Theory Versus Data

One of my favorite blogs, Assistant Village Idiot, has a post on Teaching Theory Before Data.  An excerpt: 

I had no idea it was this bad.  I have been hearing that parents were puzzled at math methods being taught to their children, but I figured it was just a mild inefficiency of method that they were not familiar with. We forget things, and when Jonathan and Ben were in more advanced maths I had to stare at things a while and look at the previous chapters (which I never did in high school) to figure it out.  But they were in Christian schools which taught math in more old-fashioned ways.  I recognised what was in front of me, but had forgotten it.  I could get it back. (Though they usually got there first while we were staring at it together.)

Holly Math Nerd, who I have seen quoted before on the internet, has an essay I can only describe as chilling, Light Bulb Moments Are Not Accidents.

Some of you are familiar with Richard Feynman's experience on the California State Curriculum Commission in 1964 New Textbooks For the "New" Mathematics. This is the same type of error allowed to continue unchecked for 60 years.  It stems from the idea that the theory should be taught first, before there is any data to apply it to.  Children's brains don't work that way.  Heck, our brains don't work that way. Even in later years, when children have some abstract reasoning ability, you don't teach the idea of the periodic table and expect the student to figure it out, labeling it as they go.  You put the periodic table in front of them and then start pointing out the patterns and connections.

If you want to teach maps, you start with places the child already knows, not the idea of a map.   

I've read pieces from Holly before and like the way she approaches problems but had missed this essay and was not familiar with Feynman's piece.  Read both.  An excerpt from Holly who tutors math, about her experience with a fifth grader:

This is the part that’s hard to explain to people who haven’t watched it happen: the so-called “conceptual” method didn’t deepen her understanding. It buried it.

It increased cognitive load, scattered attention, and replaced a stable procedure with constant decision-making.

The standard algorithm didn’t feel old-fashioned to her. It felt like relief.

And this is where parents enter the picture.

Even if they want to help their kids “the Common Core way,” many of them can’t. They don’t understand the methods well enough to teach them, and they’re often explicitly told not to show the way they learned.

When a child gets stuck, there is no parental fallback system — no shared language to fall back on.

UPDATE: Feb 15 - Holly just published a follow up essay on this topic.  It contains photos from a copybook used from 1814-50 to practice math concepts.  It shows the same method I used to learn basic math.

This got me thinking through my own experience learning math, something I've pondered before, but these articles added something new to my thinking.

In elementary school I was a whiz when it came to arithmetic.  When I was in 4th or 5th grade, my teachers arranged for me to teach a class of (I think) third graders about fractions.  I quickly got to the point where I could do addition, multiplication, division in my head using shortcuts I'd come up with and was very good at pattern recognition with groups of numbers.

I'd always attributed this to some combination of native ability and my fascination, from a young age, with baseball statistics.  I collected baseball cards and spent hours looking at the stats and would pour over the major league stats published by the papers once a week.  I learned how to calculate batting average, slugging percentage, and earned run average on paper and, to a large extent, in my head.  I realized that the patterns of numbers on a baseball card told stories even if you didn't know the position of a player, their physical appearance, or age.  I don't remember anything about theory; what captivated me was my interest in baseball and how to use the data.

It was only many years later, in my 30s or 40s, that I came to understand that my mind works on inductive, not deductive, reasoning.  Maybe that isn't exactly the correct terminology, but what I mean is I become interested in granular information and build my view of the world from that information; I don't start from general principles and I have little patience for abstract theory.  That has its advantages and disadvantages but I didn't choose one over the other, it's just the way I think.

Perhaps that is why what happened in 7th grade turned my math world upside down.  This would have been the 1963-64 school year (aligning with the timing of Feynman's article) and our math textbook that year looked very different from what I'd been using up until then.  We were told that the school system was introducing "new math", a completely new way of learning the subject, and we were the first class to be exposed to it.  What I remember is being completely lost.  The subject was taught in an abstract way that I could not understand.  From my perspective, it was not linked to anything useful or practical. I went from being a whiz to becoming a clod and never got my bearings back for the rest of my education when it came to math and I never became proficient in algebra and calculus.

At the same time, my facility with basic arithmetic functions became even sharper over the years and when it came to my business career proved very useful.  I can look at a page of financial data and quickly spot something that "just doesn't look right" and that leads me to ask questions, as well as spotting outright errors.  In my later years, when I did in depth reviews of operations and plant managers were putting up charts full of data I could hone in effectively on what to inquire about.  I also noticed that in power point cultures, on charts that had both text and statistics, the stats often didn't match the story in the text.  I came to realize that many people view stats as adornments or illustrations of the words in their narrative and don't think through the data in and of itself.  Journalist are notorious for this.  Back when I still read the New York Times, I entertained myself by finding examples of how far I would have to read an article before finding data that did not support, and in some cases contradicted, the words.

I also had a period where I spent a lot of time with epidemiological and toxicology studies, and data from environmental sites and found the basic skill sets from arithmetic served me well.  I may not have been the best at calculating statistical significance, but had a pretty good gut feel for it when reviewing methodology and results. 

Over the years, I've wondered if there was something I was missing once hitting seventh grade or whether a different teaching approach might have resulted in my being successful.  Still don't know but these articles about theory versus data have made me think about things a bit differently because it fits in with how I've come to understand how my mind works (or doesn't).