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September 14, 2010

Constructivist math in our society

Nick Diaz

I learned math under a solid, old-fashioned, time-honored, traditional program taught by the dear good Jesuit priests and brothers in charge of my elementary education in my native Cuba. It didn’t matter whether the math curriculum was from a textbook, or from Moses and the Ten Commandments; my teachers taught it and taught it well.


Despite the time-honored, “traditional” approach, math sometimes did not make sense to me. It never went beyond memorizing facts, memorizing formulas, and manipulating numbers. There was no meaning, no understanding, no answer to my questions other than, “This is simply the way it is.” In short, I grew up not liking math that much, because I didn’t understand it. I neither enjoyed nor appreciated its challenge. I didn’t hate math; I simply did not like it that much.


This went on for a several years, before and after moving to Frederick County in 1973. I wasn’t a “math guru” or specialist then. I (sort of) enjoyed teaching math, yet I also liked science, social studies, and language. For a number of years, math was just another subject to be taught at the upper elementary and junior high level.


Gradually, however, my personal and professional pendulum had a 180-degree swing, for better or worse.


Better, because I became engrossed in the art of problem solving. I became a student of mathematical relationships, how it works, why it works, how number theory, algebra, geometry, probability – how they fit together.


Worse, because I ended up spending too much time and effort in explaining my “discoveries” to students who really didn’t care that much for the details. I was already past the age of 30, and my students didn’t appreciate my efforts too much. For a few years, I was spinning wheels, not realizing that much of the spinning ends up in the throwing of lots of mud.


From traditionalist to constructivist, from one extreme to the other. Why was my “constructivist” period so unsuccessful? Analysis needed.


Constructivist math programs assume two facts, which are the major weaknesses of these programs and transcend many socio-economic groups.


First, constructivist math proponents assume all basic math facts are acquired, though no mastery is required at any specific level. Unfortunately, a teacher must fill in this gap with the dreaded “memorization of facts” as measured in the equally dreaded “drill and kill” timed facts tests that frustrate students who reputedly cannot memorize well.


Second, constructivist curriculum creators assume that all children come from math-rich backgrounds and have a well-developed math sense. This is the most serious mistake. Consider the following:


Children come to school unable to recognize coins and dollar amounts or to make simple change because they have not had the opportunity to “shop.” Few people pay in cash anymore. If people pay cash, the register figures out the change. There is no need to learn. Most of us have scary stories about the stereotypical sales clerk whom we’ve helped count change when the cash register goes down.


Strike one against the math sense/math rich background.


Children don’t know the simple linear measurements such as inches and feet. Simply forget metric measurement because it’s considered “foreign;” therefore, it’s irrelevant in our American microcosm. Children don’t think of time, clothing sizes, shoe sizes, height, and weight as measurement. Children don’t understand liquid or dry measurement because it is seldom used. There are too few parents who take the time to help children cook, help them garden (flowers are planted so many inches or feet apart), mark how tall they’ve grown on the kitchen doorframe, or make them aware of measurement in any way.


Strike two against the math sense/math rich background.


Few children are aware of time. Even middle school students have a difficult time reading an analogue clock. As a matter of fact, few children have ever seen an analog clock! There is no, “You have 45 minutes to play and then you need to come home,” or “The show starts at 4:10. If we leave now, do you think we’ll have enough time to pick up your sister?” Elapsed time has no meaning. Computers, cell phones, palmcorders, and Blackberries (the electric kind!) keep everyone organized and on time. Who needs clocks or timers other than educators and athletic coaches?


Strike three against the math sense/math rich environment.


How to fix this mess? Someone must step up to resolve this situation. There has to be a “marriage” between the two approaches to math. Perhaps we can take the best of each program? Can we insist that parents help develop the number sense/math rich background necessary to constructivist math? Can we teach parents to hold their children accountable for basic facts as is required in traditionalist math? Why is it the children who “cannot memorize” basic math facts, according to their parents, are the same ones who can rattle off sports statistics, Ripley’s weird facts, the Guinness Book of Records, and the words to every dirty song they hear on MTV?


On the other hand, before I lay the problem and solution solely into the parents’ laps, we teachers have to step up, too. Can we maintain our standards, and not always give the child partial credit for the least thing that is correct on a test? For example, must we reward the child who remembered to “label” the word problem’s answer, the child who chose the right operation even though the answer was incorrect, and the child who understands the concept but can’t compute the answer? From my Jesuit math, there is a right answer and lots of wrong ones.


Constructivist math at the elementary level tends to trade off accurate computation for accurate method.


What is the administrator’s role in all of this? Perhaps he/she is listening to the teachers’ concerns, actively helping them resolve this dilemma, and supporting them in the face of irate or confused parents. Sometimes, I doubt that.


I’m more afraid that the problem will become larger. What is the state’s educational role other than financial? How much input should the State Board of Education have regarding the actual curriculum used in public schools?


What is the federal government’s role other than financial? Should that government have any say in curriculum? Personally, I’d like to keep as much government as possible out of these decisions because the farther up the political line this goes the fewer educators and more accountants and political handlers are involved. The situation becomes all about dollars and cents, and political rhetoric, at that level. Is that where math curriculum debate needs to go to get resolved? Will the debate go that far? Can we keep it from going that far? Am I being ridiculous?


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