Tag Archives: Calculus

Scenes from AB: Help from the class

One question I often get from teachers in Desmos PD sessions is whether they can turn off the option for students to see other responses from the class when they submit a text or choice response.

Screen Shot 2017-08-25 at 11.35.21 PMSo first off, yes you can turn it on or off. When using the text input or multiple choice, you can check or uncheck the box to allow students to see 3 random responses when they submit their answer.

Teachers will often express concern that students will just copy answers off each other. I hear that. Every choice a teacher makes in a lesson’s design (whether using technology or not) should have a reason behind it, and whether you check that box or uncheck it, you should know why that particular response should or shouldn’t allow that kind of feedback.  Continue reading

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Decoding mistakes in Calculus

This year I am using mistakes to prompt discussion in class and make homework dissection more engaging. In my AP Calculus AB class, I use Active Calculus as the text, and many of its activities and exercises are perfect for an Activity Builder conversion. Such was the case when I assigned this activity to work on section 1.3 Ex 1 in Active Calculus.

The very first slide has students drawing some secant and tangent lines on a function. Most students in all three sections did pretty well with it, but I saw a few common errors I wanted to address. So channeling my Talk Less course from TMC16, I made up these two slides.

day-13-ab-errors_1 Continue reading

First Day: Speed Demon and Talking Points

Today was Day 1, folks. All students come for 10 minute mini-classes earlier in the week, so today they came in with some minor stuff (seats, etc) out of the way and we were ready to math. And we mathed.

I have two preps this year: AP Calculus AB (mostly 12th grade, 3 sections) and Algebra I (mostly 9th grade, 2 sections). My general strategy on first days is to get as much math in as I can. Especially in a day where other classes may be reading syllabi and passing out books, students will remember classes that dig in and get to it.

Each year, I start with Nathan Kraft‘s Speed Demons 3 act in order to set up average rate of change and begin a great discussion about shrinking that time interval for greater accuracy for rate of change. In the past I would play it, hold a good discussion with students about how on earth we can measure things like distance on this video, and then send them off to measure, calculate, and make conclusions at home.

This year I saw it as a good opportunity to have my table groups work on this problem together to start the year. In each section, the conversation went similarly: we acknowledge the need to measure a distance on the road, they suggest using cars, people, or telephone poles as a unit and extrapolating, they acknowledge that those units in this context are ok but flawed, and then someone suggests Google Maps. In each class, there was a burst of energy when I suggested they take out their laptops and check out the satellite. From there, paper, whiteboards, chalkboards, and rulers were flying around. Here are a few shots of the action, including a nice use of “ruler on the screen” to get a good measure.

They concluded that all cars were speeding. We had a good chat about accuracy and what could have lead to more reliable speeds. The best line of the day was a student that said which interval we used would have a lot to do with that–as in, an interval near the start, middle, or end of the car’s journey. I have been doing this problem for a few years and I had never considered different pieces of the cars’ journeys, just shrinking one interval down.

For reflection

  • Lots of great discussion at tables once real work started, but in the class discussion there was still way to much student-teacher talk and not enough student-student talk.

In Algebra I, I dipped my toe into the Talking Points pool for the first time. I used the “Being Good at Math” set from this collection Dylan Kane posted from TMC14 and credit Cheesemonkeysf. Let’s hash this out list-style…

UPS

  • Lots of great on-topic chats at the tables which is no small feat for 9th graders in a math class on day 1.
  • We had several braves souls willing to step forward and talk about changed minds in the group chat at the end. They did a good job describing their process as well.
  • I was happy with most of the attitudes they had coming in–most tended to growth over fixed mindset.

DOWNS

  • Many groups had no idea what to do when they all agreed or disagreed together after round 1.
  • I worry about making sure this type of activity sticks with them as we move into traditional content.
  • Either few students were changing their minds OR few were willing to admit it. Either way, there is room for improvement.

 

 

My big theme this year is reflection, both for me and the kids. I’m most happy that I made some inroads on that today.