Here is the project description. The students' work is published to the class blog.

**Percent of students who were able to:**

- Transcribe the data into an accurate, useful table of values: 100%
- Model the scatterplot with an appropriate regression equation: 77%
- Correctly use the equation to make predictions about future values: 60%
- Interpret the meaning of the variables in the regression equation (or would-be equation): 94%
- Interpret the meaning of the constants in the regression equation in the context of effect on the graph: 31%
- Interpret the meaning of the constants in the regression equation in the context of the data: 20%

^{x}, that the 1.1 means 10% growth? I don't have a good answer for that.

**Changes for next time to the project description:**

- Write more explicit instructions for uploading images and making and editing blog posts.
- Add a template for each problem that they can copy and paste.
- Add more implicit instructions to try several types of regressions and compare r-values to find the best one.
- Delete 'A Piece of Cake' or consider curmudgeon's comment below to just delete the 'cake' part and add a known data point that allows them to check their model.
- Delete interpreting the equation constants from the quadratics problems.
- Started out requiring four problems - one from each group - amended that to two problems. Four class periods were only enough time for them to reasonably complete two.
- Make the easier tasks (with high percentage of success based on this year) worth most of the points, so you won't have to fudge the scoring such that everyone wouldn't fail.

**Examples of Excellent Work:**

Jarrod and Stephen: Sinusoidal Regression

Harry and Matt: Exponential Regression

And...I'm on goin' on break.

ReplyDeleteIs it really important that they know that in y = (0.44)(1.1)x, that the 1.1 means 10% growth?Do they need to (either due to you or your dark Albany overlords) answer questions like: provide the equation representing a $20,000 car with 11% depreciation rate? If so, that question is important.

How much direction did you need to provide? My students could not do this w/o a lot of hand holding.

ReplyDeleteJason - Yep, they do. It seems like the question is easier forwards than backwards though, doesn't it? No matter how I teach exponential functions, I still don't have a way where they really grok it and can handle a problem cold, later.

ReplyDeleteDan - They can be pretty independent with clear enough direction, but it wasn't like I was kicked back drinking coffee while they were working, either. I do need to add some more specific directions for the technology. We spent a day together running regressions on example problems, so they knew how to start. Developing a good table was a little rough. Many needed assistance but I wouldn't just tell them "what to put." I said things like "you need a way to account for the number of months that have gone by that makes sense on a number line." I think that might have been the most valuable part of this for them - experience wrangling real data so they could do something with it.

I wouldn't toss Piece of Cake - there is a need for a regression that isn't of an immediately known or obvious type. "Is it exponential, quadratic or cubic" is a good question and brings out the utility of R^2, too. Students spend middle school and many of the standardized tests figuring out patterns. This is just another one.

ReplyDeleteMaybe the problem is in the interpretation - "cutting a cake" usually implies a circular cake cut through the center. Try rephrasing the question as using a sheet-cake or "Using A2-sized paper, draw lines to divide the paper into pieces...." Another possibility is to include a known data point that wouldn't be possible to find physically but would "check the pattern". "If your pattern is correct, you should get 18 cuts making 172 pieces."

"What shape is the St.Louis arch?"

"The suspension bridge?"

"Is this growth exponential or quadratic?"

"What function compares blood pressure to arterial diameter (turns out to be a quartic)?"

I think this gets to the most important and most realworld aspect of this project - finding an unknown equation to best fit the data - and the equation isn't obvious.

I'm not so worried about the understanding of the constants - the data will tend to obscure some of the more important insights. I think this is best left to the debriefing time when you all gather around the displays and discuss. At that time, you can push the idea that the constant is a combination of pi and ...

Don't have any thoughtful questions or constructive feedback at this point, but did want to thank you for sharing this whole project- I've really enjoyed seeing it from conception to completion, especially because the model student work helps me better understand what students should be able to know and do by the end. Enjoy your well-deserved break!

ReplyDeleteKate: I'm using your facebook data today in calculus. I'll let you know how it goes! Thanks again for posting this.

ReplyDelete=shawn cornally

Well...It's Facebook's Facebook data, but nice! I'm interested to hear what you did with it. I wish you way more than luck.

ReplyDeleteAre you going to play like it's exponential and see if they buy it? It's pretty cool that a logistic regression is actually a better fit.