Atypical AP Calculus Summer Work

Many AP teachers assign students summer work to complete prior to the start of the new school year.  Most AP Calculus teachers assign problem sets to reinforce prerequisite knowledge such as the following A.P. Calculus Summer Packet.

For the upcoming school year, rather than assign a similar set of problems, I elected to assign my students a set of readings and writings.  These assignments are meant to address the shortcomings I believe exist in most school district’s mathematics curriculum where learning is reduced to mimicking a teacher’s approach to “solving” problems.  Few students actually solve problems in the traditional sense, they simply follow a semi-scripted procedure they observed their teacher perform in class, which works well for problems that fit the script.  However, any problem that goes off-script creates confusion for many students.

If anyone has used a similar approach for their students, please let me know.  I am also interested in your thoughts on these assignments.

Summer Work

Students registered for AP Calculus AB are required to complete the following summer work prior to the first day of the new school year.  Each assignment is due on the first day of school.  Those students who attended the AP Calculus AB/BC Boot Camp may recognize some of the following items.  If you have any questions, please email me.

Summer Work Assignments:
  • Review each of the following documents.  You will be expected to be familiar with the content in each of these documents.
  • Answer the question(s) relating to each reading assignment per the directions below or on the assignment’s task sheet.
    • College Board’s AP Calculus Course Description Task Sheet #1 (250-500 words)
      • Why does the College Board emphasize conceptual understanding (the understanding of concepts coupled with the ability to make connections between, and among, other concepts, to communicate them effectively, and to utilize them in problem solving) in AP Calculus so much, even of prerequisite subjects and topics, when prior math classes emphasized procedural fluency (the ability to master procedural skills needed to perform mathematical computations and procedures)?
      • How might the emphasis on conceptual understanding benefit your success in this course, preparation for college, career achievement, and development as a lifelong learner?
      • What challenges does this emphasis present to you as a student?
    • How to Study Math (250-500 words)
      • How do you typically study for math class?  Do you study before quizzes, tests, and/or finals?  If so, how much time typically do you spend?
      • How much time per school night do you spend studying for math, not including doing homework?  Same question but including doing homework?
      • Which of these tips do you already follow when you take a mathematics course?  How are they helpful?
      • Are there any of these tips that you have not used before that might help you in AP Calculus?  Why do you think so?
      • Are there any tips that are not mentioned that you believe are helpful?  How are they helpful?
    • NRC Math Proficiency Standards Task Sheet #2 (250-500 words)
      • What were your experiences in your math classes (past & present) along each of the strands?
      • Were your experiences positive?  Why or why not?
      • Could you benefit from keeping these different dimensions of mathematical proficiency in mind as you continue with your education?
        • What parts could be challenging?
        • How could we address your challenges in the class?
    • NCTM Process Standards (250-500 words)
      • In your own words, explain each of the NCTM’s process standards for mathematics.
      • How familiar are you with each of the process standards?
      • Which of the process standards have you applied / used in prior math classes?
        • Which of these did you find easiest to use?  Why?
        • Which of these did you find hardest to use?  Why?
    • Algebra and Trigonometry Review (250-500 words)
      • Which concept(s) in algebra, if any,
        • are easiest for you?  Why?
        • are most challenging for you?  Why?
        • do you think you need to re-learn?  Why?
      • Which concept(s) in trigonometry, if any,
        • are easiest for you?  Why?
        • are most challenging for you?  Why?
        • do you think you need to re-learn?  Why?
    • All assignment submissions must:
      • 1) respond to the prompts;
      • 2) be well-written;
      • 3) adhere to the word count requirement;
      • 4) use one-inch margins, 12-point Times New Roman font, and double line spacing;
      • 5) include the assignment name and your name in a header as well as the submission date and page number in a footer on each page; and
      • 6) be consolidated into one stapled document, in the order below, with a title page labeled “AP Calculus AB Summer Work” as well as include your name and submission date.
      • Papers may be double-sided.  Unless otherwise specified, it is acceptable to write your responses to an assignment as a list of questions and their answers.  Use section headings, as needed, to separate areas of focus in your writing.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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9 Responses to Atypical AP Calculus Summer Work

  1. Jack Dieckmann says:

    Hey Dave! Interesting summer packet. I am sure it is very different than what they have gotten in the past in math or in other subjects. Given such a departure, what kind of rationale do you offer your students for so much reflection/instrospection? I like it but I am wording how students perceive where you are headed with this. Let us know when you get the results!


    • Good question. I suspect the perceptions are many and varied. BTW, I just might use the question you posed as an overarching one for students the first couple days of class.

      I emailed out the following identifying their summer work. This is as close to a rationale as I came. I hope they can read in between the lines: I suspect the ones that attended the boot camp will get it, as I discussed reasons for incorporating the NRC strands of mathematical proficiency and the NCTM process strands.

      Greetings 2012-2013 AP Calculus AB Students:

      Your summer work for AP Calculus AB is now posted. Click on the link to see specific instructions and other links for the summer work. It is unlike what you may have expected. It does not contain a collection of math problems. Instead, you are required to read a few documents and write about them.

      Please reply to this email letting me know you received it. This will save me from calling you over the summer to ensure you receive the summer work.

      Also, presentations and handouts from the AP Calculus Boot Camp are available online. For those of you who could not attend, or missed one or more days, please download and review the material. It will help you prepare for taking AP Calculus in the fall.

      I hope everyone is enjoying their summer.

      Mr. Math Teacher


  2. Dave ( also a career changer Math teacher ),a few years ahead of you. says:

    God has Blessed you if you can get them to do this.


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  6. Eric says:

    Hey Dave,

    Just stumbled upon this post and I really wish I would have read this before last school year got out and I assigned my summer work. I assigned them “review” work out of our textbook and was planning on giving them a test at the beginning of the year (next week), but feel bad about testing them on something I didn’t teach them (a cardinal sin) so it looks like I will do a diagnostic and bootcamp instead. This would be much better for next year. Keep up the good work.


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