# Wordclouds, mathematics and building a better teacher

by | Thursday, February 02, 2017

Wordcloud created from all the words in the wikipedia page for “mathematics education”

What does a teacher need to know to intelligently integrate technology in their teaching? Or better still, what is it that teachers need to know to become effective teachers?

So this morning I was playing around with a wordcloud generator. Throwing in words from our notes from the Scottsdale Design day… and I got to thinking about how it could be used as an educational tool, specifically to teach mathematics.

Now, I know what you are thinking, Wordle’s are so passe´, so yesterday. Everybody (and their uncle) uses them and it’s not clear (at least to me) most of the time what value it is bringing into teaching. So bear with me and let me see if I can explain (a) how it can be used to teach mathematics, or at least some content in mathematics; and (b) what implications it has for teacher education and teacher professional development.

I know there are many wordcloud generation sites out there, but the one I focus on is one created by Jason Davis, and is at https://www.jasondavies.com/wordcloud/

So, this morning, I uploaded our notes from the design day into it – and made a Wordle. Actually I made 3. Here they are:

(Wordle 1)

(Wordle 2)

(Wordle 3)

Now even though these may look similar, there are important differences, and not just in the placement of the words. The key difference is in relative sizes of the words in the Wordle. For instance, see the relationship between “students” and the word “flexible” in each of them. The word “students” gets larger from Wordle 1 to 3 while “flexible” becomes smaller? Why is that?

Turns out it all depends on a set of choices given by Jason, more specifically as follows:

Depending on whether you choose log n, sqrt n or n you get different designs. Why the heck is that and why do we care?

So I jumped onto Google and got the graphs for the three functions. You don’t even need a special graphing calculator or software. Google just gives it to you. Here are the graphs:

As you will see above – the main difference between these three graphs (for logx, sqrtx and x) is how the lines grow and flatten out (or not) loosely speaking. The steeper the line the greater the contrast between the larger and smaller words. In other words as we move from, n to sqrt n and log n the manner in which the words are weighted changes – based on a mathematical formula. The graph for is linear, while those for logx and sqrtx, are non-linear (i.e. not a straight line). In addition the graphs for  logx and sqrtx differ in how they slope as we move away from 0. The graph for logx flattens out faster than the graph for sqrtx. That is just a property of these functions.

Now imagine if I were to determine the size of words that go in the wordle based on each of the equations. So we let the number of times a word occurs in a text along the x axis. In the case of the the linear graph (y=x) the more times a word pops up the larger its y value would be. However, for the same value of x the the point on the axis for the other two would be different. So in the case of y=x, the difference between the most used word and the least use word would be huge, less so in the case of sqrtx – since it flattens out relatively slowly, compared at least to logx which flattens out the fastest. So here we have a great visual representation of the manner in which these 3 functions behave.

Now imagine a lesson plan that teaches students about such graphs using Wordles. How cool is that, what a wonderful way to show the presence of mathematics in, what is effectively, word counting. Thus an abstract idea of growth and ratios and equations that is mapped out in a relatively concrete manner in a wordcloud.

Now imagine a teacher who can “see” this opportunity, is willing to play and then create a lesson plan.

The point here not about wordclouds – but rather about how we see the world, in this case through a mathematical lens.

Other disciplines will provide different opportunities.

Which brings me to my main point.

That’s the teacher we want to create. That’s about creativity, flexibility, deep knowledge of content and a willingness to play. It is about being opportunistic and always being ready.

The question then becomes – what do WE, as teacher educators and faculty members in a college of teacher education, need to do to create this kind of a teacher? That is our challenge.

In fact, I would argue that this challenge goes beyond technology integration. It is really about helping develop a mindset that is always curious, always seeking new ways to think about content and presenting it to our students.

It is a challenge worthy of effort, and if we won’t do it, who will?

A few randomly selected blog posts…

## Partial to PartiallyClips

I Stumbled Upon PartiallyClips, a web-based comic strip based on clip art. The rules are simple, "No changes to the art from frame to frame ... Never use the same clip in two strips. No repeating characters." It it amazing just how well this works, despite these...

## What is this thing called text?

Steven Johnson has a great essay on the future of text title: The Glass Box And The Commonplace Book. I recommend reading the full thing but here is a quote that sort of captures his vision (though there is more, much more). Here is a great quote: WHEN TEXT IS free to...

## The end of practical obscurity

There is a somewhat troubling story in NYTimes a couple of days ago: (If You Run a Red Light, Will Everyone Know?) about CriminalSearches.com, a free service that lets people search by name through criminal archives of all 50 states and 3,500 counties in the United...

## The opposite of truth

Niels Bohr, the 1922 Nobel Laureate in Physics once said: The opposite of a correct statement is an incorrect statement. The opposite of a profound truth is another profound truth. I was reminded of this when I saw this TED video. Check it out... (h/t Andrew...

## Post-lunch session: Geetha Narayanan

Geetha Narayanan, Director Mallya Aditi International School and Srishti School of Art Design and Technology, is someone I have wanted to meet for a long time. One of the pleasures of of this conference is getting an opportunity to hear her speak ... and I was not...

## (de)Signs, a series on Slate

Slate magazine is running an interesting series by Julia Turner on signs and their design. Two articles are now up The Secret Language of Signs: They're the most useful thing you pay no attention to. Start paying attention. Lost in Penn Station: Why are the signs at...

## Infinite Regress: New ambigram / visual pun

You have wakened not out of sleep, but into a prior dream, and that dream lies within another, and so on, to infinity... The path that you are to take is endless, and you will die before you have truly awakened — Jorge Luis Borges Borges’ quote of reality being a...

## It’s all Greek to me: TPACK commercial

Last summer Matt and I created a couple of TPACK commercials for a video presentation we had been invited to make at ISTE in Denver. You can see the commercials here and here and the entire video here. Recently, Spyros Doukakis, a PhD candidate at the University of...

## Wordle, McCain v.s. Obama

As I was playing with Wordle (see previous postings here and here) I realized that it could be used for political analysis. So here are John McCain and Barack Obama's acceptance speeches as a word-map. Can you without, my telling you so, figure out which is which? A...

1. Punya,
This post highlights an amazing insight into the presence of math in “word graphing.” Thank you for sharing!

On a different note, when I taught high school, I changed the method in which my students and I went over our course syllabus. “Going over the syllabus” on day one always seemed incredibly boring, and obviously, my students never seemed highly interested. That is so wrong for our first day of class!

So, I put our syllabus into Wordle, and students spent time analyzing the word cloud, making inferences, and determining meaning. They then shared with me, and their classmates, what they thought the class was going to involve, as well as the overall themes to our course. Flipping this entire process made it more engaging and student centered.

Here is a link to they syllabus: https://www.scribd.com/document/338562496/Zoology-Syllabus-Copy
Here is a link to the word cloud: https://www.scribd.com/document/338562614/Zoology-Syllabus-Cloud1

Thanks again for sharing!