Summary of the Day
This meeting was organised by Nikesh Solanki (University of Manchester) and was held on Monday 18 March 2024. The focus of the meeting was to consider how we can develop our students’ problem-solving skills, which is one of the most desirable skills for employers. A full description of the purpose of the event can be found on the workshop’s website: Mathematics Education that Better Develops Problem-Solving Skills.
Despite the event taking place while teaching was still taking place in many places and this event being very soon after the Higher Education Teaching and Learning Series being announced, there was a healthy attendance of 23 registered participants (and some local academics who decided to drop in). In view of the fact many still had teaching responsibilities at the time, we also offered a hybrid option for attendance.
The day started with three keynote talks. The first of these was from Ouhao Chen (Associate Professor in Psychology with Education, University of Leeds). His talk outlined the theoretical framework of human cognition and its implications for mathematics education. Ouhao went on relate this to traditional instruction-based teaching and problem-based approaches. In particular, he discussed research where both methods are used. In doing so, he pointed that current research seems to suggested that a method where problems are given first and then seems to be more effective “expert” learners whereas reversing this may be better for “novice” learners.
This was followed by a talk from Dan Abramson (Professor of Practice of Mathematics Education, King’s College London) who spoke about how problem solving can be broken down into a sequence of transformations of ideas. He discussed what is required of students and educators to effectively proceed through this sequence and he mentioned considerations for applying this approach into the higher education setting.
Ewan Russell (Senior Lecturer in Mathematics, University of Liverpool) gave the final keynote talk of the morning in which he spoke about a group project unit that he has developed where students tackle real-world problems set by industrial partners. Ewan reported that with aid of this unit students had a stronger sense of developing various graduate skills (including problem solving) during the undergraduate degree.
After the keynote talks there was a networking lunch. This was followed, short talks. The first of these was given by Steven Broom who spoke about the Mathematical Problem-Solving unit that he co-leads at the University of Manchester. Heather Yorton (University of Edinburgh) gave the second short talk in which outlined on a course she co-leads aims to aims to develop various industrial problem-solving skills (e.g. modelling, mathematical analysis etc.) by tackling real world problems. Both of these talks gave the motivation for their units, an outline of their courses and how they are implemented. They also spoke about practical considerations such the complications of marking groups and they overcame those problems.
Note that titles, abstracts and slides of all the talks can be found on The Schedule section of the workshop’s website.
The day was concluded with a discussion session where we brought together what we learned throughout the day and considered how we can put it to practice in our practices. Key ideas and questions that arose during this session were:
- How do we find good problems?
- Many of the talks discussed units in which students attacked problems in groups. Building from this, we discussed how we could best encourage and facilitate problem solving in groups? It was suggested that this could be done by assigning roles to group members.
- Considering the time constraints that academics are under and the difficulty of setting an effective task, some members of the group expressed some concern about trying to find time plan strategies and devise good problem-solving tasks.
- Most of the talks during the day spoke about “non-standard” project-based units where problem solving was explicitly a skill it sought to develop. Whilst we were very impressed with these and would like to see more of them, it begged the question about how we can embed problem-solving components into “standard” units.
- Most talks focused on problem solving in applied mathematics context. Hence, it was asked how we can develop problem-solving in pure mathematics units. In fact, we asked what a “problem-solving” problem in pure mathematics even looks like.
- How can we use assessment to bring attention to problem solving? Moreover, how can assess problem solving? This led to an interesting discussion about the use of rubrics in place of standard marking schemes. Since they are more qualitative they could allow us to assess problem solving more effectively and, since they are often shared with students, they may help convey these qualities to students.
These are all topics we hope to continue exploring in the network that mention below in the Going Forward section below.
Emerging Themes
- Sequencing of teaching events: The first two talks of the day highlighted the importance of sequencing learning events and understanding the sequence of thought when attacking problems. This is an area that requires further exploration in the higher education mathematics context so we understand how to apply this theoretical framework to our contexts.
- Types of problems? As mentioned above, one of the questions raised in the discussion session asked what can be said about problem-solving in areas of mathematics aside of from applied mathematics. This raises a question about whether the methodologies discussed on the day, which were most in applied mathematics, can be translated to other contexts such as pure mathematics. If so, how? Moreover, are there differences that need to be considered i.e. are there different aspects of problem solving in pure mathematics, statistics and probability that were not discussed in the talks on that day?
- Use of rubrics (that include problem-solving): Also mentioned above, a discussion arose about the use of rubrics to help bring focus to problem-solving. It is worth exploring if and how we can use rubrics to do this.
- Group Project Units: Many of the talks discussed units in which students are required to work in groups on open problems, sometimes set by industrial partners. These problems gave students exposure to problem-solving skills as well as other graduate skills. Dr Russell’s talk suggests that these kinds of units may significantly increase students’ sense of development in such skills. This raises the question whether more institutes should establish units on this nature.
Going Forward
Network of Lecturers interested in problem solving: Following on from the workshop, we will seek to establish a network of academics with aim of exploring the ideas, questions and themes that emerged mentioned above. The purpose of the network will be to share ideas of how we can implement the ideas we have discussed and report the impact of doing so. The network will primarily function on an electronic format (e.g. MS Teams). However, my hope is that this will lead to further in-person meetings were progress on implementation of these ideas will be shared.
If you are interested in joining this network please contact Nikesh Solanki at Nikesh.solanki@manchester.ac.uk.
