Like many people, I occasionally looked for shortcuts when I struggled in mathematics classes, so it is not surprising that many of today's students use tools like ChatGPT, PhotoMath and wolframalpha to overcome difficulties. But "productive struggle" is an essential part of learning mathematics, yet these tools subvert that process. Furthermore, false impressions of student understanding will result in teaching decisions that do not meet the needs of students. One strategy that many colleges/universities are using is to forbid the use of artificial intelligence, yet most instructors believe that little is to be gained by being the "cheating police." The reality is that these tools are here and students will use them.
How can emerging technological tools be used to promote student learning rather than subvert it in precalculus/calculus courses?
I see a few ways in which technological tools can be used to promote student learning:
1.) Emphasize conceptual understanding. We should encourage students to use these technological tools as aids for understanding concepts rather than shortcuts to answers.
2.) We can create assessments that require students to demonstrate understanding and application of concepts versus relying on memorization or algorithmic procedures.
3.) We can integrate technological tools into classroom activities. A colleague of mine would give "tech problems" (using WolframAlpha) to his students. These would be things like solving a system of 4 equations, 4 unknowns and it would be an application. He required his students to interpret the results so that they understood conceptually what they learned. The technology took the place of paper and pencil calculations.
4.) Collaborative learning with technological tools can allow students to work with these tools in a group setting. Group work can involve using technology to solve complex problems, share findings, and engage in reflective discussions.
A lot of this is easier said than done, however we can share activities that we already have using technology.
Fun fact: I used ChatGPT to help create this response and to give me ideas! These technology tools, when used correctly, can be a big help!
Regarding emphasis on conceptual understanding, we have recently published a paper in the Journal of Statistics and Data Science Education titled "Teaching Statistical Inference Through a Conceptual Lens: A Spin on Existing Methods with Examples."
The paper shows how statistical software can be used to teach statistical inference concepts at the introductory level.
I like these ideas. Another thing to do is provide the solution from ChatGBT and have students find the mistake in the process. Of course, not all solutions are wrong from ChatGBT, but some of them are. Having the students analyze the results helps them to understand that technology isn't full proof and if they conceptually understand the material they can find the mistakes.
One thing I believe that is not talked about much is that students, a lot of time, don't understand when they are actually cheating. I think we just assume they know, but a lot of times they don't. Granted, this is more of an issue in a writing/research course, but it has implications in mathematics too. Like many others, I teach FTF with online homework. I think it's a good idea to talk about how the students "cheat to cheat themselves" when doing the homework. To many students, getting homework done as fast as possible is the ultimate goal and we all know this is detrimental to learning. We need to help students do homework correctly so they are prepared for assessments. They don't know this.
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