I saw my friend Duane Habecker post this image as part of a thread about “math felonies”.
I later ignited a bit of a debate about math understanding on my personal facebook page, another post on Twitter etc.
The crux of the matter is a lack of content and pedagogical understanding. Often kids are taught to satisfy a grade levels understanding but later on it would have to be re- taught. Another example- the rules of working with radicals are pretty much the same as variables but rarely taught that way. Eg you can do 3rad(2) + 4rad(2) But not 3rad(3) + 4rad(2) because the bases are different… same as 3x + 4x and not 3x+4y. If I were designing curriculum I’d always have something saying “Think ahead too…” and “look back from When..” for every topic. Well, basically I’d integrate the coherence map. 🙂
As we work on building more conceptual understanding for students across ALL grade levels, this kind of thinking – really only meant to help kids- will start to dissipate. I know it was a teacher that was really trying to help kids… and so thought of something FUN! But, it’s probably partly because he/she didn’t fully understand the process either.
Please, start with https://gfletchy.com/progression-videos/, nixthetricks.cm, achieve.org/coherencemap , teachingchannel.org for great resources that help target WHY and WHAT TO DO About misunderstanding how to teach kids certain techniques! A random example of how useful this is the map for 4.G.1
Note how it links to the High School Geometry standard G.CO.1
This is relatively easy information, but helps remind that high school teacher that it’s been a while since kids have seen these definitions, so might be good to review a bit more first.
Knowledge about the content of the standards and where they fit in the overall education career of a kid is needed. I am proud of the work I’m doing with ACT on the CASE standard and OpenSALT which will eventually be able to have this kind of visualization integrated for any competency framework as well!