Heather struggled with reconciling her explanation and the new knowledge; the ability to try and see it from another perspective was blocked out, favouring instead her own understanding of how the seasons happened. Despite the fact that she struggled to explain it, her persistence in perpetuating knowledge that she believed to be true was staggering, or as Shapiro writes, “relat[ing] it to already existing ideas or to language which [she] already possesses” (Shapiro, 1988, p.99). As a result and as information for my own practice, I take this as a cry to have kids explain their thinking as much as possible, and to rely on tools like the Thinking Routines to help clarify and to get students to talk about their understandings at every opportunity, in order to expel the myths that may come up as a result of digging deeper.<\/p>\n
I chose to explore equivalence and how the equals sign can be taken to mean \u201cresulting in\u201d or \u201ccomputes to\u201d. Vermeulen and Meyer describe this as students having an operational view of the equals sign, despite its relational meaning. Essentially, seeing the equals sign as a function of computation, and as such, students being likely to \u201creject equations such as 8=8 as false, because there is no obvious action\u201d (Vermeulen & Meyer 2017). Many factors perpetuate this misconception, but they \u201c\u2026attribute an operational view of the equal sign to the use of calculators and direct verbal-to-written translation of mathematical sentences\u201d (Vermeulen & Meyer 2017). The article by Vermeulen and Meyer had me thinking quite a bit about my own practice, not only with respect to technology, but also in the language I choose to use.<\/p>\n
In thinking about how this affects educators, Vermeulen and Meyer write, \u201cwe are of the opinion that the results obtained from both teachers and students do suggest that, owing to these teachers\u2019 limited MKfT of the equal sign, they were not aware that their teaching could, and possibly did, promote students\u2019 misconceptions of the equal sign, nor were they able to identify students\u2019 misconceptions or suggest how to prevent, reduce or rectify these misconceptions\u201d (Vermeulen & Meyer 2017). As a teacher of young children, this is particularly striking, because it brings to light the fact that in something as simple as the way I chose to vocalize and draw attention to equivalence can help promote or expel the myths of math as solely arithmetic and computation.<\/p>\n
Technology creates opportunities for students to be able to visualize the problem (and it\u2019s potential solutions) in a different way, making room for them to be critical of their own misconceptions. In the case of algebraic equations and equivalence, the idea of a balance or see-saw helps the students envisage this concept. Sakow and Ruveyda write, \u201cModern tools like tablet apps may help middle school teachers end the thirty-year stagnation and put these algebraic misconceptions to rest at last\u201d (Sakow & Ruveyda, 2015). In fact, there is an app that the article outlines as particularly effective to this end. Though I\u2019m sure there are many such apps that use the same see-saw analogy, I particularly appreciate that \u201cMathScaled\u2019s weights change in value from problem to problem, erasing student notions of specific values for variables. Furthermore, the app allows students to save screenshots of their work to assist the teacher in efficiently assessing understanding and providing individualized support\u201d (Sakow & Ruveyda, 2015). It is the constantly changing factors and reframing of the problems that allows the concept to solidify, and for the students to hone their skills in this respect.<\/p>\n
<\/p>\n
References<\/strong><\/p>\n Matthew Sakow, & Ruveyda Karaman. (2015). Exploring Algebraic Misconceptions with Technology.\u00a0Mathematics Teaching in the Middle School,<\/em>\u00a021<\/em>(4), 222-229. doi:10.5951\/mathteacmiddscho.21.4.0222<\/p>\n Shapiro, B. L. (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. Developments and dilemmas in science education, 96-120.<\/p>\n Cornelis Vermeulen & Bronwin Meyer (2017). The Equal Sign: Teachers\u2019 Knowledge and Students\u2019 Misconceptions<\/a>. African Journal of Research in Mathematics, Science and Technology Education\u00a0<\/a>Vol. 21 , Iss. 2.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Heather struggled with reconciling her explanation and the new knowledge; the ability to try and see it from another perspective was blocked out, favouring instead her own understanding of how the seasons happened. Despite the fact that she struggled to explain it, her persistence in perpetuating knowledge that she believed to be true was staggering, […]<\/p>\n","protected":false},"author":55933,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669382],"tags":[],"class_list":["post-4444","post","type-post","status-publish","format-standard","hentry","category-a-conceptual-challenges"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/users\/55933"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/comments?post=4444"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4444\/revisions"}],"predecessor-version":[{"id":4446,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/4444\/revisions\/4446"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/media?parent=4444"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/categories?post=4444"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/tags?post=4444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}