Monday, August 3, 2015

Spaced Practice and Repercussions for Teaching

I've been reading John Hattie's book, Visible Learning, in which he ranks the effect sizes of different strategies that help student achievement. One of the strategies that is pretty high on the list is that it is better to give students spaced (or distributed) practice as opposed to mass practice. In other words, rather than having a student practice something over and over again in one day, it is much better to spread that practice out over multiple days or weeks. (You can read one of these studies here.) The main benefit is that spaced practice helps with long-term retention.

While this research certainly gives some justification for providing students with multiple opportunities to revisit older topics, I am left to wonder if this should change how I structure my lessons and assessments. I, like many others, teach by units. My students might spend a month on fractions followed by a test. They then get a month of algebra followed by another test. We, as teachers, create this span of time when all learning about a particular topic must happen. We don't always give students the time to practice these ideas, particularly the more challenging ones that almost always happen at the end of the unit and right before the test.

Based on what I've read about spaced practice, I would propose that teachers shouldn't give tests at the end of a unit. Perhaps students need time to practice these skills over several weeks before you should assess them. This is something I'm going to explore this year with some of the concepts that were challenging for my students last year.

Note: This is probably not an original idea and I'm sure someone else out there has probably explored it. If you have any resources to share on the subject, I'd greatly appreciate it!

Another note: I do allow my students to retake quizzes which I had hoped would send the message that learning doesn't stop after the quiz is taken. However, very few of my students have taken advantage of this in the past. I am hoping to correct that this year with some ideas from Dylan Wiliam, Ashli Black, and others.

Update: Henri Piccioto has written about this and calls it "lagging homework". He also reinforces the idea that quizzing should happen much later then when the material was taught. Thanks to Mary Bourassa and Chris Robinson for helping me find his work!

Sunday, August 2, 2015

Movie Popcorn

I ordered a small popcorn at the movie theater and the cashier asked me if I'd like the large size for only $1 more. I knew that this had to be the better deal, so I took it. I mean, what if I had gotten the small popcorn and ran out during the movie? That would be unacceptable.

However, as I left the theater, I noticed that I didn't actually eat all of the popcorn. There was about two and a half inches of popcorn left at the bottom of the bucket. I could take it home with me, but stale popcorn doesn't sound too appetizing and I decide to throw it away. Did I just get ripped off? Should I have just bought the small popcorn?

There's a couple of ways of modifying this task to address the needs of different grade levels. It all depends on what information is given to the students. If you can just give the students the number of cups of popcorn in each bucket, then this is a fairly simple unit price problem. If you just give dimensions of the buckets, you will need to derive and use formulas. It would also be extremely helpful to use a spreadsheet.

6th Grade Version:

Info required...

Questions to explore...

What is the unit price for each size?
What is the percent change in size, price, unit price?
What is the least amount of popcorn from the large container (in cups) you would need to eat so that you don't get ripped off? (This is not as interesting a question as the 8th grade version because you can't usually tell how many cups of popcorn are left in a bucket.)

8th Grade (or beyond) Version:

Info required...

Volume of a truncated cone:

You will notice that there is a little bit of popcorn above the rim of each bucket. There is also a small gap on the bottom of each bucket. I assumed that the added and subtracted volumes of this popcorn would more or less cancel each other out. I could be wrong about this!!!

Questions to explore...

What is the capacity of each size?
What is the unit price for each size?
What is the percent change in size, price, unit price?
How many inches of popcorn would be left in the large bucket if you eat just as much as the small bucket?
What is the least amount of popcorn from the large container you would need to eat so that you don't get ripped off? In other words, how many inches of popcorn can I leave at the bottom of the bucket?

The answer....

I'm not leaving my full solution here because I'm curious to see how others might solve it. Basically, I used a spreadsheet to test different heights of popcorn eaten to determine where the unit price of the large matches the unit price of the small. If you think about it, this is further complicated because as you eat popcorn, the height AND top radius changes. You will have to come up with a formula that calculates the top radius based on the height.

I determined that you get ripped off if you leave more than two inches of popcorn at the bottom of the bucket.