For the Learning of Mathematics最新文献

Distance Mathematics Education as a Means for Tackling Impulse Control Disorder: The Case of a Young Convict. 远程数学教育作为解决冲动控制障碍的手段:一个年轻罪犯的案例。

For the Learning of Mathematics Pub Date : 2017-01-01 DOI: 10.2307/26548468

L. Ahl, Mario Sánchez Aguilar, Uffe Thomas Jankvist

引用次数: 3

Key Ideas and Memorability in Proof. 关键思想和记忆证明。

For the Learning of Mathematics Pub Date : 2014-01-01 DOI: 10.2307/j.ctvc778jw.19

G. Hanna, J. Mason

引用次数: 13

Generic Proving: Reflections on Scope and Method. 通用证明:关于范围和方法的思考。

For the Learning of Mathematics Pub Date : 2013-01-01 DOI: 10.1515/9781400865307-017

U. Leron, O. Zaslavsky

{"title":"Generic Proving: Reflections on Scope and Method.","authors":"U. Leron, O. Zaslavsky","doi":"10.1515/9781400865307-017","DOIUrl":"https://doi.org/10.1515/9781400865307-017","url":null,"abstract":"For the Learning of Mathematics 33, 3 (November, 2013) FLM Publishing Association, Fredericton, New Brunswick, Canada A generic proof is, roughly, a proof carried out on a generic example. We introduce the term generic proving to denote any mathematical or educational activity surrounding a generic proof. The notions of generic example, generic proof, and proof by generic example have been discussed by a number of scholars (e.g., Balacheff, 1988; Mason & Pimm, 1984; Rowland, 1998; Malek & MovshovitzHadar, 2011). All acknowledge the role of proof not only in terms of validating the conclusion of a theorem but, just as importantly, as a means to gain insights to why the theorem is true. In particular, we support and extend the argument made by Rowland (1998) that a generic proof does carry a substantial “proof power”, and may in fact lie on the same continuum as the working mathematician’s proof. In the same vein, we analyze possible ways that generic proof and proving may help in unpacking and making accessible to students at all levels the main ideas of a proof [1]. The article is organized as a reflection on three examples, or “mathematical case studies”, which reveal increasingly more subtle facets of generic proving. The first mathematical case study is a simple and elementary theorem of numbers (also discussed in Rowland, 1998). The second example, a decomposition theorem on permutations, is still elementary in the sense of not requiring subject-matter knowledge beyond high school mathematics, but is more sophisticated in terms of the proof techniques required. The third example, Lagrange’s theorem from elementary group theory, is more sophisticated both in terms of the proof techniques and the subject matter knowledge required. All the examples are introduced in a self-contained manner and all the terminology is explained and exemplified. In the second part of the article, we reflect in more depth on the mathematical case studies of the first part, in an attempt to explicate some of the general features of generic proofs. For example, in an attempt to characterize the mathematical content of generic proofs, we look for commonalities with professional mathematicians’ proofs as they appear in research journals and in university-level textbooks and lectures. For another example, we ask—and try to give some partial answers—about the scope of generic proving: what kind of proofs can be more or less helpfully approached via a generic version? The article has been written in the form of a thought experiment. It is, however, solidly based in the experience of the authors in running many workshops with students and in international conferences on exactly these examples and ideas. Several researchers have previously discussed the more theoretical aspects of generic proofs. This research, while relevant to the topic at hand, would take us away from our mathematical and pedagogical focus [2].","PeriodicalId":38628,"journal":{"name":"For the Learning of Mathematics","volume":"33 1","pages":"198-215"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/9781400865307-017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66835514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 50

Mathematics Education:Theory, Practice & Memories Over 50 Years 数学教育:50年来的理论、实践与记忆

For the Learning of Mathematics Pub Date : 2010-01-01 DOI: 10.1163/9789460910319_002

J. Mason

引用次数: 18

Does Practice Make Perfect 熟能生巧吗?

For the Learning of Mathematics Pub Date : 2004-01-01 DOI: 10.1007/1-4020-7910-9_36

Shiqi Li

引用次数: 13

A Conversation with Paulo Freire. 保罗·弗莱雷的对话。

For the Learning of Mathematics Pub Date : 1997-01-01 DOI: 10.1007/978-1-349-17771-4_12

P. Freire, Ubiratan D’ambrosio, Maria do Carmo Mendonca

引用次数: 86

Beyond Questions and Answers: Prompting Reflections and Deepening Understandings of Mathematics Using Multiple-Entry Logs 超越问题和答案:促使反思和加深理解数学使用多条目日志

For the Learning of Mathematics Pub Date : 1992-01-01 DOI: 10.7282/T37D2SMR

A. Powell, Mahendra Ramnauth

{"title":"Beyond Questions and Answers: Prompting Reflections and Deepening Understandings of Mathematics Using Multiple-Entry Logs","authors":"A. Powell, Mahendra Ramnauth","doi":"10.7282/T37D2SMR","DOIUrl":"https://doi.org/10.7282/T37D2SMR","url":null,"abstract":"There is little discussion in mathematics education about me~hods of effective tutoring; in particular, in so-called o~hce hour or tutmial sessions Nevertheless, these sessiOns are as much occasions for interactive instruction as classr?oms are, and deserve theoretical and pedagogical attentwn By initiating discussion in this area we invite others to contribute critically to these beginnings Clearly, d1scusstons m th1s area will inform and be informed by classroom interactions .. For this reason, though we focus on office-hom or tutorial interactions, we do indicate how t~e pedagogical tool we describe infmms classroom practice During office-hour or tutorial sessions, students customarily set specific goals that, with the tacit agreement of an mstructm or tutor, govern the interactions of these sessions . These goals typically center on questions or problems for which students seek immediate answers or solutions. Two problematic features often characteiize interactions of these sessions. First, matters of mechanics or techniques constrain the mathematical dialogue and second in this \"dialogue,\" the instructm or tutor d~es most of ~he talking or explaining Stemming conspicuously from the first feature IS the state of affairs that instmctors and tutors operate rather like machines, pmducing worked-out solutions each time students pose questions: \"How do you do problem 15 on page 35?\" or, on rare occasions, \"I was able to solve this problem to here but cannot see how to complete it Would you show me how to continue?\" Curricular emphases on content over process and answers over understandings contribute to fmming academic cultures in which students respond to mathematics learning in these ways ~o.r~over the pace and superficiality of many courses mh1b1t efforts to engage students in justifying techniques, ~n demonstrating derivations of formulae, or in intenogatmg and negotiating meanings of mathematical objects and processes Students either ~gnore these gestures or plead, Just show me how to do 11. After the exam, I may think about why it works.\" The second problematic feature of office-hour or tutorial sessions concerns who performs most of the actions does most of the talking, and therefore, acquires most ~f the learning Usually, we, instructors and tutors, dominate these sessions with our action and talk Consequently, we, ~ot stud~nts, do most of the cognizing: thinking, explainmg, solvmg, and so forth. That is, we appropriate available opportunities to re-experience and re-conceive mathematics. Fm~e~~ore, ~is appropriated time and space offer us the possibility of mcreasing our insight into a piece of n:athematics while students, in awe, mostly listen to our display of knowledge and, when it occurs, witness om mathematical growth On the whole, then, the benefits of office-hom· or tutorial sessions mostly accme to us How can instructors and tutors go beyond question-andanswer sessions and provide time and space fm students to reflect deeply on, g","PeriodicalId":38628,"journal":{"name":"For the Learning of Mathematics","volume":"12 1","pages":"12-18"},"PeriodicalIF":0.0,"publicationDate":"1992-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71383814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 31

Two Theories of "Theory" in Mathematics Education: Using Kuhn and Lakatos to Examine Four Foundational Issues. 数学教育中的两种“理论”:用库恩和拉卡托斯考察四个基本问题。

For the Learning of Mathematics Pub Date : 1988-01-01 DOI: 10.2307/40247923

R. Orton

引用次数: 6