You Need To Master Fundamentals Before You Can Think Critically

Christopher Gearson wrote a one-sided article for U.S. News and World Report praising the Common Core.  It’s entitled “High School Students Need to Think, Not Memorize.”  He writes:

In math, the shift is away from lectures and rote working of equations to the practical application of mathematical processes, often in teams, to real-world situations. High school math students might use probability to make decisions, geometry to design a bridge, and statistics to create surveys.

In order not to “bore” kids and get them to think creatively it seems that we are putting the cart before the horse.

You need to master fundamentals of any given subject, including math, before you can think critically about the subject.  For instance consider this news release from Carnegie Mellon University in June – “Carnegie Mellon-Led Research Team Finds Knowledge of Fractions and Long Division Predicts Long-Term Math Success.”

A research team led by Carnegie Mellon University’s Robert Siegler has identified a major source of the gap – U. S. students’ inadequate knowledge of fractions and division. Although fractions and division are taught in elementary school, even many college students have poor knowledge of them. The research team found that fifth graders’ understanding of fractions and division predicted high school students’ knowledge of algebra and overall math achievement, even after statistically controlling for parents’ education and income and for the children’s own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication. Published in Psychological Science, the findings demonstrate an immediate need to improve teaching and learning of fractions and division.

You can’t bypass rote memorization and working of equations in order to learn this. One of TAE’s friends, Niki Hayes, brought some great points in an email this morning about how little this approach has helped kids, I thought I would share:

…the effort to focus on concepts rather than procedures (knowledge of fundamental mental math for quick recall of multiplication facts, for example) has been the philosophy since 1989. That year, the National Council of Teachers of Mathematics published their landmark “national math standards for K-12.” The whole new focus for the nation was to be on process–the “joyful journey”– rather than “rote memorization” and cold, accurate answers. It was said by NCTM leadership that analytical and linear mathematical learning had (for 2,000 years) been focused on white males (and Asians). This was declared in spite of the discipline of mathematics having been created by diverse cultures from around the world for two millennia.

The equity focus was to be on girls and minorities (except Asians, who learned like white males). Everyone “knew” that girls and African Americans, especially, learned in groups with projects and lots of cooperative talking over the problems as they “discovered” the answers for themselves.

How’s that worked for us? Let’s see: Up to 40% of all university students and up to 90% of all community college students must take remedial math now.

The silly notion that “memorization” is bad, having to learn specific skills in a discipline is always boring, and a giant leap to creative thinking is possible for all students is beyond common sense. Results matter. We are seeing the results of our intellectual pursuit of higher thinking which are not built on a solid foundation of knowledge and skills that sets up conceptual understanding.

Here’s an analogy: Let’s have all music students be taught to play an instrument by ear, rather than forcing them to memorize and drill on notes and scales. We could then see what would happen to the musical achievements of our students and our country’s frustration when trying to figure out “what’s wrong with the kids and teachers.”

HT: Betty Peters