The best way to teach kids math is not in a classroom

Go. Out.
Go. Out.
Image: AP Photo/Patrick Semansky
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As a semi-retired engineer, I often lament efforts to remove shop, technical drawing and other hands-on classes from students’ schedules when they might otherwise understand math as just a dry academic offering. The concept that shop classes serve solely as “industrial education” fail to note its vital role in preparing future architects, engineers, scientists and more. It is classes like shop that reinforce the connection between the tangible and the symbolic—math comes alive when numbers appear as dimensions that you can see and touch. Shapes and angles are observable, and how they meet, fit and feel is appealing to the senses.

A narrowing of experience is happening in lower grades. My friend’s son was struggling with the concepts of area and perimeter, and his teacher expected each student to memorize “P = 2xL + 2xW” and “A=LxW” and take it from there. My friend took his son out to a tennis court with chalk and a tape measure. They measured the perimeter, walked around it, and marked each meter off with chalk. Then they marked off squares and counted them: how many in a row, how many rows and how many total. The lad returned to class with an indelible understanding of how to use perimeter to build a fence and area to buy carpet or paint. He didn’t need a formula because he had a physical concept.

My friend’s son was in a class that evidently “saved time” by avoiding the physical embodiments of distance, space, science, and the connectedness of the world. They went straight to the mathematical symbols and operated on the premise that all one needs to do is memorize a suitable set of rules and operate on them—independent of a vision of the reality that they represent. None of the third graders were successful under the efforts of the teacher who was just following the lesson plan.

The major task of early learning is to build a robust mind-bridge between the tangible, observable world and the symbolic world of words and numbers that we later use as a means of building more complex models. As I spend time with my toddler grandson, I am impressed by his reasoning and observation skills, even though he is barely verbal. I realize that we begin life with non-verbal reasoning according to our observations and sensations—it is only later that we substitute the symbols of language to represent the observed reality.

Neuroscientists have told us for decades that memories and reasoning are a result of connections. Memories are stronger and longer lasting when multiple observations and senses are involved. I would argue that it is a fallacy to assume that we can achieve depth in key subjects by narrowing the breadth of education. By creating artificial walls between subjects, we are attempting to teach in a manner that mimics how the teachers may have learned their subjects late in their academic careers—but it may not be an effective way to learn in younger years. Such segregation of concepts and topics may appear to be efficient, but I would argue that it is less effective.

Lists of independent facts without a network of connections are hard to follow and harder to retain. The problem reminds me of trying to dig a deep, narrow hole in dry sand. As the hole goes down, the sides collapse and fill it back in. It is possible to dig a deep hole, but only if it stretches out to the sides.

I gave a graduation speech many years ago. When asked, “What is the biggest thing you learned after you left school and became a practicing engineer?” my response was that in school, when you have an exam, you at least know what subject you are taking the exam in. In real life, you don’t know if the solution of the day will come from math, physics, chemistry, or just as likely human behavior or the quality of product instructions.

To be sure, shop classes present obstacles. The equipment is costly, the teaching skills are not so common, and the use of modern power tools and even sharp hand tools, present risk and potential liability.

We may be on the edge of a time when the tangible and symbolic are joined by the virtual. Computer generated “reality” in the form of 3D creation may be this century’s “shop class.” The math is a bit less apparent, even though there is a huge amount of math going on in the background, but the relationships of dimensions and shapes are visible. With the availability of 3D printing, even some of the tactile sensations of a shop project may be available. A virtual “shop” also reduces safety concerns, and potentially adds hours of availability. It may also be more appealing, because virtual projects are not bound by the cost barriers that could prohibit the disadvantaged from obtaining necessary materials—a very grand imagination and ambition can be accommodated at no additional costs.

I have used various forms of Computer Aided Design tools for some 30 years and I look forward the continued “democratization” of those tools through less expensive computers and less expensive software. Systems capable of CAD cost about three years engineering salary in the beginning. More powerful computers and more powerful software is available now for a few hundred dollars each. Most video games are more complex than the early CAD systems, and gaming-capable computers are easily 10 times as powerful. We have lost an important bridge between the tangible and symbolic, but with the introduction and growth of a virtual component, we may be able restore that bridge and extend it.