{"title":"On Learning to Teach... and Teaching to Learn.","authors":"M. Ollerton","doi":"10.2307/j.ctt2005xr8.12","DOIUrl":"https://doi.org/10.2307/j.ctt2005xr8.12","url":null,"abstract":"","PeriodicalId":36730,"journal":{"name":"Mathematics Teaching-Research Journal","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90162867","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}
{"title":"Learning from others","authors":"Paul Andrews, Judy Sayers","doi":"10.5749/j.ctt2204rbz.8","DOIUrl":"https://doi.org/10.5749/j.ctt2204rbz.8","url":null,"abstract":"This paper shares a European perspective on teaching linear equations in Finland, Flanders, and Hungary. Observing other cultures different from our own provides us with new insights that allow us to challenge the orthodoxy. The case study teacher approaches reported here lead us to question why we, the English, continue to teach analytical approaches for solving arithmetic equations when our European colleagues all seem to start with the algebraic.","PeriodicalId":36730,"journal":{"name":"Mathematics Teaching-Research Journal","volume":"38 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72460150","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}
{"title":"Relational Understanding and Instrumental Understanding.","authors":"R. Skemp","doi":"10.4324/9780203396391-18","DOIUrl":"https://doi.org/10.4324/9780203396391-18","url":null,"abstract":"One gets faux amis between English as spoken in different parts of the world. An Englishman asking in America for a biscuit would be given what we call a scone. To get what we call a biscuit, he would have to ask for a cookie. And between English as used in mathematics and in everyday life there are such words as field, group, ring, ideal. A person who is unaware that the word he is using is a faux ami can make inconvenient mistakes. We expect history to be true, but not a story. We take books without paying from a library, but not from a bookshop; and so on. But in the foregoing examples there are cues which might put one on guard: difference of language, or of country, or of context. If, however, the same word is used in the same language, country and context, with two meanings whose difference is non-trivial but as basic as the difference between the meaning of (say) ‘histoire’ and ‘story’, which is a difference between fact and fiction, one may expect serious confusion. Two such words can be identified in the context of mathematics; and it is the alternative meanings attached to these words,","PeriodicalId":36730,"journal":{"name":"Mathematics Teaching-Research Journal","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89522242","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}
{"title":"Goals of Learning and Qualities of Understanding.","authors":"R. Skemp","doi":"10.4324/9780203396391-19","DOIUrl":"https://doi.org/10.4324/9780203396391-19","url":null,"abstract":"","PeriodicalId":36730,"journal":{"name":"Mathematics Teaching-Research Journal","volume":"48 1","pages":"171-183"},"PeriodicalIF":0.0,"publicationDate":"1979-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86562321","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}
{"title":"Trial and Error:","authors":"Shmuel M. Avital, G. Amit","doi":"10.2307/j.ctv1hw3xxc.7","DOIUrl":"https://doi.org/10.2307/j.ctv1hw3xxc.7","url":null,"abstract":"","PeriodicalId":36730,"journal":{"name":"Mathematics Teaching-Research Journal","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88008835","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}
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