In this study, I examined the relationship between teachers’ mathematical knowledge and instruction. Twenty-one K–8 teachers who were enrolled in a master’s program were followed for 3 years to study how their mathematical knowledge and teaching changed over time. The results of multilevel growth models indicated that gains in teachers’ mathematical knowledge predicted changes in the quality of their lesson design, their mathematical agenda, and the classroom climate. Analyses of interviews and classroom observation data conducted with a subgroup of teachers revealed that in addition to the gains teachers made in their mathematical knowledge, their exit level of knowledge played a significant role in the quality of the changes in their practices.

#2Barbara Hug(UIUC: University of Illinois at Urbana–Champaign)H-Index: 10

Last. Sarah Theule Lubienski(UIUC: University of Illinois at Urbana–Champaign)H-Index: 24

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This study examines the impact of a new master's degree program on the instructional practices of K-8 in-service teachers. This 2.5-year master's program was designed to deepen in-service teachers' knowledge in science and mathematics and promote greater use of reform-oriented instruction. Teachers' instructional practices were captured annually through classroom observations, student reports, and teacher self-reports. Based on the results of the first 2 years of program implementation, there wa...

This longitudinal study examines growth in teacher knowledge as measured by two popular assessments—Learning Mathematics for Teaching (LMT) and Diagnostic Teacher Assessments in Mathematics and Science (DTAMS). Using data collected from 24 teachers, we compare the extent to which each assessment captured teacher learning during a K-8 mathematics content/pedagogy hybrid course and a general mathematics content course. Teachers made large gains on both measures, but the LMT better captured gains m...

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers’ knowledge for teaching algebra. The three categories of knowledge—school, advanced, and teaching—build on the work of Ball and others for elementary s...

This paper investigates the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the mathematical quality of instruction by comparing the enactment of a fractions problem taught by two teachers with differing MKT. It was found that MKT seem to support teachers' precise use of mathematical language and to prevent errors; the curriculum materials provided a rich representational context for mathematical work. However, teachers' orientations toward mathematics and m...

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to hi...

The set of papers presented in this issue comprise a multiple-case study which attends to instructional resources—teacher knowledge and curriculum materials—to understand how they individually and jointly contribute to instructional quality. We approach this inquiry by comparing lessons taught by teachers with differing mathematical knowledge for teaching who were using either the same or different editions of a US Standards-based curriculum. This introductory paper situates the work reported in...

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum material...

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were teaching from the same curriculum materials, the teacher with higher MKT had more complete and concise ways to describe key concepts, had multiple ways to re...

An instructional vision is the discourse that teachers or others currently employ to characterize the kind of “ideal classroom practice” to which they aspire but have not yet necessarily mastered. ...

Abstract Teachers’ noticing is an important skill for learning from and improving their teaching. We investigated what teachers noticed in short video clips of a real classroom teacher’s interaction with students around a mathematics problem by collecting data from 496 U.S. fourth- and fifth-grade teachers from 48 states. Our analyses indicated that 67.5% of teachers’ responses focused on content-specific teaching and learning events, whereas 14% of them attended to the content-specific issues a...

Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers’ knowledge of key concepts underlying fraction arithmetic. Teachers’ explanations were coded based on the accuracy of their explanations and the kinds of concepts and representations they used in their responses. The results showed that teachers’ understanding of fraction arithm...

#2Tenzin Doleck(SFU: Simon Fraser University)H-Index: 13

Prior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid s...

#2Ian Thacker(SC: University of Southern California)H-Index: 4

The success of professional development programs has typically been determined based on their impact on teacher learning, without much attention being given to the data sources used. Large-scale st...

Last. Richard Rasiej(SC: University of Southern California)

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Instruments designed to measure teachers’ knowledge for teaching mathematics have been widely used to evaluate the impact of professional development and to investigate the role of teachers’ knowledge in teaching and student learning. These instruments assess a mixture of content knowledge and pedagogical content knowledge. However, little attention has been given to the content alignment between such instruments and curricular standards, particularly in regard to how content knowledge and pedag...

Researchers have been interested in students’ transition to calculus since the early 1900s. One line of inquiry highlights students’ understandings of high school mathematics as impeding or supporting their successful transition to university mathematics. This paper addresses an underlying question in this line of inquiry: does school mathematics provide opportunities for students to develop productive meanings for calculus? This article reports on U.S. calculus students’ responses to items that...

#2Ji-Won Lee(UCI: University of California, Irvine)H-Index: 25

This study examines the association between mathematical knowledge for teaching and instructional quality in a sample of first-year elementary school teachers. Ten teachers completed the mathematical knowledge for teaching (MKT) survey at the end of teacher preparation. Three mathematics lessons taught during their first year of teaching were videotaped and scored using the Mathematical Quality of Instruction. Findings replicate prior studies that were conducted with more experienced teachers. A...

Using correct definitions of the mathematical concepts is crucial for learning and teaching of any mathematical content. Being able to make mathematically correct definition of the concepts is an indicator of teachers’ content knowledge. The purpose of this study is to determine how preservice middle school mathematics teachers define the concept of algebraic expression and equation. The participants of this case study were 35 preservice middle school mathematics teachers. The data were collecte...

Last. Andrés Pinzón(University of Los Andes)H-Index: 2

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ABSTRACTThe quality of students’ learning experience depends on the learning activities that their teachers plan prior to classroom delivery. This article characterises the lesson planning practices of a group of 27 mathematics teachers. The questionnaire and the associated information coding and analysis procedures designed for that purpose may be applicable to lesson planning characterisation involving larger groups of teachers and of other disciplines. Some of the study group’s needs and diff...