Remythologizing Mystery in Mathematics: Teaching for Open Landscapes versus Concealment

Abstract

Mathematics is full of mystery. We illuminate the myth to expose two conflicting senses of mystery at work in mathematics and its education practices. There is a sense of boundlessness with mathematics-the idea that we never fully know. There is also a practice of concealment, in which an answer or solution is known by special people who may support or provide a scaffold for students' navigation to the "special" knowledge, but may also challenge their access to it by erecting barriers and boundaries. In remythologizing mystery, we identify that the valorization of mystery in mathematics is rooted in the wonder of exploring boundless landscapes and is used misleadingly to justify school mathematics with the other sense of mystery-uncovering the concealed.

Values and Valuing in Mathematics Education

“…One hopes the reader will also be challenged to think broadly on the notion of mathematical values, a crucial element of the foundational frame that holds what we understand as western mathematics. Andersson, A., & Wagner, D. (2018) Clarkson, P. C. (1980). Interpreting test results.…”

“…However, one that to me is undervalued is mystery. Many people either regard mathematics as mysterious because they do not understand it, or dislike it and hence do not want to understand it (Andersson and Wagner 2018). And yet as Alan suggested in his book it is the sense of mystery and its counterpart openness that bring understanding to the bigger picture of how mathematics sits within our broader culture.…”

“…In activities related to mystery, mathematical ideas are usually already outlined and described by someone else (c.f. Andersson and Wagner 2018). In the sentimental dimension, progress relates to activities where students have the sense of having the opportunity to develop own ideas through questioning and exploring.…”

A joke on precision? Revisiting “precision” in the school mathematics discourse

“…It appeared in documents describing classroom tasks or test items that require only one correct solution. The one-preciselycorrect-solution practice is common in Swedish textbooks as well as in other contexts (Andersson & Wagner, 2018), such as the majority of tasks (43 of the 53 items) in the 2014/2015 National Test (Skolverket, 2015) (see Fig. 1 below for an example).…”

“…Despite pedagogical efforts to appreciate diversity in mathematical activity (e.g., Stein, Engle, Smith, & Hughes, 2008), mathematical tasks eventually tend to become a matter of being right or wrong (de Freitas & Sinclair, 2014;Andersson & Wagner, 2018). When students ultimately are expected to produce a one-precisely-correct-solution, they are at the same time exposed to the risk of being "precisely wrong" (Ryan, 2019).…”