Table of Contents

Unit 3: Reasoning and Explaining (MP2 and MP3)

3.2.2 Levels of Explanation: Bridging Level 1 and 2

Single Case or Example

When learning to explain their thinking, students will provide one example and believe it is enough evidence to argue their conjecture. This is referred to as a “perceptual proof” (Sowder & Harel, 1998).

View the student work below for examples of a perceptual proof:

Student writing on posters:
Even. Yay 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. All cookies have partners. Even means there are no numbers left out when you count by twos.

Boo! Odd, Boo! Not all ghosts have partners. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29. Odd means there is a number left out when you count by 1s, 3s, 5s, 7s, or 9s

Time to View

In the video below, Jason and Jonathan use a single example to demonstrate what an odd number is.

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Notice that in the two examples presented, students are satisfied with one case as sufficient evidence to validate their claim.