Why do fractions cause so much mathemaphobia?

[Jerbearrrrrr]

Sorry if this is the wrong place to post. Kinda wanted to rant.
I just wanted to express something that's been bugging me for a long time.

Where does mathemaphobia really come from? I guess it's from how easy it is to get stuff wrong. If you're asked to discuss a poem, you can write some poop and get half the marks.

Are fractions the root cause of a lot of mathemaphobia? I'm talking about experiences with arithmetic as a kid of age n, for say 10<n<14.

Addition is fine.
Multiplication is fine.
Raising to powers is fine.
Division is not fine. Long divison? Don't even go there. Multiplication by 1/m? What?

Then the child discovers calculators, so this is all irrelevant anyway. Onto the next chapter, where a general number is represented by a letter. Algebraic fractions are like the end of the universe to some people.

2x+3x=5x is fine
2x*3x=15x² is fine.
(2x)²=4x² is usually fine after you tell them to write 2x*2x, which is the defn of square (they won't disagree).
2x/3x=??!??! invariably.

Why is it that people can compute 6/9 = "six ninths" = 2/3, it's such a leap of imagination to do 2x/3x=2/3?

And of course even if that's sorted out, there's the dreaded
$$\frac{2x+1}{3x} = \frac{2+1}{3}$$
and the
$$\frac{2x}{3x+1} = \frac{2x}{3x}+\frac{2x}{1}$$

And then there's adding fractions...no one knows how to do that. 1/2 + 3/4 is doable, but not 1/2x + 3/4x, god no.

I remember a double maths lesson when I was ten. It was about an hour's worth of cutting paper circles up into pizza slices, and seeing, for example, that two 1/6ths fit on top of a 1/3rd slice.

And from that, the teacher said, we deduce that "we may multiply or divide the top and bottom by the same thing, and the answer is the same". And the next lesson was how to apply this to for example, adding fractions.
That ends up solving 90% of routine algebra in high school.

Why does no one else remember that lesson (or its analogue)?
What is it about fractions that make people's brains turn into mush?
Has anyone else encountered reasonably intelligent people who just can't apply themselves to adding fractions?
Even in calculus problems, people make the same mistakes over and over...

Sorry for the long post. Someone move it to where ever it's meant to be. Not even expecting a reply, just wanted to express frustration.

 

[Werg22]

Frustration? Why? Why do you care if people can't add fractions?

 

[alice22]

Probably for a similar reason as to why the OP posted:-

[tex]\frac{2x+1}{3x} = \frac{2+1}{3}[\tex]

When I am pretty sure he intended to post something else, sometimes people struggle to do things which others find easy.

 

[Mark44]

Frustration? Why? Why do you care if people can't add fractions?

It's like asking, Why do you care if people can't read? The answer is that people are better off if they are literate and "numerate," to be able to count and at least do arithmetic.

John Allen Paulos, in his book Innumeracy, bemoaned the fact that many of the people who are considered to be intellectuals, are completely ignorant of any mathematics developed in the last 400 years. And these are university graduates. Contrast this with the abilities of 6th graders of 100 years ago, who were expected to be able to do very complicated problems with fractions, decimals, weights and measures, percentages, all without the use of anything more sophisticated than paper and pen or pencil.

Are fractions the root cause of a lot of mathemaphobia? I'm talking about experiences with arithmetic as a kid of age n, for say 10<n<14.

Addition is fine.
Multiplication is fine.

I'm not convince that multiplication is fine in all cases. Teaching in college for a number of years, I have run into a lot of students who were uncertain of such products as 8 x 7 or 9 x 6 and others. There has been a movement by some in mathematics pedagogy in the past 25 years to de-emphasize the importance of memorization of the times table. This definitely has an impact on arithmetic operations with fractions and algebra skills such as simplifying rational expressions by factorization.

Certainly division is problematic, possibly for the reason above. If you can't multiply, you really have a hard time with division. I recall meeting a young woman who had a room in a house I lived in back in 1976. She was an Art major, about to get her BA degree. When she learned I was studying math, she confessed that she never learned how to do long division. I was stunned that someone could make it all the way through a degree program at a state university of some renown without knowing one of the basic skills in arithmetic. Keep in mind that this was only a couple of years after the introduction of relatively cheap pocket calculators, so she would have gone through elementary and high school before calculators were around.

One of the things that I always thought could make a real difference was to make arithmetic more hands-on, such as by using Cuisenaire rods (http://en.wikipedia.org/wiki/Cuisenaire_rods) to get across the basic ideas of arithmetic in a more concrete fashion. Even something as simple as an egg carton with marbles could get across the idea that 4/12 is the same as 1/3, or that 1/6 + 1/6 = 1/3. As far as I know, there aren't many primary schools that employ strategies such as these, possibly because so many who go into primary education have very limited mathematics skills themselves.

 

[Diffy]

Why is it that people can compute 6/9 = "six ninths" = 2/3, it's such a leap of imagination to do 2x/3x=2/3?

Probably because some math nerd will point out that you are correct as long as x <> 0.