Fantasy High School Part 3 (Statways)
I’m returning here to a perennial topic of mine: High School Curriculum Reform.
If you want to catch up on the previous installments:
For some background, I find if you look at a typical criticisms of the status quo like NCTM’s Catalyzing Change in High School Mathematics, there is a ton of writing within it devoted to chronicling all the problems we have currently, a lot of energy around attacking tracking, a cataloging of essential concepts that doesn’t vary much from what is currently in the common core high school sections (Geometry should focus around transformations etc.) and then some very vague and brief hand waving about what new curriculum or pathways might look like. Maybe we should do Geometry first, or maybe we should go with an integrated 2.5 years!?! of math. This lack of a detailed vision of what should replace the current sequence is very common.
I also believe that there really are good reason to change the curriculum sequence. However, my heart is with the more radical proponents of change rather than with the NCTM suggestions above which to me don’t sound very exciting or frankly different than what is already occurring with the exception of reducing required math classes from 3 years and removing an honors model. At the same time, I have some qualms about the possible effect on rigor any change might cause and am looking for interesting models of what innovative shifts could look like. I need concrete details to feel more confident about any major new directions.
In the midst of all of this, there was another survey release from MAA pointing out some interesting context about the HS landscape: https://www.mathvalues.org/masterblog/launchings201908
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We still have 9% of high schools that do not offer a course at the level of Algebra 2 and 10% that do not offer a course equivalent to precalculus or Algebra 3.
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Just over half, 53%, of high schools offer any AP Calculus
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NCTM recommends that high school math teachers have taken college courses in seven subjects: calculus, abstract algebra, geometry, discrete mathematics, number theory, probability, and statistics. The survey revealed that only 39% of those teaching Algebra 2 or above have taken courses in all seven subjects, although 83% have taken courses in at least five of those courses. The courses least likely to be taken are number theory (63%) and discrete mathematics (67%).
This is yet another reality check about both the current actual state of teaching and some of the barriers in the way of reform.
Statways
All of which brings me to the following video by Nils Ahbel Its a bit long but worth the listen especially the back half.
Another Link for Resources: http://www.ahbel.com/alternative-to-precalculus/
This is perhaps the clearest explication of a version of a Statistics pathway that I’ve seen yet. That’s significant because Statistics are the most commonly mentioned variant folks are looking at to emphasize more in High School.
For me Statistics is the odd stepchild of Mathematics. I’ve never personally enjoyed it as much as other areas (perhaps I really need to give it another chance). My current thinking is that in a way its one of the best examples of real mathematically modelling that you can access early on BUT
- Its easy to reduce Stats to taking surveys, reading graphs and talking policy issues without ever moving beyond this stage.
- The model is actually somewhat complex and its possible to get lost in the weeds.
- The case for practical utility is overplayed. Sophisticated statistical analysis doesn’t occur as commonly as represented. There is an open question in my mind whether to defer Stats until its needed to complement Social Science etc.
That all said I thought Nils’s take was really nuanced and interesting. He manages to weave real data sets and simulations into problems that seem accessible: i.e. examining hiring and firing decisions for Bias. I also found his usage of modelling to be persuasive. I have a lot more faith after watching that this is a viable alternative if expertise is built up around teaching and curriculum to go along with it.
The open question remains: is this a bespoke class but a talented teacher or something that can really be replicated and scaled out?
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