Clip 28/41: Standard 3: Construct Arguments & Critiques Using Graphs, Equations, & Tables Part 1

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments...They justify their conclusions, communicate them to others, and respond to the arguments of others.

Jake Disston and Jesse Ragent work with their middle school students to deepen their understanding of the connections between different representations of functions—graphs, t-charts, and equations. In this clip, he challenges his students to work at their tables to group the cards they have in front of them, creating as many different groupings as they can and devising language to describe each group. As the first student reports it becomes clear that while there is some understanding of the information, there still remains plenty of misunderstanding and confusion. Disston models the need for teachers to honor all responses in class discussion. He brings the incorrect notion of the student's "linear" grouping of the quadratics into proper focus and clarity in a way that does not denigrate the student's thinking. Ragent reviews group work protocols for turn-taking and talking, asking students to "think out loud, giving mathematical reasons for the selections" they make using language generated by the class.

See this video in the context of an entire lesson.

(Parts 1 & 2)