{"title":"Problem solving and reasoning","authors":"J. Greeno, H. Simon","doi":"10.4135/9781526483775.n6","DOIUrl":"https://doi.org/10.4135/9781526483775.n6","url":null,"abstract":"Abstract : This long chapter reviews research on problem solving and reasoning; the intended use is as text material for advanced students and others needing a moderately detailed introduction to the topics. The orientation is primarily psychological, with significant attention given to results from artificial intelligence. Major theoretical concepts, such as problem representation, the problem space, strategic knowledge, and problem-solving search, are developed in detail; and major empirical methods such as thinking-aloud protocols, problem-behavior graphs, and use of error patterns and latencies, are described and illustrated. Sections of the chapter include: Problems with well specified goals and procedures, Problems of design and arrangement, Inductive problem solving, and Evaluation of deductive arguments. (Author)","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128260949","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":"Mathematics across the curriculum","authors":"Vivienne Mulholland","doi":"10.1080/0300443920820104","DOIUrl":"https://doi.org/10.1080/0300443920820104","url":null,"abstract":"Mathematics has traditionally been taught through a subject based approach. The advent of the National Curriculum has brought about a need for change to a topic based cross‐curricular strategy, to deal with mathematics in real‐life problems. One way of approaching this with young children is to introduce an imaginary world in which they are asked to help solve the open ended real‐life problems of the inhabitants. In this way the children are able not only to pose further problems arising from the initial task, but also to develop their own strategies to the solution of them, linking across the curriculum as they do so. In this way children appear capable of posing and solving problems at a much earlier age.","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124955222","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":"Children and families: partners in learning","authors":"","doi":"10.4135/9781526483775.n11","DOIUrl":"https://doi.org/10.4135/9781526483775.n11","url":null,"abstract":"","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116812456","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":"Inclusive practice in mathematics","authors":"","doi":"10.4135/9781526483775.n8","DOIUrl":"https://doi.org/10.4135/9781526483775.n8","url":null,"abstract":"","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131404843","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":"Becoming a leader of mathematical learning","authors":"","doi":"10.4135/9781526483775.n1","DOIUrl":"https://doi.org/10.4135/9781526483775.n1","url":null,"abstract":"","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126854361","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":"Overcoming barriers to learning in mathematics","authors":"","doi":"10.4135/9781526483775.n9","DOIUrl":"https://doi.org/10.4135/9781526483775.n9","url":null,"abstract":"'Within the school curriculum learning mathematics is uniquely challenging in that it is highly organised, sequential and progressive. Simpler elements must be learned successfully before moving on to others. ‘It is a subject where one learns the parts; the parts build on each other to make a whole; knowing the whole enables one to reflect with more understanding on the parts, which in turn strengthens the whole. Knowing the whole also enables an understanding of the sequences and interactions of the parts and the way they support each other so that the getting there clarifies the stages of the journey.' (Chinn and Ashcroft, 1998: 4.)","PeriodicalId":286431,"journal":{"name":"Leading Primary Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126123456","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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