Tag Archives: Technology

If I see one more f’ing Smart board disabling a chalkboard…

…I’m gonna ‘splode. Ladies and gentlemen, an interactive whiteboard is a supplemental technology, not a replacement technology.

From today's New York Times

From a post a year ago


Mathematical storytelling

I tend to tell stories when I teach. Most of the time, they are relevant to the topic at hand. As a seventh-grade teacher, I specialized in telling a story that ended with a mathematical twist, and I was particularly pleased with myself when students:

  1. didn’t see see it coming, and
  2. wanted to argue with each other right away about how the story was going to end

Ask my college students and they would likely recognize that aspect of my teaching, although I tone it down a bit for adults.

In the past six months, I have found a wealth of examples of amazing storytellers in mathematics. I met Dan Meyer and Karim Ani. Each of them uses the language of acts for describing lessons (although they don’t quite agree with each other on the meaning). And I (along with several hundred thousand others) discovered Vi Hart. Fabulous, smart mathematical storytellers; each and every one.

Out of this rich stew of stories comes the following. It’s the first of several I’ve got brewing. Help me make them better, will you?

UPDATE: In response to initial feedback in the comments, I revised the original video and posted it above. Two changes: (1) Sloppy audio levels were fixed (this is embarrassingly easy to do in iMovie), and (2) The video ends with the two pricetags sharing screen space-for easy reference. I’m unsure whether the second change is an improvement. See comments below.

Canvas v D2L round 1: Assignments

This is the first in a series of brief posts documenting my semester-long experiment with a new Instructional Management System (IMS). This IMS is called Canvas. It’s from Instructure. I wrote about it last spring. Individual instructors can use it for free.

D2L (or Desire 2 Learn) is the adopted IMS in our state college and university system. I have hated it for years and have complained loudly to faculty and students about its bad design.

I learned of Canvas and decided I could either complain for another year or do something about it. I am doing something about it.

First, the caveats…

When you go outside of the adopted IMS, please note that you’re on your own w/r/t FERPA. I have alerted my students that if I use Canvas to post their grades, their data will be stored outside of the institution, and that if they are uncomfortable with that, they should let me know and I will not use that feature of Canvas. (In previous semesters, I have not posted grades in D2L, so technically it’s a wash for them.) No student has indicated this to me so far.

Caveats out of the way, it’s time for round 1.

Round 1: Assignments

From a design and usability perspective, let’s think about how students use an IMS. They go there, I imagine, with one of two questions 85% of the time. The most common one (sadly) is probably What is my grade? More on that in a later round. The second most common has got to be What is due next week?

D2L has no Assignments area.

I’ll say that again. D2L has no Assignments area.

There is no choice that answers the question, What is due next week?

Can you read those choices? If you want to know what is due, what do you choose? It turns out you need to choose Content.

When you do, you get a screen that looks like this:

See those due dates, for example the one for Homework 2.1, about halfway down the image?

I typed those due dates into the titles of the links. There is no system for keeping track of due dates in D2L.

Now let’s look at Canvas. Remember that you are a student and you want to know what’s due next week. You see this menu:

You click Assignments. You see this:

See those due dates? They are part of the structure of Canvas. Assignments have a special place, and they have due dates (or not, depending on what the instructor wants to do).

But this isn’t really the best organization of things. You don’t want to have to pan through all of the categories of assignments to find the one thing that is due this week. No you would rather see things laid out in calendar format. Well, my friend, you’re in luck:

Round 1 goes to Canvas for sure.

Michael Phelps v. Morton Salt girl: The grudge match

An article in the latest issue of Mathematics Teacher advocates fighting fire with fire in the competition between math class and the media for students’ attention. We are exhorted to Present Examples in High-Resolution Video, to Connect to Students’ Interests, to Show Appealing Faces and to Hold Students’ Attention

As examples of Connecting to Students’ Interests, H. Wells Wulsin offers,

Monitoring a breeding bunny population would show the process of exponential growth. Baseball batting averages could introduce percentages. Such applications of mathematics to daily life would help students build important links between new ideas and the concepts they already understand.

The article continues. Under Showing Appealing Faces, Wulsin advocates,

What if Michael Phelps calculated the volume of an Olympic swimming pool or Beyoncé computed the time delay needed for speakers at an outdoor concert? Why not let Danica Patrick figure the monthly payment on an auto loan?

I have to confess that I find the whole piece a little depressing for two reasons.

(1) Dissemination of the 1989 standards

I can cite examples of rabbit population contexts for exponential growth going back to the original NSF-funded curricula of the early 1990’s. But I doubt the example below is the first time bunnies appeared in an algebra book.

Bunnies in Connected Mathematics, circa 1998

And baseball batting averages date back much, much farther back in Algebra I curriculum.

Batting averages in Algebra I, Modern Edition, circa 1970. Note the annotation at the bottom of the page.

Is this the progress we have made in disseminating the vision of the 1989 NCTM Curriculum and Evaluation Standards? Have we made so little progress that these examples still make for a viable opinion piece in Mathematics Teacher?

(2) Lipstick on a pig

The present guru of high-resolution video in math class is Dan Meyer. I worry that when people look at Meyer’s work, they see the glitzy exterior, not the instructional techniques the technology supports.

Dan is a handsome enough guy (Show Appealing Faces) and his escalators problem has high-enough production values (Present Examples in High-Resolution Video). But that’s not what his work is really about. It’s about storytelling-about putting students in a situation where they ask the mathematical question that we know will be productive. High-resolution video makes this easier to do, but it’s not the core of the idea.

The core of the idea is that we are engaged with the story. We see Dan about to go up the down escalator and it makes us wonder (1) whether he’ll do it without falling flat on his face and (2) if he does do it, how long will it take? The viewer is invested in the narrative.

So here’s a question that points out the distinction I think is important.

Why does Michael Phelps care what the volume of the swimming pool is?

There is no story here; no narrative. If I don’t believe Michael Phelps cares about the volume of the pool (and I do not believe that-just to be clear), then why should I care about the volume of the pool?

Making Michael Phelps (or Beyoncé, or Danica Patrick, or even Danica McKellar) the handsome spokesman for the same old word problem hardly advances an agenda of real and engaging mathematics for real students, nor one of turning students into believers that a mathematical perspective on their everyday world might be (1) useful or (2) intellectually stimulating. It’s just lipstick on a pig.

You may or may not be bored by my salt problem. But there’s a reason for computing the volumes. There’s a story-someone is going to fill that container by opening a brand-new box of salt. It’s unclear at the outset whether it will all fit in there-the new container is shorter but wider.

While we don’t need to compute the volume to find out whether the salt will fit, we can. And the more carefully we measure and compute, the better we should expect our prediction to be. And in a middle school classroom, this is likely to get some students’ competitive juices flowing.

Why do we want to know the volumes of these containers? Because we want to correctly predict how the story is going to end, and because we want to be more right than our classmates.

I would gladly put the Morton Salt girl up against Michael Phelps in a year-long curricular grudge match. Which will engage students with more mathematics over the course of 180 school days: filling Tupperware with salt or pep talks from Olympians?

Meet my new online lover

I have complained about D2L-my college’s online course management system-before. It is based on a mid-90’s file-centric paradigm that has become clunky and awkward in the age of Facebook.

But I recently came across a new system-Canvas. I spent an hour messing around with it yesterday and it seems to do everything I have wanted from D2L, including:

  1. Integration of its various areas. If I start a discussion, that discussion becomes part of the course’s homepage. If I post a new document for students to read, it becomes part of the course’s homepage. Etc.
  2. It has an Assignments section. (Can you believe that D2L has no Assignments section? Really?)

    Canvas's sections

    D2L's sections

  3. Students can choose to integrate each course into the rest of their online world however they like. If they want to receive a tweet each time a new document gets put up, they can. If they want a daily summary email of everything that happened in the course, they can have that. Facebook, texts, any way a student wants to be notified (even if not at all)-they can have it.

    Canvas plays nicely with all of these.

And can we talk about graphic design?

My College Algebra homepage on D2L

A homepage for a sample class in Canvas.

Individual instructors can establish their own free Canvas accounts for use in their courses.

I am signed up for the fall. I’ll report back on how I’m getting along with my new lover.