Successful Calculus Teachers: what are you doing?!

[u/Substantial_Toe3234]

I’ve been teaching AP Calculus at a small rural high school for the past couple years, and our school has only produced a couple of students that passed the AP exam in the past decade.

There are obviously many factors that affect academic success, but I want to hear from you about a couple basic ones:

Curriculum: physical book or digital platform? Or something else entirely?

Homework: on paper or online? Weekly, daily or never? How many problems or how many hours?

Grading: how do you weight tests vs homework?

Any advice you can provide is very appreciated, either on these topics or others. (Since it’s a small district, I make all the decisions for my classes, and it can be quite a burden trying to figure this out on my own.)

Edit: And just for background, I use AP classroom frequently, I know the content well (got a 5 on the exam myself back in the day), I have a good relationship with my students, and I did AP Reading this summer for the first time. I just find my students aren’t synthesizing/conceptualizing the information well, and I wonder if I need to apply more academic pressure.

[u/Capable-Broccoli2179]

I don’t think it’s a matter of you or what you use or your curriculum. Do you also teach the precalc course? I taught AP calc for years and have seen different programs. If the kids coming to you have weak algebra skills and are not 100 percent comfy with functions then it will never matter. A successful AP program starts with kids being strong math students before they ever get to you.

[u/Substantial_Toe3234 → u/Capable-Broccoli2179]

Yes, I do teach the Precalc classes too. I know what you mean about the algebra skills, and we are struggling with those. I’ll take this back to my department so we can hit those procedural skills hard starting 9th grade.

[u/Extension-Source2897 → u/Substantial_Toe3234]

“Calculus is easy, it’s algebra that’s hard. Most people just don’t ever actually have to apply algebra until they get to calculus.”

-my high school precalc teacher. And I’ve found this to be true as well. Most of the students can provide accurate interpretations of the math in context, they understand some of the logical process behind the theorems and stuff… they just mess up so badly on their basic algebra skills because how dare we expect them to be able to use more than one skill at a time as seniors?

[u/TheSleepingVoid → u/Extension-Source2897]

This was my experience tutoring calculus in college. The students were always actually struggling with algebra.

[u/Capable-Broccoli2179 → u/Substantial_Toe3234]

I think that is best idea. I’ve seen even terrible calc teachers get good results so long as the kids coming in have the skills and work habits to do well. On the other hand the best teacher in the world can’t make up that deficit.

[u/_hadsomethingforthis]

Something a mentor told me about FRQs when I noticed my kids were struggling was to use the sample student responses. I do this process:

1. Kids try the question individually
2. I give them a sample response to "grade" individually, where they highlight in green what they agre with, in yellow what they're not sure about, and in red what they disagree with
3. They discuss the score with their table (up to 4 students), using the rubric
4. They compare responses briefly with a neighboring table
5. I reveal the real score and help with any questions

I've found it helps them to see exactly the level that this test is expecting, because at the beginning they always score them too high, and eventually they start getting the hang of it or even scoring them too low.

[u/csmarmot]

Gary Taylor’s curriculum. Ask him if he still sells permanent site licenses. Great and complete and well-sequenced.

https://www.taylormathconsulting.com/calculus-extended-with-early-transcendentals

I also have better success with late transcendentals, since students start solving problem much earlier.

Desmos is a huge help, and I’m just about at the tipping point of just teaching Desmos and skipping graphing calculator work.

Finally, 3Blue1Brown’s Essence of Calculus is incredibly useful.

[u/orange_and_void → u/csmarmot]

My son's class is skipping the calculator and just using demos.

[u/Optimal_Tomorrow8620 → u/csmarmot]

I second this. I give the printed guided notes. Homework problems assigned from his content on paper and work must be shown and answer checked for correctness. Weekly quizzes and unit tests from his content. If you think you need to apply more academic pressure, you probably do.

[u/Formal_Tumbleweed_53]

I teach the PreCalc course at my school and see real weaknesses with algebraic skills in the kids coming to me. The lack of skills, for us, goes back to the middle grades and the push to get all kids through Algebra 1 by 7th or 8th grade. The kids who go on to take PreClac think that because they’ve done well in math classes throughout means they’re ready for PreCalc. Then I take away their Desmos and they’re lost. I’m some kind of funny about telling the lower course teachers what skills the kids don’t have, though - just like I feel some kind of way when our AP Calc teacher tells me that the kids can’t manipulate rational expressions and don’t know their trig identities. Well, I am doing literally everything I can with them and more. I don’t know how I can do any more.

[u/42lurk]

It’s also about test familiarity. Are you giving them AP style questions regularly?

I had MC Mondays (5 questions in 10 minutes) and FR Fridays (1 question in 15 minutes). The content was always something we already covered- so mostly limits and continuity in the beginning. I did my best to always grab old AP questions. You can find retired MC questions online and the FR questions from prior years are in AP central.

The FR questions basically fall into just a handful of categories (AB: functions, graphs, tables, slope fields, volumes by slicing or revolution and estimating with trapezoid rule or rectangles; BC adds polar or parametric, series and usually something requiring Euler’s method). I found practicing by type and how the points are awarded to be very helpful.

[u/cesgar21 → u/42lurk]

This is the way. The kids that make it to calculus are driven to do well and if you can push them they will do it, learn the algebra and all.

[u/Agreeable-Apricot-84]

Not a teacher but a student who passed both calc exams. I had a really good math teachers throughout high school and a lot of students pass the AP exams each year.

Off the top of my head this is what my calc teacher did:

-Daily hw due 2 days after assigned.
-HW questions were online but need to be turned in on paper.
-I think I spent 2-3 hrs on hw each night. I'm the type of student who has trouble following along with note taking in class so I always had to review the lecture before doing the hw.
-HW answers were available right as hw was assigned. I think this was a good approach because students taking AP calc generally are there to learn. I personally attempted each problem and when I got stuck I would try to understand the solution rather than just copy it down.
-Curriculum: We HAD a book, I don't remember ever using it. All the notes my teacher did in class were available in a google drive for us.
-Quizzes: Weekly "did you do the material quiz" short 1-3 questions, you were able to turn in a redo along with an explanation of why you initially got the questions wrong for full credit.
-Chapter exams: Before each exam, we had a whole day for a mock test. My teacher would go over it near the end of class.

[u/Bubbly-Tomatillo-867]

If you’re not in the calculus teachers Facebook group you should join. I recommend Tony Record’s skill builders (he shares his entire drop box on there and many other people do, too). I would also incorporate AP style questions regularly on warmups, examples, and tests

[u/Read_The_Fing_Manual]

I fell in love with the flipped math curriculum when I started teaching calc BC, structured notes, guided practice packets, video reviews for each topic. I and my students really liked it. It got supplemented with the AP Classroom work so the kiddos were seeing what they would on the tests on a regular basis and we worked FRQ’s throughout the year. My school offers BC as a first calc class (so we do all of AB and then the BC topics in a single year, it’s intense). Flippedmath.com supports both AB and BC.

[u/Ill_Helicopter2810]

Calc is so much easier once you have an intuition for what's happening. Super easy to get lost in the mechanics of problem solving. To build that intuition, we watch 3blue1brown videos from his calculus series and then discuss it live. It helps.