Maggie's Farm

The irony about the teacher talking about different approaches etc leading a student to conclude that 3X4=11 is that in most cases, the 3X4=11 answer was achieved by a S.W.A.G. Which to those who are not STEM majors, is a scientific wild-assed guess.

A further irony is that while the teacher may imagine a dialogue with students about explaining approaches etc., in most cases elementary and middle school students have no interest whatsoever in discussing their approaches. In most cases a teacher will have to drag such explanations out of students. In general, students would rather have their teeth pulled instead of explaining how they came up with a given math answer.

Too many adult educators make the assumption that what THEY like to do in learning is also what children like to do. For example, the rote and repetition used in learning to read by the phonics approach is to an adult sensibility, deadly and boring. By contrast, young children like repetition, as their knowledge base is much less than that of an adult. For a child, repetition reinforces what they have learned. For an adult, repetition is boring. How many times does a four or five year old like to have the same story being read? How soon does the adult get tired of reading the same story over and over?

In the last 40 years, math educators have added a smorgasbord of topics to be covered in the lower grades. For an adult with at least a BA in math, which would describe math educators in Colleges of Education [I hope], one more math topic is like reading one more article in the newspaper. The more the merrier, especially since they devote as much time to the new topic as they would to reading another newspaper article- as they have already been exposed to the topic. Which is not the case for the younger students.


Unfortunately, this does not go over as well for the elementary or middle school student. One more topic covered in a cursory, superficial manner - no "drill and kill" here- is one more topic that a student doesn't understand very well- if at all.

Students would be better served by learning fewer math topics in a more thorough manner.

Disclaimer: I taught math for two years.

There is something to be said for "exploration." Unfortunately for exploration-oriented teachers, the best explorations are those which teachers do not script, but when a student spontaneously discovers something. Moreover, when the discovery comes from the student's own endeavors, not from a teacher's prodding, the discovery sticks better.

But in general, most kids just want to be told how to do it. It is faster than discovery/floundering. There is a reason why Direct Instruction has lasted for several thousand years. By and large, it works.

My first 8 years of learning math were run of the mill to me, but I at least got a good grounding in the basic arithmetic operations. In high school I got exposed to New Math [UICSM]. From the beginning, we had to write proofs. In 9th grade, proofs involved the commutative, associative and distributive properties of addition and multiplication. My enjoyment of math increased greatly. At the same time, I recognize that not all students can handle writing proofs- for many or even most it is "math misery," to quote a fellow student.

My thorough knowledge of the times tables, coupled with proofs about distributive properties etc., led me to explorations in estimating. As a result, I can come faster to a ballpark estimate than most people can with an exact answer on a calculator. It's a useful skill. [I can often beat them on an exact answer.]

But it couldn't have been acquired without already knowing the times tables.

There is also a problem in teaching math at the elementary level- for many elementary school teachers, math was their worst subject. While they may not know their times tables very well, they are even less able to explain the mathematical nuances that College of Ed Math educators want elementary school students to handle.

Which reminds me of sitting in math ed courses in my middle age years. We prospective math teachers were told that we were being taught the- let us call it- New Reform method of teaching math. I said to myself, what happened to the New Math I learned when I was in high school? How many iterations of New Reform method of teaching math have we gone through? I suspect a new model ever 5 years- or less. New Improved. Yeah, right.