Calculus III covers material from calc I/II, but in 3D. One part of calc III is to graph in 3D. A program called Maple is used to draw the graph, then students draw this on their exam. For 6 years, a lecture approach was used to cover this topic. Overall, students did not do well on this part of the exam (approximately C-D average). Students had no comprehension as to why the graph looked the way it did and were not able to draw basic shapes. Also, students were not able to explain if the graph made sense; did the technology provide a correct graph.

F15, I asked myself "Why do students need to know how to do this? What is it they need to get out of this activity?" They need to know why technology is providing the answer it does and if the answer makes sense. More time was spent having students analyze the equation and explain WHY the graph in Maple looks the way it does. They also had to explain if the graph was correct or not. Students practiced analyzing in class and average on this exam problem went up to a B. David Weaver assisted me with this change.

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## Comments

The EDU terminology for providing a meaningful reason is called a "Rationale", and when students generate their own rationale (which is what you did), that is when it is most powerful. And of couse, the in-class time spent reinforcing this helped too! Well done, Becky!

Becky, a couple of things stand out here that makes this a model of instructional intervention. First is that instead of "covering the topic", you got really clear as to what was the purpose of the students understanding this topic, and that informed how you approched the subject. There was a clear learning outcome. The second is that you switched from a more passive lecture approach to a more active learning approach where students had to practice what they would be tested on later, practicing if they can analyze what was going on and evaluating if it was correct (higher order Bloom's skills than just understanding). This opened up opportunities for feedback so that students could self-assess if they were learning it and where their learning gaps were so that they knew where to focus their learning efforts. No surprise they showed marked improvement! Well done.

Hi Becky,

This is a nice study as it emphasizes a point I was making in a CATS comment about psychology statistics. Students can do process, but they have trouble linking process to a visualization of the underlying abstractions that the process is intended to map. I think that focusing on the "why" issue is wonderful.

Your work illustrates the power of shared learning among faculty as well. Isn't it great how a physics faculty, being available and open to experience your material, can give you that alternative insight?

Additionally, you trigger a further thought. More related to my issues than yours, but something we need to ponder as we continue to expand on-line presence of courses. In my face-to-face course teaching statistics (our psychology mathematics), I focus intensely on the visual/geometric relations of each of the definitional formulas. But what I am finding difficult is trying to convey this sense in an on-line environment. As your CATS tries to address: when students don't understand the conceptual abstractions underlying the symbols on the paper, they fall back on mere process to "get by" in the class.

Anyway, your intervention is an important contribution to helping students avoid the "process" strategy. Thanks for sharing!

HI Becky, This is really interesting. Since I am not familiar with the assigment, could you attach more information on the actual assignment and the graph. I am curious to see what this looks like. Thanks! Olga

Olga, thanks for the response. I have uploaded the old question along with the new question for the same problem.

Becky, this is great, Erik made the perfect comments about your objective, etc. Boy, if I had these experiences in my MAT courses maybe I would be a mathmetician!

Becky I love that you are encouraging your students to question "why" and link the importance between just letting technology do the problem versus using it as a tool but understanding the answer and if it accurate. Many of my students did that with their calculators and why I don't let my 081 student use a calculator for half of the semester so they will embrace the patterns and comprehension rather than using the calculator as a crutch :-)