Mathematical Learning At Tertiary Level: Students’ Perceptions Of The Effectiveness Of Experienced Learning And Teaching Strategies

Author(s):

Svein Arne Sikko(presenting / submitting)Birgit Pepin(presenting)

Conference:

ECER 2013

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 05, Mathematics at University Level

Paper Session

Time:

2013-09-11

11:00-12:30

Room:

D-405

Chair:

Birgit Pepin

Contribution

The transition from secondary to higher education mathematics has been widely studied and it appears to be a difficult phase for many students (e.g. Gueudet, 2008). In addition to causing disappointment and distress for students personally, student failure and/or drop-out represent a significant loss of money for the university/college, a concern for teachers and a loss of potential for society as a whole (Gamache, 2002). It is said that students coming into higher education are more numerous and have more diverse backgrounds than previously, and they have different and often vague views of mathematics, its learning and its role in their future careers and lives (Kajander & Lovric, 2005). Students often struggle with university studies because they have a distorted perception of what learning is and what the acquisition of knowledge entails and many students see knowledge as a collection of facts that can be absorbed passively (Gamache, 2002). Moreover, undergraduate mathematics does not yet seem to accommodate the diversity of its student body in its offerings and learning mode opportunities (Barton, Ell, Kensington-Miller, & Thomas, 2012).

In this study we investigate how students perceive their ‘learning milieus’ and examine how they develop as mathematics learners, at transition and through their first year university mathematics. In this paper we report on the results from the second of two data points performed in the second year of the project. The question we ask is "Which forms of study did the students perceive as having been most useful in their first year of study?"

In terms of learning-and-teaching practices, face-to-face lectures remain a standard component of most higher education mathematics courses, despite being widely criticised, and even with advances in information technology and access to the internet, and it is claimed that lectures often are, in practice, where students’ learning starts (Pritchard, 2010). These criticisms relate to the lecture as a mode of teaching (mathematics) which promotes superficial learning and ‘transmissive’ teaching, an environment where ‘right-and-wrong’ answers are encouraged, amongst others. However, there is evidence that lectures, appropriately ‘conducted’, are likely to provide opportunities for student learning, for students to take responsibility for their own learning and to engage in activities that are conducive to collaborative learning (e.g. Barton et al., 2012).

Research (e.g. Crawford , Gordon, Nicholas, & Prosser, 1998) shows that students’ views of mathematical learning and knowledge relate to their experiences of learning as a whole, and Schoenfeld (1998), for example, proposes an environment that fosters “a community of sense-making in which exploring ideas is highly valued” (p.61) and in his mathematical problem-solving courses teachers encourage students to conjecture and propose solutions where the validity and accuracy of the solutions are decided by the group. Barton et al.’s study (2012) shows that lecturers are crucial in establishing new social norms (Yackel & Cobb, 1996) where the lecture goals are changed from ‘covering the content’ to ‘developing mathematical understanding’ which includes active engagement of students and where “students spend some time working in informal groups engaged in mathematical activity” (p.6).

Method

The larger study was conceptualised in collaboration with the TransMaths project at the University of Manchester. The research design was based on a theoretical framework of mixed methodology involving student longitudinal survey; student biographical interviews; and case studies of practice, all at two data points (DP1 and DP2). The data chosen for the presented study were the questionnaire/survey data and selected interviews, from students at two different institutions: one ‘old’ university; and one university college. Students studied for different courses, most of them mathematically demanding, and selected ones for mathematics teacher education. In order to develop deeper insights into students’ experiences, the study implied robust elected methodological principles: - the principle of ‘extended time’ survey: this involved following students’ development from their first weeks at university throughout their first year and into the second; - the principle of ‘continuity’ in observation and interview: selected students were ‘followed’ inside sessions (e.g. lectures, tutorials) and outside these sessions (informal group discussions/sessions); - the principle of ‘seeing it through the student’s eyes’ in observation and interview probing; - the principle of ‘reflective investigation’: this included discussing what they had written down, or submitted, or said before, in a reflective discussion.

Expected Outcomes

Firstly, the findings showed that students perceived to be learning most when they were ‘doing’ the mathematics, and in particular when they were working together with their peers in small groups. Students largely welcomed collective work and team-based learning, and it appeared that they felt safe in these groups where they could ask questions, seek help from and provide help to others. This supports previous research findings (e.g. D’Souza & Wood, 2003) in terms of the benefits of collaborative learning for the creation of an environment of active, involved and goal-directed learning. Secondly, many students claimed that they learnt little from lectures. A common thread in answers from all students, regardless the institution, was that students felt that the pace was too high and hence they could not follow the teachers’ explanations. As lectures were typically held in large auditoria, students apparently had little opportunities for asking questions. The social and socio-mathematical norms (Yackel & Cobb, 1996) of the lectures these students experienced did not help them to engage and understand the mathematics, and students would have benefitted from more innovative practices (e.g. skilled questioning; active student involvement) or ‘resources’ (e.g. technology, Borba & Llinares, 2012), to ‘re-invigorating’ large-group lectures.

References

Barton, B., Ell, F., Kensington-Miller, B., & Thomas, M. (2012). Teaching undergraduate mathematics: Perspectives and interactions.Retrieved from http://www.tlri.org.nz/sites/default/files/projects/9285_Summary.pdf Borba, M.C., & Llinares, S. (2012). Online mathematics teacher education: overview of an emergent field of research. ZDM Mathematics Education, 44, 697-704 Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998). Qualtiatively different experiences of learning mathematics at university. Learning and Instruction, 8, 455-465 D’Souza, S.M., & Wood, L.N. (2003). Tertiary students’ views about group work in mathematics. Educational Research, Risks and Dilemmas – New Zealand Association for Research in Education (NZARE) and Australian Association for Research in Education (AARE) Joint Conference. Retrieved from http://www.aare.edu.au/03pap/dso03154.pdf Gamache, P. (2002). University Students as Creators of Personal Knowledge: an alternative epistemological view. Teaching in Higher Education, 7(3), 277-294 Gueudet, G. (2008). Investigating the secondary-tertiary transition. Educational Studies in Mathematics, 67, 237-254. Kajander, A., & Lovric, M. (2005). Transition from secondary to tertiary mathematics: McMaster University experience. International Journal of Mathematical Education in Science and Technology, 36 (2-3), 149-160 Pepin, B, Lysø, K.O., & Sikko, S.A. (2012). Student educational experiences at transition from upper secondary to higher education mathematics. In F.Rønning, R.Disen, H.Hoveid, & I. Pareliussen (Eds.), FoU i praksis 2011. Rapport fra konferanse om praksisrettet FoU i lærerutdanning (pp.275-285). Trondheim: Tapir Akademisk Forlag Pritchard, D. (2010). Where learning starts? A framework for thinking about lectures in university mathematics. International Journal of Mathematics Education in Science and Technology,41, 609-623 Schoenfeld, A. (1998). Toward a Theory of Teaching-in-context. Issues in Education, 4(1),1-94 Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477

Author Information

Svein Arne Sikko (presenting / submitting)

HiST

ALT

Trondheim

Birgit Pepin (presenting)

Høgskolen i Sør-Trøndelag

Avdeling for læreutdanning og tegnspråk