I saw a video on youtube called "Math Education: An Inconvenient Truth" and felt like it needed a response from someone whose career is in math education. This is the perspective of one college p...
I saw a video on youtube called "Math Education: An Inconvenient Truth" and felt like it needed a response from someone whose career is in math education. This is the perspective of one college professor.
And about the "standard algorithm" for multiplication where we write:
16 32 ___
Etc. A little thought leads to the realization that this really is just 32*16=(30+2)*16=30*16+2*16. Hence the "standard algorithm" is identical with this method of multiplication.
Oh, and interestingly, the "standard algorithm" isn't really standard after all. Talk to folks from other countries sometime and ask them to multiply and divide for you. Their algorithm may be quite different seeming from yours. In fact, of course, it's all really the same because mulitplication is truly only one well-defined operation. How you arrive at the answer may appear different, but in the end, at root, they are all the same.
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It's not about one method vs. another method and which one is right or better. If we truly valued math, sciences and rational thought we (as a society) would decide that it was worth taking the time to recognise the different strokes for different folks and allow schoolkids the opportunity to see behind the veil of math mumbo-jumbo to the "why" and not focus so much on the "how" Seriously. .
Here in Toronto, most schools teach the tried and true algorithms that the OP favoured. But as a tutor for 10 years, I know that many students (at the high-school as well as university level) have major problems doing arithmetic with fractions - and have only the vaguest notions of how fractions are related to decimals.
I nodded throughout your video. I suspect that part of the problem of "math phobia" and the failure to make sense of (or integrate) random bits of math facts & formulae is that elementary school teachers need no college/university background in math. You end up with people who don't understand or like math "teaching" math to the young and impressionable. Which likely leads to the "one size fits all"/"my way or the highway" nonsense and bickering.
Elementary school teachers are required to take math classes in the States, but it is minimal. They are also required to take a course specifically for teaching math for elementary teachers. Sadly, many of these classes are taught by math grad students, as if the course is just math. But it's not. It's about how to TEACH math and virtually none of those grad students have even experienced teaching much and certainly don't know what will really help these (generally math phobic) folks.
I guess I wouldn't focus on formulas. But I would definitely whole-heartedly agree with the statement: "it's bad if those other methods make it harder to understand more complicated mathematics." I don't think they do, but I certainly agree with the hypothetical.
I'm guessing you and I are very nearly the same age. I grew up with the same stuff as you, I suppose. We had "TLU"s and I remember some of them were very hard. But I also remember in 3rd/4th grade having races in multiplying numbers. I remember we had 45 second to do a huge number and I always froze on 9*6.
You do know your strategy is basically "partial products" right? EM is trying to get kids to do it just like that. To come up with it, like you did. What works for each person.
Of course, the "standard algorithm" is a part of EM, so either the school system didn't know what they were talking about, or they were trying to say something else that didn't get across.
I completely agree about common sense (in the head) comes first, then memorization. That's exactly what I said in my video.
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If we truly valued math, sciences and rational thought we (as a society) would decide that it was worth taking the time to recognise the different strokes for different folks and allow schoolkids the opportunity to see behind the veil of math mumbo-jumbo to the "why" and not focus so much on the "how"
Seriously.
.
I suspect that part of the problem of "math phobia" and the failure to make sense of (or integrate) random bits of math facts & formulae is that elementary school teachers need no college/university background in math. You end up with people who don't understand or like math "teaching" math to the young and impressionable. Which likely leads to the "one size fits all"/"my way or the highway" nonsense and bickering.
You do know your strategy is basically "partial products" right? EM is trying to get kids to do it just like that. To come up with it, like you did. What works for each person.
I completely agree about common sense (in the head) comes first, then memorization. That's exactly what I said in my video.