I am a teacher by day, and an adjunct by night. One evening, while looking out into the sea of college freshmen, during one of my "lectures" I noticed that their faces all had that glazed over look, they were not as engaged and all around looking miserable. The college students humor me by laughing at my horrible jokes, and will even ask questions when they need, but I did not feel the room at all that night. Later that week I was on Twitter scrolling through, and found an interesting Tweet by Robert Kaplinsky, "Who ever felt that lecture was the pinnacle of education?! If anything, we should be giving them our best instruction to prepare them." Although lecturing is sometimes necessary to convey content, it should not be the sole way students of any age are taught.
Rubric:
Curve Sketching Rubric
Project Example:
First & Second Derivative Test Project
With that in mind, I also remembered that last year while teaching the same topic on curve sketching. I was so excited by my examples and how to do the problems, that after I was done with the class I quickly assigned the odd problems from the text book. Not thinking that each problem took about 15 minutes to complete, and giving 15 problems at 15 minutes a piece meant almost 4 hours worth of homework. I did a complete disservice to those students with the assignment, and quickly had to apologize. After reflecting on the previous year, and thinking about how I wanted this current semester to go, I figured out a new way of teaching the problem set and I feel I came up with a more interesting and collaborative way to practice the skill of curve sketching using derivatives.
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Group 4's Project and Discussion were both great!
Read below for more on the interactions of the group and the language used. |
Students were randomly assigned into 6 groups of 4. I created a Google Drive Folder for each group and then made some adjustments to the problems from the text and my unit review. Each group was assigned two functions to use the first and second derivative test, creating the curve sketching information that they needed. Groups were to find the relative maxima, relative minima, any inflection points, where there was concavity up or down, and where the function was decreasing and increasing. The groups added comments and edits, gave each other feedback and created a great collaborative final answer for their functions. They also were to sketch the curve with Desmos, and find all of the points that they solved for mathematically on the picture instead of all by hand. I had each group member turn in their perspective rough draft to have students show more than just participation in the online document, but the collaboration piece was key. A lot of the discussions were really powerful with well thought out questions, leading to deeper understanding of the tables and sign charts groups created. They learned from each other how to successfully apply the derivative tests to the function and what pieces would ultimately help them sketch the graph. the groups also made their sign charts each in different modes through technology or taking a picture of their hand drawn chart.
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| Student Sign Charts were interesting and creatively made. |
Another Group's Sign Chart |
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After everyone had turned in their Google Doc, I also wanted to get a feel for the students' outlook from completing their group project. I created a Google Form and asked several questions about how they felt the project went. A majority of the feedback that came back said the group project was enjoyable, and it helped that students with understanding the process. I also saw a lot of good computational thinking in the form of their summative assessment following our fourth unit, and I think that I will use this project in years to come. My new goal is to create one collaborative or group project for each unit of my course to engage my college learners in a more enriching fashion. Next year I plan to facilitate another learning experience that will enhance my college course, and make the course even more engaging.
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