Stephen Hwang

University of Delaware | UDel UD · Department of Mathematical Sciences

In this systematic literature review, we reviewed 48 original empirical papers focusing on Korean students’ and teachers’ mathematical problem-posing (MPP) in classrooms. All the included papers were published in peer-reviewed mathematics education research journals and located through comprehensive database searches and individual journal searches...

In 1994, Ed Silver published a seminal paper entitled “On Mathematical Problem Posing.” Silver both helped to lay a foundation for problem-posing research and pointed out key directions that problem-posing research could explore. This chapter provides a brief review of the problem-posing literature in the past three decades, showing that there have...

Problem posing, the process of formulating and expressing problems based on a given situation, is an essential practice in mathematics and other disciplines. Although this is acknowledged in policy documents, problem-posing tasks are neither substantively nor consistently included in school mathematics. In this chapter, we consider problem posing f...

In discussing theories of teaching, we take the position that there is a two-way street between what we call theory for teaching and teaching for theory . We articulate the linkages between these two dynamic processes through a particular conceptualization of professional knowledge for teaching carried by tangible artifacts. Within this context we...

The chapter brings together the individual chapter perspectives on theorizing teaching and thus initiating exchanges among the authors on outstanding issues and discrepancies to provide insights for how research on teaching may move forward. The Delphi study conducted for this aim was based on summaries of the answers of all individual chapters on...

If you have carefully worked through the ideas in the previous chapters, the many questions researchers often ask about what methods to use boil down to one central question: How can I best test my hypotheses? The answers to questions such as “Should I do an ethnography or an experiment?” and “Should I use qualitative data or quantitative data?” ar...

Building on the ideas in Chap. 1, we describe formulating, testing, and revising hypotheses as a continuing cycle of clarifying what you want to study, making predictions about what you might find together with developing your reasons for these predictions, imagining tests of these predictions, revising your predictions and rationales, and so on. M...

Theoretical frameworks can be confounding. They are supposed to be very important, but it is not always clear what they are or why you need them. Using ideas from Chaps. 1 and 2 , we describe them as local theories that are custom-designed for your study. Although they might use parts of larger well-known theories, they are created by individual re...

Every researcher wants their study to matter—to make a positive difference for their professional communities. To ensure your study matters, you can formulate clear hypotheses and choose methods that will test them well, as described in Chaps. 1, 2, 3 and 4. You can go further, however, by considering some of the terms commonly used to describe the...

spiepr Abs1 Every day people do research as they gather information to learn about something of interest. In the scientific world, however, research means something different than simply gathering information. Scientific research is characterized by its careful planning and observing, by its relentless efforts to understand and explain, and by its...

This paper proceeds from the position that elementary- and middle-school students can learn and should be exposed to algebraic ideas and that a fruitful mechanism for this is to help them to see the algebra in arithmetic. After a brief survey of the literature on helping students see algebra in arithmetic, the main focus of the paper is on the use...

This study examined how expert and novice (preservice) teachers solved mathematical modelling tasks as well as how they noticed written artifacts of student thinking that were in response to the mathematical modelling tasks. Some teachers in both groups were aware of the openness and underdetermination of the modelling tasks and that these characte...

This study investigated the changes in six teachers’ beliefs and instructional practices regarding teaching through problem posing. They participated in a series of four problem-posing workshops and volunteered to share a videotaped lesson that integrated problem posing in the final workshop. We examined teachers’ familiarity with and confidence ab...

The purpose of this paper is to provide a theoretical stance on integrating implementation and research. Implementation should be made integral to research because viewing research and implementation as an integrated whole is a more useful perspective for educational research and practice. A consequence of this position is a marked blurring of the...

Fostering conceptual understanding in mathematics classrooms is an important goal in mathematics education. To support this goal, we need to be able to diagnose and assess the extent to which students have conceptual understanding. In this study we employed a problem-posing task and a problem-solving task in order to diagnose and assess preservice...

A correction to this paper has been published: https://doi.org/10.1007/s11858-021-01265-y

Problem posing, the process of formulating problems based on a given situation, is an essential practice in mathematics and other disciplines. Although this is acknowledged in policy documents, problem posing is neither substantively nor consistently included in the school mathematics curriculum. In this paper, we first comment on the state of prob...

Any effort to integrate problem-posing instruction in school mathematics must attend to teachers’ beliefs about the advantages of teaching through problem posing and especially their beliefs about the challenges of teaching in this way. This study investigated teachers who were learning how to teach mathematics through problem posing. The primary f...

Significant research in science and mathematics education should advance the field’s knowledge and understanding of the teaching and learning of science and mathematics. How, then, should the significance of a research question in science and mathematics education be assessed? And, when disseminating the findings of research, how should the signifi...

(...) In this editorial, we discuss the first of the five overarching problems: defining and measuring learning opportunities precisely enough to study how to maximize the quality of the opportunities experienced by every student.

Although often asked tactfully, a frequent question posed to authors by JRME reviewers is “So what?” Through this simple and well-known question, reviewers are asking: What difference do your findings make? How do your results advance the field? “So what?” is the most basic of questions, often perceived by novice researchers as the most difficult q...

In our recent editorials (Cai et al., 2019a, 2019b), we discussed the important roles that research questions and theoretical frameworks play in conceptualizing, carrying out, and reporting mathematics education research. In this editorial, we discuss the methodological choices that arise when one has articulated research questions and constructed...

In our March editorial (Cai et al., 2019), we discussed the nature of significant research questions in mathematics education. We asserted that the choice of a suitable theoretical framework is critical to establishing the significance of a research question. In this editorial, we continue our series on high-quality research in mathematics educatio...

In this study, we used two pattern-related problem-posing tasks to investigate the mathematical problem posing of fifth-, sixth-, seventh-, and eighth-grade Chinese students. We also explored their teachers’ predictions about their students’ problem posing. We found that students in higher grades were more likely than those in lower grades to pose...

Research journals play significant roles in the advancement of academic fields of inquiry. This chapter starts with a brief description of the Journal for Research in Mathematics Education. Most importantly, this chapter provides practical guides to promoting and disseminating significant research in mathematics education. The guides provided in th...

In 2002, the National Research Council (NRC) released Scientific Research in Education , a report that proposed six principles to serve as guidelines for all scientific inquiry in education. The first of these principles was to “pose significant questions that can be investigated empirically” (p. 3). The report argued that the significance of a que...

Teachers are at the heart of implementing any educational innovation or improvement. One critical need is to investigate how teachers learn to use problem posing to teach mathematics in the classroom. This article conceptualizes issues about mathematical problem posing (MPP) and about learning to teach through problem posing. It highlights signific...

We concluded our November editorial (Cai et al., 2018b) with a promise to consider research paradigms that could bring us closer to the new world we have envisioned where research is intertwined with practice. We will call the paradigms we have in mind research pathways to avoid the range of complicated connotations often applied to the term paradi...

In this editorial, we elaborate our vision of the changing roles of researchers and teachers in a future world in which research has a much more direct and meaningful impact on practice (Cai et al., 2017). In previous editorials, we have described characteristics of this future world, including setting research agendas based on instructional proble...

In our May editorial (Cai et al., 2018a), we explored how collaborations among teacher-researcher partnerships could harness emerging technological resources to address the problem of isolation in the work of teachers and researchers. In particular, we described a professional knowledge base (Cai et al., 2018b) and a mechanism by which that knowled...

In our March editorial (Cai et al., 2018), we considered the problem of isolation in the work of teachers and researchers. In particular, we proposed ways to take advantage of emerging technological resources, such as online archives of student data linked to instructional activities and indexed by learning goals, to produce a professional knowledg...

In our November 2017 editorial (Cai et al., 2017), we presented a vision of a future in which research has a significant impact on practice. In the world we described, researchers and teachers work together, sharing similar goals and incentive structures. A critical feature of this brave new world is the existence of an online professional knowledg...

This editorial discusses the critical idea of replication in educational research.

We began our editorials in 2017 seeking answers to one complex but important question: How can we improve the impact of research on practice? In our first editorial, we suggested that a first step would be to better define the problem by developing a better understanding of the fundamental reasons for the divide between research and practice (Cai e...

In our May editorial (Cai et al., 2017), we argued that a promising way of closing the gap between research and practice is for researchers to develop and test sequences of learning opportunities, at a grain size useful to teachers, that help students move toward well-defined learning goals. We wish to take this argument one step further. If resear...

In our last editorial, we considered the impact of research on students' learning. In clarifying our perspective, we answered the question of “impact of research on what” to include both cognitive and noncognitive outcomes in students as well as long-term impact on students that goes well beyond short-term cognitive impact. A natural next step is t...

In our first editorial (Cai et al., 2017), we highlighted the long-standing, critical issue of improving the impact of educational research on practice. We took a broad view of impact, defining it as research having an effect on how students learn mathematics by informing how practitioners, policymakers, other researchers, and the public think abou...

How can research have a larger impact on educational practice? What kinds of research can have the greatest impact on educational practice? These are perennially thought-provoking questions for mathematics education researchers (e.g., Battista et al., 2007; Boerst et al., 2010; Heck et al., 2012; Heid et al., 2006; Herbel-Eisenmann et al., 2016; La...

In this exploratory study, we developed a portrait of the challenges and strategic responses of secondary mathematics teacher educators (MTEs) in Chinese universities. The MTEs reported encountering more challenges when teaching pedagogical courses and supervising student teachers than when teaching college mathematics courses and teaching mathemat...

This study examines how standards-based mathematics textbooks used in China and the United States implement problem-posing tasks. We analyzed the problem-posing tasks in two US standards-based mathematics textbook series, Everyday Mathematics and Investigations in Number, Data, and Space, and two Chinese standards-based mathematics textbook series,...

Coherence has been identified as an important factor in fostering students' learning of mathematics. In this chapter, by applying classroom discourse theories, we propose a framework for examining instructional coherence through a fine-grained analysis of a video-taped lesson from China. The lesson was chosen because it has been recognized as a mod...

This chapter synthesizes the current state of knowledge in problemposing research and suggests questions and directions for future study. We discuss ten questions representing rich areas for problem-posing research: (a) Why is problem posing important in school mathematics? (b) Are teachers and students capable of posing important mathematical prob...

The goal for this monograph has been to present the state of the art in large-scale studies in mathematics education. Although the chapters collected here are not intended to be a comprehensive compendium of such research, this selection of work does serve both to represent large-scale studies in the field of mathematics education and to raise awar...

Learning is fundamentally about growth and change. Longitudinal studies of mathematics learning must therefore conceptualize, measure, analyze, and interpret changes in students’ mathematical thinking. This chapter provides a perspective on how researchers can deal with issues entailed in researching such change over time, drawing on the authors’ e...

This paper explores how curriculum and classroom conceptual and procedural emphases affect the learning of algebra for students of color. Using data from a longitudinal study of the Connected Mathematics Program (CMP), we apply cross-sectional HLM to lend explanatory power to the longitudinal analysis afforded by growth curve modeling that we have...

Over the years our community has benefitted greatly from the application of survey methods to the discernment of patterns in student mathematics performance, attitudes, and to some degree, policies and practices. In particular, such research has helped us discover differential patterns in socioeconomic, gender, and ethnic groups and point out that,...

In recent years, funding agencies like the Institute of Educational Sciences and the National Science Foundation have increasingly emphasized large-scale studies with experimental and quasi-experimental designs looking for 'objective truths'. Educational researchers have recently begun to use large-scale studies to understand what really works, fro...

This study examined 361 Chinese and 345 Singaporean sixth-grade students’ performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies of...

Mathematics education has existed as an independent field of research for over a century. Although young compared with some other domains of research, mathematics education research has nevertheless developed into a fertile and active discipline. In particular, the last 40 years have seen a rapid expansion of output from a growing body of mathemati...

Lack of appropriate and adequate mathematical knowledge in elementary teachers is a major concern in mathematics education. At their first meeting in Kalamazoo the working group on Developing Elementary Teachers’ Mathematical Knowledge for Teaching identified five significant issues to explore from multiple, diverse perspectives: (1) selecting/crea...

This study analyzed teachers’ intentions for and reflections on their use of Standards-based [Connected Mathematics Program (CMP)] textbooks and traditional (non-CMP) mathematics textbooks to guide instruction. In this investigation of the interplay between textbooks and instruction, we focused on learning goals, instructional tasks, teachers’ anti...

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evide...

In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of p...

This study examined US and Chinese 6th grade students’ generalization skills in solving pattern-based problems, their generative thinking in problem posing, and the relationships between students’ performance on problem solving and problem posing tasks. Across the problem solving tasks, Chinese students had higher success rates than US students. Th...