Category Archives: math

Homework Ideas for a New Year

Last year I wrote about how I was going to start lagging homework in my AP Calculus class. To recap real quick: problem sets covered the information from the prior week, assignments were given out on Mondays, solutions were posted on Thursdays, assignments were due on Friday, feedback (but no grade) was given over the weekend and returned on Monday, if students did the work (and corrections) they got full credit.

Overall, the process worked well, but I still dealt with the majority of my class waiting until Thursday evening to work through the problems (which meant I never had kids in tutoring sessions or class asking questions on current homework assignments). In order to combat this phenomenon, I’ve decided to chunk their weekly homework assignment into daily portions that will be checked and stamped for effort at the beginning of class each day. Assignments will still be collected and responded to on Fridays and solutions will be posted for them on Thursday. I know this seems somewhat punitive but was the only solution I could figure out. If you have any other ideas of how this could work, it would be much appreciated!

Here’s an example of what an assignment will look like:

15-16 Recap: AP Calculus

As promised, this is post #2 today to make up for missing yesterday. This one will actually be about teaching, but since I apparently can’t do anything the easy way, I’ll be doing a series of 3 posts about what went well and what could be improved upon in AP Calculus (both AB  and BC flavors), General Physics, and AP Physics. So today, let’s start with AP Calculus. Lot’s of stuff to ponder, as I write this, I’m seeing that a few of these need some more unpacking, thankfully it’s #MTBoSBlaugust!

What Went Well

  • I lagged homework in AB (one of the few things I’ve written about in the past and something I need to write about more in the upcoming few days).
  • I posted full solutions to homework assignments in AB the night before the assignment was due and most of my students turned in fully corrected and annotated assignments on time.
  • I had students do 3 full 6 question FRQ exams and a full 45 question multiple choice exam prior to the actual AP exam in May. Gave them a lot of exposure to the type of problems they were going to see on the real exam and what they needed to spend the weeks prior to the exam focusing on.
  • I improved my pass rate.
  • Students did a lot of really good group work on VNPS.
  • I wrote a lot of good problems throughout the year to dig into student’s conceptual understanding.
  • I wrote some good notes and activity structures throughout the year.

What Can Improve

  • Students had difficulty transferring what they learned from lessons and the more skill based, formulaic problems they saw in their homework to the conceptually deeper AP style problems I gave them on assessments, midterms, and finals.
  • I’m not totally happy with the sequence of topics right now (might need to pick Jonathan’s brain more about the reasoning behind his sequencing).
  • By the time the third FRQ rolled around, a few of my students thought it would be useful to just memorize a bunch of FRQ solutions available on the internet (their ability to do stuff like this but not complete a simple homework assignment on time is staggering) and hope that they showed up. Luckily for them it did. Unluckily for them, those same problems weren’t on the AP exam (shocker!) and they got a 1 since they didn’t really study and prep.
  • I had a 4 person BC class that I structured more as an independent study course than a normal course. They were pretty productive most of the year, but didn’t do as well on the AP exam as they could have if they pushed themselves more throughout the year.
  • I had some students walk into an assessment (I use SBG), put their name on their paper, turn it in, and say they were going to reassess it next week. This is the first time this has happened in 4 years. Needless to say, it brought about a crisis of faith in the system and led to some long talks with these students about personal accountability in a high stakes class (due to the subject matter difficulty and exam at the end of the course) that sometimes feels like a low stakes class (due to reassessments).

 

Homework! Oh, Homework!

Recently I came across Henri Picciotto’s writing on lagging homework. To say that this idea piqued my interest is an understatement. It had me up well past midnight last night trying to figure out how it would work in my AP Calculus classes. It fit so nicely with what I had been reading in Make It Stick (like this book needs any more publicity on the MTBoS) on spaced practice that it’s at least worth a shot to begin the year. So here’s what I have so far.

In class students will work through a new topic for a day or two, depending on the complexity. Whenever they’re done with the topic they’ll do an exit slip during the last few minutes of class as a check for understanding. They will then have the opportunity to self evaluate by placing their exit slip into one of three folders: Got It, Kind Of, Not Yet. I’ll give a quick pass through these and make sure I agree with their self evaluations. The following class period I’ll spend the first few minutes working with the Not Yet group on some remediation, while the Got It group works on extension problems and the Kind Of group works together on fixing their small mistakes and then moves on to the extension problems.

On the first day of each week, the class will get a handout due on Friday. That handout will cover material that was taught the previous week. So during the first week of school, in class they’ll be learning about evaluating limits, but at home they’ll be doing precalculus review problems. During the second week of school they’ll be learning about continuity, but their homework will be on the limit evaluation problems from the week prior.

I want to be able to give written feedback (without a grade) to my students on their homework prior to them taking an assessment on it, so that will have to come on week three.

So the work flow will be something like this:
Week 1 In Class → Week 2 At Home→ Week 3 Assessment

Classes don’t start for me until after Labor Day, so I have time to tweak and rework these ideas so your thoughts, comments, and questions would be really helpful.

Here’s the handout I’m planning on giving students explaining the system to them:

The Block Game as Formative Assessment

I’ve used the Antiderivative Block Game in my calculus classes to help students practice their ability to quickly take basic derivatives and integrals (shout out to Maria Anderson, Bowman Dickson, and CheeseMonkeySF.) So far, I’ve seen Words into Math, Exponent Block and Factor Pair Block, and the aforementioned Antiderivative Block. In John Scammell‘s Twitter Math Camp morning session we had been talking about formative assessment and on the last day he asked us to create or investigate different formative assessments and the block game came to mind.

So, here is the list of other potential block games my cohorts and I came up with:

  • Unit circle/Trig
  • Logarithmic to exponential
  • Fractions/Decimals/Percents
  • Distributive Property
  • Binomials/Trinomials
  • Graphs/Equations

Have you created any block games that you use in your classes or found any that I haven’t listed here? Please comment and let me know. Hopefully I’ll be creating these block games over the rest of my summer break and you can play test them this school year.