Old New Math

“New Math” was new in 1923, writes Chris Correa.

In 1923, the state of U.S. mathematics education was not good. Fewer than half the sevnth-grade students in the U.S. could correctly convert one fifth into a decimal.

A New York Times article from December 9, 1923 reported the Teachers College was going to solve the problem by introducing a new kind of mathematics teaching into U.S. classrooms. Teachers would “abandon drilling” and “bring mathematics close to every-day life” to improve students’ mathematics achievement. As the article explains, children are not attracted to “abstruse mental operation,” so concrete and applicable mathematics problems would increase their motivation and deepen their understanding.

The National Council of Teachers of Mathematics reforms sound exactly like the reforms of 1923, Correa notes.

Featured in Week 14 of the Carnival of Education.

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Comments

  1. The reason kids do poorly in math can be for a number of reasons, only one of which is how you go about teaching the material. Labels don’t help much either, since “New Math” has been used several times over the years. You really need to look at exactly what is being taught and what level of mastery is required year-to-year.

    The big problem with the current form of New, New Math or reform math is that it lowers expectations of knowledge and mastery and hides it with flowery terms like “critical thinking”, “discovery”, and “real-world problem solving”. Looking at many state defined frameworks and standards does not help much because they are not specific. You need to see exactly what problems they expect the kids to solve each year before they can move on to the next grade. When comparing two methods, you have to set the two textbooks or workbooks side-by-side for each grade, look at the tests, and look at the performance expectations. Compare the questions with the specific California math standards or the Singapore Math workbooks. Arguing over teaching methodologies doesn’t matter much if the content and expectations vary greatly.

    The big fallacy for most ed school math teaching systems is that they think that there is some magic way to proficiency in math without a lot of individual hard work and practice. They attempt this by redefining math. How one teaches (or facilitates) and learns become more important than basic skills to the point where basic skills are never mastered. They also spiral the material which allows many students to slip along to the next grades without mastering the material, thereby increasing the capability gap and slowing down the better students.

    The goal in lower school math is to prepare every student to take a full, real course in algebra by eighth grade. Many schools provide some sort of pre-algebra or pseudo-algebra course, but it isn’t the same. It just guarantees that the only students able to take college prep, honors or AP math courses in high school are those who get help at home or with tutors.

    Yearly mastery in content and skills is critical in math. One can ignore teaching methodologies completely and work backwards from AP math to see exactly what kind of algebra course is required for eighth grade. Not every student will be able or willing to take algebra in eighth grade, but the lower school darn well better provide a proper path to that course for ALL students. Unfortunately, modern reform math programs do not do that, no matter how much integration, discovery, or critical thinking they use.

  2. Mike in Texas says:

    Steve wrote:

    “real-world problem solving”.

    “Real world problem solving” is what’s on the standardized tests being pushed by the “reformers”

    I wonder if I would be labeled “old school”? I think you need to learn the basic facts, how to add, subtract, multiply and divide before you can conquer the other stuff.

  3. I think you need to learn the basic facts, how to add, subtract, multiply and divide before you can conquer the other stuff.

    Learn, yes. Master, no. That’s what calculators are for.

    I was never all that good in arithmetic, only in other maths. I was so happy, and proficient, when the state curriculum switched to algebra and geometry in grade 8-9. Of course, I secretly mastered that material on my own long before, but never could multiply 283 and 506 in my head. Teachers couldn’t believe it.

    Is to reasonable to require a civil engineer to be a journeyman carpenter or bricklayer first? No.

  4. MiT wrote:

    “Real world problem solving” is what’s on the standardized tests being pushed by the “reformers”

    “I wonder if I would be labeled “old school”? I think you need to learn the basic facts, how to add, subtract, multiply and divide before you can conquer the other stuff.”

    The simplistic categories are “traditional” versus “progressive” and one of the distinctions between the two is a different approach to the basics; bottom-up (from the basics) for the traditionalists and top-down (integrated or thematic) for the progressives. A top-down approach is most dangerous for math because it will fail at both ends of the basic knowledge-concepts spectrum.

    As for standardized testing, there are both kinds of tests; conceptual, integrated, or top-down approach and those that cover just the basic facts and skills. I have seen them both. Our state uses the NSRE exams, which is of the integrated or top-down approach, and pushed by the progressive educational reformers in our state. In math, this means that they give more general problems where you can get full credit (I’ve seen the rubric) even if you get the answer wrong. You have to explain what you are doing and the test graders try to break down the integrated problems into scores for number sense, problem solving, and so forth. The test is rather short and it’s hard to believe that the results don’t vary quite a bit due to small changes in questions and graders.

    On the other end are tests like the NAEP test which cover just the basics. My favorite is the 4th grade question that asks how many fourths in a whole? About 50 percent got that wrong. This test doesn’t ask any conceptual or big picture knowledge questions. Many feel (myself included) that if you can’t get these basics right, then why bother asking higher-level conceptual questions that are hard to grade anyways. Some feel that there is other knowledge that makes it OK not to know these basics. I don’t.

    For either type of test, however, the questions are trivial. One “conceptual” NSRE 4th grade math question showed a bar graph with 4 bars; the results of a student election. Bob got 16 votes, Sue got 12, and so forth. Question one: Who won the election? Question two: How many total votes were cast? I think the allotted time was 20 minutes. It’s hard to believe thinking back when I looked at the exam, but it was either 15 or 20 minutes.

    NCLB doesn’t specify what type of test should be given; it is up to each individual state. My problem with NCLB is not that it requires testing. It’s that the tests are selected and/or designed by those who are being held accountable for the tests, have very easy questions, and are graded very easily. This will institutionalize very slow improvement towards a minimal goal. I am all for testing. It’s just that the tests have to be improved and the expectations raised.

    When people complain about standardized testing, they should make it clear whether they are opposed to any kind of testing or whether they are opposed to only a certain type of test or questions.

  5. “Learn, yes. Master, no. That’s what calculators are for.”

    The basics in math are not just add, subtract, multiply, and divide. Reasonable people can disagree about how many digits you need and how many problems you have to solve by hand for long division, but that is not what is going on here. It’s much more than that.

    I’ve seen these arguments for the last 30 years; between hand work and calculator or computer use. There are some who feel that everything has to be done by hand before you can use a calculator or computer. Then, there are some on the other end who feel that calculators will magically make mastery of any basics by hand unnecessary. However, it is not just a matter of finding some middle ground. Each topic has to analyzed separately.

    One of the problems is that teachers think that the calculator will make math easier. Actually, it should make math harder, requiring students to understand more advanced calculation techniques. That is not what is happening. I was in college when they changed over from slide rules to calculators. Life got more difficult, not easier. Tests now required symbolic manipulation and the 5 page hand calculated homeworks turned into 30-40 page calculator homeworks that involved much more sophisticated methods that couldn’t be done before.

    “Is to reasonable to require a civil engineer to be a journeyman carpenter or bricklayer first? No.”

    Well, why does a CE need to go to college and take all of those engineering courses? Civil Engineering is just a bunch of code books isn’t it? Do you really need all of those basic engineering courses just to plug numbers into empirical formulas. You could have a computer program to do that and just go to vocational school.

    Perhaps you would like it better if you started off as a freshman in college with the code books and the professors would try to work their way down to the engineering basics. Wouldn’t that be fun and effective? Civil engineers can disagree about what knowledge, skills, and mastery (by hand or by computer) are necessary. But, do you want educators, with little or no understanding of your field, deciding that for you?

  6. “The big problem with the current form of New, New Math or reform math is that it lowers expectations of knowledge and mastery and hides it with flowery terms like “critical thinking”, “discovery”, and “real-world problem solving”. Looking at many state defined frameworks and standards does not help much because they are not specific. You need to see exactly what problems they expect the kids to solve each year before they can move on to the next grade.”

    I always look forward to Steve’s comments. They are some of the most lucid writing on education.

    I wonder if progressive/constructivist education is some kind of Hydra-headed monster that we are condemned to live with forever. I see so much criticism and loathing of this ideology but it does seem to make a dent.

    I wonder if Steve could outline a strategy or make suggestions on how to combat this monster?

  7. “I wonder if Steve could outline a strategy or make suggestions on how to combat this monster?”

    How can you change a monopoly that has certain unassailable assumptions and allows no way for change? Even our school committee would have a very difficult time doing that. You could say I’m pessimistic. This pedagogy is what ed schools teach their students as being the one and only way. Is it possible to become a teacher without being indoctrinated? I have seen an analysis of some ed school courses and texts. It’s quite amazing.

    Many parents, however, have a quite different opinion over what constitutes a good basic education. The affluent get to choose. The poor do not. Is it OK to let the affluent kids go to private schools and not the rest? Do they think these parents are just stupid or elitist? If they think (deep down) that these students will get a better education elsewhere, then why not allow the others to choose? Our public schools are trying to stop kids from going to charter schools because our schools are “high performing” according to the state’s trivial standardized tests. Do they believe that these parents are stupid and that the child won’t get a better education? No, this is all about money and control of everything: philosophy, basic assumptions, and curricula.

    I have seen some very weird charter schools, mostly because our state would never allow a charter school that set high standards. They can’t risk the mass exodus from the public schools. Some think that choice won’t work because choice will only be choice for a few. (In other words, supply won’t meet demand. The question is why is there this demand in the first place?) Generally, these people are the ones too eager to call choice a failure “a priori” – to go back to what? Full vouchers are probably politically impossible unless the poor demand it (which they should do). Charters, unfettered by restrictions, are the most likely way to break the monopoly, but they have a big battle to fight. Parents need to form their own union and assert some power.

  8. Michelle Dulak Thomson says:

    beeman,

    . . . never could multiply 283 and 506 in my head.

    Not to belabor the obvious, but the question would’ve been whether you could do it with a sheet of paper and a pencil.

    Would you agree that students ought to be able to multiply 2 two-digit integers w/o a calculator? Because if you can do that, you can multiply any two integers with any number of digits; it just might take awhile 😉

  9. methods says:

    My mathematics professor, R.L. Moore, seldom deviated from the outstanding (unsolved) problem set but spoke out of the blue one day to the “new math” fad saying there wasn’t anything new in it. I’m not sure what he’d think about the “new new math” but he was a renowned pugilist at The University of Texas.