Contrasting undergraduate mathematics students’ approaches to learning and their interactions within two student-centred learning environments

Figures & data

Table 1. Summary of the instructional practices of Courses A and XA (slightly modified from Lahdenperä et al., 2019).

	Course A	Course XA
Stage	First year	First year
No. of students enrolled	approx. 200	approx. 200
Content	Analysis course emphasizing exact definitions and proof construction	Linear algebra course emphasizing skills such as reading mathematical text, oral and written communication, and proof construction
Lecturer	Mathematician and mathematics educator acknowledged for their excellent teaching by both students and the university	Mathematician and mathematics educator acknowledged for their excellent teaching by both students and the university
Lectures	4 h a week; lectures focus on how to approach the main content of the course	3 h a week; lectures come after students have solved problems; the lectures are based on students’ discussions and focus on a holistic understanding of the main content of the course
Course material	A general Analysis book	Course book written by the lecturer
Task design	Students solve problems every week prior to and during small group sessions; tasks are designed by the lecturer	Students start a new topic every week with approachable problems that teach content and study skills; more challenging problems follow the lecture; tasks are designed by the lecturer
Form of support^a	Two-hour small group sessions (approx. 20 students) twice a week with a tutor	Open learning space on a drop-in basis with tutors
Tutors^a	Older mathematics students	Older mathematics students who attend weekly pedagogical meetings with the lecturer
Assessment	Final grade based on a written exam; bonus points from completed course tasks	Final grade based on a written exam; bonus points from completed course tasks

^a Later in the analysis process, form of support and tutors are combined as guidance.

Table 2. Students’ background information (N = 16).

Subgroup	ID	Major subject	Study year
Deep approach (n = 7)	6	Mathematics	1st
	7	Mathematics	1st
	8	Mathematics	1st
	11	Mathematics	1st
	18	Science	>5th
	19	Mathematics	1st
	24	Science	3rd
Surface approach (n = 4)	1	Other	≥5th
	3	Science	1st
	9	Other	1st
	17	Mathematics	1st
Context-sensitive surface approach (n = 5)	2	Other	3rd
	4	Science	3rd
	5	Mathematics	1st
	16	Mathematics	1st
	21	Other	≥5th

Lahdenperä, J., Postareff, L., & Rämö, L. (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.

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Data availability

Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available.