# America Needs to Study Fractions

Recent research finds that a solid grade school knowledge of fractions and long-form division accurately predicts later success in high school math. Christie Nicholson reports

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What part of math was most intimidating when you were in grade school? Maybe it was fractions. Or even worse, long-form division. Somehow splitting numbers really seemed complicated.

And the U.S. might be paying for kids’ inability to overcome those early challenges: a new study finds that Americans are falling significantly behind in math aptitude compared with China, Finland, the Netherlands and Canada. And the root cause is deficiencies in knowledge of fractions and division.

Nearly 600 children were tested once when they were 10 to 12 years old and again five years later. Researchers found that a fifth graders’ understanding of fractions and division accurately predicts their high school competency in general math achievement.

The researchers controlled for parents’ education and income as well as for the students’ gender, IQ and knowledge of addition, subtraction and multiplication. The study is in the journal Psychological Science.

The researchers note that it’s clear we need to improve instruction in fractions, ratios and proportions along with long division.

So let's get back to the fact that we know that 1/2 is equivalent to 3/6 is equivalent to 502/1004, which is equivalent to 9/18. And that is just a fraction of the hard work we need to do.

—Christie Nicholson

[The above text is an exact transcript of this podcast.]

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1. 1. threedeevus 04:02 PM 6/16/12

You may want to check the 502/1004 for an extra zero. :)

2. 2. Rob Hooft in reply to threedeevus 04:34 PM 6/16/12

... or a missing one :-p

3. 3. Nic Hendricks 06:32 PM 6/16/12

This is actually potentially fascinating. I read recently that fractions seem to be more intuitive than addition (and I'm going to guess, division) for most people (I don't remember where I originally read this, but here is another article: http://www.sciencedaily.com/releases/2009/04/090407174805.htm )
Learning addition and division boil down to mastering a symbolic (writing) trick - "carry your (1)'s". On the other hand, fractions and multiplication more directly manipulate tangible numbers.
My own hypothesis is that a lot of us are visual learners, and fractions are more easily analyzed visually than addition is, especially once you get into big numbers. Everyone knows what a half looks like. You can convert fractions into a pie chart; or in other words, basically you're comparing the relative sizes of two numbers.
Addition of anything beyond the fingers is by definition a symbolic calculation - you pretty much have to rely on writing stuff down. In other words, your memory alone is probably not good enough to quickly calculate 356+271. Savants are a boundary case - they are people with ridiculously good memory, so for the moment let's leave them out. (Actually, I've never asked a blind person how they do math...)
I'd like to see these studies used to support the the use of more creative methods in schools to get kids familiar with manipulating numbers. You can't learn if you're afraid to make mistakes or break things, or if you can't touch things. It's so easy to play with fractions, but so many kids are told, "fractions are hard," or, "you're doing it wrong." No wonder they're not motivated to learn them.

4. 4. Kayaker 07:14 PM 6/16/12

I have wondered how many of the folks who frequent Mickey D's understand the size ranking of a third-pound Angus burger versus a quarter-pounder.

Surveying customers might make interesting NIH/USDA/NSF funded research for a grad student.

5. 5. jerryhamilt@yahoo.com 08:05 PM 6/16/12

Wood Workers are already up to par! Thank's

6. 6. fixerdave 10:28 PM 6/16/12

Does this study distinguish between causal and casual? Is the lack of fraction understanding the cause of later math problems, or is it just an indicator? That's important, because if it's just an indicator then ramping up fraction education is just going to torture kids even more, and probably turn them off math.

Besides that, you crazy Americans should have a major advantage when it comes to fractions, what with SAE wrench and imperial-measured building material. Maybe the failings in fractions is the result of too many kids skipping shop class for academic tracks, what with the demand for university educated fast-food attendants and all.

If you want your kid to understand fractions, pick up a tape measure and go build something out of wood. Problem solved.

7. 7. Bellecon 11:35 PM 6/16/12

If you want your kid to understand fractions, pick up a tape measure and go build something out of wood. Problem solved.

Or sew something, or make a quilt or double the recipe or figure the tip....10% plus one half of 10% used to be good for a dessert at our table.....if parents can't do this how do they show thier children? Artithmetic was so much easier to help my children with than those silly Engllish language rules :)

8. 8. jtdwyer in reply to fixerdave 08:15 AM 6/17/12

I agree. The referenced article abstract begins:
"Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential..."

The ability to test young students' abilities using fractions and long division to successfully predict long term mathematical education prospects does not establish that focusing on early teaching of fractions and long division will improve long term prospects. That strategy could in fact alienate a large segment of students who might subsequently have even less interest in learning mathematics.

What is most essential is understanding why this correlation between fifth grade skills in computing fractions and long division and high school math competency. Correctly understanding the actual cause of this correlation is necessary to determine how educational strategies might be improved.

Perhaps, for example, those students who successfully learn fractions and long division were taught in elementary schools or by teachers who use more successful methods or have enhanced math concept communication skills. Many other possibilities exist - pounding on fractions may not produce the desired results.

9. 9. promytius 09:05 AM 6/17/12

I'm sorry, were you saying something? I was texting, and who cares anyway, all I gotta do is pass this stupid test and get out of school and cheat somebody out of some serious bucks. Fractions? That's for losers, and for people trying to figure out why they can't make ends meet; 3/5 goes to rent, 1/5 to fuel, 2 fifths for food, and another 2/6 for medical, then there's the credit cards, they take at least 3/10, and the cable bill is 3/16, and
why is my wallet empty? What's three fifths of nothing?
We're stupid, that's WHY we can't do math, or even find America on a global map. We can't even speel gud; can you spell 'doom'?

10. 10. jbairddo 11:12 AM 6/17/12

As to the relationship between divisions and fractions, aren't fractions the same as division we gave up on. 1/2 if is .5 and 2/3 is .666666666....... oh, forget about it, leave it at 2/3.

11. 11. lowndesw 11:50 AM 6/17/12

Well, it's obvious that if you test these little darlings and some don't do as well as everyone else, then you have hurt their SELF ESTEEM, and that is CHILD ABUSE. So, lets give them a test (that satisfies all the old fogies) then give everyone an A+ on the test (that prevents the stupid little darlings from having their self esteem endangered, if that was possible), then everyone is happy and we can go get some ice cream and watch cartoons.

The hell of it is that "fractions" are a bunch easier to learn than Chinese. Take your choice. You already speak Mandarin?? Write it , too?? Can you do fractions in Chinese??

12. 12. lowndesw in reply to threedeevus 12:42 PM 6/17/12

Looks OK to me. Did YOU study fractions??

13. 13. TTLG 01:01 PM 6/17/12

The kids with these particular skills did better on a specific test, but what sort of skills did the test look for? How does the test correlate with achievement in science/technology? Are these skills causing success or are they simply indications of school quality or type of upbringing?

In over 30 years in physics and engineering, I do not think I have once used either fractions or long division professionally. So I would take a long, hard look at this before I wasted valuable school time teaching something that has no use unless it is found to be a true foundation for better understanding of numbers, which I sincerely doubt to be the case.

14. 14. tharter in reply to jtdwyer 01:30 PM 6/17/12

Seems like the simplest thing to do is just go look at what the countries that don't have this problem are doing. If they're teaching fractions, the by gosh teach fractions! I'm not saying you're wrong of course, not at all, but there should be little mystery here. Of course actually DOING it might be a bit more problematic. Given how little the US spends on primary education relative to many of these other countries, well, you get what you pay for.

15. 15. tharter in reply to TTLG 01:35 PM 6/17/12

Yes, but a lack of understanding them prevents you from understanding things you DO need to know how to do, or at least concepts you DO need to understand. For instance you certainly cannot have the faintest idea of how integration works, any concept of statistics whatsoever, or comprehend linear algebra without understanding how to manipulate and combine different ratios etc. Surely you must use some of those techniques in any 'hard' science or most engineering disciplines.

16. 16. jtdwyer in reply to tharter 02:25 PM 6/17/12

Certainly that's the simplest thing to do but it would also be completely ineffective unless there is a direct causal relationship between fractional computation skills and success in later general math achievement.

In my personal experience, I suspect it is the poor quality of all early math instruction that produces poor achievement later on. Focusing on one small aspect of mathematics instruction is not likely to improve general results in math skills. I'd expect our elementary educators would become focused on some 'no fraction of children left behind' program.

17. 17. tharter in reply to jtdwyer 02:58 PM 6/17/12

I don't know that. In fact their hypothesis looks reasonable to me. They've established a correlation between this one particular aspect of arithmetical knowledge and later performance in general math skills. If it was just "our math education is crappy" then why would this one particular correlation be standing out? I agree there's no specific evidence of causation, but presumably one would focus on the strongest existing hypothesis first. Given that I'm skeptical it is POSSIBLE to establish causation with any certainty I'd think the best possible approach would be to take some students somewhere and give them a solid tutoring in division/fractions and see what happens. If the theory is correct then they should average better performance in math later on. Admittedly it is a long and tedious experiment, but I can't see what else you could do. Of course we could simply improve all math teaching across the board, but we didn't need any experiment to tell us to try that. At least if this is true it gives us a specific area to focus attention on. That may produce better results with less resource expenditure, always a good thing.

18. 18. jtdwyer in reply to tharter 09:49 AM 6/18/12

I suggest that those whose early math education is good 'get' fractions (normalized for ability, etc.), while those whose math education is 'crappy' do not. That would certainly make fraction skills a good predictor of later math achievement, but not its cause.

IMO, for there to be a direct causal relationship to fraction skills and success in later general math achievement, factions would almost certainly have be critical to understanding higher math concepts. As some previous commentator said, he never paid any attention to fractions but had a successful career as an engineer. Others suggest that fractions are critical to mastering carpentry...

While I'm no educator, it seems to me that our educational system has become largely focused on passing specific tests rather than general learning...

19. 19. tharter in reply to jtdwyer 10:24 AM 6/18/12

Well, I DO hold a degree in math. I'd say yes, fractions and the whole set of concepts related to ratios are quite key to pretty much anything beyond some simple arithmetic.

For example: differentiation and integration rely on the concept of being able to add (in this case conceptually infinitely many) fractional values together to sum to unity, you can't understand even 1st semester calculus without understanding why and how 1/2 + 1/3 + 1/4 + ... 1/n where n goes to infinity adds up to one.

Likewise even basic statistics will require you know how fractions work, as again you're inevitably going to have to understand for instance how to sum 3 or more independent probabilities (which are always fractions) and that will involve multiplying them (division).

Similarly you can't work with even simple vectors or matrices in any significant way without running square into basic division, nor even do fairly simple high school algebra without it. Linear Algebra (another low level math class that will be required for almost any sort of engineering or hard science) will thus be impossible to grasp without understanding division.

It is really a pretty basic core concept that will pop up everywhere in basic mathematics. I don't actually understand how the previous poster could state that he was an 'engineer' and never used a fraction TBH. No doubt there are jobs that don't involve doing any math yourself but SOMEONE had to do it. You're certainly not going to build any sort of structure or do any kind of non-trivial electronics etc without that kind of fundamental knowledge.

20. 20. jtdwyer in reply to tharter 07:53 PM 6/18/12

I'll have to defer to your experience with advanced mathematics education, but then I never completed a basic algebra course. My elementary education was somewhat spotty in the 4 elementary schools I attended... I have worked fairly extensively with statistics and I don't think I ever had to perform computations on common fractions except expressed as decimal numbers.

At any rate, even the referenced study abstract stresses that it identified fractional and division skills as _predictors_ of future math achievement without mentioning them as causal factors. It also states "Implications of these findings for understanding and improving mathematics learning are discussed," but unfortunately does not mention any more. Even this article states "The researchers note that it’s clear we need to improve instruction in fractions, ratios and proportions along with long division," implying to me that causation could involve more generalized issues with math instruction than specifically fractions and division...

21. 21. tharter in reply to jtdwyer 08:15 AM 6/19/12

Well, there are a few different possibilities. There are a few different basic concepts one has to understand in order to have any real comprehension of math, one of which would be ratios (fractions). If this is the most slippery concept then it is the one people are least likely to have mastered. In that case you'd expect it to be a reasonable predictor. People who don't grasp other basic concepts might be equally disadvantaged, but those same people probably ALSO don't understand fractions.

Mainly I'm just saying that the causal link between not understanding fractions and poor performance later in math will be fairly clear when you examine which concepts are built on each other. Sort of like I don't really need to spend a lot of time speculating on why my stuff is wet if there's a big hole in my roof, I just fix the hole.

22. 22. jtdwyer in reply to tharter 08:45 AM 6/19/12

In my experience, if you simply put a patch on your roof directly above your wet stuff you may find that's not exactly where the leak is...

23. 23. kgagne 10:11 PM 6/19/12

Why is she saying "kidses" and "parentses"?

24. 24. jtdwyer in reply to kgagne 03:15 AM 6/20/12

Actually, kids', fifth graders’, students' & parents' are plural possessive forms.

25. 25. tharter in reply to jtdwyer 08:07 AM 6/20/12

Does this mean we all fail at English too? ;)

Honestly, my observation is that we all have it easy, and that's got a heck of a lot to do with people just not being motivated to break down and really learn stuff...

26. 26. jtdwyer in reply to tharter 04:06 PM 6/20/12

I don't know - I hated English and math, and just about everything else in almost all the schools I attended. It seems I wasn't motivated until my tour of duty in Viet Nam... I agree that most of us have it relatively easy most of the time...

27. 27. tucanofulano 06:16 PM 6/20/12

Best way to learn the subject = betting on horse racing at odds

28. 28. tharter in reply to jtdwyer 10:00 AM 6/21/12

When I was in Kenya I'd meet teenagers there. A lot of them walk miles to school, they have to pay out of pocket (very hard there to do, they're slowly making grade school free, but just getting there is costly in time, clothing, etc). Of course there are some students there who don't seem too motivated, but most of them work their butts off and even with the schools being mud huts with a few old tattered books half the time you run into kids that are mostly REALLY motivated. You won't find too many that don't figure out there arithmetic. It is almost a matter of life and death really. The uneducated ones have very little future. I never ever heard a single complaint about school. They know exactly which side of the bread is buttered.

29. 29. 123456 04:19 AM 6/30/12

a

30. 30. clangton 09:58 PM 1/8/13

How about learning fractions verbally (also called mental math). When our daughter was in High School and about to take the SAT I found an ancient (from 1890's) book that taught Fractions verbally (or mentally if you insist). What a cool book that was! She learned fractions and I redid the book in modern lingo and published it - Verbal Fractions, without pencil of paper. Believe it or not, it is possible to be able to do all kinds of complicated looking fraction problems without any writing, all in your head.

Every one should be able to do this. This is the foundation of math for most children and those who don't get "fractions", usually end up hating math in general. You can find my book - Verbal Fractions on Amazon.
Charan Langton

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