Tuesday, July 13, 2010

Unit 1 - Stats (Help Wanted!)

OK, so last year we opened our year-long course with Statistics and I think we are going to do that again. It was a great way to start the year because it lends itself to real-world connections, group-work, and class discussions. It also lays a foundation for us to talk about how we observe patterns and then predict from them…which leads to our patterns unit…which leads to our function stuff. Then we kind of bring it all back full circle by ending our year with probability where we start to talk about “given a certain pattern or approximate pattern or even just random data, what is the probability that…”

Our approach last year, however, was a bit haphazard. We hit all of our objectives but I’m not sure we effectively connected them. I woke a few weeks ago with some ideas on how to make it a more connected unit of study, but I am going to need some feedback on actual research questions that will work in the context. So, let me lay out our goals and the plan I’m considering and then I will throw my questions at ya.

State Standards
The standards we cover in this unit are:
M.O.A1.2.19 – Students will gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusion
M.O.A1.2.17 – Students will perform a linear regression (with and without technology),
· compare and evaluate methods of fitting lines to data.
· identify the equation for the line of regression,
· examine the correlation coefficient to determine how well the line fits the data
· use the equation to predict specific values of a variable.

We basically introduce the concept of linear regression but revisit it when we cover linear functions in the winter months.

SBG Target Skills
So, given this set of objectives for the unit of study, these are the target skills I’ve broken down (including skills that touch on our state’s 21st Century Skill Objectives) that we intend to address:
1. Communicating about mathematics
2. Working in cooperative groups
3. Gather data using appropriate sampling methods (CSO 19)
4. Create histograms (CSO 19)
5. Create box plots (CSO 19)
6. Create scatter plots (CSO 19)
7. Find line of best fit without technology (CSO 17)
8. Find line of best fit with technology (CSO 17)
9. Determine correlation coefficient (CSO 17)
10. Create normal curve distributions (CSO 19)
11. Draw conclusions from graphs (CSO 19)

Scope/Sequence for the Unit with Class Activities
My mindset here was that I wanted to work through the idea of collecting data first, and then allow the students to work in teams to do some data collection of their own. Then I wanted to introduce display method #1 (Histograms), practice creating them a bit, and then have the students use the data they collected to create Histograms. Then I wanted to repeat this process with the other data display methods mandated (and thus, assessed) in our state. I can imagine a certain amount of objection here to my “blindly” following my state standards. Let me defend my choice here by stating that while I believe there are certainly other equally (or more) significant methods of data display that I will be completely disregarding through this approach, I presume that others have followed the objectives in previous years exposing students to those other methods so I’m going to focus on successfully teaching what is designated for this course with the assumption that it fits well into the scope of previous and subsequent courses.
My idea here is that for each concept we teach, there will be a sort of repetitive cycle of: Learn New Concept, Practice New Concept, Work with your Team to Apply it to Your Group Project. Ultimately, I’d like them to each write individual reports on their group projects. Perhaps a graphic will explain my thinking better.
You’ll notice a lot of little notes to myself in there about tasks to teach them in the computer lab and such. This is clearly my working document. But my problem comes in the nature of the topic for the big project. Here’s where I am desperately hoping that the blogosphere and twitterverse comes in rescue me.

OK, so I am giving teams some flexibility to create their own topics, but I need to have some samples (in fact, enough for every group if necessary) to help with brainstorming. The problem comes in finding topics that fit the criteria I am going for:
· A topic that they could easily poll an accessible population (i.e. student body)
· A topic that would appeal to adolescents
· A topic that would involve numerical data that would work well with a histogram and a box plot
· A topic that could have a second variable (i.e.age) easily attached to look for correlation

I’m not sure what I’m hoping for…kind of a “I’ll know it when I see it” thing. I thought about “How many contacts do you have in your cell phone?” or something similar. Then we could look for a correlation in that one might assume seniors have more contacts than freshmen, but perhaps not. I don’t know. Help!


  1. There is a project that I have taken/modified from the NCTM archive that I love (and the kids go absolutely bananas for). It's a bungee-jumping project for practicing scatter plots and linear regression. Each team takes a doll (in my case, I give them crazy-looking rubber chickens that squeak when you squeeze them) and a bunch of rubber bands and a meter stick, and they have to measure / record / determine the effect of # rubberbands on the max height dropped. I give them the height of the balcony we will eventually be launching the rubber chickens from, and they don't get to test it out in advance by the balcony, only in the classroom. The day they finish the project we make a big deal out of going outside, and I find a teacher to be the official judge / a kid to be the video recorder as I drop the chickens one by one and the kids watch underneath on ground floor... Closest to the ground without hitting wins!

    It is hands-down one of the coolest projects, and the kids will never forget what slope and y-intercept mean again. They also have to figure out what data to collect and how to do it (the directions don't give that many details), so it's a good meta-processing project as well.

    If you want a copy of my project, you can email me at mimiyang at gmail dot com. Otherwise, good luck!

    http://www.blip.tv/dashboard/episode/2764759 (Year 1 video, short)
    http://www.blip.tv/dashboard/episode/2800907 (Year 2 video, student made and so longerrr)

  2. Actually, that sounds like an amazing project! I spend about a month to two months on linear functions around February so I would probably want to wait til then. We use that time to kinda of spiral back and connect it to the scatter plots and lines of best fit we learned about in September, but with more discussion of the equation, slope, y-intercept and so on. It would fit better in there than in the stats unit but would be a perfect connector between the two. :)

    I will definitely email you for more details. :)
    Thanks for the comment/feedback.

  3. BTW, Mimi...the math teacher Twitter world was throwing your name around this morning...wondering if you are on Twitter???

  4. My seniors had fun with a project about texting speed. Gave them a sentence or two to text while being timed, tried to find correlations between gender, age, thumb length, # of months texting experience, and type of phone (T9 vs. not). Totally stole this from somewhere (can't remember right now) but if you're interested I can look for the file :)

  5. Grace, I love that idea. Look around and see if you can find the file. I may not use it for the big project, but it would be a great mini-lesson on correlations. :) Thanks!

  6. Oh, and JamiDanielle: not on twitter, for sanity's sake. (I need a *little bit* of breathing room from teaching, sometimes.)

    Maybe in the future... :) You should surely email me about the chicken project when the time comes. IT'S MY FAVORITE!