“Traditionalists” (as they like to style themselves) are incapable of grasping the fact that high school math exists, and that most high school math teachers aren’t constructivists.
The above quote was from a blog written by a math teacher, and was a post about an article that Katharine Beals and I wrote which was published in online Atlantic in 2015. It caused a stir among those who don’t like what “traditionalists” have to say about teaching math.
In fact, we do know that most high school math teachers do not teach in the inquiry-based manner. What we also know is that in K-6, much of math has been dominated by the math reform ideology as embodied in many textbooks. Constance Kamii’s belief that teaching the standard algorithms to young children does them harm by eclipsing understanding has set the stage for how math has been and is being taught in the lower grades. What has happened in K-6 math over the past 30 years or so, is in part an increase in inquiry-based, student-centered learning, but in larger part an obsession with understanding.
What we “traditionalists” do notice about high school math is that many entering freshman do not know basic computation rules, and are dependent on calculators. In an eighth grade algebra class which I teach (and which is equivalent to 9th grade high school algebra), I had a student who had great difficulty multiplying two-digit numbers. He used a convoluted method that took up much time. Thirty years ago, most entering high school freshmen had the mastery of such elementary procedures.
The blogger whose quote I posted also states that Beals and I do not believe that “math zombies” exist. By “math zombies” the blogger is referring to students who can reproduce procedures but lack the “understanding” to apply the concepts underlying the procedures to new or novel problems. Yes, such students exist. They are on the novice scale of learning; there are levels of understanding that accumulate with experience. Judging novices in terms of the expectation of expert performance seems to be the goal of those who are in the “understanding uber alles” mode.
Also,–based on my observations and those of people I know who teach mathematics in college–it is interesting that the so-called “math zombies” are generally the ones who don’t need remedial math in college.