Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics

Hiebert, James; Carpenter, Thomas P.; Fennema, Élizabeth; Fuson, Karen C.; Human, Paul; Murray, Hanlie; Olivier, Alwyn; Wearne, Diana

doi:10.2307/1176776

Cited by 89 publications

(102 citation statements)

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“…Many researchers in the field of mathematics education hold similar viewpoints (cf. Cobb, 1995;Freudenthal, 1991;Gravemeijer, 1994;Hiebert et al, 1996;Müller & Wittmann, 1995;Resnick, Bill, & Lesgold, 1992;Reys, Reys, Nohda, & Emori, 1995). In the Netherlands these ideas have been incorporated in the theoretical framework of Realistic Mathematics Education (RME) (Freudenthal, 1973(Freudenthal, , 1991Gravemeijer, 1994;Treffers, 1987Treffers, , 1991.…”

Section: In the International Handbook On Mathematics Educationmentioning

confidence: 99%

“…These verbal labels not only facilitated classroom communication about the different solutions but also prompted pupils to first look thoughtfully at a problem before solving it, which is an important issue in RME and in other research on solving problems (cf. Hiebert et al, 1996). In some cases children were required both to label and to solve problems, and in other cases they were asked only to write down the names of the strategies they would use to solve the problems.…”

Section: Realistic Versus Gradual Program Designmentioning

confidence: 99%

“…Strategy labels and classroom discussion as described earlier were used to stimulate a flexible problem-solving attitude (cf. Hiebert et al, 1996).…”

Section: Realistic Program Designmentioning

confidence: 99%

See 2 more Smart Citations

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

Klein¹,

Beishuizen²,

Treffers³

1998

Journal for Research in Mathematics Education

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In this study we compare 2 experimental programs for teaching mental addition and subtraction in the Dutch 2nd grade (N = 275). The goal of both programs is greater flexibility in mental arithmetic through use of the empty number line as a new mental model. The programs differ in instructional design to enable comparison of 2 contrasting instructional concepts. The Realistic Program Design (RPD) stimulates flexible use of solution procedures from the beginning by using realistic context problems. The Gradual Program Design (GPD) has as its purpose a gradual increase of knowledge through initial emphasis on procedural computation followed by flexible problem solving. We found that whereas RPD pupils showed a more varied use of solution procedures than the GPD pupils, this variation did not influence the procedural competence of the pupils. The empty number line appears to be a very powerful model for the learning of addition and subtraction up to 100.Key Words: Addition, subtraction; Children's strategies; Early childhood, K-4; Early number learning; Mental arithmetic; Representations, modeling; Whole numbers Becker and Selter (1996) gave an overview of recent developments in mathematics education in elementary schools. Their central thesis was that "teaching is no longer seen as a treatment and learning as the effect. Learners are people who actively construct mathematics" (p. 511). Mental arithmetic plays a central role in this respect, stimulating not only conceptual understanding and procedural proficiency but also number sense and the understanding of number relations (McIntosh, Reys, & Reys, 1992). Many researchers in the field of mathematics education hold similar viewpoints (cf. Cobb, 1995;Freudenthal, 1991;Gravemeijer, 1994;Hiebert et al., 1996;Müller & Wittmann, 1995;Resnick, Bill, & Lesgold, 1992;Reys, Reys, Nohda, & Emori, 1995). In the Netherlands these ideas have been incorporated in the theoretical framework of Realistic Mathematics Education (RME) (Freudenthal, 1973(Freudenthal, , 1991Gravemeijer, 1994;Treffers, 1987Treffers, , 1991. RME came into prominence after a national evaluation study of mathematics education in the Netherlands in primary schools (Wijnstra, 1988) 1998, Vol. 29, No. 4, 443-464 Research reported in this article was supported by the Dutch National Science Foundation Grant 575-90-607. In the International Handbook on Mathematics Education, which Journal for Research in Mathematics EducationThis material may not be copied or distributed electronically or in any other format without written permission from NCTM.Copyright © 1998 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. pointed to an unacceptably low level of procedural competency in certain domains; for example, only 55% of the Dutch third graders were capable of solving the subtraction problem 64 -28 correctly. This study also revealed a generally low level of flexibility in using arithmetic strategies. As a result of this evaluation study, Treffers and De Moor (1990) published a...

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Section: In the International Handbook On Mathematics Educationmentioning

confidence: 99%

Section: Realistic Versus Gradual Program Designmentioning

confidence: 99%

See 1 more Smart Citation

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

Klein¹,

Beishuizen²,

Treffers³

1998

Journal for Research in Mathematics Education

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“…Beyond the assumptions about inquiry noted in a previous paragraph, an inquiry learning approach in math was intended for students to experience how mathematicians work (Artigue, & Blomhøj, 2013). Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, and Wearne (1996) argued that inquiry in mathematics needed to be grounded in a fundamental aspect of mathematics, namely problem solving. In this approach, open-ended and rich mathematical tasks are designed to trigger and sustain the mathematical activity of students.…”

Section: Inquiry Learning In Mathematics Classroomsmentioning

confidence: 99%

An Action Research Project by Teacher Candidates and their Instructor into using Math Inquiry: Learning about Relations between Theory and Practice

Betts¹,

McLarty²,

Dickson³

2017

Networks: An Online Journal for Teacher Research

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“…The second general approach is to make something in students' work more problematic (Hiebert et al, 1996). That is, the software tools help students see something as problematic that they might otherwise overlook.…”

Section: Problematizing Conceptsmentioning

confidence: 99%

Why scaffolding should sometimes make tasks more difficult for learners

Reiser¹

2002

Proceedings of the Conference on Computer Support for Collaborative Learning Foundations for a CSCL Community - CSCL '02

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There has been much interest in using software tools to scaffold learners in complex tasks, that is, to provide supports that enable students to deal with more complex content and skill demands than they could otherwise handle. Many different approaches to scaffolding techniques have been presented in a broad range of software tools. I discuss two mechanisms to explain how software tools can scaffold learners. Software tools can help structure the learning task, guiding learners through key components and supporting their planning and performance. In addition, tools can shape students' performance and understanding of the task in terms of key disciplinary content and strategies, thereby problematizing this important content. While making the task more difficult in the short term, by forcing learners to address these ideas, such scaffolded tools make this work more productive opportunities for learning.

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Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics

Cited by 89 publications

References 0 publications

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design

An Action Research Project by Teacher Candidates and their Instructor into using Math Inquiry: Learning about Relations between Theory and Practice

Why scaffolding should sometimes make tasks more difficult for learners

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