Thinking and Linking by Joanne Jacobs
In Jay Mathews’ Washington Post column, he asks the National Council of Teachers of Mathematics to respond to New York City HOLD’s 10 Myths About Math Education. HOLD responds to the column.
Lovely, no long division need be taught and “invert and multiply” is too difficult to remember?
Is it any wonder our children do so poorly compared to children in other developed countries with respect to math skills? A visiting Polish Control Systems professor I had ragged in our class all the time about how “stupid” American students were. He ranted how “Kids in Poland have full calculus in high school.” We thought he was a smug, arrogant SOB. I know question my conclusion. By the way, I got an A in that class regardless of my educational handicap. If I could not invert and multiply or do long division (not of numbers but of equations) I would easily have confirmed his conclusions.
I would like to add my own myth, which might be a spin-off of Myth #9 – “NCTM math reform reflects the programs and practices in higher performing nations.”
Myth #11 NCTM math covers the same material and expects the same mastery of skills as in higher performing nations.
Compare Singapore Math with any NCTM math implementation, starting from first grade, and you will see a marked difference in the amount and difficulty of problems that the students are expected to solve. NCTM can talk all they want about real-world problem solving and higher-order thinking, but the problem is that amount of material covered by NCTM math is greatly reduced. Look at the problems that each math program expects the student to solve year-by-year and decide for yourself which student has a better understanding of mathematical concepts and better problem solving capability. My son is in third grade using Everyday Math at school and I also have him do the Singapore Math booklets at home. As one of my college professors used to say: “It is intuitively obvious to the most casual observer.”
“Testimony on the Draft 2004 Mathematics Framework” by John Hoven on behalf of the Center for Education Reform (Sep 24, 2001). Hoven finds that the “hard” 8th grade NAEP problems are at a level similar to Singapore’s grade 5.
Good job Elizabeth, etal. for your work.
Not sure how much it ties into the NCTM system, but there seems to be A LOT less HW given nowadays in math. I used to have to do problems until I dreamt about whatever property we were covering…and now the kids barely get enough to show all the different applications of a property.
Thanks for the link to Hoven’s testimony. I looked at the Singapore Math problems and was quite impressed.
My son’s in 5th grade, and he uses Saxon 76. My gut feeling is that the Singapore Math is more rigorous than Saxon 76, although it’s not quite as wide a gap as in the NAEP case.
In the public schools here in California, anyone who expects anything like Singapore Math is dreaming – and I seriously doubt that we’ll see any pledges from the union to make the math more realistic.
“Not sure how much it ties into the NCTM system, but there seems to be A LOT less HW given nowadays in math.”
I just noticed that our public schools (in a few grades anyway, since not all grades publish their day-to-day schedules) that math is taught only four days a week. It did not look like the length of the class on the other days was extended. I have been struggling with this since my son started Kindergarten. Under the guise of “developmentally appropriate” and full-inclusion, it appears to me that many K-6 schools/teachers expect a whole lot less from our kids than when I was growing up. It could be that with much wider mixed-ability groups, they don’t want to pressure the lower level IEP students and therefore cannot expect more from the better students. If they expect more from the better students, then they will get too far ahead, so they have them do optional “enrichment” work. They want to treat all kids the same, but magically provide “enough” for the better students. When I ask teachers about this differentiated learning (not instruction) process, they all admit that only a few teachers can do it. I don’t know what “it” is. In my case, “it” was to have my son do more homework or special projects – more of the same (enrichment), rather than to move on to new material (acceleration).
I don’t know why they think that the large ability gap in first grade is not going to grow much larger in the following grades. One teacher told me that the gap grows smaller to about fourth grade because all of the lower level students catch up. I think that it’s just that the better students aren’t provided for their own “developmentally appropriate” needs. However, if you lower expectations to whatever the state mandates for their standardized testing, then it’s clear that the gap between the lowest level students and the minimal testing levels should grow smaller. This is not the same as the gap between the capabilities of the lowest level students and the best students.
It could be a philosophy that they want all kids to be (automatically? magically?) self-starters who will love learning and do the work without pressure, testing, or deadlines. They don’t make any distinctions between those kids who have real problems versus those who just need a swift kick in the rear. Or, to put it another way, many kids need to learn how to be self-starters by setting deadlines and expecting more of them. Perhaps they think that “love of learning” is some sort of natural condition and that any sort of expectations is going to kill that love. I want my son to learn that many worthwhile things in life don’t come easily or naturally. The problem is that some things come easily and he doesn’t want to put in the work when things get tough.
“My son’s in 5th grade, and he uses Saxon 76. My gut feeling is that the Singapore Math is more rigorous than Saxon 76, although it’s not quite as wide a gap as in the NAEP case.”
You can’t go wrong with Saxon, although I have heard some warnings about new products published under the Saxon name. (In some ways, I like Saxon math better than Singapore math.) The complaint about Saxon is that it is boring drill and kill and the kids never learn any concepts or real unerstanding. I just tell people that they have to get the two sets of books/workbooks for the two math programs and compare them side-by-side. (Or, have a scientist, engineer, or mathematician look at them.) They have to look at the homework and test problems that the student has to be able to solve each year. Then judge who has the better conceptual understanding and problem solving skills.
Most NCTM math programs spiral the curricula and allow students to slip year-to-year without fully understanding and mastering the skills. Spiraling becomes circling for some, the ability gap between the best and worst students grows, expectations are lowered, and the better students are hurt and not properly prepared for college prep or honors math in high school. Because of the lower expectations, many students have their technical career doors slammed shut by 8th grade. Well, I guess they were just not “good” in math. No, it’s the curriculum and the low expectations.
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