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Friday, March 26, 2010

Blog Entry #7

Teuscher, D., & Reys, R. E. (2010). Slope, Rate of Change, and Steepness: Do Students Understand These Concepts? Mathematics Teacher, vol. 103 (No. 7), 519-524.

Dawn Teuscher and Robert E. Reys' article, "Slope, Rate of Change, and Steepness: Do Students Understand These Concepts?" Teuscher and Reys bring up an issue that occurs with many students, in the fact that they don't understand the similarities and differences between slope, rate of change, and steepness when it comes to graphs of functions. They performed studies on tests that reflected questions that would appear on the A.P. Calculus exam, to see how students answered questions about slope, rate of change, and steepness. Unexpectedly, there were many students who believed that rate of change was the absolute value of the slope, or how "steep" a graph was, and gave incorrect intervals for answering questions about graphs and their rates of change. Teusher and Reys summed up the article by stating that teachers needed to do a better job of using the terms, and clarifying their meanings. This, in turn, will give students a better base for higher level mathematics, and prepare them more for future studies.

Teuscher and Reys bring up an excellent point that teachers need to better convey the concepts of slope, rate of change, and steepness, and explain their meanings, and how they are related. Doing so really will help students become better prepared for exams, like the A.P. exam, and for future, more advanced, mathematics. If students are allowed to continue with the incorrect ideas of slope and rate of change, when they take higher level classes, and subjects like physics, they will have an extremely difficult time, because they will have to change their views, and will not be able to connect their learning to the "knowledge" that they have about slope and rate of change. If teachers, however, explain these concepts thoroughly, it will make Calculus and Calculus based subjects much easier for students to grasp.


  1. I was a little confused by the way the first paragraph started. The last part of the first sentence, however, worked well as a topic sentence for this paragraph. I liked how you described the main issue that the authors were addressing, and even provided an example of how students might not understand the different meanings associated with slope. I wondered if the authors addressed ways to help students develop a better understanding of these ideas besides just to explain them well. The concept of slope is difficult enough that usually students need more than teacher clarification to develop correct understanding.

    Your stance toward the main idea was clearly stated in the topic sentence of the second paragraph. I also thought you did a nice job of supporting your stance throughout the paragraph. Once again, I wondered if teacher explanation would be enough to help students develop correct conceptions about slope. What do you think?

  2. The first paragraph's topic sentence is a little unclear. However, your second paragraph is great. Reading your post made me think about how Dr. Siebert told us that we needed to be consistent with the terms we use on our own blogs and how important that was. It's interesting how relevant this issue is in all fields, not just mathematics.

  3. Different wording of a couple of sentences in the first paragraph could have helped in clarification, but that is the only thing I could think of to improve. Besides that, you had a nice logical flow, clear points, and a professional tone. Good job!