Ultra short post. Posting results for my fifth cohort of AP Calculus AB students on the fall final exam. The (nearly) identical final has been used all five years; one question was changed in year two or three.

Scores improved significantly on the final for this cohort. I believe there are a variety of factors contributing to the improvement:

- I taught 80% of these students last year in honors precalculus,
- I created practice quizzes (with fully worked solutions) and tests to aid them in preparing for all assessments to include the final, and
- I lessened use of the “flipped classroom” providing more direct instruction before students engaged with their homework.

Net-net, I am pleased with the results for this cohort.

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Updated post with following data addressing a reader’s comment re: relative distribution of former v. new students in 2015 results.

I suspect that if I ran a t-test on the former v. new data it would yield a statistically significant improvement in many of these descriptive statistics.

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## 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.

Hi Dave, great post. My knowledge of stats is a bit weak, but it appears that if you assume the survey sample is relatively constant each year (and yes, that could be a big assumption), then the data appears to indicate that the students are able to demonstrate a higher comprehension and understanding of the material over the five year span. I would conclude since the test is more or less constant, you are getting better as a teacher! Good work, and thank you for doing what you do.

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Thanks, John. As you point out, it is difficult to state with certainty exactly what the data truly represent; I need to dig deeper into the mathematics of statistics to nail that down as the data reflect entire populations (not necessarily random themselves), and not samples. Nonetheless, I believe it does point in the direction of improved teaching methods over time. Perhaps a consult with Malia is in order? 🙂

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Hey Dave, impressive results, especially considering your N in 2015 was a lot larger than previous years. The increase in students who scored in 80%-90% is dramatic! Can you show a plot of where your former students placed on this distribution? It would shed light on your first hypothesis.

Keeping the measure the same over the years has really payed off in that you now have comparable data to look at trends over time. Kudos for keeping your eye on the “long game.”

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Thanks, Jack. Glad you noticed the increase in N, which gives me the most satisfaction. I’ll update the post a little later with a chart separating former and new student placement on the distribution.

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Congratulations! I would love to hear your current assessment of the flipped classroom model for these students. Did you have the pre-calc students do FC? Are you still a fan of FC?

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Depending upon the definition of FC, I will always be a fan for advanced coursework such as honors or AP courses. In those cases, FC means read the text, especially the example exercises, and attempt all of the homework BEFORE coming to class. In class, deeper conversations about the content are then possible. Call me old-fashioned, but I believe that method is the most effective for true learning. And yes, my precalculus students experienced my version of FC last year.

If FC means videos, I am not a fan of teacher created videos. They require too much effort to produce; I already spend an inordinate amount of time creating practice assessments, many with detailed work and solutions. There are other effective sources for videos, if they are key to one’s definition of FC. As an example, for my AP Calculus AB course, I’ve used Get-A-Five (getafive DOT com) for the psst three years. This past year, however, I suspect less than 25% of my students watch the videos as I front loaded the essence of key concepts via direct instruction at the outset of a week. I walk a fine line between teacher telling and student self-directed learning. All telling / showing hamstrings student transference to slightly different exercises or problems in my experience.

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“…read the text, especially the example exercises, and attempt all of the homework BEFORE coming to class. In class, deeper conversations about the content are then possible. ”

Your students are learning skills that will serve them well in college. Good for you! But I understand how students would resist this teaching method. I bet you’ll continue to see improved performance from your students in the future.

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“But I understand how students would resist this teaching method.” Agreed. I felt similarly when I first encountered it 33 years ago. However, I believe this is the crux of what needs to change in secondary education, especially for advanced coursework in mathematics and sciences.

On Thu, Dec 24, 2015 at 2:27 PM, Reflections of a Second-career Math Teacher wrote:

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sounds good; any chance they have seen previuous exanms

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Nope. Kept very secure. No chance of being seen previously.

Sent from iDave

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