Teaching Mathematics for Understanding: Discussing Case Studies of Four Fifth-Grade Teachers

Putnam, Ralph T.; Heaton, Ruth M.; Prawat, Richard S.; Remillard, Janine T.

doi:10.1086/461723

Cited by 85 publications

(56 citation statements)

References 20 publications

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“…Studies in which teachers were presented with examples of critical classroom events revealed that an insufficient understanding of mathematical content limits teachers' capacity to explain and represent that content to students in a sense-making way, a deficit that cannot be offset by pedagogical skills. Ball (1990) and Ma (1999) demonstrated this relationship for multiplication and place values; Borko et al (1992) and Simon (1993), for division; Even (1993), Stein, Baxter, andLeinhardt (1990), andHeaton (2000), for patterns and functions; and Putnam, Heaton, Prawat, and Remillard (1992), for geometry. Given their case studies, Putnam et al con-cluded that the efforts of teachers with a limited conceptual understanding ''fell short of providing students with powerful mathematical experiences'' (p. 221).…”

Section: Findings Of Qualitative Studies On the Importance Of A Concementioning

confidence: 95%

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Baumert

Kunter

Blum

et al. 2010

American Educational Research Journal

1,508

927

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In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers' content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers' pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students' learning gains that was mediated by the provision of cognitive activation and individual learning support. American Educational Research Journal March 2010, Vol. 47, No. 1, pp. 133-180 DOI: 10.3102/0002831209345157 Ó 2010 AERA. http://aerj.aera.netat Max Planck Ins on July 27, 2011 http://aerj.aera.net Downloaded from KEYWORDS: teacher knowledge, teacher education, mathematics, instruction, cognitive activation, hierarchical modeling with latent variables S ince Lee Shulman's presidential address at the 1985 American Educational Research Association meeting-in which Shulman went beyond the generic perspective of educational psychology, emphasizing the importance of domain-specific processes of learning and instruction-educational research JÜ RGEN BAUMERT is a co-director at Max Planck Institute for Human Development, Center for Educational Research, Lentzeallee 94, 14195 Berlin, Germany; e-mail: sekbaumert@mpib-berlin.mpg.de. His research interests include research in teaching and learning, cultural comparisons, large-scale assessment, and cognitive and motivational development in adolescence. MAREIKE KUNTER is a research scientist at Max Planck Institute for Human Development, e-mail: kunter@mpib-berlin.mpg.de. Her research interests include teacher research, motivational processes in the classroom, and assessment of instructional processes. WERNER BLUM is a professor of mathematics education at University of Kassel, e-mail: blum@mathematik.uni-kassel.de. His research interests include empirical research on instructional quality in mathematics, national and international comparison studies in mathematics, approaches to application, modeling, and proofs in mathematics instruction. MARTIN BRUNNER is an associate professor at University of Luxembourg, e-mail: martin.brunner@uni.lu. His research interests include research on cognitive abilities, achievement, and achievement motivation by means of modern measurement models. THAMAR VOSS is a predoctoral research fellow at Max Planck Institute for Human Development, e-mail: voss@mpib-berlin.mpg.de. Her research interests include research on instruction and learning, teacher research, and teacher beliefs. ALEXANDER JORDAN is an academic staff member at University of Biel...

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Section: Findings Of Qualitative Studies On the Importance Of A Concementioning

confidence: 95%

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Baumert

Kunter

Blum

et al. 2010

American Educational Research Journal

1,508

927

View full text Add to dashboard Cite

show abstract

“…I think it will be very difficult to accept the variety of responses from the class while at the same time trying to teach basic mathematical concepts that have one solution. (Lesley, MJ2) Sally and Lesley were indeed anticipating the predicament or ''teaching paradox'' that researchers have said every teacher who wants to help students learn with understanding must face: that is, ''the interplay between students making sense or constructing meaning for themselves and making sure that students learn particular mathematics'' (Putnam, Heaton, Prawat, & Remillard, 1992; also see Cobb, 1988;and Edwards & Mercer, 1987). This teaching paradox became a reality for preservice teachers in this study as they found themselves responding to students' incorrect work.…”

Section: Exploring Alternatives To Correcting Students' Thinkingmentioning

confidence: 99%

Praising and correcting: prospective teachers investigate their teacherly talk

Crespo

2002

Teaching and Teacher Education

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“…It is generally accepted, and widely known about what the teacher was (teacher knowledge) will influence what will be taught by the teacher to student, and will eventually also affect students (Dougherty, 1990;Ball & McDiarmid, 1990;Fennema & Franke, 1992). In addition, pre-service teachers' beliefs about mathematics teaching and pedagogical content knowledge can influence the decisions or the selection method of teaching (Pajares, 1992;Prawat, 1992;Thompson, 1992). New teachers as they taught mostly in teaching (Lortie, 1975;Noyes, 2004).…”

Section: Mathematics Beliefsmentioning

confidence: 99%

“…Teachers' beliefs about mathematics have an enormous impact on teaching practices (Hart, 2002;Buchman, 1987;Hall, 2005;Beswick, 2006;Golafshani, 2002Golafshani, , 2005Charalambos, Philippou & Kyriakides, 2002;Ernest, 1988Ernest, , 1989Ernest, , 2000Putnam, Prawat & Remillard, 1992 ;Perrin-Glorian, Deblois & Robert, 2008). The study by Samuelsson (2008) found that nearly 80% of respondents in the study of pre-service teachers who were interviewed had negative feelings toward mathematics.…”

Section: Mathematics Beliefsmentioning

confidence: 99%

Exploring Beliefs of Pre-Service Mathematics Teachers: A Malaysian Perspective

Adnan¹,

Zakaria²

2010

ASS

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The purpose of this study was to determine the beliefs of pre-service mathematics teachers. This study involved 83 respondents from the pre-service teachers from a public higher education institution (IPTA) in Malaysia. The instruments used in this study consist 42 items of mathematics beliefs. There are three dimensions in these instruments, namely beliefs about mathematics as nature, beliefs about learning mathematics and beliefs about the teaching of mathematics. The findings showed that pre-service teacher's beliefs mathematics can be used in everyday life. For the beliefs about learning mathematics, the respondents agreed that students should be able to give reasons to support each solve mathematical problems. Finally, about the beliefs on mathematics teaching, the respondents agreed that the teaching of mathematics to students should be encouraged by explaining the mathematical ideas.

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Teaching Mathematics for Understanding: Discussing Case Studies of Four Fifth-Grade Teachers

Cited by 85 publications

References 20 publications

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

Praising and correcting: prospective teachers investigate their teacherly talk

Exploring Beliefs of Pre-Service Mathematics Teachers: A Malaysian Perspective

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