Title of case study:	Playful Learning in pre-Honours Mathematics
School/Subject:	CoSE/Mathematics
Lecturers:	Andrew Wilson and Francesco Giglio
Courses:	Mathematics 1C: Introduction to Calculus (MATHS1015) Semester 1 Mathematics 1G: Introduction to Algebra, Geometry and Networks (MATHS1016) Semester 2
Student level	Level 1 undergraduate
Class size:	200-220 for Maths 1C (higher due to study abroad students) 130-159 for Maths 1G
Location:	Online / distance (only during the pandemic & on campus/in person

 

Brief summary

There is a general perception among some students that maths is a dead subject, resulting in their low attendance of maths tutorials. Countering this notion is Andrew’s and Francesco’s development of playful learning activities utilised in these tutorials. Aimed at first year students, this method allowed for practical application of maths on cases by student groups of various interdisciplinary backgrounds. As a result, students feel more confident in their knowledge, skills and enjoy the student-led sessions.  

 

Objectives 

Our biggest goal was to transition from the traditional learning and teaching of maths to a more practical, enjoyable and mainly student-led way. Through such interactive and collaborative activities, students actively discussed and applied mathematical ideas, often not even noticing the time passing.

By implementing these activities, we further aimed to address the issue of students’ low opinion on maths as a subject, and their consequent low attendance of maths tutorials. This was critical because the courses are interdisciplinary, therefore the change in perception is more impactful. 

 

What is done? 

In each tutorial, students are randomly put into groups of 4-6, with each group receiving an envelope with an information sheet and interactive tasks rather than traditional maths exercises. These activities include matching cards with sigma notation, estimating Loch Ness's area using maps, optimising chemical reactions, and navigating a “Snakes, Ladders, and Vectors” board game. The activities allow students to engage with maths creatively while using real-world examples as shown above. For example, some groups estimate Loch Ness’s area by counting map squares, others use integrals, making the tasks solvable via various methods.

Tutors facilitate the sessions by moving between groups, encouraging participation without directly answering questions and providing solutions. Their focus is to ensure everyone contributes in some way, while engaging any disengaged student. At the end of the session, a discussion of the solutions ensues, followed by each group’s grading on their group work efforts, not the solutions. This grading depends on the group’s cooperation, communication and fostering of the whole group. Feedback is key – sessions are continuously improved based on student responses, attendance, and engagement, ensuring that activities remain relevant and effective.

Tutor preparation is also collaborative. Tutors discuss their approach to the tutorial with the lecturer, ensuring that each one of them understands their role as a facilitator of the session, rather than the leader. Role-playing as students is particularly useful. 

Even online during the pandemic, this approach proved effective with adjustments. Students accessed materials in advance, and interactive PDFs enabled screen-sharing and collaborative work, minimising breakout room challenges. Despite these challenges, students remained engaged, and the collaborative learning environment was preserved. 

 

What works well? 

The biggest positive is that the students did maths for the entire 50 minutes without realising it. What further makes the sessions successful is the group randomisation and their size (5-6 students ideally) as students are motivated to exchange their ideas, skills, and approaches instead of chatting about something else.

 

Benefits

Students

Staff

Students are doing maths throughout the entire session in an interactive, enjoyable and practical way. Students not knowing each other within groups serves as a great boost to ensure they focus on the challenges and share perspectives, ideas and skills from their own degrees. Even if students don’t do the readings/haven’t attended the lecture before, they can come to the labs and still actively participate with their knowledge. The interactive sessions lead to improved opinion on maths as a subject and its tutorials. High attendance of labs – around 80% in general. Groupwork average grade above 2.5 out of three. The activities can be applied online and in-person, as proven by their use during the pandemic.  Students also improve their professional skills, such as teamwork, communication, critical thinking and autonomy. At the beginning, students set up their expectations from the session and at the end are provided with feedback on their effectiveness of teamworking, not the maths problem itself. This further ensures they continue building that positive relationship with maths and it encourages them to still attend the sessions.  The method is very flexible; the students then go off-topic but are very engaged and interested. So, they don’t necessarily have to do the preparation before, it is their own led learning.  Students find the tutorials less confrontational, more engaging and they allow them to get to know other classmates – important because there are more than 20 degree programs involved, and these are the words of students in their feedback. Increased attendance and engagement have been proven by this method. This is also reflected in their grades. Can be applied in other maths courses and years. Especially in the Honours year where they should be reminded that learning is also about creating, not only learning – and embedding research into teaching. Can be used online for large classes and although the methods are slightly adapted, their efficiency and interactivity remain at a good level.

Significantly improved understanding of how students learn and of the whole learning process itself. It is great to see that Graduate Teaching Assistants are open to contemporary approaches which helps deliver the labs successfully. The lecturers and GTAs enjoy running these sessions more than the traditional ones. The approaches and solutions used can be utilised for own research when the topic goes beyond the students’ material. The method can be adopted very readily in higher maths years and courses. Improved students’ perception of maths thanks to the activities. The flexibility of using the activities in person and online, during the academic year and even during summer schools. Despite the class being big, it isn’t difficult to manage the individual sessions and ensure the students get the most out of them. The activities are reusable and low-cost to produce. The method is great to use in such diverse cohorts, especially first year interdisciplinary courses. Enjoyable experience even to lecturers, seeing students being in the driving seat and leading the sessions.

 

Challenges             

Students

Staff

What has to be taken into account is the fact that some students within the group might be naturally shy and unwilling to participate in such group activities – this is where tutors help combat this. Some students might prefer a traditional way of learning and teaching, but the vast majority have enjoyed themselves. Some students from the same country might start talking in their native language, therefore splitting larger groups into smaller ones. Again, this is where the tutors step in.

At first, it is time consuming to develop those activities, but once developed they are reusable and only need to be printed. It might be also a bit costly to fund the materials on your own, but it is not that expensive. To run such active learning methods successfully, the lecturer must adopt and build a horizontal leadership approach. They need to create trust with the tutoring team in order to continuously improve the activities and their own approach. Moreover, to make the labs themselves successful and most beneficial to the students, the lecturer should chat with the tutors and informally guide them to lead the sessions correctly, which is often done outside the contract hours.

 

What did you learn?

Students from diverse backgrounds have different approaches to learning. Pedagogically, there is still room for improvement in many things we still do standardly. For example, tutorials are a safer space for such changes, but lectures should also be approached in this fashion. However, this can be harder given the large number of students compared to the tutorial size. 

This traditional versus innovative approach directly impacts the lecturer’s way of presenting their research as well, so contrast between the idea of an educator and a researcher should be taken into account to unite the two. For instance, this notion helped the lecturer present his research to a broader audience.

It can be terrifying at first to give out that power of leading the sessions to students and adapt to the way they will lead the sessions. This also applies to the GTAs, who might find it even more difficult. It might be even harder to have the confidence to get the power back to finish the session. 

If the session goes really really really well, you will feel like you did nothing. If you don’t have to do a single thing, that is the perfect session, because students should figure it out themselves. They might need facilitating help with the social aspect, encouragement and a bit of guidance but no solution giving. There is the analogy of learning how to ride a bike – the students have to make mistakes but then bounce off of them and get back on the track before figuring out the solution. 

Regarding future changes, students may be allowed to design some activities themselves, hence engaging with the materials they have developed. To do that, the teaching team will launch a student-staff partnership focused on improving the student learning experience in the tutorials. This will be an experiment, requiring the teaching team to meet with the students, share their experience of designing activities, and listen and possibly support any suggestions coming from the students. The desired result is to make the students feel tutorials are their own space for learning and creating, as well as an opportunity to positively influence the learning of their peers. 

 

What advice would you give to others?

Our general advice is to constructively question how to enhance learning and teaching practice by starting with what learners truly need. Most of the traditional ways of teaching STEM subjects, such as mathematics, are indeed based on what teachers should teach with very little focus on how and what learners learn. Conventional approaches to teaching mathematical sciences often generate a gap between the desired learning outcomes set by educators and the actual engagement of the learners with the topics and concepts covered in each course. A thorough and honest evaluation of student learning in the courses we are responsible for, together with a critical observation of successful teaching and learning practices adopted by other colleagues (possibly in other subjects, why not?), may lead to a substantial and effective enhancement of our learning and teaching practice. Sometimes, such an approach brings us far away from standard, conventional practices, such as the structure of the Maths 1C and 1G labs, eventually attracting criticism and concerns. We need to be optimistic about the fact that any sensible risk taken in the direction of innovative, effective practices will be likely supported by successful outcomes in terms of student engagement, student performance and solid ILOs attainment. And all this is very rewarding and worth all the efforts and risks!

 

References

Wilson, A.  and McEwan, M.  (2019, July 18-19). Playfulness in higher education. Enhancing Student Learning Through Innovative Scholarship Conference, Edinburgh, UK.

Interview with Dr Andrew Wilson  https://www.youtube.com/watch?v=e7N0u_2Jyts