"New" Maths

[schmod]

Earlier today, my parents called me asking for help with my 8-year-old sister's maths homework.

This is it:
http://www.mrnale.com/homelink_10.3.pdf

Does this seem like a logical or reasonable approach to Mathematics?

I have no idea how one would ever possibly be able to actually extend this sort of thought all the way through to University-level mathematics.

Their method of long division is even more terrifying:
http://www.youtube.com/watch?v=eKld7lQHKRg

[Haunted]

I can't possibly imagine a more logical introduction to the concept of area, volume and higher dimensional units, what part don't you get?

Long division, it's hard, but you really have to learn how to do it without a calculator first.

[hr]

Now with 100% more corn

[Fawksie]

That exercise sheet is very poorly worded, but other than that, it seems OK. And as for long division, I was also taught to do it using the partial quotients method. The underlying method is sound, they've just confused it with the addition of their bizarre processes for multiplication and subtraction.

[mhuzzell]

I went to a Montessori school, and that looks a lot like the stuff we did. Only we used actual blocks to illustrate things.

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I FOUND JESUS... he was behind the couch the whole time!

[Mehmsy]

What happened to the good old days of teaching abstract concepts without contrived concrete examples?

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http://standrews.facebook.com/profile.php?id=37106593

[novium]

urgh, that looks like a horrid mix of something I was subjected to ("visual math") and something i've only heard about, where they tried to teach kids math starting with the whole base-X thing. Tom Lehrer wrote a song about it.

[hr]

Neither the storms of crisis, nor the breezes of ambition could ever divert him, either by hope or by fear, from the course that he had chosen

[WashingtonIrving]

Whats a base 10 block? I remember the name..

So, yeah, I can't even understand the question. My 4th year maths exams are going to go great.

[hr]

"I said farewell honey, I'll see you Judgment Day"

[purringpickles]

Quoting schmod from 00:04, 13th May 2008
Earlier today, my parents called me asking for help with my 8-year-old sister's maths homework.

This is it:
http://www.mrnale.com/homelink_10.3.pdf

Does this seem like a logical or reasonable approach to Mathematics?

I have no idea how one would ever possibly be able to actually extend this sort of thought all the way through to University-level mathematics.

Their method of long division is even more terrifying:
http://www.youtube.com/watch?v=eKld7lQHKRg

[purringpickles]

Quoting schmod from 00:04, 13th May 2008
Earlier today, my parents called me asking for help with my 8-year-old sister's maths homework.

This is it:
http://www.mrnale.com/homelink_10.3.pdf

Does this seem like a logical or reasonable approach to Mathematics?

I have no idea how one would ever possibly be able to actually extend this sort of thought all the way through to University-level mathematics.

Their method of long division is even more terrifying:
http://www.youtube.com/watch?v=eKld7lQHKRg

This looks fine to me. Out of interest, how were you taught maths? This is more interesting when we take into consideration the link provided.

[schmod]

I was taught maths in the US, mostly by older teachers who were well into their 50s and 60s.... In other words, I received a fairly similar education to what my parents did in the 1970s.

As a Mathematics and Physics student here, I can confidently say that I have a much more solid basis than students who were forced to learn via the "new" methods. I was also a "fairly average" student....

A base-10 block is a rectangular prism whose dimensions are restricted to being multiples of 10. (A 1cmx10cmx1m block is a base-10 block, while a 4x4x8cm block is not unless you treat it as a 40x40x80mm block, although the book does not delve into this area).

Although this isn't a terrible way to introduce students to the metric system and powers of ten, that connection is never made (units are always given in cm), and all geometry is taught based upon these base-10 unit blocks. As shown in the worksheet, if one wants to compute the area of a 4x3x1 prism, you are asked to consider it as 4 rows of 3 blocks, and counting the blocks, rather than simply multiplying the dimensions together! (By the time this chapter is introduced, it is assumed that the students are familiar with basic multiplication). Students are never allowed to "graduate" from this concept of base-10 blocks.

If you're familiar with computer science or higher mathematics, you should be familiar with numeric bases (Decimal, binary, hexadecimal, etc...). However, it's an awfully strange term to use in a textbook for such young students, especially when the word "base" is also being frequently discussed in an entirely different context in the same lesson.

Also, what the hell is a "long"? After pouring through the textbook, I found that it's a 1x1x10 prism, which you might be familiar with if you've ever played Tetris. This is one of many cases where the textbook extensively uses made-up terminology.

The sheet is also frustratingly ambiguous. For instance, the phrase "Take 10 cm cubes" would easily be interpreted as "Take an arbitrary number of 10-centimeter cubes." Instead, the writers of the textbook intended to say "Take ten 1-cm cubes".

The worksheet and textbook also frustratingly interchange 2 and 3 dimensional constructs, which would confuse the heck out of students who actually understand the difference between them.

#4 can be drawn several different ways, but only one particular arrangement fits on that grid.


Here's another video describing the ridiculousness:
http://www.youtube.com/watch?v=Tr1qee-bTZI

It's making its way to the UK as well:
http://www.wellingtongrey.net/miscellanea/archive/2007-06-10--the-new-physics.html

[Haunted]

I recieved teaching of volumes in a similar way at that age. Centimetre cubes featured quite regularly in lessons and after we were told that the volume is simply how many cubes there in a shape (and what the unit was) we were then shown that multiplication makes this easier for simple shapes because we are counting, say, 8 slabs of 4 cubes which is exactly the same as 8 sets of 4 which is 8x4. The sheet posted obviously has some surrounding context (i.e. definitions of longs) which would no doubt be explained in the classroom.

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Now with 100% more corn

[Gubbins]

I have to say that I don't particularly like this method. Coming from a background where we learnt times tables by rote, a lot of the concepts that aim to teach primary school children maths seem bizarre.

They seem to me to be there to ensure that the more... practically-minded students can cope with the concepts. Needless to say this doesn't necessarily benefit the more academically-minded students, but naturally most of us are quite biased there.

However, one of the major concerns I have with this style of teaching is that many parents have difficulty understanding how their child is being taught, which makes helping with homework very difficult, and can put the parent at odds with the school system.

[hr]

...then again, that is only my opinion.

[maenad]

The first link won't work for me.

I'd never heard of the partial quotients method of division. My very non-mathematical brain thinks long division looks easier, but then, that's the way I was taught.

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Tommy can you hear me?

[niall]

Long division is a must, otherwise Polynomial division is even more alien!

I had to teach some of my friends how to do long division and then polynomial division for our exams in January! (I'm 4 years older than most the people on my current course)

[Fawksie]

Polynomial division is brilliant fun.

[WashingtonIrving]

It used to be I could do polynomial division but not long division. Weird. I was actually never taught long division.

Actually, its amazing how many mathematicians (including myself) are awful at basic arithmetic. But when you get to uni you aren't working with numbers really, its all symbols, so you get out of the habit. I don't make much use of a calculator either. I've got pages of maths revision in front of me right now and the only numbers are for powers.

Then again, losing marks for writing 2+2=5 is irritating..

[hr]

"I said farewell honey, I'll see you Judgment Day"

[WashingtonIrving]

It used to be I could do polynomial division but not long division. Weird. I was actually never taught long division.

Actually, its amazing how many mathematicians (including myself) are awful at basic arithmetic. But when you get to uni you aren't working with numbers really, its all symbols, so you get out of the habit. I don't make much use of a calculator either. I've got pages of maths revision in front of me right now and the only numbers are for powers.

Then again, losing marks for writing 2+2=5 is irritating..

[hr]

"I said farewell honey, I'll see you Judgment Day"

[Guest]

Exact same maths I did 15 years ago. This thread fails.

[mhuzzell]

Quoting Mehmsy from 01:43, 13th May 2008
What happened to the good old days of teaching abstract concepts without contrived concrete examples?

His sister is eight. I'm not sure it's even possible to teach this stuff to an (average) 8-year-old without using concrete examples. From all I've heard about educational theory (which is a hell of a lot more than I ever cared to), children usually only even begin to develop abstract reasoning around age 10 or 11, and it's not fully developed for years after that.

[hr]

I FOUND JESUS... he was behind the couch the whole time!

[schmod]

Quoting mhuzzell from 01:03, 16th May 2008
His sister is eight. I'm not sure it's even possible to teach this stuff to an (average) 8-year-old without using concrete examples. From all I've heard about educational theory (which is a hell of a lot more than I ever cared to), children usually only even begin to develop abstract reasoning around age 10 or 11, and it's not fully developed for years after that.

Concrete examples are great if they help develop at least a basic understanding abstract concepts.

In this case, I don't feel that either is being done.

"Jack builds a rectangular prism out of base-10 blocks" is NOT a real-world example that helps students draw real-world analogies to the concepts they are being taught.


I might as well phrase questions like "Jack is an ideal massless particle, surrounded by a uniform magnetic field B (which we'll refer to from here on as Betty)"


Muddling real-world examples with abstract constructs (eg. base-10 blocks) reduces the educational value of the lesson down to virtually nothing. Students don't know how to deal with areas or volumes by any means apart from counting base-10 blocks, and even then, don't actually have a firm understanding of their application in the real world.


Toward the end middle school, I remember being taught how to calculate compound interest. After the lesson, the textbook contained a page of word problems that we were supposed to complete. The first problem dealt with a library that compounded its overdue fees on a daily interval. The second was the same, but compounded continuously.

After reading out the problem, and realizing just how absurd it was, she told us to tear the page out of our textbooks so that none of the teachers in the future would be able to give such a ridiculous lesson, and offered extra credit to anybody who could provide evidence of a library that actually employed such a scheme.

She was also notorious for rescuing discarded textbooks out of the dumpster, and teaching from them years after they had been deemed "unfit," often ignoring the new books entirely. Shockingly, her students consistently scored the highest on the standardized tests that the new books were designed to help with, and to great amusement, she was hailed by the board as the only one who was using the new books "properly," because her students scored so much better than everybody else.