Joanne Lobato

• San Diego State University

In this chapter, we trace the evolution of transfer research in the field of mathematics education (and associated domains, such as science education and computer science education), from the rejection of the transfer of learning construct to the recent flowering of research from progressive transfer perspectives. In the main body of the chapter, w...

This book provides a common language for and makes connections between transfer research in mathematics education and transfer research in related fields. It generates renewed excitement for and increased visibility of transfer research, by showcasing and aggregating leading-edge research from the transfer research community. This book also helps...

On-line math videos for student learning are abundant; yet they are surprisingly uniform in their expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of on-line math videos that are dialogue-intensive and focus on the development of mathematical meaning and problem solving. Each video...

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...

Even in the resource-rich, more ideal conditions of many design-based classroom interventions, unexpected events can lead to disappointing results in student learning. However, if later iterations in a design research study are more successful, the previous failures can provide opportunities for comparisons to reveal subtle differences in instructi...

Despite recent research interest in student-created diagrams, little research has systematically investigated students' diagram-construction processes, meaning the order and manner in which students create markings as they physically generate diagrams. In this study, we characterize the various processes students use to create diagrams that represe...

Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats noti...

A review of Early Algebraization: A Global Dialogue From Multiple Perspectives, edited by Jinfa Cai and Eric Knuth.

As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the generali...

Although any mainstream thought is subject to theoretical challenges, the challenges to the mainstream cognitive perspective on transfer have had an unfortunate divisive effect. This article takes a pragmatic view that transfer perspectives are simply designed objects (Plomp & Nieveen, 2007), which provide different information for different purpos...

Despite the proliferation of mathematics standards internationally and despite general agreement on the importance of teaching for conceptual understanding, conceptual learning goals for many K-12 mathematics topics have not been well-articulated. This article presents a coherent set of five conceptual learning goals for a complex mathematical doma...

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 article is a response to Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008) and to one of the task group reports on which it was based, the report of the Task Group on Learning Processes. The author uses Maxwell's two views of causality—regularity and process—to explore three major issues raised in the...

We present a case study of teaching and learning fraction addition on number lines in one 6th-grade classroom that used the Connected Mathematics Project Bits and Pieces II materials. Our main research questions were (1) What were the primary cognitive structures through which the teacher and students interpreted the lessons? and (2) Were the teach...

Teaching so that knowledge generalizes beyond initial learning experiences is a central goal of education. Yet teachers frequently bemoan the inability of students to use their mathematical knowledge to solve real world applications or to successfully tackle novel extension problems. Furthermore, researchers have been more successful in showing how...

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which se...

A central and enduring goal of education is to provide learning experiences that are useful beyond the specific conditions of initial learning. For example, the design of innovative curricular materials and pedagogical approaches is often aimed at help-ing students develop robust understandings that will generalize to decision making and problem so...

This paper demonstrates how differences in the nature of students' generalizations of their learning experiences are related to differences in features of the classroom environment that regularly direct students' attention toward certain mathematical properties when a variety of features compete for students' attention. Transfer is a controversial...

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as pedagogica...

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properti...

Limitations with current approaches to the investigation of the transfer of learning in design experiments constrain the type of information that is available to researchers as they make design decisions. This article addresses these limitations by presenting a reconceptualization of transfer, called actor-oriented transfer, which emerged from desi...

This paper extends recent efforts to critique and reconceive transfer by using an empirical study to rethink the surface/structure distinction of the traditional transfer paradigm. The findings suggest that what researchers typically consider a surface feature can present conceptual complexities for students that are more structural in nature than...

We use the notion offocusing phenomena to help explain how a teacher’s actions were connected to her students’ interpretations of a linear equation. This study was conducted in a high-school classroom that regularly emphasised dependency relationships in real-world situations. Seven interviews revealed a majority view ofy = b + mx as astorage conta...

When technology is implemented in classrooms, students often form ideas that are unexpected and unwanted by the teachers and the designers of the technology. This article advances the notion of the focusing effect of technology as a way of systematically accounting for the role of technology in such situations. A focusing effect refers to the direc...

Much research on student understanding of functions has been characterized by a "multi-representational" perspective that investigates students' efforts to make connections among conventionally accepted mathematical representations such as graphs, tables, and equations. In contrast, a "quantitative" perspective explores students' efforts to identif...

During a recent visit to a sixthgrade classroom, students were observed estimating the sums of columns of multidigit numbers by first painstakingly computing the exact sum of each column of numbers on paper, then rounding the answers to obtain estimates. Apparently the students were not bothered by the fact that it didn't make much sense to round t...

This paper reports the analysis of data collected as one component of the Learner's Perspective Study (LPS) of classroom practice in eighth-grade mathematics classes in ten cultures. In this paper, the utility of characterising a nation's or a teacher's classroom practice with a single lesson pattern or script is problematised as a result of the an...

We discuss three ways to coordinate descriptions of mathematical knowledge with psychometric models (i.e., statistical models for tests) when building assessments. The three examples are sequenced to move from more coarse-grained to more fine-grained descriptions of mathematical knowledge and to move from models that simply scale to those that both...