I promised Unit 3 LTs by the end of the week, and I think I made it on time :) There's nothing like cutting it close. I had hoped to have units 4 and 5 done by this time as well, but we'll just have to see where I can get.
Here they are. More thoughts at the bottom!
UNIT 3: DESCRIPTIVE STATISTICS
Section 3.1: One-Variable Statistics
Standards
Addressed: S.ID.1, S.ID.2, S.ID.3
3.1A: I can create
plots (dot, box, histogram) to represent data.
3.1B: I can find and
interpret the mean, median, IQR, and standard deviation.
3.1C: I can compare
the shape, spread, and center of data sets using the mean, median, IQR, and
standard deviation.
Section 3.2: Two-Variable Categorical Data
Standards Addressed: S.ID.5
3.2A: I can create a
two-way frequency table for categorical data with two categories.
3.2B: I can find and
interpret relative frequencies (joint, marginal, and conditional) in the
context of the data.
Section 3.3: Two-Variable Quantitative Data
Standards
Addressed: S.ID.6, S.ID.7, S.ID.8,
S.ID.9
3.3A: I can represent
data with a scatter plot.
3.3B: I can find a
line of best fit and use it to solve problems in the context of the data.
3.3C: I can interpret
the meaning of the slope and the intercepts.
3.3D: I can find and analyze
the meaning of the residuals and the correlation coefficient.
3.3E: I can make
inferences about correlation and causation.
Thoughts/Notes:
- It makes sense to me to study 1-variable statistics separately, so I'm mostly OK with the organization of 3.1. We did get a quite decent twitter conversation on whether or not students should be required to calculate standard deviation by hand. Any further comments on that are welcome. Thank you to those who already participated and gave me ideas.
- I had planned on doing all two-variable statistics as one section, but there is a lot there! And it seems weird to me to have 1 standard on categorical data when the rest are on quantitative data. Hard for me to make that fit well. There is so much with the quantitative data though that I couldn't combine them. I hate having 5 LTs in one section (it feels so big) but I feel like I still haven't done the standards justice. Also I think Section 3.2 being so short will provide an opportunity for a different structure of class. Maybe we will do a project assessment instead of a test
Please, please, please leave your thoughts in the comments or tweet me (@kathrynfreed) Like I have said with every other unit, I really truly want to make these the best goals I can for my students. I appreciate all of your feedback whether praising my awesome-ness (not usually) or giving me advice for improvement (usually), I really like how you guys can always make me think more--even when I think my brain is dead! Thanks for that!
-Kathryn
I've also found it a bit awkward to split statistics into only a couple units. One issue I found in going 1-var then 2-var is that students start seeing a histogram/box as only useful for "1-var". Like if you take a two way table and graph each column... somehow it's back to you only studying "1-var" even though you're doing a comparison. But that could just be me not making things clear enough.
ReplyDeleteAn alternative I've tried is to split into "statistical display" and "statistical analysis". So tables, scatterplots, histograms, all of that together along with the basic measures of central tendency and spread. When that's done, move to actual analysis, which comprises interpretation, solving problems and making inferences. I don't know that it's necessarily any better, but it is another way of looking at it. I do think what you have is fine, particularly if you'll do vary up the assessment for the shorter unit.
As far as standard deviation by hand, I kind of like it, to emphasize it's based on the mean, whereas the IQR is based on the median/quartiles... it's not HARD to calculate either, there's just a bunch of steps. Someone suggested an excel spreadsheet based on a frequency table, that makes sense to me as a compromise position too. Again, that's me, take it with a grain of salt.
Just a closing remark, causation can be a hella fun class. Depending on the strength of the students, direction of causation (and confirmation bias) can be illustrated through the Wason Card Problem, and debates about how to deal with the "placebo effect" can be (legally) interesting.
Wason: http://www.skepdic.com/refuge/ctlessons/lesson3.html
@Greg - Thanks for all the ideas! I really like the idea of display vs. analysis, but not sure I'm ready to put it into effect next year (just because I feel less statistically fluent). I might throw it out there at our next Algebra meeting on Wednesday to see what others think.
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