Ineffectiveness in Research in Math Education

Author: Kilpatrick
Source: For the Learning of Mathematics, Vol. 2, No. 2, (Nov., 1981) pp. 22-29

In the article, Kilpatrick asks the question, 'Why is research in mathematics education so ineffective?' In short, Kilpatrick asserts that the two main reasons are inattention to theory and the disconnect between researchers in math education and practitioners (teachers).  Kilpatrick offers the ‘lens model’ as a way to show how it is both the researcher’s intended purpose and the lens through which the reader interprets research that determines if research is basic or applied.  The ineffectiveness of basic and applied research is found in the connections (or lack thereof) between research and theory and the connection between research and practice. Such ineffectiveness can be seen in the way that ‘new (the article is published in 1981) academic studies are not grounded in common theoretical frameworks and a therefore a community of researchers in mathematics education is not forming. The effect of research on educational practice is mediated by through theory as it is only with a common theory that research can be applied by the reader. Research needs to be more explicit and coherent in its assumptions, frame of reference and point of view so that readers can use a theoretical frame to judge similarities between research and their own situations. Kilpatrick uses a contrast between mathematics and mathematical educational research to help explain the ineffectiveness of research; according to this analogy, researchers need to develop more precise intellectual tools and the practice the ability to adapt tools to various problems and have a realistic expectation of the types of problems that such tools are able to address. Moreover, distinguishing that research in mathematical education is different than mathematics is key as the latter is technical but the former is social.

STOP: Virus

The article includes an example of how teachers mistakenly assume that studying math improves one’s ability to think logically in other domains. Kilpatrick describes how it is the way that teachers understand a theory that has a profound impact on math education; as theories disseminate through books or talks, “Gradually the idea comes into the culture of mathematics education and is picked up by teachers in practice. Sometimes the ideas I banned from colleges of education but lurks in a culture like a virus to strike down the receptive practitioner.”

Kilpatrick uses the term virus to show how an illness can infiltrate a population. This also reminds me of a ‘computer virus.’ I think a part of the trouble is that teachers are often presented viruses in work emails or district workshops.  Similar to a sales pitch, teachers hear, ‘It is important to teach this new concept or work with this type of learner because_______.’  British Columbia adopted a new curriculum this year and so there are a number of terms that teachers are talking about in the lunchroom. One virus or ‘buzz’ word that is ‘coding’ and all of the amazing things that teaching computer coding is supposed to achieve. I have taken a picture of a poster that was given out in a recent school district workshop (the intention is for it to be widely distributed). Linking to Kilpatrick’s example that teachers mistakenly assume teaching math can be generalized to teaching logic in many domains, generalizing problem-solving (which one often assumes is linked to logical thinking) is one of the supposed benefits. Almost insidiously, the limits of such generalizing or transferring potential are left out of the workshop and the poster. In my work, I hear the experiences of children from many schools. Sometimes the curriculum that teachers are presented with at district workshops/emails is taught as little more than a set of instructions to make one thing on a screen move to another location on a screen. I am currently planning a ‘Girls Who Code’ module that starts in February and so this fear of being ‘susceptible to a virus’ is frightening. If I am not careful, I could be teaching children little more than how to follow a recipe. What does successful teaching look like if I cannot trust that the purposes of such learning are embedded in theory? It makes me ask what am I teaching? And what for?

Questions:

1.     In the contexts where you have taught and researched, have you seen a ‘virus’ or idea about education that started in theory but had negative or unexpected implications?

2.     This article was written in 1981. In your research thus far, does your experience reflect Kilpatrick's claim that many math education studies are not imbedded in theory?