Mathematical Concepts Through Images

What I’ve Been Reading:

I’ve been putting off this post for a long time.

I’ve never used images in my teaching before; nor have I, before, really considered using images in my teaching. So, because of this, it was tough to get started on this post.


The following animation I came across one day on Wikipedia when I was reading about pi. It demonstrates the relationship between diameter, circumference and pi………. very effectively.

This (the relationship between diameter, circumference and pi), from my experience, is something students have trouble understanding/visualising.

The current book we’re using in class doesn’t do a great job of explaining this relationship. And, to make things harder for the students, I too have a tough time explaining it.

It’s (the animation) something I’m definitely going to use next school year when I teach area of a circle again.

The next image, I’m planning to use when I teach functions again next school year.

In many ways, a function is comparable to a machine (or at least this type of machine) (and by the way, I have no idea what this machine does.) They both take an input. They both do things to this input. And, finally, they both give an output.

I might need to photoshop input and output arrows into the image. Input on the left and output on the right. I might also need to photoshop a function into the image (just above the machine) so that students better understand the analogy.

Image Credits:

Looking Back on Course 3

The Workshop with Andrew Churches and Kim Cofino
One of the big things that I left this workshop with was the project plan (and assessment rubric) that my group wrote up and the subsequent project that we implemented.

My team was made up of three science teachers, one mathematics teacher and me, an IT teacher. Two of the science teachers taught chemistry and the other taught biology. Anyway, as you might expect, our project was chemistry-related.

I just want to insert here that I’ve never studied chemistry before.

After we were all given the green light to begin our projects, one of the chemistry teachers threw out (onto the table) chemical bonding as a possible topic on top of which we could base our project. I had never heard of chemical bonding before in my life.

After a couple of laughs and a bit of discussion, it was decided: chemical bonding was to be the topic.

I’m going to stop here on this thread. But, before I do, I just want to mention that the project plan, in its current form, really isn’t of much use to me and my students, as we study technology. So, when I get the time, I think I’m going to spawn a new version of the plan. In this new version, the topic being dealt with will be computer networks; specifically, the different types of topologies (and maybe protocols.)

I’ve embedded at the bottom of this post the project plan that we came up with.

More Reflection
I’ve been introduced to a variety of social media in Course 3 that I’ve never encountered before. Digital stories and infographics are two of these. Both are powerful ideas. (To read about how I plan on integrating digital stories and inforgraphics into the classroom, please refer to my posts below.)

Course 3 also introduced me to the idea of visual literacy for the very first time. Wow. What an incredibly important ability (is that the right word?) visual literacy is.

As a result of all the visual literacy reading we had to do, I’ve changed the way I blog. I’ve changed the way I take pictures. I’ve changed the way I make presentations. I’ve also changed my mind on what I regard as a beautiful blog, what I regard as a beautiful presentation and so on.

Bring on Course 4!

Image Credits:

We’re Going on a Bear Hunt (2TechKrew Remix)

What I’ve Been Reading:

We’re Going on a Jaguar Hunt
In my grade 2 technology class, we’re doing a remix of the well known children’s book, We’re Going on a Bear Hunt. (I didn’t think any of my classes were doing anything remixish until I sat down today and thought about each and what they’re doing… the wonders of reflection.)

The name. Where do I start.

Grade 2 have been learning about rainforests in homeroom. They have also been learning about the animals that inhabit rainforests. And the jaguar is one of these (or at least I hope the jaguar is one of these……………….. Just checked. Yes, jaguars inhabit rainforests of Central and South America.)

Stone Zoo Jaguar Pattern

What About the Book (the Real One)? What Is It About?
The real book is about a family that goes off in search of adventure (I think that’s right.) After venturing through some pretty inhospitable habitats, they encounter a giant bear in a cave that scares them, and chases them all the way home, through all those inhospitable habitats. I think that’s the way the story goes.

Anyway, in our remix of the book, a class of Saint Maur students go off on an adventure, passing through all these different habitats (including a rainforest) and then at some point, encounter a jaguar that scares them all the way back to their classroom.

Technical Stuff
We’re doing all the pages of the book in Paint. (I must say, the new version of paint that comes with Windows 7 is pretty nice. They’ve made some huge improvements to it, such as the variety of brushes on offer.)

Next, we’re uploading the pictures to VoiceThread, ordering them and then overlaying some narration.

I have two grade 2 classes and neither of them have finished the project yet (by the way, I’ve assigned one page to each student, including narration.) But, once they’re finished, I’ll be sure to link to them right here on my blog.

Image Credits:

Infographics in the Classroom

What I’ve Been Reading:

I really like this infographic. One reason is because, more so than other infographics I’ve come across, it communicates its dataset effectively. At a glance, you can clearly see the regression of Palestine over the decades.

This infographic, on the other hand, while having a nice design, fails at communicating its dataset effectively (in my opinion). To learn anything about Wilshire Boulevard, Los Angeles, I really need to examine the infographic.

The data behind the second infographic appears to be unrelated, a random bunch of statistics, and maybe it’s harder (I’m guessing it is) to communicate all this effectively in a single infographic.

Back to the Point
In my grade seven math class, currently, we’re learning about functions, plotting functions, gradients and y-intercepts.

I was thinking, once the students have learnt about positive and negative gradients, a nice exercise might be to give them an infographic, like the one above (the one of Palestine), and have them plot the data.

The exercise could be extended by asking the students to find the equation of the resulting slope or line. (I might need to remind them before they start the exercise that their graphs need to be linear.)

I’m thinking, the complete opposite or the complete reverse could happen also: students are given a plotted function and then asked to go ahead and make an infographic that represents this data.

Second Idea
I haven’t really given this idea much thought. At least, not as much as the idea above.

A very relevant infographic exercise/project for my students (and for other international school students in Japan) would be to develop an infographic that shows Japan’s declining population.

At first, I thought the exercise/project would be best suited to geography. But now, I’m thinking it could work in math and technology too.

It could even become a cross-curricular project where, for example, students are given time in geography class to gather the data (and make sense of it) and then given time in technology class to create the graphic.

Image Credits:

Storytelling in the Modern Age

What I’ve Been Reading:

This week, I’ve been reading about digital storytelling and, I must say, the idea is very cool. In this post, I’m going to look at how I could use digital storytelling in my classroom. I’m also going to look at a few questions that popped up while doing the readings.

Crystal Phoenix

Do Digital Stories Need to Be Personal?
What I mean is, if I were to make a digital story, would it have to be about me? My Grade 4s have just finished a unit on the Aztecs. If they were to make videos about the lives of the Aztecs, would these be regarded as digital stories?

The answer to all these questions is: digital stories can be about anything.

Here, for example, is a digital story about the great mathematician, Pythagoras.

And, here, for example, is a bunch of digital stories about the lives of those involved in organ donation.

Where Could Digital Stories Be Used in My Classroom?
My grade 4 technology class are about to finish a project on the Aztecs that’s taken about six weeks to complete. (I see the class once a week.) They’ve made a bunch of awesome posters using research they did in their homerooms.

The posters are all quite different. Some students chose to base their poster on the games that the Aztecs used to play. Others chose to write about (present?) the various roles that used to exist within Aztec society.

Back to the Question
I’m thinking the next time we do this project, instead of making posters, what about making digital stories?

PowerPoint, iMovie, Movie Maker and even VoiceThread are all tools the students could use to to bring their digital story ideas to life.

One thing I like about digital stories that posters simply can’t offer is sound. And from doing COETAIL for nine months, I’ve come to realise that, in digital media today, sound is integral.

Closing Remarks
Here are some guidelines for digital storytelling that I’ll be sure to follow in the future when making digital stories with my classes:

  • Digital stories can be instructional, persuasive, historical or reflective. Digital stories can be about anything.
  • Digital storytelling is best suited to the individual.
  • Digital stories are typically between two and four minutes in length.

Image Credits:

PowerPoint Design Principles

What I’ve Been Reading:


A few months back, I gave a presentation on Moodle to the teachers in my school. In this post, I’m going to look back at that presentation and evaluate it using some of the guidelines Reynolds gives us in the two articles above.

Note to Self:
Insert link here to presentation.
Here’s a link to the presentation.
In fact, no, I’m going to embed it.
Nope, not working. Here’s a link to the presentation.

Don’t use templates.
This is one of the first tips he gives us.

But what does this mean? What exactly is a template? I did use a built-in style on this presentation – does that count as a template?

Well, after playing around with PowerPoint, I discovered that templates aren’t styles and styles aren’t templates.

It appears that templates are ready to go presentations – all you need to do is add the content and delete the slides you don’t need.

So, for the time being, my presentation’s in the clear.

Enjoying the Sunshine

Don’t make the text difficult to read.
Well, this is one guideline that I think my presentation follows pretty well.

I’m pretty sure it was back in university that I learnt about the importance of contrast in interface design – colour contrast is what I mean. And ever since then it’s been a design principle I think about when creating basically anything on the computer.

The contrast of the bright orange and white against the dark grey would have been one of the major reasons I chose this particular style.

Avoid three-dimensional charts.
My presentation doesn’t have any three-dimensional charts. In fact, it doesn’t have any pictures at all. None. Just text. I’m wondering what Reynolds’ take on this would be?

I have a feeling that good presentations, just like good blog posts, should always have a couple of images to break up the text.

But what if you can’t find any good images? Is a presentation with no images better than a presentation with poor images?

Anyway, it’s something to remember for next time.

Use declarative sentences at the top of each slide.
This is something I definitely didn’t do.

The fourth slide in the presentation has the title “Facts and Figures” (not the most creative title I know) and deals with the usage statistics of Moodle.

A more appropriate title for the slide might have been something like “49,952 schools and companies are using Moodle.”

Again, something to remember for next time.

Image Credits:

Writing for the Web

What I’ve Been Reading:


In this post, I’m going to reflect on a few questions that came up while I was reading Agger’s article on visual literacy. I will also look at a couple of interesting points that he brought up (if patience allows).

Short Sentence Fragments?
Leaves the Reader Asking a Few Questions

In the article, we’re told that we should use short sentence fragments when writing online. But what are short sentence fragments? (English definitely wasn’t one of my stronger subjects back in school.)

According to this site, a sentence fragment is an incomplete sentence and because of this “incompleteness” leaves the reader asking a few questions.

Let me think of a sentence fragment to start this block of text with…

Got it. (Check above.)

I know it’s a sentence fragment because it triggers the question “What leaves the reader asking a few questions?”

It’s definitely harder than it looks. (There’s one right there.) Coming up with sentence fragments that is.


When Writing Online, What’s the Ideal Paragraph Length?
I don’t know. Is it five sentences? Is it six?

This is another question I was left asking after reading Agger’s article.

According to Gerry McGovern, a website content development company, the ideal paragraph length when writing online is about 45 words. So what does 45 words look like? Well, the opening paragraph to this post is 37. And, by the time I’ve finished writing this sentence, this paragraph will be a little over 45 words.

Isn’t It the Easiest to Read?
One thing I definitely remember from back when I was studying computer science is that Times New Roman is supposed to be the easiest font to read.

In the article, Agger suggests using a font that’s been designed for screen reading and he gives Verdana, Trebuchet and Georgia as examples.

So which one is it? What font should I be using?

The consensus seems to be that if you’re writing for the Web only then you should use a sans-serif font like Verdana or Trebuchet. And that if you’re writing something that is going to be eventually printed, then you should use a serif font like Times New Roman.

Once I’ve published this post, I’m going to change my WordPress theme to one that employs a sans-serif font.

Image Credits: