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As Long as We Remember...

August 18, 2009

A Brave New World Sixth Grade Math

Nick Diaz

The job of the typical middle and high school mathematics teacher is a challenging one, as evidenced by the kinds of questions and statements made by students, parents, and school administrators; these are the people who comprise our “constituency,” if I may.


For most of my 30 years with Frederick County Public Schools (FCPS), I was a mathematics teacher at the middle school level. Most of those years were invested in the teaching of sixth-grade students, fresh from six years at the elementary school level. Sixth grade is a frightening time for so many students, and yes, for many of their parents as well.


– Where will my locker be?


– Can I memorize my locker combination?


– Will I get to class on time?


– Will I make friends? Will everyone hate me?


– What if the 8th graders pick on me? (In other words, will I end up stuffed in a locker?)


Adjustment to a large public middle school for most children is a chore, a career goal, in and of itself.


In addition, we mean old sixth-grade math teachers make it doubly difficult for students to make that adjustment due to the nature of mathematics as a discipline, and also because of the subject-oriented background of middle and high school teachers. This is in direct contrast to the more common student-centered attitude of many elementary school teachers of mathematics.


Math, as a middle school course, regardless of “level,” is much more difficult and demanding than the math taught at the elementary school. There are many reasons for this increased difficulty:


1.) Class time allowance. Typically, a math period at the middle school ranges from 50-to-90 minutes, depending on many scheduling factors. A 50-minute math period one day could be followed by a 90-minute math class the next.


2.) Amount of material covered in course. Middle school math teachers reasonably expect students to have mastered (not just having been exposed to) most of the more routine computational skills.


3.) Sixth-grade math is typically the beginning of the study of mathematics as a discipline, as opposed to the learning of arithmetic.


What is arithmetic? It’s the mastery of algorithms – a definite list of well-defined instructions for completing a task. Given an initial state, this task will proceed through a defined series of successive states, eventually terminating in an end-state. Mastery of arithmetic and its common algorithms is what middle school math teachers expect students to demonstrate, right from the beginning.


On the other hand, what is mathematics? Nineteenth-century math guru Benjamin Peirce referred to math (or “maths”) as “the science that draws necessary conclusions.” To me, math is the tool mankind uses to improve its understanding of the world and to make sense out of its perceived randomness. It is in sixth grade that students are introduced to mathematics, and taken beyond arithmetic.


So, why is it that middle-school math teachers consistently find themselves fending off questions and protests from students and parents, particularly the latter, such as:


– Why does my child have to learn this vocabulary, (or these axioms, or these laws, or these rules, or these abstractions)? He’ll never be a mathematician!


– Can’t you get through life without fractions? (It’s a commonly known fact that five out of three people do not understand fractions…)


– I’ve always been bad at math. How do you expect him/her to understand this stuff? (A common complaint by mothers, particularly about their daughters).


– Why does my precious child have to learn this stuff when he/she can just use a calculator?


And the best of all, the most common ailment:


– My child always got A’s and B’s through elementary school, so why is he/she getting C’s and D’s (or worse…) now?


The implication of this last statement is that, of course, the child would be getting A’s and B’s if only you, the teacher, weren’t such a mean and/or bad teacher. If Johnny gets a “C” in 6th-grade math, he won’t get into Harvard or MIT… Laughable, but I’m not exaggerating that much, people!


So, why is it that so many students, who previously had performed reasonably well in elementary school math, now find math difficult to fathom, understand, and apply at a satisfactory level?


It could be because math, as a discipline, requires a student to perform two activities that cause great pain and suffering: reading and thinking!


I’ve been guilty for almost four decades of imparting such pain and suffering on poor, downtrodden little children, by expecting them to read and think, as well as to listen, apply, conclude, deduce and induce, evaluate, elucidate, interpolate, and extrapolate.


In other words, being able to multiply a four-digit number by a two-digit number is not enough to secure a good grade in middle-school math, although it certainly does not hurt.


Thinking mathematically does not equal computing, is not performing arithmetic, and is not performing empty, meaningless algorithms. On one hand, middle school math teachers want all students to perform the four basic operations with ease; on the other hand, they want students to understand that mathematics extends the mind well beyond the mechanical, and into the intellectual realm.


Middle school math teachers want thinkers, not mechanics, in our math classes. Mathematicians are basically lazy people; my best, most proficient and efficient math students have always been a bunch of lazy bums, like me. I’m the head bum. I take delight in being surpassed in laziness, the good laziness, by many of them, more often than I would care to admit.


By “laziness” I mean “efficiency,” which I define as “the ability and willingness to perform the greatest amount of work, in the least possible amount of time, of the highest quality, and with the least amount of effort.”


To parents and grandparents of students entering sixth grade, allow me to recommend that you go into your school building in the near future and make it a point to know your child’s sixth-grade math teacher.  Establish lines of communication right away, and, most importantly, support the teacher in his/her effort to expand your child’s intellectual horizons via mathematics, as opposed to arithmetic.


Questions or comments? Contact me at


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