Tag Archives: Pedagogy

A Close Look at Patterning


The Big Ideas in Patterningimage

In Ontario, there are five math curriculum strands that must be covered each year in elementary school. Of the five, I always gave patterning short shrift. I never really understood why having the kids make strings of red, yellow, and blue beads was relevant, and it was usually something I left to the last minute, or something I had the kids do while I assessed students or worked with small groups on “important” math.

Then, last year, I decided to find out more about it, and this past May, I presented my research and exploration of patterning at the Ontario Association of Mathematics Educators conference in Toronto. Unfortunately, I only had about 70 minutes, which, judging by the saucer eyes I saw staring back at me, was only enough time to turn my workshop participants on their heads and send them out the door, walking on their hands.

Therefore, over the next few months, I’d like to use my blog to go into more depth and engage in some discussion about what I’ve learned and the activities I’m developing.

The first thing I want to share is my list of what I consider to be the big ideas that students should learn about patterning. These are compiled and cobbled together from the NCTM standards, readings from Van de Walle and Small, and research by Joanne Mulligan. I have no idea, anymore, which ideas are theirs or mine, so lets just assume it’s all part of a Jungian zeitgeist and carry on.

  1. patterns are models
  2. patterns model relationships and structures
  3. patterns simultaneously represent consistency and change in those relationships and structures
  4. understanding pattern means being able to recognize, extend, replicate, predict and exploit those relationships and structures
  5. understanding pattern means being able to identify, diagnose, and perhaps repair breakdowns in those relationships and structures

These are some pretty big ideas indeed, and they seem a bit too grand to be achieved by stringing beads together. They are very likely not something most primary teachers keep in mind when chanting “red, yellow, blue, red, yellow, blue” with their students, during calendar time.

But as I post, I will endeavour to always refer back to these ideas, and we’ll see what other, perhaps more effective ways there are to discover and explore them. More to come.

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Experiments Will Make You Smarter


The first theme from Brockman’s collection of intelligence-fostering essays, This Will Make You Smarter, is that we would all be better off if we saw the world the way a scientist does. There are three essays in particular that extol the objective processes of the scientific method and experimentation as the procedures for doing everything, from allaying irrational fears to overthrowing fascist governments.

Full disclosure, so that you’re not changing the entire way you think based on my interpretation of a small data set. These essays are all very short, and are not to be considered exhaustive. But, they do encourage a lot of deep thinking and reflection, in me anyway.

The Controlled Experiment – Timo Hannay

This essay is about following the scientific method to make decisions in our lives. Hannay asserts that we are too quick to judge, and those judgments are based on prejudice, preconceptions, and a lack of imagination. According to him, we should be striving to be more objective and data driven, rather than going by some introspective gut feeling, or asking around to see what others think. I believe that his assertions are based on data collected in controlled experiments, but I only have his word for it.

The Double-Blind Control Experiment – Richard Dawkins

imageDawkins is of a like mind, but twice so. I will infer he has been reading the same journals as Hannay. He wants us to be critical. He also thinks we need to be more objective in the face of personal opinion, because of the bias inherent in it. He wants us to stop generalizing from a handful of anecdotes, in favour of coming to conclusions based on evidence. For him, it all comes down to improving the population’s understanding of how controlled experiments work (specifically, I believe, how they filter out as much bias and external influence as possible, ensuring that true causality is established), so that we develop a healthy, habitual skepticism that will keep us from being tricked or lied to.

Promoting a Scientific Lifestyle – Max Tegmark

In this entry, Tegmark laments the “fact” that scientists are pretty much useless at getting their message out to the public, and that, when the message is disseminated, it has often been watered down, misinterpreted, or bastardized (I’m generalizing here, but HELLOOO, every last initiative in education I’ve seen in the past 15 years).

He laments this because so many of the decisions we make in our lives are based on inaccurate and incomplete information. He believes we are too busy, too biased and set in our ways, and too overwhelmed by the volume of information available. I’m going to add too skeptical of things we think will make our lives complicated, boring, or inconvenient.

These restrictions of our intellectual development, he believes, result in us being easily manipulated into voting for stubborn politicians who turn their backs against evidence that undermines their biases. We allow ourselves to be duped by sound bites and propaganda that play into our fears and prejudices. And we end up blindly following charlatans and buying books about wish fulfillment, looking for the simple, quick fix to all our problems. If he had his way, scientists the world over would be using the same tactics as politicians and corporations to get their messages out, and that message would be “Look, smarten up.”

My purpose behind this blog entry is to explore how these ideas might influence me and my pedagogy. What would be the result of teaching students about controlled experimentation and critical thinking? Shall I question the authority of these experts before I make any decisions?

Visions of riot shields and fire hoses come to mind when I think about challenging authority. Is that what these folks mean? Do they mean rebel against authority? Don’t trust anyone over 30? I don’t want a child to touch the stove because he’s been taught to be skeptical of me when I say it’s hot. I don’t want him to find out on his own. Or do they actually mean to question authority? Well heck, I do that all the time.

Questioning is not necessarily the act of open rebellion some politicians and other community leaders make it out to be. It is just the act of asking questions. “Why is that the case? How do you know? Based on what evidence? Have you considered other data? Which ones?” I don’t really have a problem with this, as long as I have substantiated responses to provide. And as long as the student isn’t just questioning for the sake of being a disturbance, and can provide her own evidence to the contrary, if necessary. Anyone who does question can certainly be given the opportunity to find out the answers for himself, through research and experimentation. I’m comfortable with this, because I’m fine with finding out I was wrong.

Which brings me to an idea these writers have not touched upon, but I believe must be pointed out. If we are going to question others, then we must also question ourselves. Riot police are called out when two factions of self-righteous people clash. But, those who scream that they know better than the authorities inevitably end up authorities themselves, with their own violent detractors to repel. Humility and openness to others’ skepticism seem much more productive than arrogance and close-minded certainty. When we experiment, we suppose. We are bound to find some of our suppositions were wrong.

In the end, I agree with these three arguments, and yes, to acknowledge my bias, this is mostly because they match my experiences. But, when I say experiences, I mean from both perspectives. I have been on the receiving end of ignorant dictates (from several education ministers and their leaders since ’95). And, I have been guilty of an unbending, near-sighted hubris of my own (Dear Editor). I’ve made myself the authority and then been challenged because of it (Literacy Coach). I’ve challenged and been shut out. I’ve lead the charge, only to find myself the first to bare the brunt of a counter attack (Facebook Page).

If I choose to see those experiences as experiments, then I can look at them objectively. I can question myself and decide how to conduct the next experiment better. I can assess for bias. I can restrict parameters. I can gather data. I can learn.

I can use that learning to question.

I can use that questioning to teach.

Flash Cards Good, Part 1


In the past, I was an Early Literacy Intervention teacher. I worked with the weakest readers, half an hour a day, in small group sessions. One of the things I had to do was improve their sight vocabulary. I used the standard Dolch lists (words selected for their frequency in child centered texts and their irregular spellings), doing what most primary teachers would do; I wrote the words on flash cards, and drilled, drilled, drilled.

We went through each deck of cards, a few at a time, reading and spelling the words over and over. We played games like snap and memory, and whatever else I could think of, to get these words into their heads and out of their mouths.

What a waste of six weeks.

No matter what I did, whenever those same words appeared in the books I assigned, my students almost never read them properly. They never read them fast. And sometimes they didn’t even recognize them as words they had studied.

So, after permanently altering my hairline, I had to reflect and find out why this ‘tried and true’ technique didn’t work for these kids (all the time wondering if it ever has).

Here is the conclusion I drew from these results. The students I was working with could not transfer the discrete skill of simple recall to the act of reading meaningful sentences. They were perfectly fine at recognizing and naming these words in the context of a meaningless list, but they couldn’t recognize, name, or even guess at those same words outside of the specific drill activity.

Now, in this role, I became somewhat of a self-proclaimed expert on conducting and analyzing running records (having the child read aloud from an unfamiliar text while I manually record everything that the child says and does, so as to determine strengths and weaknesses in the child’s reading behaviours). The most important component of a running record is determining which cuing system(s) the child uses, be it phonics (visual), grammar (syntactical), or context (meaningful), or any combination of the three. A strong reader will use all three systems, seamlessly switching from one to another, depending on the demands of the text.

And duh, sight word flash cards only focus on the visual cuing system, and poorly at that, as there is no focus on the phonic relationships at all. It’s just, “Here’s a word, say it.” No wonder these kids don’t recognize these sight words in contexts that demand grammatical and semantic knowledge!

How did I address this? In Part 2, I will describe a sight word flashcard method I developed, which incorporates all three cuing systems, in order to teach the whole word, not just how it looks on paper.

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