Sessions

Tanya Evans

Handout

In this address, I focus on a systemic issue facing tertiary mathematics education - a lack of research-informed evidence-based approaches to teaching and learning. The issue highlights the disciplinary disconnect as many research mathematicians do not research in mathematics education. A consequence of this is that many mathematicians contribute to the academic inertia by teaching in a traditional transmitting method - the mode of teaching they are familiar with - simply replicating the teaching they received. In contrast - on the other end of the spectrum - there is increasing experimentation with new modes of delivery by enthusiastic innovators who, in some cases, lack the skills required for conducting rigorous educational research as part of their innovative endeavours. Innovations are often based on integration of new technological gadgets for use in mathematics education with only anecdotal evidence about their merits.

Rapidly accelerating advances of emerging technologies are likely to exacerbate the problem. Globally, the higher education sector is challenged to keep up with the times and reassess its sustainability in a technological era. Blended learning, the integration of face-to-face and online instruction, is now widely adopted as the ‘new normal’ in course delivery across tertiary institutions. Yet the people who are tasked with educational modernisation are not generally supported by mathematics education researchers in their attempts to try out new technology-assisted instruction.

In addressing this disciplinary disconnect, I outline a proposal for a field of research in university mathematics education that aims to bridge the gap by focusing on the following research themes:

Theme 1: Developing frameworks for conducting evaluation research in a realistic university setting for testing an innovation that aims to integrate insights from broader educational research. I will talk about a suitable methodology for this type of developmental research, which is gaining prominence as an effective approach in mathematics education – design (-based) research (Bakker, 2018). To demonstrate how this methodology can be used, I draw on my recent work, in which an innovation involving regular online pre-lecture quizzes was designed, developed, implemented and evaluated. The aim of the intervention was to optimise the effect of distributed (spaced) practice on long-term memory retention. At the completion of the first iteration of design research, our findings suggest that this relatively small change in course instruction can improve efficiency and effectiveness of educational exchange (Evans, Kensington-Miller, & Novak, 2019).

Theme 2: Investigating the mechanisms involved in successful professional development projects in mathematics departments and developing frameworks for dissemination of effective/efficient teaching and learning practices in a realistic departmental setting. This largely unexplored area of research, if developed, can potentially have a major impact on the university mathematics education. I will talk about my current research project with Barbara Jaworski involving a professional development discussion group in the Department of Mathematics at the University of Auckland. This project draws on the pioneering research in this domain that was conducted at the university in the last 10 years (Barton, Oates, Paterson, & Thomas, 2014; Oates & Evans, 2017; Paterson & Evans, 2013; Schoenfeld, Thomas, & Barton, 2016).

Chris Sangwin

For nearly twenty years I have been developing and researching online assessment for mathematics as a contemporary tool through which to engage students and, I hope, improve mathematics education. Online assessment has grown from a cottage industry, to a mainstream activity with almost every major university textbook now accompanied by online assessments. All tools have their strengths and weaknesses, including the paper based exam. Online assessment has been highly successful in providing immediate feedback about the correctness of students’ answers. As such, online assessment is proving to be a very useful tool for building basic skills and procedural understanding. This talk will provide some examples of our use of online assessment in Edinburgh with year 1 students in skills-heavy methods-based courses. However, there are some important things still missing. In particular, the assessment of free-form proof is poorly supported in 2019 by online assessment tools. More seriously, these tools risk polarising the nature of what is learned and potentially impoverishing the curriculum as a result. In this talk I will explore these issues by discussing the role of playfulness in mathematics education. Playfulness here is taken in the sense of “playing in the match” or “playing in the concert” rather than childishness. That is to say, I will explore play as a desirable and important end goal.

Harry Wiggins

Teaching is more than a job. It is a human responsibility and one of the greatest responsibilities in a civilized society. Science education has the opportunity to explain the mysteries of the world. Science educators train young minds to explore, to question, to investigate and to discover. Educators therefore have the opportunity to impact young minds in countless ways. As Albert Einstein said: “Education is not the learning of facts, but the training of the mind to think.”

However teaching, particularly mathematics, at university presents a lecture with several dilemmas that needs to be tackled:

Classroom environment

Course content and assessment

Electronic world

One of the biggest dilemmas facing undergraduate lecturers is teaching large classes. With large classes you typically encounter students with many differently learning styles. Is it possible to cater for all of these learning styles? Also, as educators how can you find the perfect balance of interactivity? It is estimated that 60 percent of people are passive learners. Saryon and Snell (1997) found that students receiving an interactive and student-centered lecturing style are more likely to have a higher impact of learning compared to more traditional styles. So as a mathematics lecturer, how do you solve this classroom catch-22?

Coupled with the classroom environment, we also have to be aware that we are teaching generation Z. They prefer instant gratification. Generation Z wants to see value in content and needs affirmation and recognition. How can this dilemma be resolved? It is a real catch-22, as most mathematics problems needs grit, determination and can take a while to be solved, which clearly clashes with the personality of modern students. This is another classroom catch-22 to take note of and try to solve.

The delivery of content, for example mathematical topics, creates even more catch-22 dilemmas. Are we using effective teaching pedagogies? Is the content organized in a sensible manner? Is there sufficient motivation for tackling the topics in the syllabus? Can we resolve the abstract and hierarchical nature of the material that accompanies the syllabus? Or how important is content really? This is emphasized by a quote by Maya Angelou who said “I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.” So is our content really preparing students for the fourth industrial revolution and equipping them with the skills needed for jobs that don’t exist yet?

Another important educational issue is that of assessment. Assessment refers to a wide variety of methods to evaluate or measure students learning progress or skills acquisition of students. So as an educator you need to ask what kind of assessment is good or necessary. When is assessing enough or too much? What are the costs in terms of feedback, money, time and human resources? These dilemmas need to be resolved to find the best fit for the course and the students.

Finally, education technology is ubiquitous and becoming more and more present in classrooms across the world. However, is using technology hampering or helping teaching? What are the right educational tools to be used in the classroom and which tools are the wrong ones to incorporate? Does using technology make an impact on students? These classroom dilemmas require reflection and appropriate research to fully understand the impact to help educators finding and using the correct tools for their courses and students.

In summary, my talk will tackle these catch-22 topics of teaching. Especially, why reflecting on these issues are important and how these considerations have influenced and shaped my tertiary mathematics teaching. Teaching is a craft that can always be improved. Reflection is a powerful tool that we can all use to improve our own teaching to help students to reach their full potential.

Lastly, using these examples, I will make the case that all universities should have lecturers in the field of education who not only understand the content but also have the ability to better their respective institutions. That is educators who can suggest and implement changes to improve teaching on a bigger scale. Using reflection as a tool of measurement changes we can create and implement initiatives to improve learning environments that will benefit students, educators and ultimately society.

Jessica M. Libertini, Amanda Beecher

Teaching mathematics to students whose majors do not require calculus can be challenging. Historically, many universities taught precalculus or statistics to fulfill general education requirements, but these topics were often divorced from application. In lieu of these typical non-calculus university mathematics courses, the Virginia Military Institute developed Math that Matters, a two course sequence grounded in evidence-based pedagogy and leveraging topics of interest at a local, national, and international level. These new courses were designed to develop learners who appreciate the value and usefulness of mathematics and feel empowered to engage in quantitative problem-solving in their careers and lives. In these courses, students learn to harness the power of basic statistics, data science, mathematical modeling, and technology to frame, solve, and communicate the answers to contextualized problems that were suggested by faculty specializing in diverse fields including art history, physical education, and biology. In this session, participants will learn about our courses and how we created them. We will also demonstrate a lesson and facilitate the work of participants as they take a module (set of lessons) and learn how to engage their local faculty to personalize Math that Matters lessons for their own school.

Janine Sprakel

At a time when more and more of our lives rely on mathematical skills, fewer Australians study and enjoy mathematics. The CHOOSEMATHS Project has taken a multi-layered approach to addressing the issue. Through a national strategy involving mentoring, awareness campaigns, schools outreach and an awards program, we have worked with parents, students, teachers and the public to raise the profile of mathematics and encourage Australians, particularly girls and young women, to engage with mathematics. We’ve learnt a great deal, much of which teachers can implement readily in their classrooms.

Chris Matthews

Embedding Indigenous perspectives in the curriculum, particularly the mathematics curriculum, is often seen as political correctness to appease past wrongdoings. This usually goes hand-in-hand with the perception that Aboriginal and Torres Strait Islander peoples had no form of mathematics and hence, teaching from this perspective is pointless. This presentation will explore the connection between mathematics and culture, how Terra Nullius has shaped our education system and how this maintains the status quo of poor educational outcomes for Aboriginal and Torres Strait Islander students. Prof. Chris Matthews will demonstrate how taking a cultural approach to the teaching and learning of mathematics leads to deep learning for all students. The presentation will then explore the connections between mathematics and Aboriginal culture, how this can be used to transform mathematics education for Aboriginal students and how this education is important for all students.

Cristina Varsavsky

The series of Southern Hemisphere Conferences on Undergraduate Mathematics and Statistics Teaching and Learning has its origins in Queensland, Australia. It was in November 1997 that a group of mathematicians from the Universities of Southern Queensland, Central Queensland, Queensland University of Technology and Bond University had the bold idea to convene academics around the country who are passionate about mathematics education to engage in discussions around the theme What can we do to improve learning? The conference was labelled as DELTA’97 to capture the concept of continuous change experienced by educators.

The first Symposium on Undergraduate Mathematics was held at the Gardens Point campus of Queensland University of Technology in Brisbane (Cretchley et al., 1997). The level of participation showed that many teachers of undergraduate mathematics and statistics students were concerned about teaching matters, eager to share experiences and learn from others. The strong participation allowed for a solid three-day program with two sessions running in parallel. Key to the success of that first gathering was the international flavour given to the event, with keynotes by Deborah Hughes-Hallet of Harvard University and Jerry Uhl of the University of Illinois, as well as a few delegates and contributors from the United States, South Africa and New Zealand.

The success of the first symposium proved the need for an ongoing forum to share good practice and discuss latest developments relevant to the teaching and learning of mathematics and statistics. Education was rarely discussed in corridors and tea rooms in mathematics and statistics departments, so the symposium appealed to many academics from around the country who found their tribe in this emerging community. We are indebted to the organisers of DELTA’97 for their passion for elevating mathematics education and for committing their time and energy to bring to fruition a second symposium. This was held in November 1999 in the Laguna Keys Resort on the Whitsunday Coast in Queensland. The Challenge of Diversity, with special reference to catering for differing learning styles, developing dynamic curricula, flexible delivery and the role of technology to support these endeavours, was the integrating theme. Again, the invited international speakers Adrian Oldknow of Kings College at the University of London and David Smith of Duke University, the forums led by international coordinators, and the greater participation of international delegates gave this gathering a stronger international flavour. In addition, all contributed papers were published in a book of proceedings, documenting the breadth and depth of the research and innovation taking place in Australia and elsewhere in addressing the challenges of diversity (Spunde, Cretchley & Hubbard, 1999).

This second symposium cemented the identity of the DELTA community, which grew from strength to strength from then on. The strong participation of and commitment from South Africa and New Zealand delegates, led to continue these gathering every two years, with locations rotating around Australia, New Zealand and South Africa. The informal collaboration between these Southern Hemisphere countries has grown organically into the formation of the International DELTA Committee who oversees the delivery of the conferences and ensures their continuity. One of the guidelines given to future hosts is to choose venues that are conducive to support network building and continue conversations outside the formal sessions.

The third conference, now re-labelled Southern Hemisphere Symposium on Undergraduate Mathematics Teaching, was held within the world famous Kruger National Park, South Africa, in July 2001, around the theme Gearing for flexibility. The organisers decided to call it Warthog DELTA, and so commenced a trend of naming the gatherings based on their geographical setting. One of the objectives was to use this international meeting as a platform to gain momentum in African countries to increase cooperation on the topic of mathematics education. This conference was also a first in publishing selected research papers in the Journal of the South African Mathematical Society Quaestions Mathematicae (Angelow, Engelbrecht & Harding, 2001), with all other contributions included in the DELTA’01 Communications (Engelbrecht, 2001). The symposium was attended by 120 delegates from 24 different countries, with five guest speakers from the US, UK, Tanzania and South Africa.

By the third event, the DELTA series of conferences had already gained a truly international reputation as the forum for the exchange of ideas, challenges and good practices in undergraduate mathematics and statistics teaching and learning. The DELTA community had by now a clear and strong identity. From then on, the conferences continued to be held without interruption on a biennial basis, and have maintained the highest standard. DELTA’03 was the Remarkable DELTA, held in Queenstown, New Zealand, set against the imposing Remarkables mountains (Holton & Reilly, 2003). It focused on the theme From all angles, encouraging discussions about the complexities involved in mathematics education. Kingfisher DELTA’05 returned to its birth place, Queensland, this time on the pristine Fraser Island and with the theme Blending beyond the boundaries. In addition to the Conference Proceedings (Bulmer, MacGillivray & Varsavsky, 2005), selected papers were published in a Special Issue of the International Journal of Mathematical education in Science and Technology (iJMEST) (Bulmer, 2005). The partnership with iJMEST continued since then, disseminating the work of the DELTA community to the broader readership of the journal.

In 2007, DELTA reached to South America. The Calafate DELTA was held in the picturesque Patagonian town of Calafate, the gateway to the World Heritage Glaciers Park. The theme Vision and change for the new century offered the opportunity to look for new solutions to challenges that persisted over time (Darcy-Warmington et al., 2007; Martinez-Luaces & Varsavsky, 2007). The Gordon’s Bay DELTA was held in 2009 in this beautiful coastal town close to Cape Town in South Africa with the theme Mathematics in a dynamic environment (Wessels, 2009; Oates & Engelbrecht, 2009). The Volcanic DELTA 2011 took place on the edge of Lake Rotorua, with the theme Te Ara Mokoroa, a Maori phrase which describes “The long abiding path of knowledge” aiming to stimulate all participants no matter where they might be on that path (Reilly & Oates, 2011; Thomas & Hannah, 2011). Back in Australia in 2013, Lighthouse DELTA was set in the tourist coastal town of Kiama, and attempted to shine the light through the fog of issues and challenges we all faced (King, Loch & Rylands, 2013; Matthews, 2013). In 2015 Elephant Delta took the community to beautiful Port Elizabeth on the south-eastern coast of South Africa (Blignout & Kizito, 2015; Mofolo-Mbokane, 2015). The eleventh and second last conference was held for the second time in South America; it was hosted in Gramado, a holiday resort “German” town in what is known as the Romantic Route in Southern Brazil, which evoked the truly international and collaborative flavour of the DELTA community. Finally, this year we are gathering by the Swan River in Freemantle, on the Australian Western coast (another first!). This year’s theme, Reflections of Change, brings to mind the need to constantly research our practices to ensure we provide high quality mathematics education to our students.

The DELTA community should be proud of the impressive body of work it produced over the years, which is documented comprehensively on the DELTA website (Delta conferences, 2019) and the iJMEST special issues. However, there is so much more work to be done. Mathematics, as a discipline, is being subject to extreme pressures for change: pressure to modernise teaching practice, demands from the serviced disciplines, dealing with changing student profile, bridging the gap for underprepared students, students questioning relevance of what they are taught, and the list goes on. The challenges faced by teachers on a daily basis are complex, and the solutions require patience, creativity, commitment and resilience to cope with trials that do not work. It is not a surprise that many of the topics discussed at the first gathering in Queensland are still being discussed today, but they are situated in a forever changing higher education landscape and the continuously evolving technological environment, and so requiring more nuanced solutions.

DELTA is not a formal organisation. It is a community of practitioners, working at the coalface with students who come from all walks of life and who study mathematics or statistics for many different reasons. Members include university mathematicians and statisticians, educational researchers, tutors and students who share the joy, successes, disappointments and challenges of mathematics teaching at university level, and who collaborate in research projects across the world. The community remained vibrant over 22 years due to the willingness and commitment of their members who take turns to host international meetings every two years to advance the teaching and learning of undergraduate mathematics and statistics so that our graduates are adequately equipped for their next stage in life.