{"title":"The emergence of the analytic-structural way of thinking in linear algebra as a blended space","authors":"Margherita Piroi","doi":"10.1007/s10649-024-10354-0","DOIUrl":null,"url":null,"abstract":"<p>This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall linear algebra topics she had learned the previous year. Following the theory of conceptual blending, the presented case study is used as a model for the description of the emergence of the analytic-structural mode. It shows how the evolution of the used signs and their relationships suggests that the analytic-structural mode emerges as a blend between the other two ways of thinking.</p>","PeriodicalId":48107,"journal":{"name":"Educational Studies in Mathematics","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Educational Studies in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10649-024-10354-0","RegionNum":2,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall linear algebra topics she had learned the previous year. Following the theory of conceptual blending, the presented case study is used as a model for the description of the emergence of the analytic-structural mode. It shows how the evolution of the used signs and their relationships suggests that the analytic-structural mode emerges as a blend between the other two ways of thinking.
期刊介绍：
Educational Studies in Mathematics presents new ideas and developments of major importance to those working in the field of mathematics education. It seeks to reflect both the variety of research concerns within this field and the range of methods used to study them. It deals with methodological, pedagogical/didactical, political and socio-cultural aspects of teaching and learning of mathematics, rather than with specific programmes for teaching mathematics. Within this range, Educational Studies in Mathematics is open to all research approaches. The emphasis is on high-level articles which are of more than local or national interest.? All contributions to this journal are peer reviewed.
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