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Accountable;1392008 wrote: It's funny to me how many mechanics and carpenters claim to suck at math, when they use it seamlessly every day at work.


Glass cutter here........cutting is only half the job, economic cutting is the real job...so I must be a good mathematician

yaaarrrgg;1391992 wrote: IMO, the big problem with math education is there needs to be more emphasis on the conceptual and geometric meaning of math, less on memorization.

When I tutored math, I discovered that college students who struggled at math were not bad at knowing their times tables. What they struggled with was knowing when to add, when to multiply. They struggled with what it all meant at the geometric level. Which is why story problems give kids the most trouble. At that level a table full of numbers won't help a person at all.

The invention of the computer has made rote memorization in math pretty much obsolete. Machines are better at this aspect than humans. My TI92 calculator can solve differential equations. The only natural thing left for the human is understanding the concepts, not really crunching the numbers


Again, both right and wrong at the same time. You talk of knowing concepts, which is much the same as patterns, but without a memorized set of times tables, you don't see the patterns at all. I asked a student what 200 X 300 was. He grabbed a calculator and replied, "0.6 repeating." I knew, of course that it couldn't possibly be that since it had to be a large number. I also knew that it would begin with a six and have four zeros. I even knew what the student had done, pushed the divide button instead of multiply. But the point is that the student didn't know. He argued that "machines can't be wrong" as well.

Without times tables, patterns are invisible.

Saint_;1392037 wrote: Again, both right and wrong at the same time. You talk of knowing concepts, which is much the same as patterns, but without a memorized set of times tables, you don't see the patterns at all. I asked a student what 200 X 300 was. He grabbed a calculator and replied, "0.6 repeating." I knew, of course that it couldn't possibly be that since it had to be a large number. I also knew that it would begin with a six and have four zeros. I even knew what the student had done, pushed the divide button instead of multiply. But the point is that the student didn't know. He argued that "machines can't be wrong" as well.

Without times tables, patterns are invisible.I think that story proves how important it is for kids to have an interest in mathematics. The only way I can see that happening is for parents and teachers to convey the correct message when teaching it. The fact is that children and teenagers alike, in the US, are primed solely to emphasize the answers as opposed to the concepts behind mathematics. It's the very immediate reaction to reach for a calculator.

We can argue that this priming has nothing to do with mathematics at all and that our standard for evaluating teachers and schools are from test scores alone. Sculpting these children to purely "ace a test" gives the absolute wrong answer if not literally then by the sheer fact to ask a question that assumes only one answer is missing the point of everything that is honestly cool about learning which is to have perspective, not some symbol that denotes a correct answer as if a cookie is to be thrown in the air afterwards

K.Snyder;1392038 wrote: I think that story proves how important it is for kids to have an interest in mathematics. The only way I can see that happening is for parents and teachers to convey the correct message when teaching it. The fact is that children and teenagers alike, in the US, are primed solely to emphasize the answers as opposed to the concepts behind mathematics. It's the very immediate reaction to reach for a calculator.

We can argue that this priming has nothing to do with mathematics at all and that our standard for evaluating teachers and schools are from test scores alone. Sculpting these children to purely "ace a test" gives the absolute wrong answer if not literally then by the sheer fact to ask a question that assumes only one answer is missing the point of everything that is honestly cool about learning which is to have perspective, not some symbol that denotes a correct answer as if a cookie is to be thrown in the air afterwards


Really outstanding post. :yh_worshp:yh_hugs:yh_dance

:yh_clap



You get a cookie. =^..^=

Saint_;1392042 wrote: Really outstanding post. :yh_worshp:yh_hugs:yh_dance

:yh_clap



You get a cookie. =^..^=:yh_bigsmi

A cookie sounds nice

Bruv;1392009 wrote: Glass cutter here........cutting is only half the job, economic cutting is the real job...so I must be a good mathematician
You are where it counts.

Measure twice cut once. Minimize waste, minimize costs, maximize profit.

Saint_;1392037 wrote: Again, both right and wrong at the same time. You talk of knowing concepts, which is much the same as patterns, but without a memorized set of times tables, you don't see the patterns at all. I asked a student what 200 X 300 was. He grabbed a calculator and replied, "0.6 repeating." I knew, of course that it couldn't possibly be that since it had to be a large number. I also knew that it would begin with a six and have four zeros. I even knew what the student had done, pushed the divide button instead of multiply. But the point is that the student didn't know. He argued that "machines can't be wrong" as well.

Without times tables, patterns are invisible.


I would take a completely different moral from that example. For one, was the student given an education that started with his addition and times tables? If so, doesn't that undermine your conclusion more than it supports it?

I would say the problem here is the student doesn't understand the basic meaning of multiplication. There's no way to visualize what the student believed to be true. I think schools should spend a couple weeks on something called "eye-balling it" or "sanity in numbers." It should teach broad rules of thumb on what makes basic sense. Teach things like:

Between 0 and 1, multiplication shrinks the number

Greater than 1, multiplication grows the number

The problems stem from teaching the concept as "number" instead of "matrix". If you teach matrix manipulation in school reception classes then all this falls into place.

Teach them about sets at the same time, so it doesn't come as a surprise when they're older.

As early as you can. We taught my daughter real early, and she is great. She is a over achiever in math. a+ student. so make it fun and teach them early.

Well said, I remember my mother making a game out of it. When I wanted something from her, she wanted times tables from me. "Mom, can I have a cookie?" "Sure! What's 7 times 9?"

Yes, there's no reason students shouldn't be taking calculus by the age of 15(being conservative, which highlights America's lackluster schools).

In any case, my experience with some of these textbooks is that they use only one way of teaching the material when mathematics has many many formulas that can achieve the same desired outcome. I suppose the thought is that the classroom doesn't have enough time to go over the many possible techniques or am I wrong? If so why do so many textbooks have only one example for achieving an answer when there are probably more than 4 on every equation?