Historically, I would say that the least amount of learning occurs during exam week. This year, however, I have tried to make this statement false through giving my students a new final exam. When the first group presented, not only did I see, hear and was taught about unique examples of how to use calculus, I can actually say the group still LEARNED through the assessment.
Below is a video of their PowerPoint presentation, which they used as well as supplemented with dialogue.
After the presentation they opened the floor to me by giving me 10 minutes of questioning. Most of the questions they answered swift and correctly, until I asked “Do all functions, on a closed interval, have an absolute maximum?” . Their answer was “Yes”. Of course this is incorrect.
Now here is how the learning occurred… First I will address the traditional way of assessment:
If this was a traditional final exam, I would have marked this question wrong and moved on to the next question and continued marking. These students would never have received any feedback, as in the past, I have yet to see many students come back to see WHAT they did incorrectly on a final exam. These students would have then gone on to university/college with this false knowledge.
How it has changed this year…
I didn’t let this false information continue. I then asked, “What if I told you, I could draw a function on a closed interval without an absolute maximum?” The girls looked at each other with confused eyes, and pondered the idea. After some passing minutes, one replied accusing me of a liar. I wanted to ensure they didn't continue on with this false information, so I then asked, “Is there any kind of function that continues upward on forever?”. One quickly answered, “WAIT! A function could have a vertical asymptote and therefore have no absolute maximum. I guess you weren’t lying”, the other girl smiled and agreed.
After this, I wanted to ensure they had a true understanding and therefore I asked, “Can a function, without any asymptotes, on a closed interval, not have an absolute maximum?” The enlightenment has occurred! Both girls whispered quietly, and then turned and replied “If the curve has an open point at the highest point, then it would not have an absolute maximum”.
Learning had occurred, and yet it was a final exam.
I continued with my questioning, which they answered correctly, and I am happy to say that this experience has been a success with the first group!
