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Life in the time of COVID: Thoughts on current trends and future directions in mathematics education

This is a reflective, personal, and possibly somewhat self-indulgent piece, prompted by my thinking on current trends evidenced in recent editorial experiences with, and contributions, to several journals and book publications that report on contemporary mathematics practice and research internationally. As such, it is not intended as a definitive ‘state-of-play’ (in the sense of a meta-analysis or a systematic review of the literature), but as a means of considering some of the questions raised by these studies and using these to frame some potentially useful directions for future research, which I hope may be of interest and value to Bolema readers and researchers. A key observation underpinning my motivation for this piece mirrors the well-known historical example of the birth of Calculus, which grew somewhat independently, but contemporarily aligned, in the seventeenth century in England and France, with the work of mathematical giants, Newton and Leibniz. My editorial duties and contributing authorship to journals and books across a wide range of international platforms have led me to observe some common trends by researchers and teachers, who are similarly sometimes seemingly unaware of common approaches and influences in other countries and domains. These observations prompted the idea to highlight some of the common findings of these studies, and point out some questions these studies pose for future research.

Studies and publications referenced here include, but are not limited to, my work as Associate Editor for two journals: the Bolema Journal, and the International Journal of Mathematical Education in Science and Technology (IJMEST)1 1 Available at: https://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=tmes20. Acess in: 30 oct. 2021. , the latter of which has produced three Special Issues in 2021 (Two showcasing selected papers from conference proceedings: (Herenga Delta 2021, the 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (12 articles, see EVANS; OATES, 2021EVANS, T.; OATES, G. Herenga Delta 2021: values and variables in mathematics and statistics education in a time of disruption. International Journal of Mathematical Education in Science and Technology, London, Special Issue, 2021 (in press).); INDRUM 2020 (International Network for Didactic Research in University Mathematics, eight articles; HAUSBERGER; BOSCH, 2021HAUSBERGER, T.; BOSCH, M. (Eds.). INDRUM 2020 (International Network for Didactic Research in University Mathematics). International Journal of Mathematical Education in Science and Technology, London, Special Issue, 2021 (in press).), and a third Special Classroom Notes Issue examining issues arising from the COVID-19 pandemic, Takeaways from teaching through a global pandemic – practical examples of lasting value in tertiary mathematics education, 21 articles; SEATON; LOCH; LUGOSI 2021SEATON, K.; LOCH, B.; LUGOSI, E. (Eds.). Takeaways from teaching through a global pandemic – practical examples of lasting value in tertiary mathematics education. International Journal of Mathematical Education in Science and Technology, London, Special Issue. 2021 (in press).). Other contemporary works include my role as Guest Editor (see OATES; SEAH, 2021OATES, G.; SEAH, R. Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Australian Journal of Education, Melbourne, 2021 (in press).) for a Special Issue of the Australian Journal of Education, with seven articles examining Learning progression/trajectories in mathematics and science education; as a contributing author to a chapter (GALLIGAN et al., 2020GALLIGAN, L.; COUPLAND, M.; DUNNE, P.; OATES, G.; HERNANDEZ MARTINEZ, P. Research into teaching and learning of tertiary mathematics and statistics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education Australasia 2016-2019. Singapore: Springer Nature, 2020. p. 269-292.) which reviewed recent research in tertiary mathematics in the latest four-yearly MERGA2 2 Mathematics Education Research Group of Australasia. Available at: https://www.merga.net.au/. Access in: 30 oct. 2021. review of Australasian-focused research (BOBIS et al., 2020BOBIS, J.; WAY, J.; ATTARD, C.; ANDERSON, J.; MCMASTER, H.; CARTWRIGHT, K. Research in Mathematics Education in Australasia 2016–2019. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 1-5., Research in Mathematics Education in Australasia (RiMEA) 2016–2019); and two chapters with a technology focus, the first a chapter in The Handbook of Cognitive Science,3 3 Available at: https://meteor.springer.com/project/dashboard.jsf;jsessionid=JD8w3bmv4IjhMfVsbzapuRMWxh7rU4QDpc1lQVHG.spr-prod-app-16?id=1030&tab=About. Access in: 30 oct. 2021. which explores the role of the internet in the process of developing students into independent learners, through the different forms of blended learning and how humans and media interact in the learning process (ENGELBRECHT; OATES, 2021ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press).); and a second chapter which examines, and provides explicit examples of an authentic assessment to promote active online learning and a critical reflection for pre-service teachers in a mathematics pedagogy course (OATES; DENNY, 2021OATES, G.; DENNY, P. Authentic assessment to promote online collaboration and critical reflection. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 69-94. Global Education in the 21st century Series.).

Not surprisingly, given their publication over 2020 to 2021, a consistent theme in many of these works, and indeed a motivating driver behind some (e.g., SEATON; LOCH; LUGOSI, 2021SEATON, K.; LOCH, B.; LUGOSI, E. (Eds.). Takeaways from teaching through a global pandemic – practical examples of lasting value in tertiary mathematics education. International Journal of Mathematical Education in Science and Technology, London, Special Issue. 2021 (in press).), is the pervasive effect of the COVID-19 pandemic on mathematics education. Even before the role of technology was forced into stark relief by the need for most schools and universities to suddenly go online, many studies had been debating the role technology played in shaping, and the potential for it to change, the ways in which we teach and learn mathematics (e.g., ATTARD et al., 2020ATTARD, C.; CALDER, N.; HOLMES, K.; LARKIN, K.; TRENHOLM, S. Teaching and learning mathematics with digital technologies. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 319-347.; BORBA et al., 2016BORBA, M. C.; ASKAR, P.; ENGELBRECHT, J.; GADANIDIS, G.; LLINARES, S.; SÁNCHEZ AGUILAR, M. Blended learning, e-learning and mobile learning in mathematics education. ZDM Mathematics Education, Switzerland, v. 48, n. 5, p. 589-610, 2016.; BORBA; CHIARI; ALMEIDA, 2018BORBA, M. C.; CHIARI, A. S. S.; ALMEIDA, H. R. F. L. Interactions in virtual learning environments: new roles for digital technology. Educational Studies in Mathematics, Switzerland, v. 98, p. 269-286, 2018.; ENGELBRECHT; LLINARES; BORBA, 2020ENGELBRECHT, J.; LLINARES, S.; BORBA, M. C. Transformation of the mathematics classroom with the internet. ZDM Mathematics Education, Switzerland, v. 52, n. 5, p. 825-841, 2020.). In hindsight, such studies may be seen as foreshadowing, or setting the stage for the sudden demands the pandemic thrust upon us, reflecting the observation by Borba, Chiari and Almeida (2018BORBA, M. C.; CHIARI, A. S. S.; ALMEIDA, H. R. F. L. Interactions in virtual learning environments: new roles for digital technology. Educational Studies in Mathematics, Switzerland, v. 98, p. 269-286, 2018.) that technological developments were transforming societies and educational processes well before COVID had emerged. In 2019, there was a call for papers for a special issue of ZDM, with a central theme to investigate the evolvement and transformation of the classroom with the growing integration of the internet into the learning process. However, in their editorial piece for the 16 articles that subsequently appeared in Volume 52(5) Online mathematics education and e-learning4 4 Available at: https://link-springer-com.ezproxy.utas.edu.au/journal/11858/volumes-and-issues/52-5. Access in: 30 oct. 2021. , Engelbrecht et al. (2020)ENGELBRECHT, J.; BORBA, M. C.; LLINARES, S.; KAISER, G. Will 2020 be remembered as the year in which education was changed? ZDM, Switzerland, v. 52, p. 821-824, 2020. note how the COVID-19 pandemic risks trampling over many of the aspirational transformations described in these studies. They ponder if 2020 will be remembered as the year in which education changed, observing that while the crisis provided an opportunity for change, the radical transformation to online teaching and learning caused by the COVID-19 pandemic “is not the [evolving] way we would have liked to conduct this transition” (p. 3) to more effective forms of blended learning.

Such questions are also highlighted by others over this period, with respect to both teaching and learning, and research. Successive editorials in 2020 issues of the Bolema journal (v. 34, n. 67; v. 34, n. 68) question the effects of the pandemic, with Miarka and Maltempi (2020)MIARKA, R.; MALTEMPI, M. What will become of mathematics education after coronavirus? Bolema, Rio Claro, v. 34, n. 67, p. ii-iv, 2020. for example questioning, in the early stages of the pandemic, if learning would ever return to the previous ‘normal’? With respect to the impact on research and Bolema publications, they ponder how, like teaching, research might adapt to the virtual world forced on us by the pandemic, and further, what are the methodological challenges of such processes? Later in the year, as the fuller impact and long-suffering nature of the pandemic became more apparent, Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020. built on the questions posed by Miarka and Maltempi (2020)MIARKA, R.; MALTEMPI, M. What will become of mathematics education after coronavirus? Bolema, Rio Claro, v. 34, n. 67, p. ii-iv, 2020., suggesting five aspects in which they see mathematics education is being, or might be affected by the pandemic. The first is a predictable increase in research into the actions taken by teachers in general (and those of mathematics in particular) in response to the pandemic. Such research is exemplified in the 21 articles featured in the 2021 IJMEST Classroom Notes Special Issue (SEATON; LOCH; LUGOSI, 2021SEATON, K.; LOCH, B.; LUGOSI, E. (Eds.). Takeaways from teaching through a global pandemic – practical examples of lasting value in tertiary mathematics education. International Journal of Mathematical Education in Science and Technology, London, Special Issue. 2021 (in press).), which provide a collective snapshot of contemporary practices and responses to COVID in undergraduate mathematics teaching. The focus of these articles is consistent with the eight themes identified as directions for future research by Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., namely: approaches to teaching; goals of mathematics education; relation of mathematics education with other practices; professional development of teachers; technology; equity, diversity, inclusion; affect; and assessment. The critical nature of one of these themes, assessment issues in tertiary mathematics, is evidenced by the more than half of the articles in the Classroom Notes Special Issue (12 out of 21 articles) with an assessment focus. These articles consider both formative assessment (e.g., how might students monitor their progress in a self-directed online environment?) and summative assessment (e.g., with respect to maintaining integrity in online examinations). Wider assessment issues and the pandemic also underpinned the September 2020 call for papers in a commissioned book (Volume 6) in the Global Education in the 21st Century Series (BARKATSAS; MCLAUGHLIN, 2021BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic assessment and evaluation approaches and practices in a digital era: a kaleidoscope of perspectives. v. 6. Boston: Brill, 2021. Global Education in the 21st Century Series.), with the objectives to:

  • Explore authentic assessment research, approaches, and practices at all levels of education.

  • Explore program evaluation and teacher evaluation research, approaches, and practices at all levels of education.

  • Disseminate mixed method studies, qualitative studies, quantitative studies, discipline-based narratives, and case studies of sustainable authentic assessment and evaluation approaches and practices (including Covid-19 studies) at all levels of education.

Assessment was the primary focus of the 17 articles featured in this publication, but connections to other themes are also clear, with several chapters exploring technology-supported approaches to foster active learning, collaboration, and visualization (e.g., ERSOZLU; LEDGER; HOBBS, 2021ERSOZLU, Z.; LEDGER, S.; HOBBS, L. Virtual simulation in ITE: technology driven authentic assessment and moderation of practice. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 53-68. Global Education in the 21st century Series.; OATES; DENNY, 2021OATES, G.; DENNY, P. Authentic assessment to promote online collaboration and critical reflection. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 69-94. Global Education in the 21st century Series.; SEAH; HORNE, 2021SEAH, R.; HORNE, M. How much do they know about 3d objects: using authentic assessment to inform teaching practice? In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 240-261. Global Education in the 21st century Series.), while others examined cultural and equity issues, and affective factors (e.g., SANTOS; FORTUNATO; MENA, 2021SANTOS, F. P.; FORTUNATO, I.; MENA, J. Teacher performance evaluation approach from a Brazilian perspective: a literature review. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 315-328. Global Education in the 21st century Series.; WILKS-SMITH, 2021WILKS-SMITH, N. Translanguaging pedagogies for multilingual learner assessment. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 285-311. Global Education in the 21st century Series.). Exemplifying the aspects highlighted by Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020., and the themes of Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., questions raised in these studies include how common classroom-based collaborative pedagogies and formative assessment techniques may be adapted for online use (OATES; DENNY, 2021OATES, G.; DENNY, P. Authentic assessment to promote online collaboration and critical reflection. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 69-94. Global Education in the 21st century Series.), and the need for greater investigation on the impact of teacher practice on student learning, especially in the Brazilian context, where the authors suggest it is a missing component. “There is a need of substantial analysis on teachers’ practice by observing pedagogical strategies used, teachers’ dispositions and beliefs, test scores, or students’ surveys” (SANTOS; FORTUNATO; MENA, 2021SANTOS, F. P.; FORTUNATO, I.; MENA, J. Teacher performance evaluation approach from a Brazilian perspective: a literature review. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 315-328. Global Education in the 21st century Series., p. 326).

In respect of changes in teaching and delivery, Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020. observe that while many seemingly successful actions have been taken in response to the pandemic, from a research perspective we have little evidence of the effects of such moves. For example, how might the use of virtual environments affect the learning of school mathematics from the point of view of learning and learning outcomes? Such questions are also emphasized by Engelbrecht and Oates (2021)ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press)., whose article focuses on the ways in which computer-mediated networks support social interaction, cooperation, and collaboration, for learning and knowledge building. They observe how the physical classroom as we have known is changing and describe how the sudden switch to fully online learning has amplified perspectives such as self-determined and self-directed learning for students (heutagogy, see for example, BLASCHKE, 2019BLASCHKE, L. M. The pedagogy–andragogy–heutagogy continuum and technology-supported personal learning environments. In: JUNG, I. (Ed.). Open and distance education theory revisited. Singapore: Springer, 2019. p. 75-84.), including self-regulation (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021.), and questions on how to develop and evaluate the effectiveness of blended or hybrid learning environments (ENGELBRECHT; OATES, 2021ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press).). Traditionally, online learning environments have been largely asynchronous (i.e., where learning is conducted in the students’ own time), but COVID-19 has thrust the spotlight more closely on how we might develop synchronous online learning, with capacity for instructor-student and peer-to-peer interaction? Engelbrecht and Oates (2021)ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press). conclude by framing several issues that require further research in this respect, many of which resonate closely with the second aspect highlighted by Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020., namely, what is the effect of technology on the teaching and learning of mathematics when technology, in addition to being a resource (as has been frequently the case to date), becomes the main means of education? Key questions here centered around epistemic factors, and the mathematical and cognitive value of online tools and approaches, including:

  • What technology should students use to support their own mathematical learning as well as collaboratively the learning for other students? How might they make effective choices with the multitude of options available in informal contexts?

  • How can social media tools be combined with the best practices in teaching and contribute effectively to student engagement, and the development of deeper mathematical understanding? (ENGELBRECHT; OATES, 2021ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press)., p. 31)

Three other aspects of mathematics education identified by Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020. are not discussed in detail here, but their importance and commonality are evidenced in other studies so are worth repeating, even if briefly. The third aspect they identify is the emergence of new teaching and learning problems introduced by the pandemic, or existing problems that the pandemic has amplified, issues which feature strongly in the most significant theme found by Bakker, Cai and Zenger (2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., see next discussion). Their fourth aspect, echoed by Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021. is with respect to questions about our mathematics research discipline, and the impact on higher education research and publication rates (FONT; SALA, 2020FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.). Their final aspect considers the impact of the pandemic on conferences and other mathematics education congresses. In this latter respect, Evans and Oates (2021EVANS, T.; OATES, G. Herenga Delta 2021: values and variables in mathematics and statistics education in a time of disruption. International Journal of Mathematical Education in Science and Technology, London, Special Issue, 2021 (in press)., p. 1) observe that the pandemic “has been a period when optimism was often elusive and when challenges sometimes seemed insuperable and overwhelming. The resilience of the Delta research and teaching community5 5 The Biennial Delta Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. Available at: https://www.herengadelta.org/. Access in: 30 oct. 2021. is being tested”. While Font and Sala (2020)FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020. recognize these challenges, they also optimistically note the emergence of an increased number of virtual conferences, with benefits (notwithstanding time-zone challenges) of increased international participation, and greater access for participants from developing nations, a point of equity highlighted by Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021..

In a similar fashion to the way in which COVID-19 intersected with the publication of the ZDM special issue, influences from the COVID-19 pandemic can be seen in the approach and focus of several other studies initiated prior to the pandemic outbreak. In the precursor to the study by Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021. cited earlier for example, the researchers note how reporting of results from their initial survey conducted in 2019 (planned for presentation at 2020 NTCM and ICME), was shaken up by the crisis. In 2019, they asked the question “On what themes should research in mathematics education focus in the coming decade?” (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., p. 2) They received 229 responses from 44 countries, and their initial analysis identified the 8 themes listed earlier, as a focus for future research: They were, however, prevented from presenting their results, and the researchers thus pondered how respondents might think differently about the themes formulated for the future due to the pandemic? They decided to resurvey their participants, asking the question “Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how?” (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., p. 2). They observe that the general gist of responses in 2020 was that the pandemic had:

… functioned as a magnifying glass, … on themes that were already considered important … systemic societal and educational problems were said to have become better visible to a wider community, and urge us to think about the potential of a new normal (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., p. 5).

With respect to teaching and learning, the responses in 2020 supported the findings and questions raised by other studies cited previously (e.g., FONT; SALA, 2020FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.; ENGELBRECHT; OATES, 2021ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press).), with for example more emphasis on interaction, collaboration, higher-order and critical thinking (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021.). With respect to research, Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021. describe how several respondents felt that the pandemic has highlighted the extent to which mathematics education research has been less than accessible or insufficiently responsive to the needs of practitioners and students in the past, and more so now in respect of immediate concerns. They ask if we perhaps “need a particular type of communication research within mathematics education to learn how to convey particular key ideas or solid findings?” (BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021., p. 13).

Not all studies over this period explicitly referenced the pandemic, but even within many of these, similar issues are evident. The RiMEA review (BOBIS et al., 2020BOBIS, J.; WAY, J.; ATTARD, C.; ANDERSON, J.; MCMASTER, H.; CARTWRIGHT, K. Research in Mathematics Education in Australasia 2016–2019. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 1-5.) encompasses 14 chapters presenting critical analyses of research in mathematics education in Australasia over the years 1026 to 2019 (i.e., the period leading up to the pandemic), and serves to highlight significant enduring trends and forecast possible directions for future research. While the chapters are not explicitly organized around themes, their collective focus resonates with those themes described previously (e.g., BAKKER; CAI; ZENGER, 2021BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021.; FONT; SALA, 2020FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.). In their discussion entitled Focusing our understanding of Initial teacher Education, Way et al. (2020)WAY, J.; CAVANAGH, M.; ELL, F.; LIVY, S.; MCMASTER, H. Advancing Our Understanding of Initial Teacher Education Through Research. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds..). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 91-115. echoes the observation of dos Santos, Fortunato and Mena (2021)SANTOS, F. P.; FORTUNATO, I.; MENA, J. Teacher performance evaluation approach from a Brazilian perspective: a literature review. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 315-328. Global Education in the 21st century Series. with respect to teachers’ practice, noting very few studies that have been specifically designed to deeply explore the experiences of pre-service teachers from their own perspectives, as distinct from the practices of teacher educators. They see a need for “more longitudinal studies with rich data drawn directly from pre-service teachers…across a range of institutions” (WAY et al., 2020WAY, J.; CAVANAGH, M.; ELL, F.; LIVY, S.; MCMASTER, H. Advancing Our Understanding of Initial Teacher Education Through Research. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds..). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 91-115., p. 108). Several of the chapters likewise mirror calls for increased development and evaluation of pedagogies as described earlier (BAKER et al., 2021; ENGELBRECHT; OATES, 2021ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics. Switzerland: Springer, 2021 (in press).; FONT; SALA, 2020FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.). Attard et al. (2020)ATTARD, C.; CALDER, N.; HOLMES, K.; LARKIN, K.; TRENHOLM, S. Teaching and learning mathematics with digital technologies. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 319-347. for example make several recommendations for future research directions in respect of teaching and learning with digital technologies, including:

  • Investigation of how digital technologies are being used to develop mathematical content knowledge in pre-service early childhood and primary teachers.

  • Develop deeper understanding of how technology can be used to position students to have more voice and control in mathematics classrooms and promote rich, two-way interaction (ATTARD et al., 2020ATTARD, C.; CALDER, N.; HOLMES, K.; LARKIN, K.; TRENHOLM, S. Teaching and learning mathematics with digital technologies. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019. Singapore: Springer, 2020. p. 319-347., p. 341).

In their chapter reviewing studies on tertiary mathematics and statistics, Galligan et al. (2020GALLIGAN, L.; COUPLAND, M.; DUNNE, P.; OATES, G.; HERNANDEZ MARTINEZ, P. Research into teaching and learning of tertiary mathematics and statistics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education Australasia 2016-2019. Singapore: Springer Nature, 2020. p. 269-292., p. 285) conclude by posing six questions for further research in tertiary mathematics and statistics education, including studies which examine “the co-evolution of pen-enabled technology, the flipped classroom, and blended learning to create learning cultures to assist students to gain a deep understanding of mathematics”. As noted earlier, the COVID-19 crisis may have disrupted this co-evolution with its sudden demands for online learning, but the questions of how to effectively develop cultures of effective blended-learning remains paramount. In another of their concluding questions, Galligan et al. (2020)GALLIGAN, L.; COUPLAND, M.; DUNNE, P.; OATES, G.; HERNANDEZ MARTINEZ, P. Research into teaching and learning of tertiary mathematics and statistics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education Australasia 2016-2019. Singapore: Springer Nature, 2020. p. 269-292. add support for studies to investigate the effects of the pandemic on our mathematics education research and community (e.g., FONT; SALA, 2020FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.; MIARKA; MALTEMPI, 2020MIARKA, R.; MALTEMPI, M. What will become of mathematics education after coronavirus? Bolema, Rio Claro, v. 34, n. 67, p. ii-iv, 2020.), to seek “better understandings of some of the higher-level contexts of mathematics and the application of mathematics and statistics in work-integrated learning contexts and HDR research” (GALLIGAN et al., p. 285). In their discussion of Innovative and Powerful Pedagogical practices in Mathematics Education, Hunter et al. (2020)HUNTER, J.; MILLER, J.; CHOY, B. H.; HUNTER, R. Innovative and Powerful Pedagogical Practices in Mathematics Education. Innovative and powerful pedagogical practices in mathematics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD (Eds.). Research in Mathematics Education in Australasia 2012-2015. Singapore: Springer, 2020. p. 293-318. may well be considered as presaging some of the issues accentuated by the pandemic, when they argue that we “need effective pedagogy for all learners and … ambitious, future-focused teaching in mathematics education” (HUNTER et al., 2020HUNTER, J.; MILLER, J.; CHOY, B. H.; HUNTER, R. Innovative and Powerful Pedagogical Practices in Mathematics Education. Innovative and powerful pedagogical practices in mathematics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD (Eds.). Research in Mathematics Education in Australasia 2012-2015. Singapore: Springer, 2020. p. 293-318., p. 293). They call for studies which challenge the status-quo of current practices (as COVID-19 has demanded), and importantly, how we might know if the developing practices are transferable from one context to another? We need to distinguish “the difference between knowledge that something can work and knowledge of how to actually make it work reliably over diverse contexts and populations” (BRYK, 2015BRYK, A. S. Accelerating how we learn to improve. Educational Researcher, Washington, D.C., v. 44, n. 9, p. 467-477, 2015., p. 469, apudHUNTER et al., 2020HUNTER, J.; MILLER, J.; CHOY, B. H.; HUNTER, R. Innovative and Powerful Pedagogical Practices in Mathematics Education. Innovative and powerful pedagogical practices in mathematics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD (Eds.). Research in Mathematics Education in Australasia 2012-2015. Singapore: Springer, 2020. p. 293-318., p. 313). Hunter et al. (2020)HUNTER, J.; MILLER, J.; CHOY, B. H.; HUNTER, R. Innovative and Powerful Pedagogical Practices in Mathematics Education. Innovative and powerful pedagogical practices in mathematics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD (Eds.). Research in Mathematics Education in Australasia 2012-2015. Singapore: Springer, 2020. p. 293-318. suggest we may need to adopt different research paradigms to examine such questions, and how this can be done is itself seen as a fruitful line of future research.

Finally in this discussion, I consider here the emerging body of research and interest in using learning progressions and trajectories (LP/Ts), with associated questions of how these may be used to better inform student learning (e.g., CONFREY; SHAH; BELCHER, 2021CONFREY, J.; SHAH, M.; BELCHER, M. Using Learning Trajectory-Based Ratio Curriculum and Diagnostic Assessments for Promoting Learner-Centred Instruction. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era. Boston: Brill, 2021. p. 187-216.; SEAH; HORNE, 2021SEAH, R.; HORNE, M. How much do they know about 3d objects: using authentic assessment to inform teaching practice? In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 240-261. Global Education in the 21st century Series.). In support of the call for papers showcasing LP/T’s in the AJE Special Issue (see the editorial by OATES; SEAH, 2021OATES, G.; SEAH, R. Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Australian Journal of Education, Melbourne, 2021 (in press).), and mirroring the earlier call by Bakker, Cai and Zenger (2021)BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021. for greater practical accessibility of research, the Special Issue guest editors cite the observation by Confrey et al., (2019CONFREY, J., MCGOWAN, W., SHAD, M., BELCHER, M., HENNESSEY, M., & MALONEY, A. P. Using digital diagnostic classroom assessments based on learning trajectories to drive instruction and deepen teacher knowledge. In: SIEMON, D.; BARKATSAS, T.; SEAH, R. (Eds.). Researching and Using Learning Progressions (Trajectories) in Mathematics Education. Boston: Brill Sense Publishers, 2019. p. 75-100., p. 76, apudOATES; SEAH, 2021OATES, G.; SEAH, R. Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Australian Journal of Education, Melbourne, 2021 (in press)., p. 1), that despite considerable research into teaching and learning, “much of the accumulated knowledge is neither readily accessible nor actionable, by most classroom teachers” in the primary and secondary years. The AJE Special Issue features seven articles which showcase a range of theoretical perspectives and methods of investigation, reflecting the recognized potential of using LP/Ts research in generating a closer link between research and practice. A common thread through these articles is the value of LP/Ts in highlighting the need for linking of curricula content, both within, and between subjects. However, the guest editors observe that, at the present time, there is insufficient evidence in respect of the impact learning progressions may have on planned curricula developments, and emphasize the need for further research into LP/Ts’ applications in the classroom context. They frame two key questions worth further investigation:

  • how does LP/Ts research assist teachers in planning activities and implementing differentiated instructions to support the diversity of needs within the classroom?

  • considering the increasing emphasis on STEM education, what is the potential for LP/Ts research as a framework for interdisciplinary collaboration between mathematics and science discipline, to explicitly nurture its growth from the early childhood years onwards (OATES; SEAH, 2021OATES, G.; SEAH, R. Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Australian Journal of Education, Melbourne, 2021 (in press)., p. 3).

In addition, we might note that these studies have so far focused predominantly on teaching, with the impact of LP/Ts on student learning in the long term still largely unexplored.

In summary, this discussion has highlighted many issues of contemporary interest for mathematics education, for example issues associated with constraints of online learning caused by the pandemic, and it has identified several areas of interest and significance in future research. For me, a key factor in many of the studies discussed here is both the way in which the pandemic has questioned our current practice, and to what extent it will shape and influence our future practice? As we emerge from the immediate and somewhat frantic responses thrust on us by the crisis, future research should ask to what extent have our classrooms and research practices changed? Have we really entered a ‘new normal’ as it is often described, and, if so, in what ways is it better, or perhaps less effective than before? And if we have indeed entered a new normal, how are we equipping and supporting our teachers, students, and researchers to adapt to, and thrive in this new environment? To what extent do our Initial Teacher Education courses reflect the new and emerging practices we have described, for example are we now better equipping our teachers to teach online with effective, technology-based pedagogies? How have our research approaches and methodologies developed to investigate these questions appropriately? I look forward to seeing studies emerging, and more specifically, as an Associate Editor, submitted to Bolema, that look to address such questions.

References

  • ATTARD, C.; CALDER, N.; HOLMES, K.; LARKIN, K.; TRENHOLM, S. Teaching and learning mathematics with digital technologies. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019 Singapore: Springer, 2020. p. 319-347.
  • BAKKER, A.; CAI, J.; ZENGER, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Switzerland, v. 107, n. 1, p. 1-24, 2021.
  • BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic assessment and evaluation approaches and practices in a digital era: a kaleidoscope of perspectives. v. 6. Boston: Brill, 2021. Global Education in the 21st Century Series.
  • BLASCHKE, L. M. The pedagogy–andragogy–heutagogy continuum and technology-supported personal learning environments. In: JUNG, I. (Ed.). Open and distance education theory revisited Singapore: Springer, 2019. p. 75-84.
  • BOBIS, J.; WAY, J.; ATTARD, C.; ANDERSON, J.; MCMASTER, H.; CARTWRIGHT, K. Research in Mathematics Education in Australasia 2016–2019. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education in Australasia 2016–2019 Singapore: Springer, 2020. p. 1-5.
  • BORBA, M. C.; ASKAR, P.; ENGELBRECHT, J.; GADANIDIS, G.; LLINARES, S.; SÁNCHEZ AGUILAR, M. Blended learning, e-learning and mobile learning in mathematics education. ZDM Mathematics Education, Switzerland, v. 48, n. 5, p. 589-610, 2016.
  • BORBA, M. C.; CHIARI, A. S. S.; ALMEIDA, H. R. F. L. Interactions in virtual learning environments: new roles for digital technology. Educational Studies in Mathematics, Switzerland, v. 98, p. 269-286, 2018.
  • BRYK, A. S. Accelerating how we learn to improve. Educational Researcher, Washington, D.C., v. 44, n. 9, p. 467-477, 2015.
  • CONFREY, J., MCGOWAN, W., SHAD, M., BELCHER, M., HENNESSEY, M., & MALONEY, A. P. Using digital diagnostic classroom assessments based on learning trajectories to drive instruction and deepen teacher knowledge. In: SIEMON, D.; BARKATSAS, T.; SEAH, R. (Eds.). Researching and Using Learning Progressions (Trajectories) in Mathematics Education Boston: Brill Sense Publishers, 2019. p. 75-100.
  • CONFREY, J.; SHAH, M.; BELCHER, M. Using Learning Trajectory-Based Ratio Curriculum and Diagnostic Assessments for Promoting Learner-Centred Instruction. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era Boston: Brill, 2021. p. 187-216.
  • ENGELBRECHT, J.; BORBA, M. C.; LLINARES, S.; KAISER, G. Will 2020 be remembered as the year in which education was changed? ZDM, Switzerland, v. 52, p. 821-824, 2020.
  • ENGELBRECHT, J.; LLINARES, S.; BORBA, M. C. Transformation of the mathematics classroom with the internet. ZDM Mathematics Education, Switzerland, v. 52, n. 5, p. 825-841, 2020.
  • ENGELBRECHT, J.; OATES, G. Student collaboration in blending digital technology into the learning of mathematics. In: DANESI, M. (Ed.). Handbook of Cognitive Mathematics Switzerland: Springer, 2021 (in press).
  • EVANS, T.; OATES, G. Herenga Delta 2021: values and variables in mathematics and statistics education in a time of disruption. International Journal of Mathematical Education in Science and Technology, London, Special Issue, 2021 (in press).
  • ERSOZLU, Z.; LEDGER, S.; HOBBS, L. Virtual simulation in ITE: technology driven authentic assessment and moderation of practice. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 53-68. Global Education in the 21st century Series.
  • FONT, V.; SALA, G. 2021. A year of uncertainties for mathematics education. Bolema, Rio Claro, v. 34, n. 68, p. i-v, 2020.
  • GALLIGAN, L.; COUPLAND, M.; DUNNE, P.; OATES, G.; HERNANDEZ MARTINEZ, P. Research into teaching and learning of tertiary mathematics and statistics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds.). Research in Mathematics Education Australasia 2016-2019 Singapore: Springer Nature, 2020. p. 269-292.
  • HUNTER, J.; MILLER, J.; CHOY, B. H.; HUNTER, R. Innovative and Powerful Pedagogical Practices in Mathematics Education. Innovative and powerful pedagogical practices in mathematics education. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD (Eds.). Research in Mathematics Education in Australasia 2012-2015 Singapore: Springer, 2020. p. 293-318.
  • HAUSBERGER, T.; BOSCH, M. (Eds.). INDRUM 2020 (International Network for Didactic Research in University Mathematics). International Journal of Mathematical Education in Science and Technology, London, Special Issue, 2021 (in press).
  • MIARKA, R.; MALTEMPI, M. What will become of mathematics education after coronavirus? Bolema, Rio Claro, v. 34, n. 67, p. ii-iv, 2020.
  • OATES, G.; DENNY, P. Authentic assessment to promote online collaboration and critical reflection. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 69-94. Global Education in the 21st century Series.
  • OATES, G.; SEAH, R. Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Australian Journal of Education, Melbourne, 2021 (in press).
  • SANTOS, F. P.; FORTUNATO, I.; MENA, J. Teacher performance evaluation approach from a Brazilian perspective: a literature review. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 315-328. Global Education in the 21st century Series.
  • SEAH, R.; HORNE, M. How much do they know about 3d objects: using authentic assessment to inform teaching practice? In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 240-261. Global Education in the 21st century Series.
  • SEATON, K.; LOCH, B.; LUGOSI, E. (Eds.). Takeaways from teaching through a global pandemic – practical examples of lasting value in tertiary mathematics education. International Journal of Mathematical Education in Science and Technology, London, Special Issue. 2021 (in press).
  • WAY, J.; CAVANAGH, M.; ELL, F.; LIVY, S.; MCMASTER, H. Advancing Our Understanding of Initial Teacher Education Through Research. In: WAY, J.; ANDERSON, J.; BOBIS, J.; MCMASTER, H.; CARTWRIGHT, K.; ATTARD, C. (Eds..). Research in Mathematics Education in Australasia 2016–2019 Singapore: Springer, 2020. p. 91-115.
  • WILKS-SMITH, N. Translanguaging pedagogies for multilingual learner assessment. In: BARKATSAS, T.; MCLAUGHLIN, T. (Eds.). Authentic Assessment and Evaluation Approaches and Practices in a Digital Era: A Kaleidoscope of Perspectives. v. 6. Boston: Brill/Sense, 2021. p. 285-311. Global Education in the 21st century Series.

Publication Dates

  • Publication in this collection
    05 Jan 2022
  • Date of issue
    Sep-Dec 2021
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