More of the Same, Dept.

A recent article in “Smart Brief” argues that if you change parents’ attitudes about math, you will change the childrens’. This makes sense, but the devil is in the details as they say. The study the author describes (and which she conducted) to substantiate this, views the changing of parents’ attitudes as educating them in the alternative strategies that students are forced to learn in lieu of the standard math algorithms. The standard math algorithms are now delayed until 4th, 5th and 6th grades per the prevailing interpretation of Common Core–and the textbooks that put this interpretation into practice.

The starting thesis for the article is as follows:

“Many parents’ beliefs about effective mathematics instruction are inconsistent with current research.”

Depends what “current research” you’re looking at I guess. I wouldn’t know reading this article, because the author doesn’t cite any. She refers to parents’ attitudes toward the Common Core math standards as a “misunderstanding”. Interesting choice of words. I’d say that it’s probably a case that the people who think the “understanding uber alles” approach of the Common Core math standards is effective, is a misunderstanding. A misunderstanding about what understanding in math is about.

“Parents try to explain computation the way they learned it a generation ago. Children partially learned a different strategy or algorithm earlier that day but can’t put all of the pieces together. They can’t make sense of the procedural-based traditional algorithm parents are showing them. Parents can’t make sense of the concept-based algorithm or invented strategy the child is showing them. The session often ends in tears.”

What the article doesn’t choose to say is that the standard algorithms that the parent teaches their frustrated children generally works well. She says the opposite–they can’t make sense of it. Characterizing the standard algorithms as something the students can’t make sense of is inaccurate. And the standard algorithms for multiplication, division, addition and subtraction can be explained (and were in the older textbooks) in terms of their conceptual underpinnings.

As far as what the author refers to as “concept-based algorithms” or “invented strategies” (which the students likely didn’t invent but had them thrust upon them by a CC-aligned textbook), these are nothing new. They were taught also in earlier eras, but after the standard algorithms were taught and mastered. There were strategies like “making tens” or adding from left to right. For example 56 + 79 can be done by adding 50 + 70 (or 120) and 6 + 9 )or 15). The partial sums are added to get 120+15 or 135.

Ironically, some of these techniques were sometimes discovered by the students themselves. Now, however, it is a mish-mash of these techniques, taught to ensure that students “understand” what is happening with place value. The belief is that teaching the standard algorithms first obscures the conceptual understanding.

Adding to that students’ confusion, they are also required to make drawings of what is going on, in the belief that “visualizing” the math is understanding. What results is confusion of a plethora of techniques, like a dinner of side dishes. The standard algorithms do not stand out as main dishes, but just another side dish and they often are left wondering which side dish would be most appropriate for the problem at hand.

I had an algebra student who had to multiply two two-digit numbers. He used a convoluted partial products technique that took up much space on his paper and which he had trouble doing. I tried to show him the standard algorithm, but the habits were set and it was just more confusion.

The thrust of the “study” the article examines is that by educating parents (and pre-service math teachers) in the alternative methods and strategies, it boosted parents’ confidence as well as their children’s. I would like to see the study, Actually, I wouldn’t. I’ve seen similar ones. They lack control groups in general, and contain an inherent confirmation bias.

The author, Carol Buckley, is identified as an associate professor of mathematics at Messiah College in Pennsylvania. I looked her up. She has a B.S. in Elementary Education and an M.Ed. in Curriculum and Instruction from Shippensburg University; and an Ed.D in Educational Leadership from Immaculata University. But no degrees in math.


2 thoughts on “More of the Same, Dept.

  1. Students tell their parents they don’t understand discovery math and they teach them what they know – traditional algorithms. This is unlikely to work well because any technique has to be taught over time in incremental steps and parents are conflicting with what’s taught at school. When the child gets back to the discovery approach at school, things only get worse, especially if the teacher intervenes.

    Parents wouldn’t intervene unless they saw a problem. How would changing parents’ attitudes help? Would they then tell the student to go back to school and ask the teacher for help? Does she really mean that parents should learn their discovery techniques to help at home (“educating them”)? They need to have a program to do that. I remember thinking when my son was young that schools held open math nights because they want us to be helpers at home and do far more than turn off the TV and make sure that the math homework was done. But modern K-6 math curricula have little to no math homework any more. What specifically do they want us parents to do? We are not mind readers.

    Ignoring the fact that some of us STEM parents know far, far more than pretend mathematics professors, they come up with a new way of teaching that they KNOW parents don’t understand, but then complain about parents giving conflicting instruction when problems arise. The first question is when did they decide that parents have to be home content helpers and teachers? Why is that necessary? What happens to kids whose parents don’t have the time or ability? Is it just an attitude they expect to change or do they want us to learn to be push their nonsense at home?

    “The thrust of the “study” the article examines is that by educating parents (and pre-service math teachers) in the alternative methods and strategies, it boosted parents’ confidence as well as their children’s.”

    So the kids being taught by the parents have no math problem? It’s just a confidence” issue? Never mind that they can’t DO the problems, you just have to “Trust the Spiral” or whatever the latest mantra is.

    Poof! Problem gone!

    If you do it well enough, then students will end up blaming themselves when the world changes in high school and college. I saw it happen. “I’m so stupid!” Nobody asks us parents of the best math students what we had to do at home or with tutors. It was not discovery math.

    Liked by 1 person

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