6 days on the road and I’m a gonna make it home tonight…. (great old song)
4 days at ASCD annual conference in Philly and 2 days giving workshops at Harvard University to a series of groups from around the University…
Once I catch my breath I will respond to the fantastic array of comments on my last 2 blog entries on curriculum. I also will share with you some of the discussion at Harvard.
But here’s a tidbit from my conversation with Harvard math professors: they see shocking deficits in 2 areas of student performance. See if you can guess…
First area: endless errors and conceptual confusion on fractions and decimals! It’s just like the misconception research in science: even our best and brightest are not learning these things with understanding.
Secondly: students do not seem to understand the rationale behind simplifying a complex result; they often think it is an arbitrary demand!
Both of these weaknesses are at the heart of the common core standards emphasis on conceptual understanding and at the heart of the defects of ‘coverage’ with plug and chug. It also relates to the Harold Fawcett material I referenced in the previous blog. Far too many students do not understand WHY key axioms/formulae/rules/methods exist and how to use one’s knowledge heuristically to solve real problems, as I have written here a few times.
Here is my simple 20 minute short-answer test for conceptual understanding; try it if you are a math teacher or supervisor in grades 8 and up:

• Why can’t you divide by zero?
• Why these axioms and not others in geometry? (Where did these axioms come from and why do we accept them?)
• How can you possibly do anything with ‘undefined terms’? How do we know what to do with and how can we represent points, lines, planes if we can’t define them?
• Why was the calculus invented? What problems needed solving that algebra and trig couldn’t?
• Similarly, what does algebra do that arithmetic can’t?
• Why do we have negative and imaginary numbers? Why isn’t that just nonsense?

It was very gratifying to learn of the interest in my work in Romance Languages, math, engineering, and physics at Harvard. Maybe there’s hope?