MJ McDermott is vocalization about the stream state of math education, as the in isolation adult . KCPQ does not validate this video. Math Education: An Inconvenient Truth
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October 6th, 2009 at 6:53 am
I doubt that they “know” this. I encourage you to ask them. Note that the definition that you use of exponents has some difficulties, as it does not apply to rational exponents. How could they extend this to more general situations? For example, consider x^1/2 * x ^1/2. Why would this work? What is a valid justification?
October 6th, 2009 at 6:53 am
So they should generalize that what is true for whole numbers is true for all rationals? Why would this be true? What is x is negative? I don’t think I can draw similar conclusions.
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I do agree with you about the reasoning. However, this is not what is advocated in the video by McDermott. She’s focused on the rules, not the underlying reasoning.
October 6th, 2009 at 6:53 am
Its a little hard to ask them since it was years ago (and I only taught them for 3 days). However even if they didn’t “know” that, they could deduce it easily from what I taught them. As for that example, try starting w/ x^1 and rewriting, to get x^(2/2), then rewrite 2 as 1+1, x^((1+1)/2)=x^((1/2)+(1/2)), using the reverse of the exponent addition rule, finally get x^(1/2)*x^(1/2).
October 6th, 2009 at 6:53 am
I don’t think you’re providing a general proof. You’re just providing examples. Note that students would have to think about the domain of x. However, students often just think that x must be either a whole number (or perhaps the integers). I don’t think anything that we’re discussing is obvious to students. Most math majors I’ve worked with are oblivious to the domain of the variables they work with. I suggest more use of quantifiers.
October 6th, 2009 at 6:53 am
Not what that proof suggests, it gives them a way to think about x^(1/2)*x^(1/2). Once I’ve shown them that x^1= x^(1/2)*x^(1/2), then I go to work on figuring out what x^(1/2) is say x=36, for example. (assuming they’ve already learned square roots, which they should have by now) it’s not had to see that 6×6=36, so if x=36 then x^(1/2)=6, well sqrt(36)=6, what bout x=-36? Well can you think of a (Real) number that when multiplied to itself gives -36 as an answer?
October 6th, 2009 at 6:53 am
Your correct that what I gave isn’t a proof, but it’s the framework for one. Which I would complete, (500 character limit sucks lol). And again, nail on the head about them not thinking about the domain of x. That comes from the poor teaching/curriculum at the HS level. Something I would be sure they’re used to thinking about by now in the curriculum.
October 6th, 2009 at 6:53 am
Note that this thinking is type of reasoning is not what the above video is about. It is about finding the best algorithm, not understanding the underlying reasoning.
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BTW I interviewed some first grade students today. The majority of them know everything that is in their traditional textbook. They’ll be bored out of their minds this year. Good luck getting them engaged in reasoning when they reach high school.
October 6th, 2009 at 6:53 am
Then maybe that majority should be in 2nd grade math? Just a thought. I wish i could’ve been in some accelerated learning type program for math since like my junior year of HS when I figured out that math was what I wanted to do for a living. I would probably have my doctorate by now (Junior year was ’05-’06).
The single greatest thing that I noticed was different about the class I taught for 3 days (by the end of those 3 days) was their curiosity had returned.
October 6th, 2009 at 6:53 am
The problem is really with the textbooks. Almost all first grade texts underestimate what first grade students could do. Why even have first grade if all students move to 2nd grade.
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Encouraging curiosity about mathematics is not what the authors of this video want. They want students to memorize these steps! Note that this is not mathematics. After all students could be simply playing some meaningless game that we call mathematics.
October 6th, 2009 at 6:53 am
lol it would have been funny if she got the answer wrong
October 6th, 2009 at 6:53 am
Yeah the texts could be better, but I also find many teachers at the HS level, that were harder to learn from than the texts they used. I taught myself triple integration right about when The Fundamental Theorem of Calculus was being taught to me in class. Must people can’t read a HS math text and learn from it I find, why is that? I’ll concede that your right about the video, but I’m pretty sure I know what’s going to happen in the class room. And its not going to improve the math situation any
October 6th, 2009 at 6:53 am
You’d be surprised what a difference one person can make. If we can just help some children develop a deeper understanding of math, we’re headed in the right way. Best of luck to you!
October 6th, 2009 at 6:53 am
Wow, i’m terrible at math, and often find myself a calculator cripple, but even i remmebered my long division and basic multiplcation.
October 6th, 2009 at 6:53 am
This is the dumbest thing I’ve ever seen. It’s just a way to sell those books. Math takes hard work and there’s pretty much no way you’re gonna get more for less.
October 6th, 2009 at 6:53 am
wow this women manages to competely destroy simple mathematics. This women seriously is lacking the mental power to uderstand that this is the best way to teach a child who is merely 10 years old. I applaud her subtle stupidity
October 6th, 2009 at 6:53 am
Clusterproblem method. Brilliant! She wants pupils to become calculators, which is good, if you COMBINE the caculus skills with understanding what you are doing. Pupils won’t learn that with standard algorithms alone. + she’s a manipulative biatch.
October 6th, 2009 at 6:53 am
she is soooo right!!! its easier and a better way to make students get to a correct answer!
October 6th, 2009 at 6:53 am
Okay agreed some ways are better than others. But both algorithms she shows are fine. I’s just that she messes it up because she uses the first algorithm smart, and the second dump, with smaller steps.
(I must admit that I’m not a big fan of the matrix kin of multiplication, cause you have no idea why it works, and the cluster version can get really messy)
October 6th, 2009 at 6:53 am
If this is a better method to teach young children fine, but it’s important for them to learn the standard algorithms too since I doubt very much the scientists at NASA use the cluster method when planning a space shuttle launch.
October 6th, 2009 at 6:53 am
both are fine…. but- wow- thats just way too much! and think about what will happen if they apply the second algorithm to later problems. like finding hypotenuses! once that kid gets to high school or college if they are still thinking spread out like that they’ll never pass a test
October 6th, 2009 at 6:53 am
I don’t think anyone at NASA is using the standard algorithm for whole number multiplication. Note that most adults use various forms of technology. What is critical is that students have an understanding of the relative size of the result, something often masked by the traditional algorithm.
October 6th, 2009 at 6:53 am
It’s easy to see why this comment stream is so long. There simlpy isn’t a single method that is one-size-fits-all. After many years of math teaching I figured out that you simply show different solution methods and encourage students to use the method that appeals to them the most. Calculators cause more issues with laziness and lack of confidence than they do anything else. Sure, adults use them on the job, but would you want production to cease simply because the TI-85 fell in the crapper?
October 6th, 2009 at 6:53 am
Of course she could have used an easier cluster, going right to 20 x 36, however, she wants to mislead you into thinking that the traditional algorithm is always the most efficient. The cluster method can often be used mentally, but the traditional algorithm often cannot be. No one algorithm is always the most efficient.
October 6th, 2009 at 6:53 am
When i was in college my physics professor actually forbade the use of a calculator, and it was the best class I ever had! I felt so much more confident about the math and physics involved and my ability to think logically, which is something that punching keys on a calculator cannot teach. I understand they are necessary from time to time. When teaching solution methods it’s crucial that students develop several skills, from knowing a few algorithms to estimating the size of a solution.
October 6th, 2009 at 6:53 am
I applaud your stupidity. Everyone who went to my school learned it the “Standard” way and we all had it mastered before we made it to mid school.
Those other ways are waste of paper, take way too many steps, and wastes too much time for making a drawing.
However, teaching a kid to “use a calculator” defeats the purpose of teaching math in the first place.