Gifted Issues Discussion homepage Forums General Discussion Thurston on maths education

Quantum, the question that springs to mind, though, is what about mastery-learners in that kind of system?

This was a long-standing disagreement between my mom (an EC master teacher) and myself, incidentally. She thought that spiraling pedagogy was vastly superior for most students, and that therefore, mastery learners needed to 'adapt' to it rather than being accommodated.


I disagree based on my own experiences, my DH's, and on my DD. She can "touch" on a subject a couple of times before she tunes it out completely. So you'd better do it right and do it THOROUGHLY when you mention it. No half-truths, no skating on the hard parts.

I realize that is really fundamentally different from the way that most primary (and for that matter, secondary) teaching works these days.

But I think that it does a disproportionate disservice to the most capable students, who more than any other group, tend to be mastery learners by nature.

If I'd had my way, my DD would not have heard the word "photosynthesis" in 3rd grade... because she THOUGHT she "knew about" that topic when she saw it again in 10th grade biology, and it was a struggle to get her to tune IN to the parts that weren't covered before. KWIM?

Same thing in mathematics. While introducing different MODES of thinking is good, introducing a surface level coverage of topics that students cannot really master yet-- isn't. IMO.

It turns everything about a student's education into one endless litany of review-review-review. Sucks ALL of the joy out of it for mastery learning students.

That is an interesting question. I am not qualified to answer as I don't have your specific child and had not dealt with those particular frustrations. I do tend to beat (not literally) the attitude out of DS and repeatedly emphasize that he must take and adapt to the world as it is and not as he prefers it to be. I also occasionally remind him that he is not THAT smart and he is simply not ready to learn everthing about a given topic, which will be cover in more depth when . . . However, I am not sure that he qualifies as a mastery-learner. He is impatient and practical and all about speed-learning and picking up what he needs at the moment and touching on all manners of interesting facts/ideas.

For what it's worth, I do disagree with the degree of spiraling in current education - it's way too much! However, some spiraling is necessary. For example, it wouldn't be practical to hold off on basic long division until you cover repeating/terminating decimals in pre-algebra or division of complex polynomials in algebra. Similar, I would not hold off on basic solids geometry until you are able to comprehend analytical geometry in a calculus course. That knowledge can be useful as a practical matter earlier in life.

It's an interesting article. I agree with much but certainly not all of it. He is unreasonably negative about acceleration and competitions. (I agree that school maths should be more broad, and that different people can be successful on different time scales.)

An interesting part was this (page 5 section 7).
This is absolutely right. (It is also, by the way, why some can learn maths much faster. They are ready for higher levels of abstraction and generality, and in fact they find it easier.) Thurston continues
I don't think it is necessarily hard to put yourself in someone else place in this way. But it's important to keep this in mind. For those of us with mathemetically precocious children, we can sometimes be stumped when they have an unexpected blind spot where they don't seem to understand or realize something that we think should be "obvious".

lol, yea this. Tuesday, DS7 invites me to sit with him as he tries out (another) math site. He's taking a test on middle school statistics. The last question is what is the mode of the data, he looks at me like "what in the world are they talking about?" I knew over a month ago he was talking this from a podcast. So, just short of sighing, I ask him "You know what mean is?" Yes. "And median?" Yes. He chuckles and says "oh yeah, mode is the most one."

Honestly, I doubt if 5% of people on the street know the difference between the three but somehow I expect a seven year old to? Or perhaps more similar to your thought, lowest common denominator has been a particular gap of his.