## About

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August 2013 - present

Education

August 2008 - May 2013

August 2008 - May 2011

September 2000 - June 2004

## Publications

Publications (81)

Past studies have suggested that in light of recent curriculum standards, many US teachers make limited use of drawn models in their mathematics instruction. To gain insight into this phenomenon, we investigated relationships between US teachers’ opportunities to learn about, knowledge of, motivation for, and instructional use of drawn models for r...

Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose view...

This research employs the novel Racial Responding in Mathematics Scale (RRMS) to study the equity beliefs of 288 teachers. A series of multiple regression analyses were conducted to investigate the relationships between four RRM constructs – affective and cognitive empathy and responding action and alignment – and racial resentment and sympathy as...

Yavuz S., Arora A., Jacobson E., Willey, C., (2024), “Teachers’ Attributions of students' mathematical success and struggle: One-Question Analysis”, Indiana Mathematics Education Research Symposium (IMERS), IU-PU-IUPU, Indianapolis, IN, March 1, 2024

Choosing appropriate strategies and implementing them correctly to solve problems are essential parts of mathematical reasoning. In this study, we examined 214 US fourth graders’ strategy choice and implementation when solving a fraction ordering task amenable to multiple strategies. The students used 12 distinct fraction comparison strategies. Of...

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 attentio...

Substantial progress has been made in assessing teachers’ knowledge by designing multiple choice items. However, scholars have also found that multiple choice items have limitations for measuring specific kinds of content knowledge for teaching. In this study, we investigated whether these limitations also existed when measuring teacher pedagogical...

We designed a multiple-choice problem to assess how students interpreted the problem (situation), chose a specific arithmetic operation (translation), and performed computation (mathematical operation). Based on the data from 1465 fifth graders, we found that although 64% of students translated the problem as a subtraction problem, only 47% chose t...

There have been many efforts to measure pedagogical content knowledge with multiple-choice survey instruments, but little is known about how different types of items contribute. In this study, we examined interviews with 9 Grade 4 teachers to develop a deeper understanding of how teachers select pedagogical representations in the context of a surve...

We found less than half of the 4th graders elected to use visual models and the accuracy was not greater than those who did not use visual models, suggesting that visual models as currently used do not deliver on their promise. We conjecture students’ unit coordination (Wilkins et al., 2020), geometry knowledge, and teachers’ fraction instruction (...

We found less than half of the 4th graders elected to use visual models and the accuracy was not greater than those who did not use visual models, suggesting that visual models as currently used do not deliver on their promise. We conjecture students’ unit coordination (Wilkins et al., 2020), geometry knowledge, and teachers’ fraction instruction (...

We found only 1 out of 214 students used the number line to determine the relative size of fractions, and only 2 students used it to support benchmark reasoning. We conclude that number lines are almost never used, and when they are used, they are mostly used as a graphical display instead of a tool to support reasoning. We call for curriculum and...

We designed a multiple-choice problem to assess how students interpreted the problem (situation), chose a specific arithmetic operation (translation), and performed computation (mathematical operation). Based on the data from 1465 fifth graders, we found that although 64% of students translated the problem as a subtraction problem, only 47% chose t...

We found only 1 out of 214 students used the number line to determine the relative size of fractions, and only 2 students used it to support benchmark reasoning. We conclude that number lines are almost never used, and when they are used, they are mostly used as a graphical display instead of a tool to support reasoning. We call for curriculum and...

The purpose of this study is to investigate the range of strategies fifth graders used to solve a word problem involving fraction multiplication. We report a detailed qualitative analysis of elementary students' written work (N = 1472). The results demonstrate that students collectively use a wide range of strategies for fraction multiplication. Im...

Research is mixed on whether understanding decimal magnitude supports operations with decimals or whether operations can be learned before and while students develop understanding of decimal magnitude. In the present study, we used a large scale, longitudinal design to investigate students' knowledge of decimal comparison and operation before and a...

Teachers' diagnostic competence is essential for effective mathematics instruction. Prior studies have examined teachers' diagnostic competence using various approaches, such as asking teachers to assess students' erroneous work or anticipate potential learning difficulties. Few studies have examined how teachers interpret the significance of stude...

In this theoretical paper, we introduce analytic pragmatism (Brandom, 2008) as a paradigm that allows for the simultaneous discussion of findings from different theoretical traditions. We illustrate the use of this paradigm by examining literature about teaching and learning fractions. This novel approach is particularly well suited for the body of...

Math that Matters is an accessible, practical, and insightful book written for current (and future) math teachers about classroom assessment and feedback. Although it includes judicious citation of current scholarly writing, it is not so much a scholarly book as a practical book aimed to influence teachers. The first three chapters describe Small’s...

Contingent argument-based approaches to validity require a unique argument for each use, in contrast to more prescriptive approaches that identify the common kinds of validity evidence researchers should consider for every use. In this article, we evaluate our use of an approach that is both prescriptive and argument-based to develop a validity arg...

In this empirical study, we report data from 44 elementary PTs' talk about linear functions in a simulated teaching context and our analysis of this talk in terms of the representations involved (i.e., graphs, equations, and tables) and whether it conveyed conceptual understanding or errors. Drawing on two complementary definitions of conceptual un...

In this theoretical paper, we introduce analytic pragmatism (Brandom, 2008) as a paradigm that allows for the simultaneous discussion of findings from different theoretical traditions. We illustrate the use of this paradigm by examining literature about teaching and learning fractions. This novel approach is particularly well suited for the body of...

Mathematics teacher education aims both to increase knowledge (cognitive constructs) and to instill productive disposition (affect-related constructs) for teaching mathematics. Prospective teachers’ knowledge and productive disposition are theoretically intertwined and together make up Mathematical Proficiency for Teaching (MPT). Although both aspe...

The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which standards-based mathematics teaching practices were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the affordances an...

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser’s (Educational Studies in Mathematics 75:241–251, 2010) study of prospective elementary teachers’ conceptions of multidigit number and examined the main claim t...

This study explores the dimensionality of mathematical knowledge needed by elementary school teachers. Specifically, we focus on the construct of Mathematical Knowledge for Teaching to investigate whether common mathematical content knowledge (the generic mathematical knowledge that is held by an educated adult), specialized content knowledge (the...

The focus of this presentation is on students’ non-symbolic representations of quantity, so things like student drawings of fraction bars or base-ten blocks. In particular, we are interested in examining the flexible use of these representations. ��Flexibility is a stated goal of the common core practice standards, some NCTM position statements, an...

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The...

Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find...

Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The authors...

In this paper, we report a proof-of-concept tool that maps research findings of student mistakes and misconceptions to the CCSSM standards. We also report findings from a pilot study that suggests the tool has promise for helping teachers predict common errors on multiple-choice items—an increasing focus in elementary classrooms preparing for stand...

This study (n = 1,044) used data from the Teacher Education and Development Study
in Mathematics (TEDS-M) to examine the relationship between field experience focus
(instruction- or exploration-focused), duration, and timing (early or not) and prospective
elementary teachers’ intertwined knowledge and beliefs about mathematics and
mathematics learn...

In this paper we explore the relationship between certification path and teaching self-efficacy for teachers of K-12 mathematics. We focused on teaching self-efficacy for a content area that spans the K-12 curriculum: fractions, ratios, and proportions. Initial findings indicated that alternate certification is significantly correlated to teaching...

Mathematics education researchers in several recent projects have used psychometric models to develop measures of newly conceptualized domains of content knowledge for teaching. In this study, we conducted a retrospective analysis across four projects to investigate the interactive process of domain conceptualization and measure design. Our analysi...

Primary teacher mathematics education aims both to increase knowledge and to shape beliefs about teaching mathematics. Prospective teachers' knowledge and beliefs are theoretically intertwined and together make up mathematical proficiency for teaching (MPT). Although both aspects of MPT represent simultaneous goals in university classes, most resea...

This study was designed to address a problem facing administrators and teacher educators working at the district level in Georgia: How can schools and districts in Georgia support teachers’ development of mathematical proficiency for teaching? This local policy problem is an instantiation of a national problem. Teachers are thought to develop exper...

A growing body of international research has documented the importance of teachers' pedagogical content knowledge for students' learning (e.g., Baumert et al, 2010). Much remains to be discovered about how teachers develop mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008). One empirical question is whether teachers develop MKT...

There is enduring international interest in the mathematical knowledge of teachers (e.g., Rowland & Ruthven, 2011). We report on data from a paper-and-pencil instrument that highlights dynamic reasoning necessary for responding to students' thinking in a particular domain—fractions and fraction arithmetic in terms of quantities. The instrument cons...

Numerous studies, primarily conducted with school children, have reported the misapplication of direct proportion reasoning strategies to situations in which two quantities do not covary in a fixed ratio relationship. In the present study, preservice middle-grades mathematics teachers (N = 28) evidenced similar difficulties in a content and methods...

Table representations of functions allow students to compare rows as well as values in the same row.

What do teachers learn ‘on the job’? And how, if at all, do they learn from ‘experience’?
Leading researchers from the UK, Europe, the USA and Canada offer international, research-based perspectives on a central problem in policy-making and professional practice – the role that experience plays in learning to teach in schools. Experience is often w...

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administere...

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state‐mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our analys...

The relationship between teaching and content is foundational to ideas about mathematical knowledge for teaching (MKT). We argue that items designed to measure such knowledge provide constrained instances that clarify how particular contextual features, which we call pedagogical context, influence the mathematical reasoning prompted by items. From...

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsáák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study inve...

We summarize the four fractions attributes and sub-attributes that contribute to them. We use the subcategories as a tool for insuring that we assess each attribute in a variety of contexts. For each attribute and sub-attribute we provide a general description and examples that illustrate reasoning with that attribute. We also provide references to...

This document elaborates four attributes for proportional reasoning that form the foundation for the items on the DTMR proportional reasoning assessment form. We summarize these attributes and the sub-attributes that contribute to each attribute. Because three of the attributes are at a macro-level in terms of grain-size, we found it useful to iden...

This study builds on previous work exploring U.S. teachers' conceptions of integrated mathematics curricula. In this study we used focus group and individual interviews to examine the mathematical processes teachers emphasized in their descriptions of implementing a new curriculum. Our results suggest that the mathematical processes teachers use in...

We analyze how middle grades teachers in a professional development program reasoned about fraction arithmetic using length and area models. We discovered that teachers' abilities to partition length and area quantities were critical. In particular, we focus on ways that teachers' used multiplication factor/product relationships, distributive reaso...

This study extends research on teachers' difficulties with fraction division by examining underlying difficulties they can have coordinating levels of units. Research on students has demonstrated that coordinating 3 levels of units is central to multiplicative reasoning, including reasoning about fractions, but similar attention to levels of units...

Mathematicians and university math educators insist that multiplication is not repeated addition; however, the interpretation works when solving most elementary school mathematical problems. Sure, mathematicians might make a distinction, but does such hair splitting matter to third graders? Should it matter to their teachers?