Let's look at an investigation of Products and Sums of Numbers in a classroom setting. In this video segment, you can observe fourth-grade students as they work in small groups and later present their work. The problem encourages students to use visual representations to search for patterns and relationships between sums of numbers and products of numbers. Students communicate their ideas to one another to explore patterns, test their conjectures, and refine their ideas. The teacher, Ms. Doolittle, asks questions and provides guidance to assist with their reasoning process, which is sometimes a necessary part of developing reasoning skills.

Read the questions below before you watch the video (you may want to view the video segment again with specific questions in mind):

• What do you think are the teacher's mathematical content goals for this lesson?
• What evidence of effective reasoning do you see? Do students justify their answers? If so, how?
• What types of help does the teacher provide? How does she encourage reasoning and justification?

Now, watch an extended video excerpt (duration 8:40), at left, of Ms. Doolittle's fourth-grade class as they reason about the relationship between square and double numbers.

  Observe reasoning in the classroom setting