{"title":"What Are and What Are Not Extrema Points? Examining Definitions and Examples","authors":"Pessia Tsamir, Dina Tirosh, Regina Ovodenko","doi":"10.1007/s10763-024-10458-2","DOIUrl":null,"url":null,"abstract":"<p>This paper reports on five secondary school mathematics prospective teachers’ conceptions of <i>extreme point</i>. The analysis of the data addressed students’ definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept images regarding what <i>is</i> and what <i>is not</i> an extreme point. Participants viewed extrema points as points that necessarily satisfy <i>f</i>′ = 0 or as points that are always at a “change in monoticity” of the function. The topic “extreme points” is both an aim and a mean to address broader issues related to mathematical definitions, examples, and nonexamples. We conclude with possible next-step ideas.</p>","PeriodicalId":14267,"journal":{"name":"International Journal of Science and Mathematics Education","volume":"44 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Science and Mathematics Education","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.1007/s10763-024-10458-2","RegionNum":3,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
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Abstract
This paper reports on five secondary school mathematics prospective teachers’ conceptions of extreme point. The analysis of the data addressed students’ definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept images regarding what is and what is not an extreme point. Participants viewed extrema points as points that necessarily satisfy f′ = 0 or as points that are always at a “change in monoticity” of the function. The topic “extreme points” is both an aim and a mean to address broader issues related to mathematical definitions, examples, and nonexamples. We conclude with possible next-step ideas.
期刊介绍：
The objective of this journal is to publish original, fully peer-reviewed articles on a variety of topics and research methods in both science and mathematics education. The journal welcomes articles that address common issues in mathematics and science education and cross-curricular dimensions more widely. Specific attention will be paid to manuscripts written by authors whose native language is not English and the editors have made arrangements for support in re-writing where appropriate. Contemporary educators highlight the importance of viewing knowledge as context-oriented and not limited to one domain. This concurs with current curriculum reforms worldwide for interdisciplinary and integrated curricula. Modern educational practice also focuses on the use of new technology in assisting instruction which may be easily implemented into such an integrated curriculum. The journal welcomes studies that explore science and mathematics education from different cultural perspectives.
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