My New Recipe for Teaching AP Calculus AB

Upon opening the AP score report for this year’s AP Calculus AB cohort earlier this week, I knew the new recipe I created for teaching the course this past school year was a keeper. I did not feel the same last year.  In fact, I do not believe I even blogged about my students’ scores after I received last year’s score report, as disappointment with the results held me back.  At the same time, the disappointment drove me to seek out a new approach to teaching the course.

To help understand my satisfaction with the new recipe, let’s first look at data for the past three year’s for which I taught the course along with the year preceding my arrival as a baseline.

Comparison Data copy

The yellow highlighted cells show the significant improvement in this past year’s cohort compared to earlier ones, as well as the difference between the this cohort’s pass rate and the national average pass rate.  Secretly, I had hoped for a 100% pass rate.  However, I was very happy to compute the 82% rate, which exceeded my minimum expected rate of 60%; I shared each of these with my fellow AP math teacher (Calculus BC and Statistics) before summer break.  I cannot recall if there was a friendly wager riding on the results though.  My memory likely will kick in as the new academic year commences this fall, where my friend may owe me a cold beverage.

The Recipe

So, what exactly is the recipe I used this past year?  In general, it consisted of a “flipped classroom” model where students completed their homework assignment before attending class, or receiving any guidance from me; some might classify the approach as incorporating a blended learning model where students integrated use of online technology with traditional in classroom instruction.  There is a fair amount of debate over what makes up blended learning, so I chose not to include it as an ingredient in my description of the initial recipe.


Every week students visited my website to view assignments for an upcoming week as shown below.

Homework Assignments

Each of the links above connected students to a detailed tutorial hosted on containing assignment instructions; links to videos; supplemental, embedded videos and slide presentations; a reading assignment; specific homework exercises; a Google form to enter select exercise solutions; another Google form for students to rate themselves on the assignment based on a provided rubric; and on occasion, a brief one to three question multiple choice online assessment with step-by-step solutions provided after they submitted their answers.

Select images of some of the material available to a student on my Sophia site follow.

Sophia Tutorial Title


Tutorial 4

Tutorial 3

Initial Review of Recipe’s Success

While the “flipped classroom” approach is challenging for many students, both in terms of access and acceptance, I believe it is a superior method for challenging topics such as calculus where up to half of students routinely fail or drop the course.  My first experience with the flipped classroom model occurred my freshman, err plebe, year at West Point where students read the textbook and completed homework before the next class period during which students presented their work among their classmates and the “P,” or professor.  The major difference between then and now, aside from 30+ years, consists of the expanse of the Internet and all the video and textual resources available to students to include step by step solutions to most textbook exercises!

With the Internet at their fingertips, my students watched one or more instructional videos on the to-be-learned calculus topic before reading the textbook, or completing the assigned homework exercises.  Other supplemental resources were available to students such as videos from college instructors or detailed slide presentations showing step by step solutions that followed along with examples from the textbook.

Many improvements, enhancements, and other changes will follow this first use of the recipe.  However, I am confident that its basic ingredient set satisfies the needs of student, teacher, parent, and administrator.  I look forward to working with a new cohort of students this coming year, where tweaks to the basic recipe will hopefully yield even greater results.

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.
This entry was posted in Mathematical Proficiency, Pedagogy and tagged , , , , , . Bookmark the permalink.

8 Responses to My New Recipe for Teaching AP Calculus AB

  1. Dave, it sounds like you are getting a real handle on this teaching thing! I am so glad to hear that, with all the struggles of the past two years, you are seeing positive results and feeling good about what you have done. Congratulations on your AP test scores. But more importantly, I hope you are starting to have greater confidence in your choice to teach. Clearly you are an excellent teacher. We need more like you.


    • Thanks so much for the kind words, Patti. It was critical that I experience success this year to make my investments of time, talent, and treasure worthwhile. I never cared so much for a job as I do for being a teacher. While it has been painful these past few years, mostly due to my desire to make a significant difference in my students’ educational outcomes, moments like these do underscore the reasons I decided to become a teacher.

      I hope all is well with you, too. BTW, I love your gravatar.


  2. CA Maestra says:

    Fantastic!! 😀

    Also, I think you meant 🙂


  3. A few questions: I attempted what you’re doing last year with my freshmen pre-AP English kids, and I met a great deal of resistance from admin and parents due to a lack of tech at home. I gave lead time on assignments, library passes so they could go to the library and watch the videos and complete assignments during school time, extended before and after school tutorials…and nothing. Though I had a 91% passing rate on our state exams, I still feel like the year was a failure because of the inability to properly implement what you’re talking about.

    How do you adjust for students with little to no access to technology at home or even the desire to access the technology provided at school? What suggestions do you have to overcome these issues? Did your district provide technology (i.e.: 1:1 or iPads/laptops in the classroom)?

    Congratulations on your and your students’ achievement! You all should be commended!
    Heather Nieto


    • Hi Heather.

      Yes, access and motivation are necessary factors for maximal success with this approach. In fact, they are correlated somewhat as a more motivated student may seek out access more readily.

      While this approach clearly succeeded with my AP students, most of whom were seniors (62%) or juniors (32%) and high SES, it would most likely have failed miserably with my algebra 1 & algebra intervention sections, as most were freshman (62%) and low SES. Maturity (freshman v. upperclassman) and SES are major contributors to motivation and access, respectively.

      For my algebra sections in second semester, I incorporated a quasi-blended learning approach. I believe it helped somewhat, but I also implemented other supports which may have had more of an effect. How much, by which, is too difficult to tease out. Student motivation clearly played a strong role as well, even when access was addressed as I had full-time access to 36 Chromebooks.

      Lastly, a 91% pass rate is nowhere near a failure! Whatever you are doing seems to be working. I believe the outcome is more important than the method. I adjust methods to optimize outcomes.



  4. Hi Dave,
    Congrats on your students’ excellent scores!
    My question: In the flipped model, if students are watching the lessons and completing the assignments at home, how are you filling up class time?


    • Thanks, Olivia. Class time is used to address gaps in understanding, answer questions, re-teach as needed, group work, assessments, etc. Homework is not graded for correctness. Students must attempt the problems and be prepared to present their work even if incorrect. We address mistakes, misconceptions, misunderstandings as part of a whole class discussion or with students working in small groups. Homework only accounts for 20% of their grade directly, yet indirectly it heavily influences the 80% from assessments.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s