Students who are ill-prepared in mathematics are entering university and creating challenges for mathematics departments.

There are lots of ideas out there on what to do about this but little evidence to guide university mathematics educators grappling with new ways to teach an old subject to an increasingly diverse student body.

But business as usual is no longer an option.

As debates rage about education and equity in primary and secondary schools, are we ignoring the potential inequities in higher education maths classrooms?

## The students we have or the ones we want?

University mathematics departments have the responsibility of teaching motivated and unmotivated students, along with prepared and unprepared ones.

Not to mention the increasing number of service units filled with students in mathematics-dependent degree programs like engineering, health and biology.

Most students in university maths classes will not become mathematicians and are not intrinsically interested in maths. While some academics are in denial about this, many have accepted the present day reality of teaching maths at university. That is, work with the students you have in your classes instead of dreaming about the students you want.

But what works for improving students’ mathematics outcomes at university?

## Engaging students

At the 9th annual Delta Conference on Undergraduate Mathematics Teaching and Learning, science education expert Dr. Sandra Laursen made a strong case for moving away from passive “sage on the stage” lecturing approaches, in favour of actively engaging students in doing maths in class.

There are a couple of different approaches you can take when teaching an undergraduate maths class. Traditionally maths classes see lecturers lecturing as students passively listen. But there is another approach called “inquiry based learning” which sees students actively engaging in problem-solving and discussion with peers.

Dr. Laursen led a large, comprehensive study on inquiry-based learning in undergraduate mathematics.

Two years of data were sourced from 300 hours of classroom observation, 1100 surveys, 220 tests, 3200 student transcripts, and 110 interviews with students and academics from 100 classes at four large, research-intensive universities that implemented this approach in mathematics.

Comparing students taught with the inquiry-based learning approach and those who weren’t, the study found the former reported better learning gains. An analysis of grades found that students in inquiry-based learning (IBL) classes did as well or better than students who did not complete any IBL classes.

But more importantly, the outcomes for different groups of students were dramatic in IBL classes compared to non-IBL classes. Implementing inquiry-based learning approaches in mathematics improved outcomes not only of high achieving students, but also females, future mathematics teachers and low achieving students.

The study found traditional approaches to teaching in university mathematics favour males and high achieving students. Student-centred approaches improved all students’ mathematical learning.

It also found that maths classes are dominated by lecturing and teacher-centred approaches – 87% of class time had students listening, compared to only 27% of IBL class time devoted to lecturer-talk. Students in IBL classes spent more time doing maths via working in small groups, presenting at the board and discussing problems with the whole class.

## Effective teaching

The evidence for changing the dominant mode of teaching mathematics at university is convincing. And the benefit of inquiry-based learning for modern student cohorts, as demonstrated by Laursen’s study, is strong.

Mathematicians are not required to have teacher training in higher education. Thus, the default teaching mode becomes teach as you were taught.

Professor Merrilyn Goos, who recently spoke at the same conference as Dr. Laursen, said that knowing mathematics is necessary, but not sufficient for being an effective teacher.

Mathematicians are beginning to shifting the paradigm with new, innovative teaching approaches. While many mathematicians may not refer to IBL or the flipped classroom trend in higher education, they are engaging students actively in mathematical problem-solving.

For example, having students make problem-solving videos to encourage communication of complex mathematical ideas. Free audience response systems are also transforming passive lectures to question and answer sessions.

The possibilities are endless for teaching mathematics to engage students. The status quo favours males and high achieving students but today’s university classrooms should invite *all* students to learn, and enjoy learning, mathematics.

The evidence is in for teaching mathematics in higher education. A less little conversation, a little more action.