For me, I think any type of word problems are difficult for me, I litterley go back and read it 10 times trying to figure out what goes where. It's almost lik everytime I read it, I don't listen to myself read? If that makes sense, like if you where talking to someone and they're drowing you out or not listening to you, I'm doing it to myself though, it comes in one ear and quickly goes out the other. Or I'll read the problem and I just DON'T understand anything
And also the shapes where you have to find there base or the height of it or whatever.
What about you? What things did you struggle with the most?

I struggled the most with Trigonometry. I understand the very rudimentary basics of Trig - that a triangle's inner angles all add up to 180 degrees, that there is a sine, cosine, and tangent (and a corresponding cosecant, secant, and cotangent), and that the entire circle equals 2pi. But I don't actually understand what a sine IS, or what it means to measure the sine of an angle, or why a circle equals 2pi. I only have those things memorized because I took Trig 3 times (once in high school, twice in college).

To me Trig was always the hardest math subject (I've taken Algebra, Pre-Calculus, Trig, Geometry, and Analytic Geometry classes). I don't know what it was about Trig that made so little sense to me, I think because a lot of it was abstract, there weren't as many concrete concepts to work with as there are in other forms of math - or at least, none of them seemed concrete to me. I am sure there is a logical explanation behind "What is a sine?" or "Why do you measure the sine of an angle, what does that mean?" but those answers were never explained to me... so as a result, those subjects make no sense to me.

Algebra makes more sense to me because I can see the rationale behind the equation. For example, I understand all the different "parts" of the equation y=mx+b. I know that m is slope, b is the y-intercept of the graph, and you can plug in x and y values to make calculations. Each piece of it was explained to me, and because I have a working understanding of what each part does and why it does it, that part of Algebra actually came pretty easily to me (when I wasn't making stupid calculation errors). Trig never made sense to me like that.

I know this sounds kind of bizarre and anathema to post in a dyscalculia forum, but I actually like doing Algebra word problems if they aren't too difficult. I get a sense of satisfaction from picking out the different information in the word problem, figuring out what they're asking for, then figuring out how to solve the problem and get the correct answer. I guess because I generally suck at math, being able to actually do a word problem makes me feel on top of the world! Word problem type questions were my favorite part of the GRE math section.
"The hardest arithmetic to master is that which enables us to count our blessings." - Eric Hoffer

Word problems are the surest test that you understand the underlying concepts.

Trig has a ton of memorization and you need to know the identities. You can solve for the identities but can easily make a sign mistake. I've figured out a way to solve them BTW and minimize errors. Trig also involves knowing how to substitute. Math mnemonics are extremely helpful with trig if you can learn that way. I can explain sine/cosine and what that means, but won't attempt over the internet. Engineers pursue that study, particularly with power, voltage, current waveforms and looking at the frequency domain. I think that it's great that you survived trig.

DS struggles with dividing fractions, long division, and money.

I had a really hard time with dividing fractions when I was a kid too, because I couldn't visualize it. I can visualize dividing whole numbers - such as 9 divided by 3, separating a quantity of 9 into 3 discreet quantities. But the idea of "dividing" fractions was not something I could picture in my head, so I had a real hard time grasping it. Once someone taught me that all you have to do to divide a fraction is flip the second fraction and multiply them across, it became a lot easier for me. I've come to terms with the fact that I may never understand some math concepts, I will just have to memorize the tricks around them and go with it!

Also, here's my little horror story about long division. In elementary school we were taught long division first, then short-hand division. I always used short-hand division, so much so that by the time I got to 6th grade I could not remember how to do long division. My teacher called me up to the board one day to work on a math problem, which involved division. I did it the short-hand way and she said, "No, don't divide like that, divide the long way."

I then had to admit, in front of the entire class, that I could not do long division. It went just like you would imagine in the cringe-worthy scene of a coming-of-age movie. All the kids laughed at me, even the teacher looked like she wanted to laugh at me, and then she made me stand up there and learn how to do long division in front of everyone. I hated her for YEARS after she did that to me, I had never been so mortified in my life. And now I can't remember how to do short-hand division anymore! I think she traumatized it out of me, haha.

As far as sine and cosine, I can draw a graph of both and I do know what the graphs of sine and cosine look like. I had a really fabulous teacher sit and try to explain the "meaning of sine" to me - why the graph looks like that, how people figured out it looked that way, what it means in real time, etc. It just never stuck with me. I probably wasn't paying much attention because I hated that stupid subject so much, I just wanted to be done with it. I do think that the real-world applications of sine and cosine graphs (such as in music, voltage, etc.) are extremely interesting... I have just never been able to fully understand them. Maybe with more dedicated brain power I would be able to figure it out.
"The hardest arithmetic to master is that which enables us to count our blessings." - Eric Hoffer

Quick answer - everything! never understood any thing other than simply counting. Einstein eat your heart out!!
Kathy
Albert Einstein said: "Many of the things you can count, don't count. Many of the things you can't count, really count!."

For word problems, there are specific, systematic, and explicit procedures you can be taught to handle word problems. One of the procedures is called RIDD and research has been performed to study that procedures effectiveness.

DS is sitting a regular classroom at the moment and I don't agree with the way his teacher presents information. Concepts are not stressed, tricks are used, and they are not taught to mastery. About one day is spent on a new concept. You either sink or swim. At the beginning of the year, I spoke with the teacher and discovered he took the min math classes required to graduate college. The lack of higher math education makes this teacher (and I suspect others) incapable of seeing the need to slow down and really stress certain topics, like fractions. You simply cannot perform algebra without a thorough knowledge of fractions.

True story, DS came home and had totally learned dividing fractions wrong. He was ganked, beyond ganked. I spent 4 afternoons working with DS to unlearn how he had been taught. To this day, if he divides fractions the way he learned at school, he will get the problem wrong. When he does things step by step, he gets the problems correct. It's horrifying to have to un f(*k my kid. He's finishing the school year and then he's home in the Fall. We will be spending some time straightening out the whole fractions thing, and he is on the cusp of mastery.

I think that it's cruel how teachers pull kids to the front of the board, particularly when they lack confidence.

DS initially learned long division by the partial division method. He can now do it normally, but I let him use a calculator. Honestly, I see no purpose in dividing 7.0098 / 2.0002 without a calculator. Yes he can do it, it takes several minutes and it's still pointless.

I struggle with basically everything that comes after 3rd grade. I don't know all of my multiplication tables, long division is like Greek to me, fractions don't make much sense, pre-algebra and on, I skated through because no one bothered to hold me back, though one teacher did fail me in her class (trig? geometry?). I just always remember dreading math class and my breathing returning to normal only after leaving the class.
I'm NOT lost, I'm just taking the scenic rout!

squeakymonster wrote:
I struggle with basically everything that comes after 3rd grade. I don't know all of my multiplication tables, long division is like Greek to me, fractions don't make much sense, pre-algebra and on, I skated through because no one bothered to hold me back, though one teacher did fail me in her class (trig? geometry?). I just always remember dreading math class and my breathing returning to normal only after leaving the class.

I can pretty much ditto everything squeaky said here. Everything past 3rd grade for me too is a blur of confusion. Never understood any of it. I definitely remember that feeling of relief once I was out of math class. I don't know what was worse--not knowing the answer--or dreading if that was the day the teacher would decide to call on me for an answer...
Algebra? When I learn decimals and fractions, you're welcome to try teaching me, but unless you have the patience of a saint and are very long-lived, good luck with that...

CheshireKat-that sounds like what happens to me. With fractions, i learn how to work out the equation(sometimes anyway)but i have no freaking clue why it works like that. Happens with other math subjects too.

I guess i dread when the teachers calls on me, and asks me the answer, and i have to say in front of the class that i dont know. Then shes all like, "Why not?" haha i take very very long to do working out
Hello...

It took me a long time to understand fractions in the context of algebra.

Sorry for another long, math-involved post, but I usually get messages to the effect that it has helped someone, at least a little.

I think of all algebra as a very limited set of moves, like learning to play chess. You only have a few pieces and they obey straightforward rules, but you have to separate the enormous possibilities that the evolving board represents from the static nature of each piece; you can't begin to deal with the board until you understand the pieces.

The key to me doing this for fractions was to understand that division is multiplication, and therefore, fractions are, too. Just like subtraction is addition, just a special case of it. Multiplication and addition are nice, clean things. Division and subtraction are not, if you treat them as their own thing.

The other big step for me was to change how I write equations when I have a lot of nested division (i.e. division of fractions.)

These two things allow all division and fraction problems to be written as unambiguous multiplication problems. The usual way teachers write these things are a shorthand to save space and increase legibility, which is not useful and introduces errors when you are trying to manipulate an equation.

In order to take advantage of all the nice, simple algebra rules for multiplication, it has to be written like multiplication, not division or fractions.

The last one is the important one. Raising to -1 means to flip the number/fraction upside down. It takes advantage of the following fact, which I will state but not prove:

It allows things that are very confusing, like this example:

to be rewritten as a few steps of multiplication.

Doing the translation with no simplification or other steps, you'd get

a and b are left alone, because there's nothing to be done.

When you get to the c and d part, you see that they're inside a portion that needs to be flipped. So you flip them, and they become

Nothing else needs to be flipped. You've just finished the actual division of fractions, and that remains is to translate it back into shorthand.

The parenthesis are redundant, because we've written this in terms of pure multiplication, no division, and we can multiply numbers in any order and you get the same answer.

So all I'm going to do is throw away the useless parenthesis, and change the order I write the letters down in so that they're grouped.

Now I need to make it look like one of the translation rules above so that I can write it as a fraction.

So I put two new sets of parenthesis in, to group the numbers together, while I pull the flip operation outside the "bc" numbers.

Now it looks like one of the original rules, and I can write it as the final fraction.

I have left out a lot of the definitional stuff about multiplication that this method relies on, which I can post if someone is interested. I don't want to take up even more space if it isn't helpful.

I like how you express division as a negative inverse and restate the problem as multiplication. I'll try to remember that if I have to call upon it in the future.

My 6th grader has no advanced knowledge of the laws of exponents. I taught DS how to multiply fractions by first teaching him what a reciprocal was and how to apply it. He practiced writing out reciprocals for several different fractions and whole numbers. No one in my son's class knows what a reciprocal is. I'm not certain the teacher knows.

We then placed division problems in standard fractional form first...Multiplied the numerator and denominator by the denominator's reciprocal. We practiced with whole numbers first and them moved on to fractions. He gets the answers correct when he does this.

He prefers the trick keep- change- flip. The problem is that he can never recall what to keep, change, or flip, and the class spent two days at most on the concept prior to cramming on a comprehensive final. There was very little practice time and the teacher tossed dividing fractions in at the very end of the semester, and hasn't taught it since.

This Spring semester, they have spent literally weeks on probability and bar graphs. The emphasis is so stinking messed up. No one with any serious math knowledge would teach this way. It does a grave disservice to the class as a whole.
Edited by heathermomster on February 28 2012 01:37 PM

LoveAlways, I have the same thing with problems. If I read, for example...'one man walks for two miles at a walking pace of two miles an hour and another man walks in the opposite direction for for mile at three miles an hour, how long is it before they both stop?' Urgh! What the hell does that mean??? Actually I don't even know if that problem makes any sense at all, because none of them do at all to me...it was just an example of how inexplicable they are to me.

I'm afraid I couldn't read the posts with actual maths in, because the words and numbers just swim about and I can't make sense of them at all. In fact I'm getting severely stressed out and feel a headache coming on by just seeing them!

I never learned the times tables. If someone asks me what 6 times 4 is I don't know, but I can work it out in my head by thinking 'that's four sixes... 6, 12, 18, 24'. Ah, 24!