The school–tertiary interface in mathematics: teaching style and assessment practice

Abstract

Issues arising in the transition from secondary school to tertiary mathematics study are increasingly coming under scrutiny. In this paper, we analyse two practical aspects of the school-tertiary interface: teaching style; and assessment. We present some of the findings arising from a 2-year national project in New Zealand titled "Analysing the Transition from Secondary to Tertiary Education in Mathematics" supported by the New Zealand Ministry of Education. The results provide evidence of similarities and differences between teachers and lecturers in their preferred teaching approaches and assessment strategies that contribute to a transitional gap between the school and tertiary sectors. The results also show that each group lacks a clear understanding of the issues involved in the transition from the other's perspective, and there is a need for improved communication between the two sectors.

“Much Palaver About Greater Than Zero and Such Stuff” – First Year Engineering Students’ Recognition of University Mathematics

“…Mismatches in mathematical content of secondary and tertiary level mathematics are also reported from other countries (Engineering Council 2000;Heck and van Gestel 2006;Hourigan and O'Donoghue 2007;Hoyles et al 2001;Kajander and Lovric 2005;Robert 1998;Thomas and Klymchuk 2012). In summarising these studies, discrepancies in the focus on distinct mathematical activities relate to oppositions between factual knowledge and use of formularies and tables, routine skills and mathematical problem solving, computational fluency and use of technology, as well as informal argumentation and mathematical proof.…”

“…While in school classrooms students might receive some formative feedback, in undergraduate mathematics courses there is commonly only summative assessment through an obligatory closed book examination. However, the content and form of these examinations might be less standardised and offer more flexibility for the lecturers than school examinations, as for instance reported by Thomas and Klymchuk (2012) from a New Zealand context. The authors contrast this with teaching to the test and a higher amount of bureaucratic work for school teachers with local assessments.…”

“…For instance, according to Jooganah and Williams (2010), mathematics in school is mainly procedural requiring from the students only little conceptual depth, while university mathematics places Bemphasis on proof and rigour requiring them to engage with and critically think about concept definitions^(p. 116). Similarly, in their comparative study of teaching and assessment at school and university, Thomas and Klymchuk (2012) observed that at school emphasis is on practice of worked examples, mathematical modelling and recalling factual knowledge, while at university conceptual reasoning, rigour and problem solving are more valued. The students in their study also found the university courses Bdeeper and more challenging^(p. 298).…”

“This is what you need to be learning”: an analysis of messages received by first-year mathematics students during their transition to university

“…Thomas and Klymchuk (2012) refer to a high percentage of students who participated in their study (77.8%) reporting differences in teaching style and/or the emphasis in university mathematics courses. This includes changes in the way resources are provided, the assessment practices, the pace that is followed and, the level of interaction.…”

“…Various researchers refer to the differences in the way learning resources are used in the two educational settings (De Guzmán et al 1998;Pampaka et al 2012;Thomas and Klymchuk 2012). For instance, a common issue is that some students do not know how to take notes when they come to university, because in high school, they were used to having a specified textbook (De Guzmán et al 1998).…”