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Henderson, Peter; Hodgen, Jeremy; Foster, Colin; Kuchemann, Dietmar – Education Endowment Foundation, 2017
This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…
Descriptors: Mathematics Skills, Elementary Education, Teaching Methods, Mathematics Instruction
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Kalinowski, Pav; Lai, Jerry; Fidler, Fiona; Cumming, Geoff – Statistics Education Research Journal, 2010
Our research in statistical cognition uses both qualitative and quantitative methods. A mixed method approach makes our research more comprehensive, and provides us with new directions, unexpected insights, and alternative explanations for previously established concepts. In this paper, we review four statistical cognition studies that used mixed…
Descriptors: Graduate Students, Qualitative Research, Psychologists, Statistical Analysis
delMas, Robert C.; Bart, William M. – Focus on Learning Problems in Mathematics, 1989
Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)
Descriptors: Achievement Tests, Cognitive Structures, College Mathematics, Higher Education
Konold, Clifford – 1989
Results of the most recent administration of the National Assessment of Educational Progress (NAEP) suggest that the majority of secondary students believe in the independence of random events. In the study reported here, a high percentage of high school and college students answered similar problems correctly. However, about half of the students…
Descriptors: College Mathematics, High Schools, Higher Education, Mathematical Concepts
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Tirosh, Dina; Graeber, Anna O. – Journal for Research in Mathematics Education, 1990
Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…
Descriptors: Arithmetic, College Mathematics, Computation, Division
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Thipkong, Siriporn; Davis, Edward J. – School Science and Mathematics, 1991
A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)
Descriptors: Algorithms, Arithmetic, Decimal Fractions, Elementary Education
Konold, Clifford – 1988
The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…
Descriptors: Cognitive Processes, Cognitive Structures, College Mathematics, Concept Formation
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Graeber, Anna O.; Tirosh, Dina – Educational Studies in Mathematics, 1990
Described are the conceptions held by United States and Israeli students about multiplication and division that may impede their work with decimals. Included are the introduction, method, division and multiplication task results, and the implications for education and textbook development. (KR)
Descriptors: Arithmetic, Elementary Education, Elementary School Mathematics, Foreign Countries
Dahlberg, Cecilia, Ed. – 1989
This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…
Descriptors: Algorithms, Arithmetic, Cognitive Structures, Concept Formation
Wilson, Patricia S. – Focus on Learning Problems in Mathematics, 1990
Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…
Descriptors: Abstract Reasoning, Cognitive Development, Cognitive Dissonance, Cognitive Structures
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Fischbein, Efraim; And Others – Educational Studies in Mathematics, 1991
To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…
Descriptors: Cognitive Structures, Cognitive Style, Comprehension, Concept Formation