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[WSS17] Rethinking Calculus Homework


As part of the Education Innovation track at Wolfram Summer School 2017, I created nine Mathematica notebooks to use as homework for my AP Calculus AB course. The notebooks cover differential calculus and focus on using the Wolfram Language (WL) to discover the key parts of the curriculum that will be further expanded on during face-to-face classes. The notebooks will be a students' first introduction to a topic.

For example, rather than taking notes on a linear motion lecture, students are guided through examples and questioned about what they find. Here is an example (download the project notebook for a further description and links to the nine notebooks):

After investigating the difference between average and instantaneous velocity, students would run the following animation (screen shot shown here) showing the vertical motion of the red ball and the corresponding position graph, focusing on the velocity as the slope of the tangent line. They would then answer the following questions.

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Here is another example students would see after sketching graphs of f ' (x):

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The notebooks follow a "dialog" format, repeating short pieces of information/investigations, student connection written in text cells, and checking work with input (code) cells. Students start with WL input given and are soon prompted for more unguided input. Student actions are prompted with red bullets, text cells are prompted with yellow background and code input cells prompted with blue background. Since much of the AP Calculus AB curriculum is hand-written, there are practice problems with text input and code input for immediate self-checking.

The nine notebooks cover the following differential calculus topics:

  • Definition of the Derivative and Differentiability
  • Differentiation Rules
  • Linear Motion
  • Trig Derivatives
  • Chain Rule
  • Implicit Differentiation
  • Exponential, Logarithmic, and Inverse Trig Derivatives
  • l'Hopital's Rule

All files were created using Mathematica 11.1

More work is need for further development for notebooks on optimization, related rates, and integral calculus.

Helpful resources included CalcLabs with Mathematica 5e, (Hollis 2012) and Hands-On Start to Wolfram Mathematica (Hastings, Mischo, Morrison 2015).

POSTED BY: Dan Uhlman
1 year ago

Great Work!

POSTED BY: l van Veen
1 year ago

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