Jinfa Cai

• Ph.D.
• Professor at University of Delaware

Em 1994, Ed Silver publicou um artigo original intitulado “On Mathematical Problem Posing”. Silver tanto ajudou a estabelecer as bases para a pesquisa de proposição de problemas como apontou direções-chave que a pesquisa de proposição de problemas poderia explorar. Este artigo fornece uma breve revisão da literatura sobre proposição de problemas na...

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students’ behavior in these three stages of problem posing, especially focusing on investigating the...

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as experienc...

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...

Resumen: Antes de la pandemia (2019), nos preguntamos: ¿En qué temas debería centrarse la investigación en educación matemática en la próxima década? Las 229 respuestas de 44 países condujeron a ocho temas más con-sideraciones sobre la investigación en educación matemática en sí. Los temas se pueden resumir como enfoques de enseñanza, objetivos, re...

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...

Providing students opportunities to engage in problem posing activities is advocated in the mathematics curriculum standards of many countries — for instance, China and the United States. This paper synthesizes research from the last two years that addresses how to integrate problem posing into the classroom so that students can gain more problem p...

In this article, we discuss how mathematics can play a role in STEM activities in K–12 classrooms. From the perspective of content, we argue that mathematics serves as a language tool to help represent/model STEM activities and explain/interpret identified solutions. From the perspective of process, we argue that mathematics serves as a thinking to...

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...

In this study we aimed to inquire into the impact of the use of early arithmetic strategies by a group of fifth-grade students, on their solving of equations involving two representations of unknowns. Pre- and post-tests consisting of equation-solving items involving two representations of unknowns (number sentences containing empty ‘brackets’, as...

In this survey paper we focus on mathematics learning in Chinese contexts, as a way to contribute to broader discussions about mathematical learning. We first review the features of Chinese students’ mathematical learning depicted in the literature, followed by a review of student mathematical learning in recent Chinese research journals. This lead...

Collaborative learning has been advocated for the last several decades. However, classroom practice has indicated that this method often comes with challenges and low efficiency, suggesting the need for better support for teachers. The aim of this study is to explore teachers’ learning about collaborative learning in a professional development (PD)...

The knowledge and skills that mathematics teacher educators (MTEs) need to have for teaching mathematics teaching is a fundamental issue that influences their preparation and development. In particular, considering that mathematics teaching comprises MTEs’ teaching work, do MTEs need to have school teaching experience and, if so, in what ways does...

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...

Problem posing has received increased attention among researchers and educators. One of the most important aspects is to understand the cognitive process of problem posing. In this study, we conceptualized a framework for the cognitive process of mathematical problem posing in three stages: (a) input—understanding the task, (b) processing—construct...

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...

Research has shown that students’ beliefs related to mathematics are connected to their affect and motivation as well as their mathematical thinking and activity. Moreover, high parental expectations have been shown to play a role in students’ positive beliefs and self-efficacy. This paper reports on two studies investigating parental expectations...

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...

Problem solving and problem posing have long been of interest to the mathematics education community. In this survey paper we first look at some of the seminal moments in the history of research on the important topics. We then use this history to position the state-of-the-art research being done in both problem solving and problem posing, before i...

This study investigated 45 undergraduate students’ mathematical problem posing based on four problem situations. This study was designed to better understand the kinds of problems they pose, and the kinds of mathematical ideas exhibited when problem posing. The findings of this study support that underprepared college students can pose mathematical...

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...

Before the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics educ...

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

In this study we aimed to understand teaching mathematics through problem posing based on an analysis of 22 teaching cases. Teaching mathematics through problem posing starts with problem-posing tasks. This study provides not only specific examples of problem-posing tasks used in classrooms but also related task variables to consider when developin...

Mathematics teacher educators (MTEs) play key roles in creating opportunities for classroom teachers learning to teach mathematics. This chapter aims to describe the development of secondary MTEs in China from two perspectives. First, an overall picture of secondary MTEs in China is depicted, including their types, responsibilities, and development...

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...

The present study investigated the efficacy of an intervention program to assist teachers in the development of conceptual and practical tools for engaging students in dialogic classroom discourse. Sixteen fourth-grade mathematics teachers received 28 h of the intervention over a semester of 4 ½ months. Compared to the nonintervention group, the in...

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...

This study explored 1634 Chinese eighth-grade students’ domain- and task-specific self-efficacy and its relationship to their problem-posing performance. In particular, the linear regression model, generalized additive model (GAM), and piecewise regression model (PRM) were used to detail the linear and non-linear relationships between these variabl...

The original version of this article unfortunately contains correction.

This study serves two purposes. The first purpose is the development and validation of a Mathematics Teachers’ Beliefs Scale (MTBS). In addition to providing a valid and reliable MTBS instrument, this study provides information on the process of developing and validating the instrument, which shall be useful for the development and validation of si...

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...

Communicating research insights is challenging and is often work that is underestimated. In this chapter, readers are invited to take the stance of writing as communicating with reviewers. After sharing how reviewers are assigned to manuscripts, the authors (experienced journal editors) discuss three of the common issues reviewers usually raise whe...

Open access to this editorial: https://link.springer.com/article/10.1007/s10649-019-09908-4

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...

This study examined over 48,000 eighth-grade Chinese students’ mathematics performance and use of learning strategies. In particular, this study explored how the use of learning strategies and their combinations are related to students’ mathematics performance in Chinese context. This study examined three kinds of learning strategies derived from t...

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 this study, we analyzed how an experienced mathematics teacher learned to teach the distributive property of multiplication over addition using problem posing. The teacher taught two lessons on this topic, one with the use of problem posing and the other without. First, we analyze the differences between the two lessons, followed by a discussion...

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...

This study investigated the impact of a problem-posing workshop on teachers’ problem-posing conceptions and skills as well as their conceptions and design of mathematics lessons that use a problem-posing approach. The findings demonstrate that although the vast majority of the teachers possessed very little experience with problem posing prior to t...

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...

Gender differences in achievement in mathematics, a traditionally male-stereotyped subject, have long been a concern for many educators around the world. Gender differences in mathematical achievement have decreased in recent decades, especially in Western countries, and become small or insignificant in large-scale tests, such as the Programme for...

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...

This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of them...

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...

Cultural beliefs about teaching do not directly dictate what teachers do, but teachers do draw upon their cultural beliefs as a normative framework of values and goals to guide their teaching. In other words, teachers’ beliefs and values concerning effective mathematics teaching influence their instructional practice. Based on the findings from a n...

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

This study investigated the relationship between three cognitive features of mathematical instruction tasks (high cognitive demand, multiple representations, and multiple solution methods) and student learning outcomes among 1,779 students from 30 Chinese fifth-grade classrooms using a new mathematics curriculum. Measures of mathematics learning ou...

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...

It is widely believed that teachers' knowledge of students' thinking has a significant impact on teachers' teaching and students' learning. However, there is far less research on how teachers acquire their knowledge of students' thinking before, during, and after lessons. This study is designed to compare the differences between expert and nonexper...

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...

Students in Shanghai ranked at the top in mathematics on the past two assessments of the Program for International Student Assessment (PISA). However, even though Asian students in general, and Chinese students in particular, ranked at the top in mathematics, we know little about Shanghai students’ subjective well-being (SWB). This paper reports tw...

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...

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers’ views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result...

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...

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing condit...

Comparing is one of the most basic intellectual activities. We consciously make comparisons to understand where we stand, both in relation to others as well as to our own past experiences. International comparative studies have completely transformed the way we see mathematics education. The focus of this ICME-13 Topical Survey is to discuss the wa...

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People’s Education Press in China over 3 deca...