they have collected.

Question: In what ways does this task encourage reasoning?

Show Answer
Our Answer:
In order to sort the buttons, students need to identify a category and a reason for sorting the buttons in a particular way. When asked, "How did you sort the buttons?", children describe their thinking and in the process demonstrate and reinforce their reasoning.

Question: What characteristics of a classroom that encourages reasoning are present in this lesson?

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Our Answer:
Students work in pairs, talk about their strategies, explain their reasoning to one another and to the teacher, and represent their thinking in written form by recording their data on graph paper. Students are expected to be able to explain and justify their reasoning. At the end of the class, students explain and justify their thinking to the class and consider various ways to sort the buttons.

Question: Ms. Gayles's questions lead students to explain their thinking and the reasons why they sorted the buttons the way they did. Can you give five examples of questions you can use to help young children clarify their thinking and explain their reasoning?

Show Answer
Our Answer:

Here are some examples:

What types of groups are you going to make?

How are these buttons the same?

How are the buttons in this group different from the buttons in that group?

How can you record your button group on the graph paper?

Can you tell me how you decided to group the buttons on your paper?

Can you show me how you did it?

Why did you put them in an L shape?

Where will you fill in the square for the next group?

Are there buttons that don't fit in your group? Why?

Could there be more than one way to describe the buttons in a group?

It's also important to ask follow-up or clarifying questions. If you ask, "What types of groups are you making?" and the students respond, "Little ones and big ones and short ones," you could ask, "Let me see –– which are big? Which are little? Which are short?"


Question: How might this activity be extended for students who demonstrate an understanding of sorting?

Show Answer
Our Answer:
There are many ways this activity could be extended. Other materials, such as pattern blocks, geo-blocks, attribute pieces, and everyday items could be used. The "What's My Rule?" game could be used with the buttons –– one person chooses buttons with a similar characteristic, and other students try to determine that characteristic. Students could use Venn Diagrams to sort buttons by more than one characteristic. The "What's My Rule?" game and Venn Diagrams could also be combined and used with numbers; for instance, one circle could be "multiples of five" and a second circle could be "even numbers," with the numbers fitting both categories placed in the area where the circles overlap.

Next  Use the Classroom Checklist

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