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Rethinking Math Basics in a Digital Age

I just returned from the Computer-based Math conference led by Conrad Wolfram. If you haven’t seen his TED talk, you really should check it out. It presents a new way to think about how we teach mathematics in this digital age. One idea that led the conference was that we need to help young people learn mathematics using the tools and learning environments of their time, not those from previous generations. These tools allow us to approach the subject in a very different way. Learners no longer need to learn all the steps and tricks of calculation before they can think mathematically about a question or problem. Computer-based mathematics, or computational mathematics, means we can extend our thinking by having computers handle the calculations – the learner’s task becomes less mechanical, more concept focused. It goes from techniques to big ideas.

Yet, though this conference was focused on rethinking mathematics education, there were a number of attendees who confused computer-assisted math, in which the computer makes it easier to do what they’re already doing, with computational mathematics. To paraphrase an analogy Seymour Papert once made, this is like using a jet-engine to speed up a horse-drawn carriage (from Looking at Technology Through School-Colored Spectacles, an article definitely worth reading), rather than to think of travel from a completely new perspective. Not only is the gain in speed limited by the limitations of the carriage, the carriage most likely will explode. A whole new perspective is needed.

So, what really are ‘the basics’ of mathematics, those core ideas and skills all people need? Is calculation really the most important skill? I realize that defining ‘the basics’ is not a simple task, but shouldn’t we feel the necessity of doing this in light of the tools that are currently available and that have re-shaped so many aspects of our lives? Skills that were deemed absolutely essential when the tools we had were different may no longer be the skills that are necessary today. As Sugata Mitra asks, how many of us need to know how to ride a horse, once an essential skill. Or to use a slide rule to determine logarithms or even how to really dial a phone.

It may once have been important to have human calculators, but it would seem that this role has been usurped by an enormous array of technology. My guess is that we’d find at least some (many?) learners who do not excel at calculating, for whatever reason (eg, not fast or interested enough) who actually are very adept and engaged by mathematical thinking. Perhaps it would be that student who loves the logical challenges of a game or even analyzing the statistics of an issue (whether political or sports related) to predict an outcome, but thinks she is ‘bad’ at math. If we accept that helping learners think mathematically and understand the mathematical information with which we’re inundated regularly, especially with the avalanche of data we’re seeing, what really are ‘the basics’? Is long division more ‘basic’ than recognizing recursive patterns in nature or historical data?

And it’s not just mathematics education that needs rethinking. It’s all areas of school and schooling and the role they play in a child’s education and total learning environment. Maybe we need to stop trying to hitch the technology engine to the horse cart of current education. New, ubiquitous technology calls for more than incremental change.

Interested in your ideas of what you think today’s ‘basics’ are and how what these would look like in a classroom.

Additional Note: For a very different view of what education ‘basics’ are, check out Hackschooling.
December 11th, 2013 @ 1:14PM

NCTM plays a leading role
The National Council of Teachers of Mathematics has long been aware of the need to change mathematics education, and has published many books and articles on this topic (e.g., a 2005 Yearbook). In the 1990s several high school curricula were created that assumed every student had access to a computer and software. Needless to say, practice in schools lags behind what many leaders have advocated.
Posted By: Andrew Zucker on December 12th, 2013 @ 4:17PM
You\'re right, Andrew, and thanks for the reminder. Although, for many years it seemed that the NCTM was taking one step forward, one step back. In the 1990\'s, it was difficult to run a workshop at NCTM conferences if you needed all participants to have access to computers. So, technology and the promise it held for rethinking math education in terms of making a more fundamental change didn\'t have a very high profile.
Posted By: Susan Einhorn on December 13th, 2013 @ 6:13PM