3D Printer and more Technology in the Classroom (plus the last Step II lesson of the semester)

 The week before Thanksgiving was pretty busy as it usually does as the semester draws to a close with all of its final presentations and final exams. I think that the first thing I want to talk about this week is my final lesson for Step II since I will be writing 5E lesson plans to close out the semester. Unlike the two previous lessons, my time management was poor. I made the strategic decision in the middle of the lesson to forego the evaluation I had prepared since our statistical examination that closes Step II will look at one evaluation in particular. The lesson was productive for my own growth. Upon reflection, I realized why my time management was so bad. On the surface, it looked like I had just allowed students too much time in the exploration section of the lesson. Looking more closely, I realized that I should have stopped the exploration section. Many students gave answers that indicated that either the lesson section's instructions were unclear or that the students ...
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A cool classroom activity and AP Stats

 This past week we had a couple of classes where we discussed the use of mathematical models in our classrooms. We also talked about where (Lowe's) to get large whiteboard panels that can be sawn into smaller whiteboards for class activities. We've used them throughout the semester and I like the way that they work. Because each group's board is usually left in a visible place in the classroom, it gives everyone a chance to look at what classmates did and assess their own ideas in comparison (I found myself doing this a bunch during the M&M activity). It's something that I think a classroom can benefit from and I hope it aids in active learning classrooms.

So, back to the classroom modeling exercise. Each group had to estimate the number of M&M's in an 89 gram bag. We had digital scales and recorded the weight of M&M's for 1-14 pieces. Then we used Excel and we got a linear fit for our data and used that to get our estimate. There were 99 pieces in the bag and we were fairly close with our estimate of 101. Every other group also had an estimate > 99. I recall them ranging from 101 to 105. 

The activity reminded me of AP Stats way back when I took it in high school. I recall that we never got to linear regressions but times have changed? In any case, I think that the experiment is absolutely awesome at conveying the idea of restricted regressions (if that's being done these days). Doing so would have increased everyone's beta for grams per M&M and would have led to estimates closer to the true value. Even if restricted regression isn't something that is covered mechanically or algorithmically or however, I think that it is a perfect example of planting important ideas for students to ponder in the sense that mathematical models should include the natural condition of an experiment; we should have all have used the factual information that the best fit line should pass through (0,0). If we had, we would have been closer to the correct answer. If I ever get the opportunity to teach AP Stats this is definitely an activity that is worthwhile. (The data my group collected: )


(Except that we can't run the restricted regression because we did not zero the scale so each measurement is the number of M&M's plus the plastic container for those M&Ms. I guess we at least got an estimate of the container's mass: 1.8765 grams)





I think that AP Stats really lends itself to the thoughtful construction of experiments that get students to think about what the regression or test stat should be. There's some cool stuff I've seen AP Stats teacher mention online where students learn some things about bias by examining interviewer callbacks where the variation occurs (solely?) due to the (racialized) name of the applicant on identical resumes.

In other news, this week is a big week in Step II; I have my second lesson of the semester. This time I'll get a full class period and a full classroom of students so the change will be marked compared to lesson one. I hope that it goes well and that students are active in the various Es of the lesson. We're covering linear expressions, their simplification and factorization via the distributive property. And we're using algebra tiles to assist the lesson. Students seemed lukewarm to them last time--the students who worked diligently through the lesson seemed to use them out of a sense of obligation to the teacher and there were groups that sort of fumbled around with them. I think that experience is starting to pay and I am better equipped to get students involved but it may just be the change in grade level from Step I. We'll see.

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