Handbook of International Research in Mathematics Education

Lyn D. English, David Kirshner, Lyn D. English, David Kirshner

• Publisher: Routledge
• Year: 2015
• Print ISBN: 9780415832038
• eBook ISBN: 9781134626717
• Topic: Education
• Subtopic: Education General

This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities.

New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook's original themes for international research in mathematics education and remains in the process a definitive resource for the field.

Section I

Priorities in International Mathematics Education Research

1 Changing Agendas in International Research in Mathematics Education

Lyn D.English

Queensland University of Technology

DavidKirshner

Louisiana State University

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies.

In opening the first chapter of the Handbook’s second edition, English (2008) argued that many of the important questions that need to be addressed in mathematics education are not being answered. In highlighting some of these concerns, a number of “catalysts for change” were identified as fuelling the need for further research. These catalysts included national and international mathematics testing, the impact of social and cultural factors (including economic and political influences), an increased focus on the professional learning of teachers, a revival of theory development, the enhanced sophistication and availability of technology, and the increased globalization of our field. To what extent these factors continue to have a significant impact on our field is open to debate, as are the global research questions demanding attention. Although responses to these issues would vary from nation to nation and indeed, from one research group to another, it is worth reflecting on some of the challenges, both the longstanding and the emerging, that appear to be shaping (or reshaping) mathematics education research.

In an introductory chapter of this nature we cannot, of course, do justice to the myriad factors impacting our field. As Heid (2012) emphasized in her final editorial for the Journal for Research in Mathematics Education, although it is desirable to identify the major problems in mathematics teaching and learning and to target appropriate research agendas, we cannot expect universal agreement on what these problems and agendas might be. What we can strive for, however, is the means to determine “great challenges, especially ones on which progress can be made in the near future” (Heid, 2012, p. 503). We touch upon just a few of these in this first chapter and leave the reader to explore each of the sections for a more in-depth and diverse coverage of global challenges facing researchers, teachers, and policy developers alike. To provide a partial guide to the issues examined by the authors, we devote the last portion of this chapter to a summary of the chapters within each of the sections.

Emerging and Continuing Challenges

One of the ongoing challenges facing all of us today is operating effectively in a world that is increasingly shaped by complex, dynamic, and powerful information systems fuelled by unprecedented developments in technology. Students’ future careers, many of which might not exist today or only in emergent forms, will require skills in interpreting, explaining, and developing structurally complex systems. Spanning a range of fields including social, economic, political, and scientific domains, such systems will demand mathematically powerful knowledge and reasoning processes, skills in dealing effectively with sophisticated technology, and the ability to think flexibly, creatively, and innovatively—all essential to life-long learning. The chapters in this Handbook explore various ways in which we might increase all students’ access to opportunities that nurture these core foundations. From school curriculum renewal, to advancing theory and research methodologies, through to capitalizing on technological developments, the authors offer international perspectives on broadening opportunities for mathematics learning and teaching.

Selecting particular issues to highlight in this opening chapter is a challenge in itself. These are many and varied, with some presenting more urgency than others depending on the unique features of a nation’s educational system. Complementing the challenges explored in each of the main sections, we address briefly two issues that we see as having a significant influence on shaping the agenda of future mathematics education: the increased international focus on STEM education and the ever-present endeavors to link research with practice.

International Developments in Science, Technology, Engineering, and Mathematics (STEM) Education

Promoting STEM education (science, engineering, mathematics, technology) has become a central concern of policy makers across the globe, with many nations formally recognizing the significant role of STEM skills across multiple economic sectors (e.g., Honey, Pearson, & Schweingruber, 2014; Marginson, Tytler, Freeman, & Roberts, 2013; National Research Council, 2014; National Science and Technology Council, 2013; Office of the Chief Scientist, 2013). In the United States, for example, the 2013 report from the Committee on STEM Education maintained that “The jobs of the future are STEM jobs,” with STEM competencies increasingly required not only within, but also outside of, specific STEM occupations (National Science and Technology Council, 2013, p. vi). Developing students’ competencies in the STEM disciplines is thus regarded as an urgent goal of many education systems, fuelled in part by current or predicted shortages in the STEM workforce and also by outcomes from international comparative assessments (e.g., OECD, 2013).

A major domain of the 2012 Programme for International Student Assessment (PISA) was mathematical literacy, with a focus on challenging problems set in real-world contexts and the mathematical thinking and processes applied to solutions (OECD, 2013). It is not surprising then, that one of the key findings of the report, STEM: Country Comparisons (Marginson et al., 2013), was that many nations with strong STEM agendas and international testing outcomes have a well-developed curriculum that focuses on inquiry, problem solving, critical thinking, creativity, and innovation. Combined with an emphasis on disciplinary thinking and literacies, these curricula display a heavy commitment to broadening STEM engagement and achievement.

While educational bodies are lobbying for greater attention to STEM education, the nature of such learning and how the component disciplines might be integrated effectively within the curriculum do not appear to have received the required research attention. Calls for more in-depth connections among the STEM disciplines appear in the Common Core State Standards for Mathematics (www.corestandards.org/Math/) and the Next Generation Science Standards (www.nextgenscience.org/) in the United States. Interestingly, the California Department of Education (STEM Task Force Report, 2014) considers STEM education to be more than “an interdisciplinary applied approach”; rather, STEM education is viewed as comprising attributes that are common to the four disciplines, namely, engaging students in “critical thinking, inquiry, problem solving, collaboration, and what is often referred to in engineering as design thinking” (p. 7). This perspective aligns with the recognition by many nations of the importance of these generic skills in advancing students’ learning across the STEM disciplines.

An aspect of concern for mathematics education within an integrative STEM approach, however, is the need to maintain a strong presence and role alongside the other disciplines. A balanced distribution of the four discipline areas is essential, otherwise mathematics could very well be in danger of being overshadowed. At present, science seems to dominate many current STEM reports. Indeed, the STEM acronym itself is frequently referred to as simply “science” (e.g., Office of the Chief Scientist, 2014). Many countries also refer to the role of STEM education as one that fosters “broad-based scientific literacy” with a key objective in their school programs being “science for all,” reflected in an increased focus on science education in elementary, junior, and middle secondary school curricula (Marginson et al., 2013, p. 70). As Marginson et al. commented, discussions on STEM education rarely adopt the form of “mathematics for all” even though mathematics underpins the other disciplines; they thus argue that “the stage of mathematics for all should be shifted further up the educational scale” (p. 70). Even the rise in engineering education, commencing in the early school years (e.g., Lachapelle & Cunningham, 2014), would appear to be oriented primarily towards the science strand at the expense of mathematics. This concern has been raised by several researchers in engineering education (e.g., English & King, 2015; Honey et al., 2014; Walkington, Nathan, Wolfgram, Alibali, & Srisurichan, 2014).

An interesting way of viewing mathematics within a unified STEM approach is evident in the California State Department (2014), where the integrative nature of each of the four disciplines is defined. Mathematics is viewed in terms of fostering “mathematically literate” students, who not only know how “to analyze, reason, and communicate ideas effectively,” but can also “mathematically pose, model, formulate, solve, and interpret questions and solutions in science, technology, and engineering” (p. 11). Although advancing mathematics learning from such a perspective is potentially rich, the discipline nevertheless remains underrepresented in terms of ways to achieve this, with science still appearing to receive considerably greater attention, as Honey et al. (2014) indicated.

One of the underutilized roles of mathematics within STEM lies in providing critical grounding for success beyond school, where skills are needed for making informed decisions on issues that are central to national and international debates on political, economic, environmental, health, and defense issues, to name a few. Together with the exponential rise in digital information within STEM, the ability to handle contradictory and potentially unreliable online data is critical (Lumley & Mendelovits, 2012). Mathematics provides the grist for making evidence-based decisions in dealing with data across disciplines. More recognition needs to be given to this powerful role of mathematics in STEM integration.

In essence, we argue that mathematics as a discipline within the current STEM climate needs to have a stronger voice. Mathematics must maintain equitable discipline representation, especially with the burgeoning of publications devoted to STEM education (e.g., Honey et al., 2014; National Research Council, 2014; Purzer, Stroble, & Cardella, 2014; International Journal of STEM Education; www.stemeducationjournal.com/). At the same time, the research conducted across all STEM disciplines needs to reach the classroom and other relevant learning environments. As we indicate in the next section, one of the most enduring challenges for mathematics education, and indeed any field, is linking research with practice.

Linking Research with Practice

The perennial nature of the research into practice challenge is evident in the numerous reports, editorials, and articles devoted to ways in which we might translate and disseminate our significant research outcomes so that they directly enhance learning and teaching (e.g., Arbaugh et al., 2010; Burkhardt & Schoenfeld, 2003; Heid, 2012). Indeed, though only Chapter 9 by Michael Fried and Miriam Amit on mathematics education reform was solicited to address this theme, it has been substantively addressed throughout the book, especially in Chapters 2, 4, 5, 7, 10, 18, 19, 20, 21, 22, and 29. Thus a general overview of the research/practice rift in this introductory chapter also serves to orient the reader to a major theme of the Handbook.

Policy concerns about the alienation of research from educational practice, and more generally about the efficacy of educational research, are deep-seated and international in scope. As reported in Vanderlinde and van Braak (2010), since the turn of the century there have been major governmental and government-funded reports filed in the UK, France, The Netherlands, and the United States, as well as multinational reports from the OECD’s Center for Educational Research and Innovation, and the Commission of the European Communities.

Because funding of educational research is tied to public and political perception of its impact on practice, researchers are necessarily attentive to criticisms that educational research results are little utilized (Onderwijsraad, 2003), of poor quality (Coalition for Evidence-Based Policy (2002), and of limited influence (Burkhardt & Schoenfeld, 2003). Still, there is little consensus as to what role educational research should play, for instance whether production of knowledge or improvement of educational practice should predominate (Mortimore, 2000; Bauer & Fisher, 2007); and whether, in principle, knowledge produced by educational research can directly delineate educational practice, or if its appropriate service is to enrich the conversation about educational possibilities (Bridges, Smeyers, & Smith, 2008; Nuthall, 2004).

To gain some perspective on the range of issues involved in the research/practice split, we turn to the work of Broekkamp and Van Hout-Wolters (2007), which identifies four quite different interpretations of the underlying concern, as summarized in Vanderlinde and van Braak (2010, p. 302):

1. Educational research yields few conclusive results; or educational research does not provide valid and reliable results that are confirmed through unambiguous and powerful evidence.
2. Educational research yields few practical results; or educational research is limited in practical use.
3. Practitioners believe that educational research is not conclusive or practical; or educational research is not meaningful for teachers.
4. Practitioners make little (appropriate) use of educational research; or practitioners do not have the skills to use educational research results.

Depending on which interpretation one subscribes to, the actions needed to affect positive change will vary widely:

1. Rethink the kinds of research questions that are pursued and/or the methodologies employed to address those questions (Levin & O’Donnell, 1999); or invest more in high-quality, validated research (Kennedy, 1997).
2. Design research studies that more effectively address the needs of practitioners (Hammersley, 2002); include practitioners as partners in research (De Vries & Pieters, 2007; Ruthven & Goodchild, 2008).
3. Do a better job of articulating the linkages of research studies to practice (Gore & Gitlin, 2004); or train teachers in the science of educational research (NRC, 2002).
4. Disseminate research results more widely (Chafouleas & Riley-Tillman, 2005); or train practitioners in the interpretation and utilization of educationa...

Table of contents

• Cover Page
• Half Title page
• Title Page
• Copyright Page
• Contents
• Acknowledgements
• List of Reviewers
• Section I Priorities in International Mathematics Education Research
• Section II Democratic Access to Mathematics Learning
• Section III Transformations in Learning Contexts
• Section IV Advances in Research Methodologies
• Section V Influences of Advanced Technologies
• Final Comment
• Index