“In mathematics and learning, the journey to the solution matters more than the correct answer”

Students of mathematics thought their instruction was unfair, so they were given the chance to redesign their basic education themselves. This resulted in improved learning outcomes.

When a student of mathematics walks into class for the first time, there are probably a hundred or so students in the room. The basics are taught to such a large number of people that the lecturer hardly ever learns everyone’s name. How can you learn anything at courses like this, let alone have your questions answered?

Mika Koskenoja, university lecturer in mathematics and a member of the Teachers’ Academy – a network of top-level teachers – has taught almost all of the courses offered in mathematics on the basic and intermediate levels at the University of Helsinki.

“I’m not a top-level researcher in the field, but I feel I have a knack for teaching. Over the years, I’ve developed my teaching a lot.”

Koskenoja alternates between teaching methods from course to course. At times, he doesn’t say much in front of class, at other times he takes his students to visit schools.

“I can experiment with this and that, but in the end it's the students who decide what works. Heeding students’ wishes and providing varied instruction keep courses attractive.”

Koskenoja often knows already during a lecture whether students have internalised the matter at hand.

“Concentrating and listening creates a certain atmosphere that you can sense in the lecture hall.”

New course arrangements brought about by discontent

Traditionally, mathematics courses are composed of lectures, calculation exercises and examinations. At the lectures, the lecturer teaches, during the exercise sessions students go over their completed assignments, and in the examinations they demonstrate what they have learnt.

However, this makes it possible to pass a course with minimum effort. Students obtain one solution to a problem, but will not necessarily find out whether their own answers were correct.

“In mathematics, much like in teaching, the journey to the solution matters more than the answer, and often there is more than one path,” Koskenoja says.

In 2015 students were fed up with the traditional exercises and wanted to redesign them. Each individual wanted to get feedback. The staff warmed to the idea and joined the development, with Koskenoja volunteering to coordinate trial courses.

Out of the students’ ideas was born the DIGest method, an online-oriented way of learning and teaching mathematics and statistics.

“The method works particularly well in courses with a lot of students. Thanks to it, you don’t have to travel around, and yet everyone gets feedback on their exercises,” says Koskenoja.

DIGest is based on peer and self-assessment. After returning their work, students assess each other’s answers on Moodle on the basis of model answers. Instead of no feedback at all, they get two sets of feedback from other students.

If those two assessments differ markedly, the teacher or an assistant will also check the answers. Finally, students assess their own performance.

“The method improved learning outcomes.”

Online teaching enhances summer course offerings

In summer 2019 Koskenoja organised his first course almost entirely implemented online. The only thing requiring students to assemble in the same place was the final examination.

What made the course special was that it was held when Koskenoja was on holiday. This overlap was made possible by video recording the lectures in advance. Exercises and assistance were taken care of by assistants. This way, students received the same amount of support as in regular lecture courses.

Today’s upper secondary school pupils are already adept at doing calculations with computers, which makes the web a natural platform for students of mathematics.

Students also communicate via course-related online platforms. Questions and solution proposals are added to course forums in the form of screen captures taken by students.

“Contact teaching is well suited to supervising theses, but online courses offer some variation.”

Thanks to online instruction, interesting courses can also be offered in the summer without interfering with teachers’ holidays.