Instructional Approaches for AP Calculus

This is the third of four posts on the new AP® Calculus AB and AP® Calculus BC Course and Exam Description (CED). If you do not yet have a copy, click the link above to download the PDF version.

In previous posts I discussed the Concept Outline from the new CED, the Big Ideas and the related Enduring Understandings (EU), Learning Objectives (LO), and Essential Knowledge (EK). The second concerned the Mathematical Practices for AP Calculus (MPACs).  The CED contains a section called AP Calculus AB and AP Calculus BC Instructional Approaches.

The instructional approaches begins with recommendations on organizing the course from three perspectives: inquiry, applications, and technology. The second part of this section gives hints on linking the Learning Objectives to the MPACs and scaffolding them.

The third section called Teaching the Broader Skills talks about justification, reasoning, modeling, interpretation, drawing conclusions, building arguments, and applications. A succinct table related these to the MPACs, suggests question techniques and other strategies for each.

This is followed by an excellent section on representative instructional strategies. A table all lists these strategies:

  • ask the expert,
  • construct and argument,
  • create a plan,
  • create representations,
  • critique reasoning,
  • debriefing,
  • discussion groups,
  • error analysis,
  • graph and switch,
  • graphic organizers,
  • guess and check,
  • identify a subtask,
  • look for a pattern,
  • marking the text,
  • model questions,
  • notation read aloud,
  • note-taking,
  • paraphrasing,
  • predict and confirm,
  • quickwrite,
  • sharing and responding,
  • simplify the problem,
  • think aloud,
  • think-pair-share,
  • use manipulates, and
  • work backwards.

A brief definition of the strategy, its purpose, and an example are included for each. Quite a list! Of course no one can do all of every day or even every month, but the list provides a succinct reference; it’s a place to find new things to try with your class. No one will do all of them, but maybe you can find some new ones you like.

The strategies are followed by a brief discussion on the importance of students being able (that is, taught) to communicate their solution and their reasoning well.

This is followed by section on using formative assessment to monitor student learning and provide ongoing feedback. It suggests ways to help you understand what students know and addressing what they do not (yet) understand. Relating these to the instructional strategies, ways to assess learning while teaching, and ways to provide good feedback to students round out this chapter.

There are further short comments on vertical teaming, using graphing calculators and other technology, and resources for strengthening teacher practice complete this chapter.

The final part of the book gives information about the format and timing of the exam. A selection of sample exam questions for AB and BC calculus is included. The applicable LOs, EKs, and MPACs are included for each question. This will help you see how the LOs, EKs, and MPACs applied in preparing the test questions. A secure practice exam is also scheduled for release later this summer and will be available at your audit website, and at College Board sponsored workshops and summer institutes. The questions are also linked to the appropriate LOs, EKs, and MPACs.

Taken together the CED gives a complete look at the new program and many resources for AP Calculus AB and BC teachers. The CED gives a good basic outline of what an AP Calculus teacher need to know. It is a good read, maybe not for the beach, but for AP teachers.

The next and last post in this series will be a little different. In it I’ll show you a good tool for organizing all this and arranging it for teaching.

The College Board has produced a series of short videos on the new CED. Click here to see these Course Overview Modules.


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