The Flawed Approach of Traditional Math, Dept.


A May 29, 2018 article about Common Core from the Yale Tribune,  references another article that appeared in the Washington Post and Chicago Tribune by Jessica Lahey. It summarizes her views about the bad rap she and others feel is being given to Common Core’s math standards:

She believes that the gap between parents and students does not necessarily lie on the Common Core itself, but on the flawed approach of conventional math education where students were taught to memorize and dutifully accept axioms and mathematical rules without completely understanding its application and the principles at work.

This view is shared by many and has become the hobby horse of the math reform movement that gained significant traction with the National Council of Teachers of Mathematics’ (NCTM’s) math standards, first published in 1989 and subsequently revised in 2000.

I have written about the mischaracterization of conventional –or traditional–math many times.   My main message is that the underlying concepts were in fact taught, and students were then given practice applying the various algorithms and problem solving procedures.  I have provided evidence of such explanations in excerpts from the math textbooks in use in the 20’s through the 60’s. Yes, the books required practice of the procedures, but they also showed the alternatives to the standard algorithms.  These were presented after mastery of the standard algorithms as a side dish to the main course.  These alternative methods are by and large the same methods that are taught today under the rubric of “Common Core Math”.  The difference is that the alternatives are generally taught before the standard algorithm in the belief that teaching the standard algorithm first eclipses the understanding of the “why and how” of the procedures.  Delaying the teaching of the standard algorithm by requiring students to use inefficient and often confusing techniques (in the name of “understanding”) can result in a confusion of what is the side dish and what is the main dish. The beauty and simplicity of the standard algorithm is lost among a smorgasbord of techniques that leave students more confused than enlightened.

In short, the ideas expressed in the two articles referenced above represent the groupthink that pervades education schools and other forms of the education establishment. The prevailing mode of thought views drills, practice and the learning of procedures as “rote learning” and prevents true “understanding”. If students “understand”, then everything else follows–the corollary of which is that understanding must come before procedure.

What is left out of such pronouncements is the difference between novice and experts. There are levels of understanding as one goes through school, and depending where one is on the spectrum between novice and expert, the level of understanding may be deep, shallow, or in between.  Procedural understanding is a level of understanding, but students who are at such level are sometimes referred to as “math zombies”.  This term is is relatively current but is what Lahey and others think is the end result of “conventional math.”  And unfortunately, their view seems to rule the roost.

For more on the notion of “understanding” and traditional math see here, and here.  Tell your friends.  Then hire a tutor.




One thought on “The Flawed Approach of Traditional Math, Dept.

  1. “Jason Zimba, one of the main writers of the Common Core math standards, explains to The Hechinger Report, that the standards enable a freedom for curriculum authors to interpret the standards in numerous ways. ‘There will be a lot of variety, and it doesn’t make sense to me to pick one thing and say it’s the Common Core,’ he asserts.”

    Zimba is wrong. The one thing you can say about Common Core is that the goal is only no remediation for College Algebra starting from Kindergarten. One implementation refers to that as their “distinguished” level of math learning. Now, many school districts are eliminating or hindering the choice of algebra in 8th grade so that STEM-goal students have to double up (somehow) in math in high school. They have no proof or examples that show this works without outside help from parents or tutors. This is systemic educational incompetence, and I haven’t even begun to talk about their understanding first/only approach.

    jl2977, who wrote the article in the student run “The Yale Tribune”, has no appreciation of what he/she had to do to get into Yale. Acceptance to Yale, like most Ivies, is not an academic sort. There are GPA/understanding-minimalist ways to get there, but they all still require much more work than what is defined by the Common Core – a fact not appreciated by jl2977.

    “One thing is for sure- whether you like it or not, Common Core is the way to go. Academic institutions need to step up and innovate new ways of learning techniques. Parents need thorough understanding of subjects to teach their children the basics, and one could benefit from getting a maths tutor.”

    Does jl2977 have any clue about how that sounds? Is this the new assumption – educators do the fun, “understanding”, group stuff and the parents and tutors have to clean up the mess. Some might claim that the Common Core will float more boats statistically, but students will never learn to fly up to Yale or any STEM degree program. This is basis of what I call a statistical, two+ generation approach to education where parents and tutors have to take an active role. I got to calculus in high school with no help from my parents. That is no longer possible, and they call it “social justice.” My son just graduated from Yale as one of their top math students, but I had to help him in K-8 in math to fix their use of MathLand and Everyday Math. All of his STEM friends had to have help at home or with tutors.


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