After discussing Day Six with Dr. Thompson, Ms. Coombs agrees that the students appear to be graphing the path of the jump instead of thinking about co-varying quantities. She and Dr. Thompson refer to this as “shape thinking.” Ms. Coombs conjectures that the earlier problems where steepness did indicate an increase (or decrease) in speed contributed to this problem. However, in their discussion, Ms. Coombs realizes that her language could have also supported this way of reasoning when she talked about speeding up or slowing down in terms of steepness. Dr. Thompson conjectures that more focus on the covariational relationship of the two variables instead of the shape of the graph would have been more productive.

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