Fractions are so 20th century

In a “60-second lecture,” a Penn professor argued that elementary students shouldn’t learn fractions. They’re too hard.

“I have a simple suggestion when it comes to teaching students in elementary school fractions — don’t. Fractions have had their day . . . but in this digital age, they are as obsolete as Roman numerals.”

Chris Correa provides a link to a non-fractional math lesson by the professor.

I’ve done quite a bit of algebra tutoring in the last few years. I’m dubious about the idea that students can skip basic math skills and go directly to higher-order skills. I don’t see it. I do see many confused and frustrated students.

By the way, Will Durant, who’s quoted in this much-commented-upon post, has started a blog to continue the discussion of constructivist math and education school follies.

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  1. How sad. After all, digital-worship is just more worship of the almighty 10th, as though none of us are appendage challenged.

  2. Fractions are one of the MOST practical of practical math topics.

    When was the last time you saw a “.66666667 cup” measure? Or (for those of us who sew) when was the last time you went to the fabric shop, needing 3.875 yards of chintz?

    Also, I live alone, so I spend a lot of my cooking time cutting recipes in halves or thirds. I can do that pretty fast, in my mind. It would take me longer (and a calculator) to do it in decimals. (And as noted above, I don’t have decimal measuring cups, so I’d either have to convert back or know what each decimal corresponded to).

    Yes, fractions are a bit of work to master. But once they’re mastered, they’re used a great deal in “real” life

  3. I would think that the skills required to add fractions would be directly relevant to learning algebra.

  4. The problem is, how are you ever going to figure out factoring if you don’t learn fractions? Even if you’ve completely switched over to the metric system and never see another fraction in your entire life, factoring is the single most useful mathematical skill I ever learned (besides counting). And it’s damned difficult to program into a machine.

  5. The ability to manipulate fractions is the the most important transitional skill between arithmetic and algebra (rational expressions) and algebra is the most important subject for a career in science and engineering. Often, you can judge an elementary math curriculum by evaluating how well it teaches fractions.

    It’s hard to tell whether Prof. DeTurck is joking, given that he teaches college courses like calculus and differential equations, but he does make oodles of money from the NSF for teacher training.

    “An original grant to the University of Pennsylvania’s Mathematics Department from NSF four years ago founded Access Science, an academically based community service project supported by Penn’s Center for Community Partnerships. The new funding, which is approximately $500,000 for three years, will allow Access Science to continue through 2006.”

    “The program has made a significant positive impact in science teaching and learning,” said Dennis DeTurck, the Penn mathematics professor who is leading the program. “The new NSF funding will enable us to expand our efforts to help individuals and groups of teachers to design and implement math and science curricula that are well-organized, engaging, hands-on and discovery-oriented.”

    … “hands-on and discovery oriented”. Maybe that gives us a clue.

    When does he expect schools to teach fractions, in algebra in high school? Does he think that non-math nerds don’t need to know how to manipulate fractions? Does he make a distinction between fractions and rational expressions? Does he think that the calculator eliminates the need for fractions?

    “Fractions have had their day … but in this digital age, they are as obsolete as Roman numerals.”

    That’s just plain stupid. Perhaps he has been hanging aroung Ed schools too long. If he is talking about those students who will never end up in a technical field, I would still disagree with him. Besides, how would he decide which fifth grade students are not going to end up in technical fields? Fractions are not difficult and he either wants to eliminate them completely or delay teaching fractions until high school.

    “DeTurck added that learning fractions in elementary school is unnecessarily confusing and frustrating to young children.”

    Which is it: Are fractions not necessary or is it just that they are too confusing. These are two separate issues.

    “I’ve done quite a bit of algebra tutoring in the last few years. I’m dubious about the idea that students can skip basic math skills and go directly to higher-order skills. I don’t see it. I do see many confused and frustrated students.”

    I don’t see DeTurck specifically advocating going directly to “higher-order skills”, but he does advocate top-down, hands-on learning. Whenever I hear someone talk about “higher-order skills”, I ask them to give me several specific examples of what they mean and explain how the student can get there without mastery of the basics. Often, people refer to higher-order thinking as some sort of Zen-like ability to figure out problems without background knowledge and skills. An example of this is a problem I saw once where the teacher wanted the kids to solve what was a simple two equation and two unknown problem using guess and check – no equations and no variables. I guess that learning how to define and solve equations and learning about linear independence gets in the way of higher-order thinking.

  6. Yet more nonsense from math “reformers.”

    I teach math at a two-year college and guys like this professor are going to help insure that I remain busy until the day I retire. Busy, as in “busy reteaching students stuff they should have learned in K-12 but didn’t.” You can’t do college-level math without the foundation of algebra.

    The “new-new math” which has taken over in K-12 over the last decade-plus is the mathematical analogue of the “whole language” movement which swept through English/Reading and produced a generation of functional illiterates as a result.

    “Let’s do away with fractions” comes across like just another attempt to dumb down the math curriculum.

    The poor kids who suffer through this kind of rot emerge from K-12 as functional innumerates. College-level math becomes a minefield through which half or more of these kids fail to pass.

  7. Maybe they’ll reserve fractions for “enrichment” classes.

  8. mike from oregon says:

    Another area that fractions play a huge part is construction. Years ago, they (the government and educators) tried to switch us over to the metric system – personally, I hate the metric system; and so too, it appears, did the HUGE majority of our country. As a result, construction is still done using feet, inches and fractions thereof. To do away with it is a HUGE disservice for the kids trying to learn how to live in our world. Just as if you lived in a European country, you’d be at a loss if you didn’t learn how to use the metric system (and become very comfortable with it).

  9. Walter E. Wallis says:

    On the other hand, when was the last time you saw an engineer consult log tables?

    But I think that algebraic equations might be more difficult without an understanding of fractions math. A lot of engineers would need their head rewired.

  10. Foobarista says:

    Gak! Math is So Hard, said the Barbie doll.

    Meanwhile, in the real world, about a billion kids in China and India are busily learning calculus. (Oh, by the way, last time I checked they use the metric system _and_ know fractions.) Maybe we could send these ed school profs to Beijing and Bangalore and bring over some genuine math teachers?

  11. To be fair, I strongly suspect that he meant teaching *operations* using fractions. The idea of 1/3 is not too difficult and much needed, but I can see his argument (although I don’t agree with it) that knowing how to add 1/3 + 1/4 is not a vital skill and it might be construed as unintuitive by students. Certainly, how much time do people need to to spend learning how to compute 5/8 divided by 5/3?

    Not too many people have to add fractions in such circumstances with unequal denominators, even using the imperial system.

  12. Tom West wrote:

    “Certainly, how much time do people need to to spend learning how to compute 5/8 divided by 5/3?”

    “Not too many people have to add fractions in such circumstances with unequal denominators, even using the imperial system.”

    I have never liked the argument that because the average grownup doesn’t need to know a certain topic, then we don’t have to teach it to kids in K-8, where there is usually no tracking. (I can hear the doors slamming already.) Fifth grade is about the point where kids start learning to manipulate fractions (add, subtract, multiply, divide). Learning how to perform these operations is critical as a lead-in to algebra. (besides being important in their own right) Decimals are no substitute. Instead of 5/8 and 5/3, what if you have 5/(X+1) divided by (x-1)/3? Do you think the rules change or that this operation is somehow mysteriously more difficult?

    This is another example of dumbing down a curriculum to meet some lowest common denominator of education. Oops, I guess the students don’t have to know about LCD anymore. What other topics can you pick out that are not really necessary?

    Manipulating fractions is easy. There aren’t many rules and it’s not difficult to understand why they work. If kids have a difficult time with them it’s because the teacher doesn’t know how to teach them. Perhaps the teacher doesn’t even know how to do perform the operations.

  13. Well, I’m a math geek, so I can’t really fathom how an adult mind can have difficulty with fractions.

    However, as seen from numerous posts about teachers difficulties with this sort of math, it’s my lack of imagination that’s at fault here, not the observation that many people have difficulty with fractions.

    If the reality is that you cannot get enough people who actually understand this stuff to teach, then you’ve got to adjust the curriculum to face what the new, if unpleasant, reality. To be brutally honest, most of the brighter people I know wouldn’t last 10 minutes in many of the classrooms and schools of today. Certainly I wouldn’t, and I’ve taught a lot of adults.

    [Just to be clear, I disagree with the removing fractions because in all honesty, I *cannot* believe that all but the smallest subset of teachers really do have problems with fractions.]

  14. In order to grasp fractions, you must understand basic math operations. You must be able to add, subtract, multiply, and divide. You can think of fractions as suspended division–1/3 is just one divided by three, after all. If large numbers of students can’t master fractions in elementary school, that indicates, to me, that they don’t understand the underlying operations. It’s a symptom of a greater problem.

    Fractions are used in everyday life; they’re so ubiquitous we don’t take great notice of them. Do you say, “It’s seventeen minutes to noon,” or do you say, “It’s quarter of”? Do you drive .25 miles down the road, or a quarter of a mile? They give a good approximation of the relation of a part to a whole, a better approximation, in my opinion, than the decimal equivalent. After all, .25 is just 25/100.

    I would think the ability to use fractions easily, and to understand what one is doing, would be essential to any scientific activity which uses measurement. I certainly want my doctor and pharmacist to be certain that they’ve chosen the right dosage for my weight.

  15. Steve LaBonne says:

    Perhaps ed. schools could have their elementary ed. majors spend less time on the kinds of stupid courses and assignments we so often hear about, and use the time saved to make sure they have a sound grasp of the fundamentals of arithmetic. Just a thought.

  16. Without fractions you CANNOT:

    Do Algebra

    Cook to a recipe

    Use a common American ruler

    Or even really understand decimals.

  17. Those who think that we should stop teaching arithmetic, fractions, etc. because “we have computers for that now” should reflect on their experiences with managers that were completely clueless about what they were managing.

    If you have never done these mathematical operations, you will be that clueless manager. You may have a computer to do math for you, but you have to know something in order to know what the computer can do for you and how to get it to do it. You have to know what operations to use, when to use them, and why to use them, and you’re more likely to learn that stuff by… using them.

    Besides, exercising your brain is almost never a waste of time. And it’s not like they’re teaching as fast as they can and need the extra time to squeeze everything in…

  18. Aside from the necessity of understanding fractions for post-arithmetic math, it’s essential that one understands fractions to read musical notation. Why is a 16th note half as long as an 8th note? Because 1/8=2/16, that’s why. The entire rhythmic notation of Western Music is based on fractions. So that’s just one more area of learning the progressives are making more difficult by eliminating the basics.