Breaking the hierarchies in mathematics education
FYMSiC Conference 2024
Johanna Rämö, johanna.ramo@uef.fi
University of Eastern Finland
Image credit: Veikko Somerpuro
Why are we teaching mathematics today?
There are several good answers to this question. Here is one I’ll be focusing on:
To teach students skills that are useful in life.
The Finnish university education
The Finnish university education
The Finnish university education
Traditional mathematics teaching in universities
Why are we teaching mathematics today?
To teach students skills that are useful in life
Why are we teaching mathematics today?
To teach students skills that are useful in life.
What is useful?
Most important skills in working life, according to Finnish alumni
Most important skills in working life, according to Finnish alumni
Ability to learn new things
Most important skills in working life, according to Finnish alumni
Ability to regulate own actions
Most important skills in working life, according to Finnish alumni
Cooperation skills
Most important skills in working life, according to Finnish alumni
Creativity
Most important skills in working life, according to Finnish alumni
Theoretical knowledge in one’s own field
Traditional teaching in Finland
Traditional mathematics teaching in universities
Hierarchies
Hierarchies
Extreme Apprenticeship (XA)
Image credit: Veikko Somerpuro
Extreme Apprenticeship (XA)
Rämö, J., Lahdenperä, J., & Häsä, J. (2020). The Extreme Apprenticeship method. PRIMUS, 31(10), 1106-1120.
Image credit: Veikko Somerpuro
The learning cycle of the XA method
Rämö et al., 2020
Tutor
Students can come and go as they wish
Drop-in sessions several days a week
Main method of teaching
Image credit: Veikko Somerpuro
Tutors are undergraduate/graduate students
Model how mathematicians work
Teach study skills
Guide by listening
Image credit: Veikko Somerpuro
Tutor
The learning space is in the main hallway of the department
Professor
Group of students
You can draw on all surfaces
Mathematical community made visible and accessible to both students and faculty
Image credit: Veikko Somerpuro
Tutors
Image credit: Susanna Oksanen
Professional development of the tutors
Image credit: Veikko Somerpuro
Results
Lahdenperä, J., Postareff, L., & Rämö, J. (2019). Supporting Quality of Learning in University Mathematics: a Comparison of Two Instructional Designs. International Journal of Research in Undergraduate Mathematics Education, 5(1), 75-96.
Results
Lahdenperä, J. (2018). Comparing male and female students’ self-efficacy and self-regulation skills in two undergraduate mathematics course contexts. In V. Durand-Guerrier, R. Hochmuth, S. Goodchild, & N. M. Hogstad (Eds.), Proceedings of INDRUM 2018.
Summary
Summary
But…
Assessment
One thing remained – the examination
Argh, why is changing assessment so difficult!
Argh, why is changing assessment so difficult!
At the same time I knew that “Assessment drives learning” (George Miller)
Argh, why is changing assessment so difficult!
At the same time I knew that “Assessment drives learning” (George Miller)
Hierarchy
Argh, why is changing assessment so difficult!
At the same time I knew that “Assessment drives learning” (George Miller)
Assessment of learning
Assessment
Au (2022). Unequal by design: High-stakes testing and the standardization of inequality
Räisäinen et al. (2016). Students' and Teacher's Experiences of the Validity and Reliability of Assessment in a Bioscience Course
“If tobacco smoking was invented today, it would not be permitted.”
Norman H Tiffin, 2015
Canadian Journal of Respiratory Therapy
If our current assessment regime was invented today, would it be permitted?
Assessment for learning
Assessment is conducted with the intention of improving learning (Wiliam, 2001)
Assessment as learning
Z. Yan, & L. Yang (Eds.), 2021. Assessment as Learning : Maximising Opportunities for Student Learning and Achievement
Our solution: self-assessment
For life-long learning, students should learn to assess their current skills with respect to their goals (see Boud et al., 2010)
DISA, Digital Self-Assessment
Häsä, J. I. A., Rämö, J., & Nieminen, J. H. (2021). Supporting quality of learning by letting students give their own grades: An innovative self-assessment model in university mathematics. In Z. Yan, & L. Yang (Eds.), Assessment as Learning : Maximising Opportunities for Student Learning and Achievement.
Part of a rubrik
Also generic skills can be learning objectives
Example of a self-assessment exercise
DISA, Digital Self-Assessment
Results on DISA self-assessment
Nieminen, J. H., Asikainen, H., & Rämö, J. (2021). Promoting deep approach to learning and self-efficacy by changing the purpose of self-assessment: a comparison of summative and formative models. Studies in Higher Education, 46(7), 1296-1311.
Nieminen, J. H., & Tuohilampi, L. (2020). ‘Finally studying for myself’–examining student agency in summative and formative self-assessment models. Assessment & Evaluation in Higher Education, 1-15.
Students reflections on self-assessment
"Now I didn’t focus on memorising things. Instead, I focused on understanding the topics, so that in the future, if necessary, I can use them / re-learn them quickly.”
"[...] I think that there wasn’t any bulimic learning. I remember the content better. “
“[…] Success in the exams isn’t only a matter of preparation. On some days, it’s more difficult to concentrate than on other days. In this kind of a course [...] the final grade doesn’t depend so much on a single performance, but every prepared solution and also the self-assessment count for the final grade.”
“[…] the exam measures just content knowledge. In self-assessment, also other kinds of skills are considered.
Different versions of self-assessment in the XA courses
More information and concrete examples:
https://digicampus.fi/course/view.php?id=4440
-> Access as a guest
Should we ban exams altogether?
Self-evident…
If I am taken ill I want to see a doctor who has taken exams and passed them
… but also:
I want doctors to be able to assess very well what they know and don’t know
Photo: Petr Kratochvil
Self-assessment vs. Exam
Life-long learning
Tuononen, T., Parpala, A., & Lindblom-Ylänne, S. (2019). Graduates' evaluations of usefulness of university education, and early career success - a longitudinal study of the transition to working life. Assessment & Evaluation in Higher Education, 44(4), 581-595.
Don’t good grades matter for getting a good job?
The most important factors in getting employed, according to Finnish alumni
The most important factors in getting employed, according to Finnish alumni
ability to verbalise one’s own skills
Thank you!
johanna.ramo@uef.fi
Image credit: Veikko Somerpuro