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Re: Math Education: An Inconvenient Truth



Uploaded by: websnarf
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Timing out some of the methods shown in the video I am responding to. http://www.wheresthemath.com/




Tags for this video: An calculators division Education elementary Inconvenient Math mathematics multiplication outsourcing Truth

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Sure, walking is ... ( 1 month ago by websnarf)
Sure, walking is what you do before you learn to run. Does that mean you skip walking and just go straight to running?
Argument from ... ( 1 month ago by websnarf)
Argument from personal incredulity. You failed to consider that I don't consider anything you think to have any relevance or value to me.
There is no quick or easy division algorithm; the TERC method does not help in any way. Better that there is one standard one that works and is checkable.
I could. Now how ... ( 1 month ago by websnarf)
I could. Now how would you *CHECK* that I didn't press the wrong buttons on my calculator?
Estimate. If ... ( 1 month ago by phillipk)
Estimate. If someone has a decent understanding of the concepts (not the necessarily the particular algorithm you're promoting) then they would see if the answer was off. How often do you do multiplication this way? I mean, I do it in my head all the time--but just estimating. I say whatever works to teach kids the concepts. Specific techniques have very limited value. Strawman because you're purposely making the other techniques look complex.
No, the lattice ... ( 1 month ago by websnarf)
No, the lattice method increases the amount of extra work, and therefore for larger numbers just continues to slow you down to a worse degree.
If these people were serious about showing better methods, they would show the Karatsuba method, which is known to be far superior to all these methods (including the standard method).
Karatsuba requires an *understanding* of algebra in the same way that the TERC method does.
More straw man. I ... ( 1 month ago by websnarf)
More straw man. I googled for TERC investigations and found it to be exactly what M.J. McDermott described in the video I responded to.
An example of their stupidity: They consider solving 2-digit multiplication to be a unique benchmark of computational fluency. There is no difference between 2 digit and 10 digit multiplication!
They then ask for students to explain why (a/2)*(2*b) = a*b without teaching fractions.
The harm being perpetrated on the younger generation is infuriating.
Good estimation ... ( 1 month ago by websnarf)
Good estimation requires techniques beyond elementary school and would add time to the computation. It would also fail the find low digit errors in large multiplications.
Wow, now you've ... ( 1 month ago by sleeper2345)
Wow, now you've actually looked at some example of the curriculum to draw conclusions! Amazing! Actually they use arrays to explain why (a/2)*(2*b) = a*b. You don't need fractions if a and b are whole numbers and a or b is even. Have you ever taught math before? What do you mean there is no difference between 2 digit and 10 digit multiplication? Other countries build on this benchmark. Of course, let's not learn from them. Let's keep doing what we're doing. Our ignorance will rule the world!
Investigations ... ( 1 month ago by sleeper2345)
Investigations introduces fraction work in 3rd grade prior to this work. They also introduce operations with positive and negative numbers in 3rd grade. When did you learn to add positive and negative numbers? I bet not in 3rd grade.
This curriculum is based on research about how students learn. You are basing your conclusions based on your personal opinion that is not grounded in empirical work. Thus, your reasoning cannot be supported. You speak from a position of ignorance.
How do arrays help ... ( 1 month ago by websnarf)
How do arrays help a fractions problem?
I am not a teacher, so I don't know how to deal with children behavioral problems but I do understand arithmetic and remember how I learned it. I learned 2 digit simultaneously with any multi-digit multiplication. There was no distinction in teaching it because there is no distinction in the actual math of it or the algorithm.
Other westernized countries teach the standard method and they perform better than American schools that don't.
Why do you bet that ... ( 1 month ago by websnarf)
Why do you bet that I didn't learn negative numbers in 3rd grade? I was a highly accelerated student; trying to peg to my rate learning is besides the point (and more straw man).
There *ARE* empirical studies that show that Washington's students (where TERC is being used) are failing relative to other states and the US failing relative to Europe.
I have seen studies in child learning and they are a joke. We don't understand it well enough to run experiments like this.
Investigations is a ... ( 1 month ago by TheBGH)
Investigations is a FAILURE. For anyone who is a parent and watched how their grade school kids were taught this crap, you will understand the failure. The net/net is the foundation needs to be formed with basics. If nebulous concepts need to be taught to learn why 2x3 is 6, we're putting the cart ahead of the horse for grade schoolers.
FWIW I got the ... ( 1 month ago by phillipk)
FWIW I got the answer way faster using this approach:
30 x 26... is 260 three times... 250+250 is 500... add 20... 260 more is 780. add 31... done
Whatever works I say.
And are you a 7 ... ( 1 month ago by websnarf)
And are you a 7 year old, and what if you messed that up somehow? I don't see you showing all your work there in a way that can be easily checked.
7 year olds should ... ( 1 month ago by phillipk)
7 year olds should start with understanding the concepts and bag memorizing formulas or algorithms. It's better to understand the problem than to even know how to solve it.
An array can easily ... ( 1 month ago by sleeper2345)
An array can easily be shifted so that you can change 6 x 4 to 3 x 8, noting that the are the same thing. The 2-digit by 2-digit multiplication is important because it is generalizable, thus it is a critical benchmark. Asian countries (high performing) apply this as a primary focus before extending it.
Other westernized countries (high performing) actually talk about mathematical ideas. We don't in the US. One researcher said, after viewing math instruction in the US "I don't see the math"
Negative numbers ... ( 1 month ago by sleeper2345)
Negative numbers are not in any traditional textbook until 6th grade at the earliest. I don't know anything about the situation in Washington, but you can bet the problem is more complex than just the curriculum. Many variable are involved.
I don't know what studies you're referring to. How about looking at a synthesis of reserch such as "How Students Learn" by the National Research Council. The TERC materials employ the recommendations and research in this document. Or look at "Adding it Up"
Understanding is ... ( 1 month ago by websnarf)
Understanding is meaningless without a foundation. The Nazis "understood" how to deal with jews because their foundations did not include realizing that jews are equally human.
If I understand different ways of how an arithmetic problem breaks down, how does it help if I don't know if I am right, or how I might check my work?
Where did you get that 20 from in the above? Is it 2*(260-250) which you didn't write down? If your arithmetic gets longer or more complicated it just gets worse.
I did this--but ... ( 1 month ago by phillipk)
I did this--but very fast--in my head:
31x26
30x26 (hold onto 26)
3x 260
250 two times is 500... plus the 2 10s I left out...
500+20+260 is 780
take that last 26 and you have 806.
Array ( 1 month ago by websnarf)
Or, more reliably:
31 x 26 = (30 + 1)*(25 + 1) = 30 * 25 + 30 + 25 + 1 = 750 + 55 + 1 = 806.
Which is a way of encoding the identity (a + b)*(c + d) = a*c + a*d + b*c + b*d via some "understanding". Which is interesting, but worthless to a student not yet ready for algebra.
where is the ... ( 1 month ago by phillipk)
where is the evidence that the so-called standard algorithm is better by any measure? Your reasoning (that it's faster) is only one measure and only measured on you. So many people make claims that are based on their own personal opinion. I don't see the evidence being demonstrated here.
Its all about ... ( 10 hours ago by ruiruivo83)
Its all about teaching people how to do math by head with the MERC method. Not faster.
Yes but what you ... ( 6 hours ago by websnarf)
Yes but what you have to realize is that those are *TWO DISADVANTAGES* not a trade off. Being able to do things in your head is worthless if its slower than a calculator and still not as good if you want to check your work afterward.
Math sooner or later must become a subject you do with a paper and pencil. What exactly are you planning to gain by delaying this?
Fast and error ... ( 2 hours ago by websnarf)
Fast and error prone? Writing was invented for a reason.


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