Abstract:

The importance of technology for education is increasing. In general, however, resistance is still observed (in teachers, teacher advisors, administration, curriculum developers…). Why? Although financial challenges often come to the fore, the case of the simple calculator suggests this may not be the core issue. Nowadays, very cheap; research shows the huge potential of ‘wisely’ used calculators (to support problem solving, number sense, mental calculation, student attitude…). But they are not widely adopted, and rarely do we seek a deep understanding of the reasons why this might be.

In the course of our research in mathematics education, we have found epistemological issues to be fundamental to understanding ‘what counts’ in education. As a focal point, we are now developing this understanding in our research on the use of technology in elementary mathematics, and especially around the introduction of simple calculators in the classroom. As a framework, we have read the works of the German philosopher, Heidegger, who distinguishes two attitudes toward technology. One focuses on technology as a “mean” and the other recognizes technology as “revealing” particular “truths.” Heidegger says that technology not only gives us (easier, faster, wider) access to the world, but always ‘thinks’ it before we do, revealing it in a certain way, exposing a particular “truth” about it. He exemplifies this with the windmill revealing the working force of the wind, and insists that the real power (and danger) of technology is not in the object or its use, but in its revelation. Technology inevitably transforms us and what we do; windmills not only harness the wind, but the peasant as well.

With this in mind, we reviewed the research literature on the calculator in elementary school mathematics. First, we found an overall focus on knowing how to use technology, Heidegger’s instrumental conception. Second, we asked what can be said about the truth revealed by such technologies, hypothesizing that reluctance might be resistance to the binding truth it reveals. We found this truth to deal with everyday “practical epistemology”: with what needs to be known (or not), but also with what it means to know and how one comes to know (to learn, to teach…). May hesitancies AND enthusiasms in the face of technology originate, in a very profound way, in such practical epistemological issues? On that point, we found very supportive evidence: Many researchers ‘incidentally’ observe how technology requires major changes in practice, that is, in the way mathematics is made and conceived of in the classroom. The calculator crystallizes a certain (“relational,” not “procedural”) understanding of mathematics, and accepting the technology is to accept its epistemology.

We now use these theoretical findings to conduct an empirical investigation to see what they may enable (e.g., in teachers’ professional development). Besides that, the study also has consequences for education at large. Other technologies (e.g., word processors) offer challenges similar to those of the calculator. But even more broadly, we bring new light to the question of the educational use of technology, showing how any implementation (online platforms, tutorials, microworlds, …) comes with its own ‘upsetting truth’, imposing epistemological shifts that some around/among us anxiously resist… or await.

Keywords:

Resistance, epistemology, calculator, mathematics, Heidegger, primary school.