## Second Time Around

We’re into this unit again with the freshmen. Teaching a course the second time around is a joy. I have a much better idea of what difficulties they’re going to have. What mistakes they’re going to make. What the misconceptions will be. More importantly, I can catch them earlier, either by changing the activities I did last year or by changing the discussions that surround each activity.1

We’ve been collecting data:

How long is five seconds?2

I started this one by asking, “Who’s really good at judging how much time has passed without looking at your cell phone?”
I had a stopwatch, told them I’d say “start” and they had to tell me when 5 seconds had passed. First person timed at 3.6 seconds. Lots of “I can do better!” type comments were shouted. We did a few more as a class, then they were off to collect five trials for each person. Collected the data. Made a histogram. Discussed the data (mean, median, mode, range, outliers, symmetry … you get the idea).

They were sent home to measure their stride length – from the front of one foot to the front of the next. Instructions included to explain how they measured this.

This one was fun to discuss the next day. One student used the boards on her hardwood floor. She marked her steps on the floor, counted the slats, and measured the width of one slat and used that to estimate her stride length. Another student walked on the snow on her sidewalk and measured the footprints. I thought the best part of the discussion was figuring out which measurements didn’t make sense. 32 inches? Nope, this person measured two steps. 12 inches? This person measured from toe to heel. 11 inches? Turns out that really was his stride length. 8 inches? The dog’s stride length.3

1The little notes I wrote last year in the teacher’s guide are like presents from a former self.
2Supplies: Graph paper and a stop watch for every two people. This is the ideal. Or you could let them use their cell phones, if phones are allowed in your school that is.
3Okay, this one actually happened last year. I miss that kid.

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### 5 Responses to Second Time Around

1. Richard G says:

That’s a fun unit. One of my favorite IMP units, really. I remember us finishing the unit by making a large pendulum (26 feet long) out in our commons area and having them use their formulas to predict the 10 swings.

Right now I’m teaching DO BEES BUILD IT BEST from year 2.

2. Hi Jackie

Different course, different country but your post reminds me of a conversation at the end of last teaching year when planning for the coming one. Something that I had not seen before.

Kids develop their understanding of units from a notion of “fit” to “compare”. At first kids work by figuring out if something fits into something else. This is their primitive concept of “unit”. Later, however, they are able to generalize. Then they can have a meaningful understanding of standard units.

Its a subtle distinction that I had not picked up but important in the development pathway.

Russel

3. J. M. says:

I was recently at the National Zoo in Washington D.C. and they have the stride of a cheetah at top speed marked out on the ground. It blew my mind. It’s about 25 feet, which makes sense, but when you stand there and see the next foot-placement 25 feet away it’s pretty cool. You should mark it out in a hallway and ask your students to guess which animal.

4. Jackie says:

I hope we get to build a pendulum this year Richard. Last year the spring musical prevented us from using the theater (which is the only space we have that’s high enough). I’m not sure which I like more, Pit or the Game of Pig (sometimes I think I’m an AP Stat teacher in waiting).

Thanks for the comment Russell, I hadn’t thought of it that way (well, not recently). Do you have time at the end of each year to prepare for the next? It sounds like you have some great conversations among your staff.

J. M. Very cool. I’m writing a note to myself for next year! (we had a few unexpected days off due to the cold and finals are next week, so I doubt I’ll be able to work it in this year).

5. Hi Jackie

Yeah I guess we do have some great conversations among staff: when the pressure is off and people have the head space to think beyond the next class. I wish that we could have these conversations during the year as well.

Yes we have a time at the end of the year to consolidate our reflections on the year just gone and to plan for the coming year.

Also we are fortunate to have one of the authors of First Steps in Mathematics working at our school. We have been drawing on her expertise as we build a better transition from Primary mathematics through Middle school mathematics into Senior school mathematics.