Take 10 with... Tanya Evans

Dr Tanya Evans from the Department of Mathematics gives us 10 minutes of her time to discuss her research on new modes of engaging students in undergraduate mathematics education.

Tanya Evans (left) with Julia Novak, Department of Mathematics
Tanya Evans (left) with Julia Novak, Department of Mathematics

1.  Describe your research topic to us in 10 words or less.

Undergraduate mathematics education: emphasis on effectiveness, efficiency and engagement.

2.  Now describe it in everyday terms!

Driven by the advances of emerging technologies, the higher education sector is forced to move with the times and look for ways to become sustainable in a technological era.

Blended learning, the integration of face-to-face and online instruction, is being widely adopted as the ‘new normal’ in course delivery across higher education. In mathematics classes, this new mode of instruction is commonly seen at all levels, yet the extent of its effectiveness raises important questions about its pedagogical merit and about the responsibility of instructors with its evaluation.

My research focuses on developing new modes of educational exchange with the emphasis on improving effectiveness, efficiency and engagement of undergraduate mathematics students.

3.  What are some of the day-to-day research activities you carry out?

Typical activities include reading papers, setting up new studies with students and/or collaborators, writing applications, collecting data (questionnaires, focus groups, video/audio recordings of lectures and professional development meetings), analysing data (quantitatively and qualitatively), and meeting with my collaborators (including online meetings at 10-11pm for my European multi-team project!).

4.  What do you enjoy most about your research?

I enjoy the challenges that I face while conducting educational research that involves myriads of factors affecting numerous variables and being able to explicate dependencies by theorising and using empirical evidence. This type of research is quite dissimilar to my previous area of research, pure mathematics, where logical implications are either true or not – there are no grey areas in pure mathematics!

5.  Tell us something that has surprised or amused you in the course of your research (it could be a discovery, an anecdote or even a funny incident).

As I am learning about experimental educational psychology, I am surprised how university level mathematics instruction is so poorly informed by findings accumulated over the last 100 years.

For example, considering the effect of distributed practice (or spaced practice) on long-term retention of learners, the main finding to date is that separating learning episodes of the same content by a period of 1 day is extremely useful for maximising long-term retention.

In reality, assessment structure in traditional mathematics courses would not have any incentives for learners to engage in a follow up learning episode within 1 day after a lecture as assessment components (e.g. assignments) would be spaced out by at least a week or more.

6.  How have you approached any challenges you’ve faced in your research?

The biggest challenge is to be able to conduct a trial in a real educational setting. Being part of the mathematics department provides me with opportunities to implement changes to instructional practice and evaluate their impact.

For example, based on robust findings pertaining to distributed (spaced) practice effect, I redeveloped our largest stage II course to include incentives for students to engage in follow up learning episodes after every lecture (assessed online quizzes between lectures). The evaluation of the impact of this new more frequent educational engagement points to significant improvement in effectiveness and efficiency in students' learning.

7.  What questions have emerged as a result?

There are so many unanswered pressing questions in mathematics education. I am particularly interested in conducting rigorous research alongside the rollout of new technology-assisted methods of instruction, which are occurring at ever increasing rates. The lack of research-informed evidence-based approaches presents as a major issue that can have unexpected consequences for student learning.

New findings from mathematics education research serve as a cautionary tale about instructional interventions based on technology that were detrimental to students' learning, reinforcing the argument that evaluating the effectiveness of instructional resources needs to be done in a far more robust and systematic way than simply relying on students’ self-reported satisfaction.

8.  What kind of impact do you hope your research will have?

At research-intensive universities, mathematics instruction is primarily done by mathematicians who are not trained to conduct educational research and are not required to have knowledge about learning theories. However, the expectation is that the mathematicians are the ones who drive innovation in teaching and learning at tertiary level, which often involves trying out new technology-assisted instruction and new modes of delivery.

I see the value of my research in providing guidance to mathematics educators in adopting research-informed evidence-based approaches to teaching and learning. This can be achieved by disseminating research findings via professional development initiatives that I am currently involved in: DATUM – an intra-departmental professional development discussion group and PROMT – Peer-Review and Observation of Mathematics Teaching.

9.  If you collaborate across the faculty or University, or even outside the University, who do you work with and how does it benefit your research?

My long-term collaborators from the University of Auckland are Dr Barbara Kensington-Miller (CLeaR) and Dr Julia Novak (Associate Dean of Teaching and Learning, Mathematics).

Internationally, I am leading the New Zealand team that was invited to join a large EU project, PLATINUM, funded by Erasmus+ involving 7 European countries. This project is designed to establish Partnerships in Learning and Teaching in University Mathematics and participants include research teams from Mathematics Departments at eight European universities.

10.  What one piece of advice would you give your younger, less experienced research self?

I wish someone would have made me aware about the 'imposter syndrome' that I was definitely experiencing when I was a young PhD student in pure mathematics, a highly competitive male-dominated field.

Useful advice would be 'Fake it till you make it' as a way to boost confidence and optimistic mind-set. It would also be immensely useful to know what I know now about the research regarding mathematics self-efficacy, which is a construct referring to learners' expectations and beliefs about their ability to develop skills, master tasks and learn mathematics.

Mathematics self-efficacy is more predictive of achievement than a surprisingly long list of other measures, including self-concept, perceived usefulness of mathematics and prior experience with mathematics.

The most robust finding in mathematics related affect is that female students have on average lower self-efficacy in mathematics than male students. Knowing about this would have changed my perspective while experiencing imposter syndrome and, perhaps, have helped me to find ways to improve my self-efficacy.