This is the second post in a series that is based on my keynote address last week at Grand Valley State University's annual Teaching and Learning with Technology Symposium with Matt Boelkins. This time, I am addressing Matt's question to me which is:

What are three things you believe must be present in a technology in order for you to use it effectively in teaching?  Is there any particular trait that makes a certain technology a non-starter?

I think my criteria for technology rests on three aspects of the same idea: Accessibility.

First of all there’s economic accessibility. This means that the technology I use must be free or cheap. There are some exceptions to this rule but by and large, I am willing to use technology that is slightly less polished or feature-filled than some other similar technology, if the first technology is significantly cheaper than the other.

An example of this is graphing tools that we use in calculus and other courses. We have these tech tools that will allow students to enter in a mathematical function —- which is the fundamental object of study in calculus and precalculus —- and visualize it as a graph, manipulate the graph and extract information from the graph. This is a technology that really I don’t think those of us who teach calculus and pre-calculus can seriously live without anymore. We want to get graphing tools into the hands of every calculus student so they can construct their own understanding of functions from a graphical standpoint, directly by using the technology.

Now for many years back in the 80s and 90s the default choice for graphing tools was the graphing calculator. Texas Instruments in particular has something of a corner on the market on graphing tools. These graphing tools have not changed significantly in 15 or 20 years, and they cost about the same as they did back in 1990, about $120 for something like a TI-86 or TI-89 graphing calculator. These have a small square monochrome screen and an attached keyboard and you can enter in functions and graph them, along with other scientific calculator features and in some cases you can write programs for them.

Nowadays on the other hand we have tools like Desmos.com which is a free, online graphing tool that does literally everything the TI-86 will do in terms of graphing, and more. It’s in color. You can create interactive sliders. You can import data and do statistical regression analysis with it. You can share your work by sending a hyperlink to it. And can be accessed on a browser or through iOS or Android apps, and let me mention again that it is completely free.

Now I ask you: Why should I use a $120 calculator when I have a free option that contains all of the features of the calculator and more besides? Desmos is economically accessible whereas the TI-86 is not.

Another form of accessibility is physical accessibility. By this I mean that the technology ought to be portable both in the sense that it’s small enough to carry around with you easily and therefore have with you all the time; and portable in the sense that it works on multiple hardware platforms. Again let’s go back to the graphing calculator. The TI-86 is smallish. It’s portable. But what if you leave it at home? What if you drop it and it breaks? Your data are not backed up somewhere, and you will have to not only go buy another calculator —- economic accessibility again —- you will have to recreate all the data you had stored on your calculator. The technology is the hardware and the hardware is the technology.

Compare it to Desmos, which is completely agnostic as to hardware. I can, for example, use Desmos on a lab computer, or a tablet or smartphone or Chromebook. If my phone runs out of battery during class, I can pull out my laptop and pick up where I left off, and vice versa. And  I have an Android phone; if I decide next week I want to switch to an iPhone, it’s no problem because the app is free and if I don’t like the app I can just go to the Desmos website.

This is what “portable” technology means in the fullest sense and I insist on physical accessbility because students are human beings with different situations and backgrounds. The technology needs to be portable so as to fit their life choices, not the other way around.

Finally there is intellectual accessibility. Technology needs to be simple above all, and easy to learn (even though it may be deep enough to challenge users to a lifetime of exploring). Again I am going to pick on graphing calculators. Let’s suppose that students in a precalculus or algebra class are learning about parabolas and they are trying to figure out the meaning of the parameters in the general equation $y = a(x-b)^2 + c$ .What do those constants do?

On a graphing calculator this requires multiple keystrokes back and forth through three layers of menus and you cannot see the graphs you are creating until finish one set of keystrokes.

Now I ask you, which one is more intellectually accessible? Which one creates a more dynamic and rich learning environment for students, and which one takes away from it, even to the point where you have to not so much use the technology as overcome it?

So those are my three big criteria: economic accessibility, physical accessibility, and intellectual accessibility and only in a very rare number of cases does any technology make it into my classroom that doesn’t tick off the boxes in all three of those areas. Particularly technologies that are expensive or otherwise require major sacrifices from users in terms of time or money or life choices are just not going to happen in my classroom.

This is all in keeping with the idea that students are human beings:

  • If I choose a technology that fails on the economic accessibility level, then I am ignoring the fact that many of my students have reasons why spending $120 on anything is a major burden; and if I can have a tool that is roughly as functional as a $120 tool, but which is free or cheap, then all other things being equal which tool should I choose if I am really aware of, and care about, my students' lives?
  • If I choose a technology that fails on the physical accessibility level, then I am saying that students' physical contexts don't matter. It's almost like saying my students themselves are not physical beings. I am saying that I want them anchored to a specific hardware in a specific location, even if that makes no sense at all.
  • If I choose a technology that fails on the intellectual accessibility level, then I am setting students up for frustration for no reason in my class; I am not choosing the technology that provides the shortest path between their minds and the mathematical concepts I want them to learn. That shows a tendency not to care about all the other cognitive burdens my students have to carry. If I have a tool that is maybe not as professional-grade as another, but makes discovering and internalizing mathematical knowledge simpler for students, then if I care about student learning and not just tool-use, I know which one I am going to pick.