Using Desmos to Support the Chain Rule

Submitted by Sara Meana on
What is the Purpose of the Assessment?

Students will be able to calculate the derivative of composite functions.

Students need to correctly apply the chain rule to calculate derivatives of composite functions.  Commonly, students "forget the chain", only applying the derivative rule to the outside function.

Describe the necessity for this assessment

The chain rule is an application of two (or more) derivative rules.  Without correct application of the chain rule, students cannot be successful in MAT220, or subsequent courses.  When analyzing previous semesters MAT220 data, one third to one half of students historically had not mastered the chain rule the first time the chain rule was assessed.

Describe how the practice will be implemented

Students will use Desmos to compare the graphical representation of the derivative, created by desmos, with the graphical representation of the derivative calculated with the rules.  Students will compare Desmos answer (correct) with their answer (maybe or maybe not correct) and then make adjustments to the equation until the Desmos answer graph and their answer graph match.

Interpret, compare, and describe the results

When comparing student work samples from Fall 2022 with Fall 2023, I noticed that students that used Desmos to check chain rule solutions had more crossed out and revised solutions than students that did not use Desmos.  That alone, is evidence of improvement!  Additionally, the percentage of students mastering the concept the first time it was assessed increased from 52% to 76%!

After analyzing, and reflecting on the outcome, what are the next steps?

With this improvement in assessment results, I intend to continue the practice of teaching students to use Desmos to confirm solutions to the chain rule.  

When comparing to end of course data, like chain rule questions on the final exam, I did not see evidence that students were checking their work with Desmos and making improvements.  I am considering adding a check box to each problem stating "I checked my answer with Desmos" or "I chose not to check my answer with Demsos".  I hypothesize that will remind students that simply forgot, and also will give me a talking point with students that are getting wrong answers but stating they checked with Desmos.


When finding derivatives using the chain rule, a common student error is to "forget the chain".  By visually confirming the derivative equation they calculated matches the derivative graph generated by Desmos, students can confirm correct rule choice and correct application of rules.  If the graphs don't match, students can then make small changes to their equation until the derivatives match.  Instead of asking a technology (like mathways or symbolab) to state the correct answer, we are leveraging technology for problem solving, and reinforcing fluency between graphical and algebraic representations.

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