The epistemological and
\nthe pedagogical
\nWhat we exactly refer to when we talk about an epistemological perspective on mathematics or mathematics education is not something easy to pinpoint. I am thus very thankful to my colleague\u2019s analysis of John Hattie\u2019s recent book for helping us to put some words around this. Throughout his long article, Proulx patiently dissects what appears as the New Zealand-born researcher\u2019s quest for ways to tell us about things that work (best) in education. I personally tend to call this a sort of pedagogical concern, a desire to guide (the Greek root ag\u014dgos).<\/p>\n
One might think of the two perspectives as complementary, but I see them as two non-intersecting lines (in a d > 2-dimensional space!), coming from very different places and going in totally different directions. Whereas for one what matters is the extent to which \u201csomething works\u201d, the other values the breadth of understanding of \u201cwhat is at work\u201d. Pedagogical findings assume the primacy of situational factors, of the container over the content. Epistemological observations presume that those conditions take their actual signification only through the matter at hand, the substance over the form. In one case, interacting with students by questioning them about a mathematical concept seems generally better than only explaining<\/p>\n
it. In the other, questioning and explaining are mysterious phenomena that can produce different kinds of mathematical activity and elicit various possibilities for a given mathematical idea. Going to the extreme, I would almost caricature this by saying that while the pedagogical looks for answers, the epistemological search for questions. Proulx\u2019s analysis gives for me a striking illustration of that.<\/p>\n
Whatever works<\/p>\n
In
\n2009, Woody Allen presented a movie (he wrote and directed it) called \u201cWhatever works\u201d. The takeaway message has to do with the importance of making room for the things that keeps us happy, and not being too judgmental about it. For me, Proulx\u2019s reading pictures Hattie and his books in that sort of light. There seems to be a lot going on in these books to create the impression that in a way what the author presents (I\u2019ll count Hattie and his team as one) \u201cworks\u201d in some way. Because he needs that.
\nPresented that way, Hattie\u2019s work might sound a little bit delusive, but it can also be taken as an epistemological posture (and that\u2019s also what Allen\u2019s movie is more or less about!). When everything fails, one solution is to redefine what being successful means! There is a form of pragmatism in Hattie\u2019s work in which the very nature of things is that of their workability. Of course, there are different ways of thinking about this, some more trivial, and other more articulated (one could think, for example, of Varela and Poerksen\u2019s (2004) \u201ctruth is what works\u201d). My favourite example of this is an oft-cited article by Anna Sfard: On two metaphors for learning and the dangers of choosing just one (Sfard, 1998).<\/p>\n
In this paper, Sfard contrasts the \u201ccognitive\u201d and the \u201cparticipative\u201d view; one situating learning inside the individual (and often: in his\/her head), while the other rather conceptualizes it as social phenomena (visible in relationships, depending on other\u2019s recognition, etc.). Although both cognitive and participative views develop from radically different and incompatible epistemological perspectives, Sfard suggests that this does not really have to matter, because when the time comes to get things going, it can be quite useful to turn to both at the same time, in order to take out of it something that works (as well as
\npossible). This is a position that Proulx and I would definitely not agree with, of course (see Proulx & Maheux 2012, in which we explain why we think this is not a good idea)!
\nIt does not look like Hattie explicitly embraces such an epistemological posture, or that he is aware of it in his writing. It is also not apparent at first sight in Sfard\u2019s writing. This is (often) an implicit kind of epistemology, one that hinges on the belief, or the assertion, that epistemology is not so important. Or perhaps this stems from the simple unawareness of the possibilities of epistemological considerations on an issue: what they can do, generate, offer as possibilities, etc. For me, they are, nevertheless, epistemological posture in full. Having that in mind while reading Proulx\u2019s analysis could help understand the presence of what appears to him as contractions in Hattie\u2019s discourse. When one\u2019s chief concern is to come up with and talk about things that work, and things that work first of all for him\/herself, the sort of consistency we expect if we look for the \u201creality\u201d of things in a different light might not apply. And this is what Proulx\u2019s comments clearly exhibit.
\n\u201cA\u201d Didacticien\u2019s Epistemology
\nI would like to conclude this brief reaction by discussing one last aspect of Proulx\u2019s paper. In his piece, he makes strong assertions about what he calls the perspective of \u201ca researcher in didactique des math\u00e9matiques\u201d. The indefinite article \u201ca\u201d in this sentence is obviously ambiguous. Is it referring to all the people who use the label (as if he was writing \u201cthe researcher\u2019s in didactique des math\u00e9matiques\u201d)? Or, is it meant to designate only one single individual (himself). The actual French phrasings he mostly uses has the same ambiguity, but sometimes tend toward the former interpretation (purposefully?). For this reason, I think it would be worth highlighting how Proulx\u2019s deeply rooted epistemological considerations, from which he produces his reading, are not necessarily present in the work of all those who claim the title of researcher in didactique des math\u00e9matiques.
\nTo begin with, even the distinction in interest between what works and what is at work could not be so simple for everybody. Many scholars, big and small names, have told me or written about the importance for them to help students, teachers, and schools, to \u201cfix\u201d them (a little, if possible) and make things better, and so on. This is even the case for some who seem to mostly focus on \u201cfundamental\u201d research, but nevertheless believe that having an impact on schools is the ultimate goal, or at least the most important and desirable one. Like so many educational researchers, they feel their work has to improve mathematic education in some way. And, like Sfard, many of them work to offer things that works as much as possible, as good as possible; and to tell people about what does not work, and so on. Proulx\u2019s visible, central and powerful interest for what is at work, how and why, strongly contrasts with this. He actually explicitly wrote about it in this journal (see Proulx 2015).
\nAs mentioned above, we can also recognize in his discussion of Hattie\u2019s contradictions the importance of the epistemological questions for Proulx. Promoting problem-solving rather than direct instruction would mean valuing \u201cdata\u201d and the possibility of tapping on more observations over what one believes in, and what one wants to see at work. Most mathematics education researchers would readily adhere to Proulx\u2019s take on this, but we all also know a great number of individuals who prefer to ignore a good amount of research in order to keep working on \u201ctheir\u201d problems, no matter how irrelevant or unsustainable they are. But beyond that, there is also the relatively simple aforementioned observation that while for some researchers, like Proulx and I, epistemological questions are quintessential to mathematics education, for others they seem inopportune, or even detrimental (e.g., because they come in the way of finding stuff that \u201cworks\u201d).
\nWe also more subtlety detect in his analysis the discourse of someone who sees research as a profoundly creative enterprise, of someone who\u2019s pretentions are not to tell us what is at work \u201creally\u201d, but to offer
\ninterpretations, distinctions, ideas (Proulx might say \u201cto generate ideas\u201d\u2026). And, finally, there are also some cleverly selected references of work in the field that hints to a conceptualization of what is at work in terms of mathematical activity; others could have been more concerned about the objects (e.g., tasks) or the intentions involved in that activity, for example.
\nThis is not to diminish in any way the importance of Proulx\u2019s reading of Hattie\u2019s work. On the contrary, it showcases its value, and its importance for our community. Proulx\u2019s analysis really is a piece of his work, and reading it is not merely a way to learn about what Hattie does in his books. It is also, and maybe mostly, learning more about Proulx\u2019s thinking, about his ideas, his perspectives, his intentions, his distinctions. The article is not just an accidental and insignificant piece he drops here as ballast. And it is not either a simply \u201cgeneric\u201d answer to Hattie\u2019s writing \u201cfrom the perspective of didactique des math\u00e9matiques\u201d. It is an original, unique opus, some lieu in which Proulx works and develops his own research in various ways. For those who know his work less, the section on problem-solving is probably the one where this is the most visible. Also, as he would say, through writing his critical essay, Hattie\u2019s work became in that sense his problem to solve!<\/p>\n","protected":false},"excerpt":{"rendered":"
The epistemological and the pedagogical What we exactly refer to when we talk about an epistemological perspective on mathematics or mathematics education is not something easy to pinpoint. I am thus very thankful to my colleague\u2019s analysis of John Hattie\u2019s recent book for helping us to put some words around this. Throughout his long article, […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[17],"tags":[19],"class_list":["post-431","post","type-post","status-publish","format-standard","hentry","category-reactions","tag-en"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"en","enabled_languages":["en","fr"],"languages":{"en":{"title":true,"content":true,"excerpt":false},"fr":{"title":false,"content":false,"excerpt":false}}},"acf":[],"_links":{"self":[{"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/posts\/431","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/comments?post=431"}],"version-history":[{"count":3,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/posts\/431\/revisions"}],"predecessor-version":[{"id":445,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/posts\/431\/revisions\/445"}],"wp:attachment":[{"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/media?parent=431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/categories?post=431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jfmaheux.uqam.ca\/chroniques\/wp-json\/wp\/v2\/tags?post=431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}