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Teaching Fractions: The Tootsie Roll Is the New Pie

Unknown Lamer posted about 7 months ago | from the all-you-need-is-lambda dept.

Education 194

theodp writes "Following up on a WSJ story, data visualization author Stephen Few illustrates why using lines or bars may be sweeter than pie when it comes to teaching kids fractions. 'Although the metaphor is easy to grasp (the slices add up to an entire pie),' explains Few, 'we know that visual perception does a poor job of comparing the sizes of slices, which is essential for learning to compare fractions. Learning that one-fifth is larger than one-sixth, which is counter-intuitive in the beginning, becomes further complicated when the individual slices of two pies — one divided into five slices and other into six — look roughly the same. Might it make more sense to use two lines divided into sections instead, which are quite easy to compare when placed near one another?' So, is the Tootsie Roll the new pie?"

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194 comments

First question from the kids (3, Insightful)

Chrisq (894406) | about 7 months ago | (#45013127)

What the fuck is a tootsie roll?

Re:First question from the kids (0)

sortius_nod (1080919) | about 7 months ago | (#45013601)

While I know what one is, why are Americans commandeering reality? They can't even keep their government open, how the fuck are they supposed to keep maths consistent?

Re: First question from the kids (3, Insightful)

StikyPad (445176) | about 7 months ago | (#45013679)

The smartest Americans know better than to go into politics, which leaves the politicians we have.

Re:First question from the kids (1)

Sockatume (732728) | about 7 months ago | (#45013983)

Advice for submitters: avoid writing while hungry, snack foods might not be the universal and inviolable constant you assume them to be when your stomach is growling.

Pies? Rolls? I'm heading into a mid-afternoon blood sugar crash here and Slashdot is not helping.

No (0)

Anonymous Coward | about 7 months ago | (#45013143)

They need to use both.

Re:No (2)

plover (150551) | about 7 months ago | (#45013293)

The pre-segmented Tootsie Roll is actually a poor choice. A person who sees it already divided into seven chunks won't understand all those divisions have to move in order to divide it by eight.

Re:No (0)

Anonymous Coward | about 7 months ago | (#45013355)

They need to use both.

They need to use neither.
Give 'em the good axiomatic definition of a fraction. And them later on give the examples with pies and tootsies.

Re:No (1)

fuzzyfuzzyfungus (1223518) | about 7 months ago | (#45013553)

They need to use neither. Give 'em the good axiomatic definition of a fraction. And them later on give the examples with pies and tootsies.

Oh, you'll loath some of the bullshit that gets added to math curricula to pad out the vocab lists...

Hey kids, because it's fucking pointless, we are going to be learning about 'proper fractions', 'improper fractions' and 'mixed numbers'! Open your copybooks now: "A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is a fraction where the numerator is larger than the denominator. A mixed number is a number written with a whole number component and a fractional component." All of these are basically just division problems that are being left unevaluated for reasons of convenience, or because the resulting decimal representation may not be entirely well behaved, so this shit is pointless; but it will be on the quiz.

Re:No (4, Informative)

Mitchell314 (1576581) | about 7 months ago | (#45013773)

Uh, there *are* legit reasons for teaching the different classifications of fractions. For example, mixed fractions are the most intuitive representation of rational numbers. Improper fractions are the simplest way to write the number down, but not the most intuitive (for the given audience). Proper fractions are the remainder part of the mixed fraction, whereas the integers are taught in different lessons.

Math is hard, and teaching math is hard. The 'intuitive' or 'obvious' way to teach math isn't necessarily a good way.

Re:No (0)

Anonymous Coward | about 7 months ago | (#45014159)

The 'intuitive' or 'obvious' way to teach math isn't necessarily a good way.

It is, in fact, the only good way to teach math. If kids don't have an intuitive and deep understanding of all the concepts, they don't truly understand it.

Re:No (1)

Archangel Michael (180766) | about 7 months ago | (#45014163)

Math is not hard. Teaching Math is not hard. Math is conceptual and until you get the concepts, actual math is just by rote, which is how math was taught to me.

Re:No (0)

Anonymous Coward | about 7 months ago | (#45013783)

They need to use neither.
Give 'em the good axiomatic definition of a fraction. And them later on give the examples with pies and tootsies.

Oh, you'll loath some of the bullshit that gets added to math curricula to pad out the vocab lists...

Hey kids, because it's fucking pointless, we are going to be learning about 'proper fractions', 'improper fractions' and 'mixed numbers'! Open your copybooks now: "A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is a fraction where the numerator is larger than the denominator. A mixed number is a number written with a whole number component and a fractional component." All of these are basically just division problems that are being left unevaluated for reasons of convenience, or because the resulting decimal representation may not be entirely well behaved, so this shit is pointless; but it will be on the quiz.

Well at least modern maths as it was teached in the 60s, 70s and 80s gave students the notion of how you construct and use mathematical objects. In their case natural numbers, integer numbers, fractions and decimal numbers. And progressing from one set to the other is made logically clear and unanmbiguous. Clarity of exposition and a rigurous theory (at their level obviously) is everything in maths. Today we have replaced clarity and rigour with hocus-pocus rules. No one is advocating with teaching university maths in kindergarten, middle school or high school. But what students learn nowadays in school is just a recipe of rules without any justification. They are simply not learning maths. And we are doing them a disservice.

Re:No (0)

colinrichardday (768814) | about 7 months ago | (#45013919)

gave students the notion of how you construct and use mathematical objects.

Do we construct mathematical objects? Did the number one not exist until I became aware of it?

Re:No (0)

Anonymous Coward | about 7 months ago | (#45014003)

gave students the notion of how you construct and use mathematical objects.

Do we construct mathematical objects? Did the number one not exist until I became aware of it?

We can debate on wether the integer numbers are constructed or not. That is a metaphysical debate. But once we have agree on what natural numbers are, and what operations we can do on them we can construct rigourously the set of integer numbers, and set of rational numbers, as well as the set of real numbers and complex numbers.

Try defining what the number one is, you'll have quite a difficult problem on your hands.
You can say 1 bottle of wine, 1 car, one airplane, one universe, 1 planet etc... but that doesn't tell you what the number one is does it ?

Re:No (1)

colinrichardday (768814) | about 7 months ago | (#45014313)

we can construct rigourously the set of integer numbers, and set of rational numbers, as well as the set of real numbers and complex numbers.

Perhaps we specify the rationals in terms of the rational numbers. Also, if we are now constructing the rational numbers, does that mean they didn't exist in Newton's time? Or if they did exist then, how do we construct them now?

Re:No (1)

Chrisq (894406) | about 7 months ago | (#45013487)

They need to use both.

I agree, some things like halving halves to make a quarter are easier to show in two dimensions.

Re:No (0)

Anonymous Coward | about 7 months ago | (#45013617)

They need to use both.

I agree, some things like halving halves to make a quarter are easier to show in two dimensions.

And how do you visualize 1/3-1/5 or 1/3+1/5 with pies or tootsie rolls ? Either metaphor (pies or tootsie rolls) is fundamentally flawed in that it captures only 1 property of fractions (fraction of a whole) and that's it.

Re:No (2)

Chrisq (894406) | about 7 months ago | (#45014137)

They need to use both.

I agree, some things like halving halves to make a quarter are easier to show in two dimensions.

And how do you visualize 1/3-1/5 or 1/3+1/5 with pies or tootsie rolls ? Either metaphor (pies or tootsie rolls) is fundamentally flawed in that it captures only 1 property of fractions (fraction of a whole) and that's it.

In UK schools they use Unifix blocks [glsed.co.uk] which are essentially the same as the "tootsie roll" examples. The way these would be used would be to make several columns of 15 blocks. One would be divided into three parts and the other into five. They could then easily illustrate adding 1/3 + 1/5 by adding one of the "three part division" to one of the "five part division". Counting would show that the answer was 8/15 and comparrison to the whole 15 parts would show that it is just over half.

This would also illustrate why you have to get the fractions to have the same denominator. Subtraction is a bit harder - they would have to take away the 3 15ths from the 5 15ths but you get the idea

Start a classroom war (5, Insightful)

Anonymous Coward | about 7 months ago | (#45013157)

The pie chart is counter intuitive? Anyone who has ever fought over pizza slices knows very well that 1/5 is larger than 1/6, even kids.

Here's a simple classroom script to teach kids about fractions:

1) Buy 2 pizzas, slice one in 8 pieces, the other in 12 pieces.

2) Take 20 students in the classroom and tell them to choose a piece from any of the pizzas.

3) Watch as war ensues

Re:Start a classroom war (-1, Troll)

Dunbal (464142) | about 7 months ago | (#45013189)

No oil and Israel is probably not involved in the pizza, so there won't be a war.

Re:Start a classroom war (1)

Anonymous Coward | about 7 months ago | (#45013395)

If it's Italian pizza, there will probably be oil. Olive oil, to be exact.

Re:Start a classroom war (5, Funny)

SJHillman (1966756) | about 7 months ago | (#45013407)

Anyone who fought over pizza knows that not all 1/8ths are created equal.

Re:Start a classroom war (1)

Hatta (162192) | about 7 months ago | (#45014297)

There's another teaching opportunity. Using nothing more than a compass and straight edge, divide the pizza into equal portions.

Stephen Few Loves his Bar charts (2)

ZahrGnosis (66741) | about 7 months ago | (#45013473)

I completely Agree... I've actually had a few public disagreements with Stephen Few (on his blog - Hi Stephen) about his love of bar charts.

He's absolutely right, technically, on the visual perception -- that it's easier to compare lengths to basically anything else (like pie slices), particularly shapes that vary in more than one dimension (is a 5x5 rectangle bigger than a 6x4? If you know the dimensions you can do the math, but if you look at the boxes it's not as easy).

BUT, where I disagree (and I seem to agree with parent AC) is that people get tired of bar charts. Kids, in particular, have amazingly short attention spans, and as any teacher knows, engaging a child in a learning experience is very important, and different students will learn different ways. Your example of buying pizzas for a class is a classic example (although war is not the standard goal). Cutting a long subway sandwich or tootsie roll may not have the same effect. In fact, it's possible that the measurements Stephen Few relies on to measure visual perception could change if we took the time early on not to cater only to what our students are already good at, but to exercise spatial considerations that could improve.

Pie charts have their place, if only to break up the monotony. Certainly we should teach kids ratios based on bars, lines, squares, and other things as well -- for the most part we already do -- but we should not say that any one way is the best, even if there's one measurement that "proves" it, at the expense of variety.

Re:Start a classroom war (5, Funny)

ohieaux (2860669) | about 7 months ago | (#45013637)

When asked if he wanted his pizza cut into 4 or six slices: "You better cut the pizza in four pieces because I'm not hungry enough to eat six." - Yogi Berra

Who cares? (2)

Russ1642 (1087959) | about 7 months ago | (#45013163)

So one method is probably a small fraction better than another method of teaching fractions. This isn't how you enhance the next generation's education. This is how you make it look like you're doing something to help when you're actually just raising a fuss over the tiniest of things. This is the plastic banana slicer of education: an answer to a question nobody asked.

Re:Who cares? (1)

SJHillman (1966756) | about 7 months ago | (#45013451)

My teachers preferred to use real-world examples, which seemed to help. Cutting a pizza into 8ths or 10ths (who the hell cuts it into fifths?). Doubling or halving chocolate chip cookie recipes (1/3 cup sugar doubled is 2/3 cup. 1/2tsp vanilla halved is 1/4tsp). Sports statistics, word problems, supermarket packaging, etc. It was all better than some arbitrary pie chart that carried no meaning beyond "this slice is bigger than that slice".

I always wanted... (0)

Anonymous Coward | about 7 months ago | (#45013937)

I remember those questions: I always wanted the pizza cut into 6ths as I didn't think I could eat 10 slices.

Now there's an advertisement for a post-secondary education.

Re:Who cares? (1)

AHuxley (892839) | about 7 months ago | (#45013779)

Recall the damage done to education in Alabama, Mississippi and South Carolina by the General Education Board after the War of Northern Aggression?
English, math and science best left for college preparatory classes.

Something weird just happened ... (4, Insightful)

MacTO (1161105) | about 7 months ago | (#45013171)

... and somebody read a school textbook.

Seriously. Textbooks have used multiple representations of fractions for years, one of which is linear, because the education research has indicated that different children learn better with different representations of fractions.

Well, at least we now know how long it takes for education research to trickle into the classroom: decades.

Re:Something weird just happened ... (3, Interesting)

Sarten-X (1102295) | about 7 months ago | (#45013375)

Teachers also use word problems, discrete objects, and liquids, ideally delivered in quick enough succession that the student's brain catches the only constant: the concept of a fraction.

I think the problem isn't education research getting into the classroom - it's exactly the opposite. Teaching is an application-focused industry [xkcd.com]. When a teacher solves a particular educational problem, the technique stays within the school district, or perhaps makes a few rounds at educational conferences. The technique rarely gets any widespread attention, hardly any formal study, and is entirely forgotten within the decade... until an "educational researcher" stumbles across it and publishes a paper describing its effectiveness, which doesn't help because the school boards aren't interested in using new experimental techniques when their budgets are already in such jeopardy.

There is no Nobel Prize for education.

Re:Something weird just happened ... (1)

fuzzyfuzzyfungus (1223518) | about 7 months ago | (#45013699)

... and somebody read a school textbook.

Seriously. Textbooks have used multiple representations of fractions for years, one of which is linear, because the education research has indicated that different children learn better with different representations of fractions.

Well, at least we now know how long it takes for education research to trickle into the classroom: decades.

It's important to remember that (assuming qualified faculty, an assumption that is...widely variable... in its truth; but is definitely nonfalse in better systems and some parts of worse ones) educational research can make it into a classroom from the top or from the bottom:

Your top-down approach (curriculum design followed by mandate, textbooks 'aligned' with that curriculum) is nominally research based; but ponderous as hell and perpetually mired in comittee and trying to appease the wackjobs in Texas and the wackjobs in California at the same time. It's primary virtue is that, sooner or later, their work trickles down to even the most burned-out and ossified classrooms; because the faculty and local admin have no choice. On the other hand, faculty enjoy some freedom to teach as their training and experience deems best, and the ones with recent educational education and/or professional development are probably familiar with the research. This happens a great deal faster, especially in situations with new teachers or districts that do a good job of encouraging faculty not to ossify. However, it can take unbounded amounts of time to have any effect in situations with lousy faculty and local administration.

Pffft, Fractions? How about Frogs AND Fractions? (1)

AdamStarks (2634757) | about 7 months ago | (#45013193)

http://twinbeard.com/frog-fractions [twinbeard.com]

Frog Fractions taught me enough fractions to pass my GED!

Thanks, Frog Fractions :-D

Re:Pffft, Fractions? How about Frogs AND Fractions (1)

i kan reed (749298) | about 7 months ago | (#45013345)

And it helped me get my insect porn business off the ground, and won me elected office!

Re:Pffft, Fractions? How about Frogs AND Fractions (0)

tepples (727027) | about 7 months ago | (#45013385)

How would one go about converting a Flash game like this to HTML5?

Re:Pffft, Fractions? How about Frogs AND Fractions (1)

pla (258480) | about 7 months ago | (#45013677)

How would one go about converting a Flash game like this to HTML5?

First, you learn HTML2 (or 3, or 4, doesn't much matter). Then you learn CSS. Then, you learn Javascript. Then, you learn HTML5. Then, you learn Flash. Then, you learn ActionScript. And finally - You break into TwinBeard HQ, steal the source code to Frog Fractions, and begin the long process of porting it.

After all that, though, you probably already have a pretty good grasp of fractions.

No, Not At All. (0)

Anonymous Coward | about 7 months ago | (#45013227)

This is a solution looking for a problem. But, more so, this solution makes the problem much worse. The pictured Tootsie roll, appears to be a square turd, with lines all over it. Though the lines don't align both sets of divisions indicate the same number of segments. It makes no sense to me, with regards to fractions, and I'd like to think that after mastering probability and statistics that I have a reasonable grasp on fractions.

What is the tootsie roll supposed to represent? The pie in the same picture clearly indicates a single slice out of nine.

Re:No, Not At All. (1)

SJHillman (1966756) | about 7 months ago | (#45013479)

I think a Hershey's bar would be a better choice if they want something that's already marked up. At least then you can break it into halves, quarters, eighths, etc (depending on which size bar you buy). Or just just a regular, unmarked tootsie roll, a ruler and something sharp enough to cut it.

Length vs volume. (2)

PlusFiveTroll (754249) | about 7 months ago | (#45013229)

The comments on the site (as of this time) give some pretty good reasons why using slices of a circle aren't the best way to describe fractions. Most of the time [wikipedia.org] it is easier for the mind to tell if two lengths are the same versus if two slices of a circle are the same. It is a much simpler calculation to determine length (line) then volume (pie piece).

Re:Length vs volume. (0)

Anonymous Coward | about 7 months ago | (#45013497)

If you're calculating volumes of pie pieces then you're doing it all wrong. You only need to look at the chord length of the arc of the pie slice, it's a simple linear length.

Re:Length vs volume. (1)

cryptizard (2629853) | about 7 months ago | (#45013635)

Oh man because 3rd graders are going to love all those word you just said. They're for sure understand that right away because you are the best educational mind of our generation.

Re:Length vs volume. (0)

Anonymous Coward | about 7 months ago | (#45014205)

My 4 year old preschooler got it.

Maybe I let him play too much DragonBox.

Re:Length vs volume. (0)

Anonymous Coward | about 7 months ago | (#45014185)

I don't quite understand why you would want to present a linear length wrapped around in a circle. If you are not going use the simplest form (the line), why not use a hexagon instead? Or a star shape? Actually, it's children, so let's make the charts animal shaped instead. Although I do like your n-sided polygon approach (the chords make a polygon).

The problem with presenting linear values with two dimensional shapes is that there are so many ways to interpret it. The angle or equivalently the arc length gives one way to measure linear values, and the area is another way. Using the chord length (the third way) is especially nice, as changing one value requires changing all the other values in a non-trivial manner. None of these three approaches give the same fractions except in special cases.

Re:Length vs volume. (1)

Arker (91948) | about 7 months ago | (#45013515)

Which is simply more reason why students need practice doing the more difficult calculation early.

This whole notion that everything in education needs to be watered down and simplified for ease of digestion simply cheats the children - who tend to be quite a bit smarter than we think, when given a chance.

Re:Length vs volume. (0)

Anonymous Coward | about 7 months ago | (#45013611)

The comments on the site (as of this time) give some pretty good reasons why using slices of a circle aren't the best way to describe fractions. Most of the time [wikipedia.org] it is easier for the mind to tell if two lengths are the same versus if two slices of a circle are the same. It is a much simpler calculation to determine length (line) then volume (pie piece).

There is not such a thing as the "best way to describe fractions". Which is why for the last hundred years, teachers and textbooks have used a variety of different representations, I'm not sure where this guy has been hiding.

As for what is "easier" to tell apart, if the kids are having trouble making the distinction between 8/10 and 9/10 then the problem is not so much HOW you represent it visually, but rather that the difference is getting small enough that some representations aren't visually different enough. So.... increase the difference. Quit comparing 4/5 to 3/5, and compare 1/2 to 1/4. Pretty easy and obvious to spot the size difference on the pie graph.
But as a counter-point to his love for bar graphs- they don't reinforce the idea that the divisions are part of a whole, whereas a pie chart does.

Re:Length vs volume. (0)

Anonymous Coward | about 7 months ago | (#45013969)

If you are using volume in the pie chart, you are doing it wrong, you use the inner angle.

Re:Length vs volume. (1)

AdamHaun (43173) | about 7 months ago | (#45014065)

They shouldn't be (and probably aren't) using numbers that are very close together to teach the concept. Instead of using 1/5 and 1/6, use 1/2 and 1/3, or 1/3 and 1/8. If the perception of length vs. area/angle matters, it's a bad choice of numbers.

Break me off a piece (0)

Anonymous Coward | about 7 months ago | (#45013251)

of that Kit Kat Bar.

No wonder kids are getting fat these days (0)

Anonymous Coward | about 7 months ago | (#45013261)

The new curriculum has math teachers slicing lemon merengue pie in class instead of teaching fractions.

Hershey bars would also work well (1)

RobertLTux (260313) | about 7 months ago | (#45013263)

any candy bar that has natural sections would work for fractions

Kit Kats would work for 2 and 4 based fractions

Only denominators with 9 (4, Funny)

Anonymous Coward | about 7 months ago | (#45013281)

There's 9 sections. What happens when you want to teach 1/4s, 1/2s, 16ths ?

That's why I think a bottle of Scotch is the new pie!

Now children, let me drink two shots, what fraction of the bottle did I just drink?

Now children, assume what's left is the whole and I drink another three shots, what fraction is left?

Now children, write a 1,000 word essay on why whiskey is the best math tutor whle I take a little snap.

A New Product Line (1)

archer, the (887288) | about 7 months ago | (#45013291)

Now Tootsie can sell a bunch of new lengths: halves, thirds, quarters, fifths, sixths, etc. Schools would just need to go out and buy a few bags.

For adults learning fractions, they could use alcohol instead, but they'd just have one fraction: fifths.

Use a single bar (0)

Anonymous Coward | about 7 months ago | (#45013319)

Between the numerator and the denominator.

Why teach fractions to kids in the first place? (1)

Anonymous Coward | about 7 months ago | (#45013373)

Students will need to learn about fraction, true...

However, there is little to no need for fraction in the real world, with one exception. The US. Due to the antiquated mesurement system, you have to know fractions, else you are doomed...

However, in the rest of the world, fraction do not have a lot of use and their teaching can be pushed later in the cursus when we this learning is easier and has less need to rely on visualisation...

Cyrille

Re:Why teach fractions to kids in the first place? (0)

Anonymous Coward | about 7 months ago | (#45013449)

dude what?

Re:Why teach fractions to kids in the first place? (1)

SJHillman (1966756) | about 7 months ago | (#45013567)

Fractions are still useful in the metric system, granted, with more limited application. Halves and quarters are fine, but what about when you need to divide a whole between seven people? Each person can get 1/7 or each person can have 0.142857142857... even rounded to only .14 that's kind of hard to figure out compared to 1/7.

Metric and decimal is great for science, but fractions still have their place in everyday life.

Re:Why teach fractions to kids in the first place? (2)

pla (258480) | about 7 months ago | (#45014029)

However, there is little to no need for fraction in the real world

Let me guess, you find the the Big Mac button confusingly similar to the Quarter Pounder button.

Hint: One has 2/3rds of the number of buns of the other one. One bun, two buns, red bun, blue bun!

Hershey Bars Are Better (1)

dmiller1984 (705720) | about 7 months ago | (#45013399)

It's much easier to get the concept of a whole with an entire Hershey bar than with an arbitrary number of Tootsie Rolls.

Re:Hershey Bars Are Better (1)

SJHillman (1966756) | about 7 months ago | (#45013603)

When we first started fractions and division (third grade or so?), we used groups of discrete units rather than cutting up a single unit. If you have ten pennies and you eat half, how many do you have left? If you have 14 pennies and you throw 1/7th of them at Johnny, how many did you throw? Most kids are still smart enough to see a group of individual objects as a "whole".

Use both (0)

Anonymous Coward | about 7 months ago | (#45013425)

If you're only going to use lines (and not pies) just use a damn tape measure. Seriously. I still have trouble reading a tape measure. I'm awesome at reading pie-charts though! Maybe if I were taught fractions with a tape measure I wouldn't have so much trouble with it now.

Who eats a Tootsie Roll in equal fractions? (0)

Anonymous Coward | about 7 months ago | (#45013469)

If you want a divisible bar, the best food for dividing into fractions is sushi rolls.

Thank you for the idea (1)

advid.net (595837) | about 7 months ago | (#45013477)

From now I'll try this way to teach fractions, let see that this evening on a 9yo.
(a child who doesn't understand why a fraction is smaller with higher numbers)

Here's a thought.... (or 2 or 3) (2)

cogeek (2425448) | about 7 months ago | (#45013495)

Math was taught and learned just fine for over 2000 years. Pretty damn arrogant to come along in the last 50 and think we know how to teach children math in a better manner than they've learned math all along. Pick your slogan, acronym, whatever. KISS (Keep It Simple Stupid), If it ain't broke, don't fix it... Nothing wrong with the way math has been taught all along. I have 4 kids that have all gone through Algebra in the last few years, and I had to go out and buy them Lego sets to learn Algebra. A true WTF moment for me. We didn't get Legos in school and still learned Algebra just fine. When they learned addition, subtraction, multiplication and division I'd help them with their homework only to hear "that's not how we do it" "our teacher taught us a different way" and we'd wind up taking 15 steps to solve a problem that should be done in 2 or 3. When people get paid to come up with "new and better" ways to do things, they have to come up with something or wind up losing that steady government paycheck. Doesn't matter that it's a worse solution than what's already in place, just that it's different.

Re:Here's a thought.... (or 2 or 3) (1)

SJHillman (1966756) | about 7 months ago | (#45013661)

People were fine cooking with fire for X thousand years just fine, pretty damned arrogant for them to invent the microwave.

Just because "that's the way it's always been done" doesn't mean it's the most efficient/effective/bestest way. Sure, it doesn't mean the old way isn't better for some people, but it's even more arrogant to assume the new way isn't better without trying it first, especially based on some anecdotal evidence.

Also, I highly doubt that math was taught the same way across any or every culture over the course of 2000 years.

Re:Here's a thought.... (or 2 or 3) (1)

cogeek (2425448) | about 7 months ago | (#45013745)

Yes, and the vast improvement in the public school system over the last 50 years certainly proves their "new way" of doing things to be so much better than the old way. American education is in a steep decline, because we've stopped teaching the basics and tried to come up with a "one-size fits all" approach. It won't work, every child is different and there are some kids that will just never get it now matter how far we dumb things down. One of the biggest causes of this is the recent belief that every kid needs to go to college. Sorry, some kids have to go to Vo-Tech and learn to fix cars, some kids have to go to beauty school and be hair stylists, and some have to get their BA's so they can ask me if I want fries with that.

Re:Here's a thought.... (or 2 or 3) (1)

cryptizard (2629853) | about 7 months ago | (#45013663)

You are so right. Who needs newfangled things like cars and cell phones. People got around just fine in biblical times I say. For that matter, who needs vaccines or medicine? Living past 30 is overrated.

Re:Here's a thought.... (or 2 or 3) (2)

cogeek (2425448) | about 7 months ago | (#45013775)

Not saying there's never room for improvement, I'm saying there's no need to fix what already works and has worked well for centuries. The constant plea from the teacher's unions is that we just need to spend more money per student when we already spend more money per student than any other civilized nation and still graduate kids that can't read and write at an elementary school grade level. One room school houses with a single teacher for all grades used to be able to teach the basics, no reason they shouldn't be able to now with the resources available.

Re:Here's a thought.... (or 2 or 3) (1)

cryptizard (2629853) | about 7 months ago | (#45014001)

Except people from back then would be legally retarded now (i.e. the Flynn Effect). Students are expected to learn more, quicker than ever before. As you say, we are spending more money per student than anyone and it just isn't working. I would actually say that teaching methods haven't changed that much in the past hundred years. Maybe the answer is to get kind of extreme and start from scratch.

Re:Here's a thought.... (or 2 or 3) (1)

AlphaWoIf_HK (3042365) | about 7 months ago | (#45014257)

Students are expected to learn more, quicker than ever before.

People expect them to learn more, but in practice, they just memorize more and then later forget it all.

As you say, we are spending more money per student than anyone and it just isn't working.

Change is difficult and expensive, so why fix something that is completely broken?

Re:Here's a thought.... (or 2 or 3) (2, Insightful)

ohieaux (2860669) | about 7 months ago | (#45014097)

Just last night I was helping my elementary age son study for a test on fractions and percents. We went through all concepts and he was still not getting it. Finally, he drew a line and started segmenting it. The teacher had shown the class "another way" to conceptualize this topic. He completely understood this approach. He then told me that his teacher told them about learning styles and tried to present the topic in multiple ways. So, while it seemed simple from one perspective to most of the class, others needed a different conceptualization.

I see no problem with exploring different approaches to learning. And, finding a better visualization for those types of learners is more than appropriate.

Re:Here's a thought.... (or 2 or 3) (1)

cogeek (2425448) | about 7 months ago | (#45014215)

I agree, nothing wrong with teaching "some students" a different way of doing it. But when the teacher's throw out a tried and true way of doing something to benefit the few, thus causing it to be more complex and difficult for the many, that's a problem. It's unfortunate that your son struggles with a method of learning that works for most other people, but that's no reason for people to advocate tossing out the entire system and starting from scratch. There will always be some people that don't get it no matter what method is used or taught.

Re:Here's a thought.... (or 2 or 3) (1)

AlphaWoIf_HK (3042365) | about 7 months ago | (#45014229)

Math was taught and learned just fine for over 2000 years.

It wasn't. Rote memorization is not ideal, and I do not consider it "just fine." Our entire education system is pretty much broken.

Re:Here's a thought.... (or 2 or 3) (2)

cogeek (2425448) | about 7 months ago | (#45014299)

Rote memorization is the only way to learn the fundamentals, addition, subtraction, multiplication, division, but those aren't taught any more. No kids are required to memorize math tables unless it's done by a parent. More complex ideas require teaching a kid how to think, but if they're busy counting on their fingers to subtract 7 from 13, more complex problems will never sink in.

Use Democrat logic... (1, Funny)

AmazinglySmooth (1668735) | about 7 months ago | (#45013619)

If we divide people into identity groups, you can truly understand how to put certain groups together! 50% white 50% female ...

Re:Use Democrat logic... (1)

cogeek (2425448) | about 7 months ago | (#45013815)

Don't think I've ever seen a better example of the English word "oxymoron" than "Democrat logic"....

One and Done (0)

Anonymous Coward | about 7 months ago | (#45013651)

posting AC as I'm away at friends....

Ok; Take a 1/3 pie slice. Enlarge it by 50%. It is still a 1/3 pie slice, in value and visually.

Now; Take a 1/3 line slice. Enlarge it by 50%. It is no longer a 1/3 line slice in visual, but still in value.

Pie pieces include both the value and the master unit in their visual.

And finally, it's a good precursor to learning about degrees and radians.

Re:One and Done (1)

SJHillman (1966756) | about 7 months ago | (#45013741)

That 1/3 pie slice is no longer 1/3 of the pie in value if you only enlarge the slice and not the rest of the pie. Sure, it's still 1/3 of a circle, but it's no longer 1/3 of the pie it was originally from. That's only good for teaching fractions of a circle, which really doesn't come up all that often until you're way past the point of learning basic fractions. The whole idea is to compare the fraction to the whole (or other parts of the whole), and if you're enlarging just one part of it, then you're throwing everybody off for no good reason.

Pretty good with fractions (1)

kilodelta (843627) | about 7 months ago | (#45013705)

Because I had it drilled into me as a kid. Now I sort of unconsciously can do most fractions.

No, Use a scale (2, Interesting)

sl4shd0rk (755837) | about 7 months ago | (#45013713)

Show them 1" on a ruler. Show them 1/4" increments. It's real easy to see 4 of those make up 1". Next show them 1/8" increments and 1/16" increment. They see pretty quickly how 16 can fit but the marks are smaller even though the number is bigger.

Now they've just learned how to read the crazy US Inch-standard system as well. Pretty handy for growing up in a slack-jawed yokel country who's politicians never let teachers adopt the metric system, but I digress...

Extra credit: show them a meter stick and listen to the gasp at how easy everything is because every little mark takes 10 units to get to the next larger unit of measure.

Re:No, Use a scale (1)

cogeek (2425448) | about 7 months ago | (#45013835)

This is a new one to me... the "US Inch-standard system?" I always grew up hearing it called the "English System of Measurement" for the country it originated in, England....

Re:No, Use a scale (0)

Anonymous Coward | about 7 months ago | (#45013941)

It's called The Imperial System

Re:No, Use a scale (0)

Anonymous Coward | about 7 months ago | (#45014093)

America is a country founded on Not Invented Here* so your imperial measurement system is not the same as the one used in Merry England. Hence calling it the English system is doubly wrong.

* See also football, spelling, etc.

Re:No, Use a scale (0)

Anonymous Coward | about 7 months ago | (#45014271)

I suppose it still is the English system of measurement, since two of the three countries still officially using it have English as the most common or official tongue. For some reason I thought Liberia wasn't a big pusher of English, but there you go.

Re:No, Use a scale (0)

Anonymous Coward | about 7 months ago | (#45014157)

Pretty handy for growing up in a slack-jawed yokel country who's politicians never let teachers adopt the metric system,

They've been teaching both systems in classrooms for decades...it's never been prohibited.

Source: My early-80s elementary schooling in Louisiana.

Re:No, Use a scale (1)

MonkeyDancer (797523) | about 7 months ago | (#45014385)

A Meter can only be evenly divided into 2 or 5.
A Foot can be divided into 2, 3, 4, or 6.

So if you ever have to measure a third of a Meter, good luck!

6/5 of a tootsie roll (1)

Overzeetop (214511) | about 7 months ago | (#45013967)

The linear idea is good for comparison side by side, but if you have a tootsie roll which is 5" long and one that is 6" long, which one is a whole tootsie roll, which one is 5/6 of a tootsie roll, and which one is 6/5 of a tootsie roll. Even if you show the individual pieces, you can't tell. With a pie, there's never any question as to whether you have more or less than a whole pie.

Why is this a story? (1)

harvestsun (2948641) | about 7 months ago | (#45014115)

This isn't a problem that needs solving. I never needed a teacher or diagram to explain to me that a half of something is larger than a quarter; that's effing obvious. "Learning that one-fifth is larger than one-sixth, which is counter-intuitive in the beginning"? WHAT? And even so, this article's point is moot, since visual representations other than pies have been around for many years. Containers of liquid, pieces of chocolate bar, etc.

The only things I needed to learn about fractions were the tricks for adding/subtracting/multiplying/dividing them. And a bigger problem is that teachers nowadays focus more on teaching the procedures than the concepts. Kids may know "you cross out a number on the top and a number on the bottom when multiplying fractions" but they don't understand WHY.

Re:Why is this a story? (1)

Jack Fretwell (3359477) | about 7 months ago | (#45014359)

Check out Fractured Fractions at www.capjax.com. Let me know if you think it helps and what could be added. __Jack jack@capjax.com
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