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Journal ArticleDOI

Teachers' Knowledge of Children's Mathematics after Implementing a Student-Centered Curriculum

01 Jun 2004-Journal of Mathematics Teacher Education (Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com.)-Vol. 7, Iss: 2, pp 121-144
TL;DR: This paper investigated the knowledge 13elementary teachers gained implementing a knowledge-centered curriculum in the context ofdistrictwide reform, finding that teachers' knowledge of nonstandard strategiessupported by the curriculum materials was strongerer and more coherent than their knowledge of students' novel nonstandard strategies.
Abstract: Our study investigated the knowledge 13elementary teachers gained implementing astudent-centered curriculum in the context ofdistrict-wide reform. Participants comprisedall the teachers in grades three, four and fiveat a single elementary school. We believed thatinvestigating teachers' responses to fictionalpedagogical scenarios involving nonstandardalgorithms would yield insights into criticalcomponents of their knowledge base. We lookedin particular at teachers' knowledge of children's mathematics. We found that teacherswere in the midst of creating a knowledge basefocused on children's mathematics and groundedin knowledge about alternative conceptualtrajectories through the elementary curriculum.Teachers' knowledge of nonstandard strategiessupported by the curriculum materials wasstronger and more coherent than their knowledgeof students' novel nonstandard strategies.Strong mathematical knowledge was notnecessarily associated with strong knowledge ofchildren's mathematics. Teachers' thinkingvaried by a topic's treatment in the writtencurriculum materials used, suggestingimplementation of the curriculum as a source oflearning.
Citations
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Journal ArticleDOI
TL;DR: This paper examined the influence of teachers' beliefs and knowledge on their error-handling practices during class discussion of mathematics, and found that although teachers' ways of handling student errors are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.
Abstract: This collective case study examines the influence of 4 third-grade teachers’ beliefs and knowledge on their error-handling practices during class discussion of mathematics. Across cases, 3 dimensions of teachers’ error-handling practices are identified and discussed in relation to teacher beliefs and knowledge: (a) intentional focus on flawed solutions in class discussion, (b) promotion of conceptual understanding through discussion of errors, and (c) mobilization of a community of learners to address errors. Study findings suggest that, although teachers’ ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.

126 citations


Cites background from "Teachers' Knowledge of Children's M..."

  • ...Based on scenarios developed by Kennedy et al. (1993) and Empson and Junk (2004), these scenarios asked teachers to anticipate the varied ways children might solve a particular problem, interpret student work, and respond to students’ difficulties....

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  • ...Empson and Junk (2004) report a study in which teachers expressed beliefs that it is a good idea to use student mistakes as opportunities for learning....

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Journal ArticleDOI
TL;DR: In this article, the authors present two extended conceptual examples of ways in which educative curriculum materials might be used to support PTs in developing the knowledge needed for teaching, and follow these examples with a set of empirically based design principles.
Abstract: Building on the work of Ball and Cohen and that of Davis and Krajcik, as well as more recent research related to teacher learning from and about curriculum materials, we seek to answer the question, How can prospective teachers (PTs) learn to read and use educative curriculum materials in ways that support them in acquiring the knowledge needed for teaching? We present two extended conceptual examples of ways in which educative curriculum materials might be used to support PTs in developing the knowledge needed for teaching. We follow these examples with a set of empirically based design principles and conclude with a brief consideration of unanswered questions related to the use of educative curriculum materials in teacher education.

65 citations


Cites background from "Teachers' Knowledge of Children's M..."

  • ...We build on this hypothesis by arguing that educative curriculum materials can provide teachers with some scaffolded expertise in children’s mathematical thinking by identifying solution methods that children tend to use (see also Empson & Junk, 2004)....

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Journal ArticleDOI
TL;DR: The authors studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers' learning or on teachers’ learning abo...
Abstract: Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers’ learning abo...

50 citations


Cites background from "Teachers' Knowledge of Children's M..."

  • ...Empson and Junk (2004) focused on the knowledge of CMT that teachers develop through their use of Investigations curriculum materials and found that teachers developed knowledge of children’s strategies that matched knowledge in the research literature. They suggest the teachers acquired this knowledge through observing children during activities in the curriculum. At the same time, connecting to CFoK within traditional mathematics curricula seems to be challenging, but possible, for teachers. Wyatt (2014) found that elementary teachers were able to add elements connecting to CFoK in their use of America’s Choice in both language arts and mathematics. However, Vomvoridi-Ivanović (2012) found that PSTs facilitating an afterschool mathematics club for Latino/a elementary-grade youth rarely made connections between textbook-like activities and students’ out-of-school experiences....

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  • ...…curriculum materials is prominent in several studies, with researchers noting ways that curricula can serve as levers for teacher learning and change (e.g., Empson & Junk, 2004; Lipka et al., 2005), and ways that more traditional curricula can constrain teacher practice (Vomvoridi-Ivanović, 2012)....

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  • ...Empson and Junk (2004) focused on the knowledge of CMT that teachers develop through their use of Investigations curriculum materials and found that teachers developed knowledge of children’s strategies that matched knowledge in the research literature....

    [...]

  • ...Empson and Junk (2004) focused on the knowledge of CMT that teachers develop through their use of Investigations curriculum materials and found that teachers developed knowledge of children’s strategies that matched knowledge in the research literature. They suggest the teachers acquired this knowledge through observing children during activities in the curriculum. At the same time, connecting to CFoK within traditional mathematics curricula seems to be challenging, but possible, for teachers. Wyatt (2014) found that elementary teachers were able to add elements connecting to CFoK in their use of America’s Choice in both language arts and mathematics....

    [...]

01 Jan 2009

46 citations


Cites background or methods from "Teachers' Knowledge of Children's M..."

  • ...Other programmes using this approach include those described by Chamberlin 2005; Empson and Junk 2004....

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  • ...…2003; Dinkelman 2003; Rogers, et al. 2007b; Williamson 2006 24 - Adler 2000; Ball and Cohen 1996; Clarke 1997; Collopy 2003; Davis and Krajcik 2005; Empson and Junk 2004; Hagedorn 2004; Kaahwa 2002; Remillard 2000; Remillard 2005 25 - Margolinas, et al. 2005 26 - Fraser, et al. 2007 27 - Barabash,…...

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Journal ArticleDOI
TL;DR: In this article, a study focused on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions, assessed and analyzed misconceptions were collected from 10 teachers at fifth-eighth grade levels in the USA.
Abstract: This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth–eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of students’ thinking. By engaging in the inquiry process of the 4 steps of identifying errors, analyzing reasons for the errors, designing approaches for correction, and taking action for correction, the teachers made obvious progress in their knowledge of students’ thinking, understood the difficulties and challenges their students had in learning mathematics, and enhanced their pedagogical content knowledge.

44 citations

References
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01 Jan 2000

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4,711 citations

Book
19 Mar 2013
TL;DR: Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.
Abstract: Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: * Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. * Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

3,480 citations

Book
01 Jan 2010
TL;DR: This book discusses subtraction with Regrouping, Multidigit Number Multiplication, and Teachers' Subject Matter Knowledge, as well as exploring the relationship between Perimeter and Area and Profound Understanding of Fundamental Mathematics.
Abstract: Author's Preface to the Anniversary Edition Series Editor's Introduction to the Anniversary Edition A Note about the Anniversary Edition Foreword Acknowledgments Introduction 1. Subtraction With Regrouping: Approaches To Teaching A Topic 2. Multidigit Number Multiplication: Dealing With Students' Mistakes 3. Generating Representations: Division By Fractions 4. Exploring New Knowledge: The Relationship Between Perimeter And Area 5. Teachers' Subject Matter Knowledge: Profound Understanding Of Fundamental Mathematics 6. Profound Understanding Of Fundamental Mathematics: When And How Is It Attained 7. Conclusion Appendix References New to the Anniversary Edition: Journal Article #1 New to the Anniversary Edition: Journal Article #2 Author Index Subject Index

2,056 citations