1. Negotiating the transition from high school to undergraduate mathematics: some reflections by Zimbabwean students Zakaria Ndemo Bindura University of Science Education

2. Description of problem Students face challenges in learning undergraduate mathematics. Discrepancies characterizing high to university mathematics has been referred to as the “shock” of the “new” inevitable (Clark & Lovric, 2009)…... Transitional phase is characterized by hurdles: change in social environment, mode of delivery and multi-quantified symbolism

3. Description of problem Transitional hurdles has resulted in low uptake of undergraduate mathematics. Students fail to grasp fundamental distinction between analytic and synthetic Current study sought to unravel the nature of transitional challenges among Zimbabwean undergraduate mathematics students.

4. Theoretical considerations Theoretical constructs explicating the nature of transitional difficulties include: Notions of set-before and met-befores (Tall, 2004), Ausbel’s theory of learning Synthetic and analytic definitions (Selden & Selden, 2003). Anthropological idea of the rite-of –passage framework.

5. Theoretical considerations Set-befores are genetic structures we are born, 3 basic set-befores (recognition, language, repetition). Pertinent to the study was language dimension in light of the multi-quantified symbolism of undergraduate mathematics learning A met-before is a current mental facility shaped by specific prior experience of the learner. There are negative and positive met-befores Ausbel’s theory of learning

6. Synthetic and analytic definitions

7. Rite-of-passage framework separation phase, refers to period when students are in high school and preparing for university. Liminal phase, is the time lapse between end of high school and beginning of university mathematics as well as time in between. Incorporation phase, covers first year university study duration – a strong synthetic model interferes with assimilation of new information Content taught at incorporation phase not compatible with robust synthetic model

8. Beinstein’s theory of pedagogical discourse Classification: refers to the strength of the boundaries between discourses and group of actors (Bernstein in Jablonka et al.,2012, p. 2) Strict separation between largely informal intuitive discourse in high school and broadly axiomatic discourse of the incorporation phase Undergraduate mathematics is a more classified knowledge system.

9. Beinstein’s theory of pedagogical discourse recognition rule refers to the need for students to understand principles for distinguishing between high school and undergraduate mathematics learning contexts. In this regard, students need to recognize the speciality of the discourse at tertiary level, as a necessary condition for their capacity at producing what counts as legitimate mathematics in the undergraduate learning contexts.

10. Research questions What are Zimbabwean undergraduate students’ perceptions of the nature of university mathematics? What are the sources of difficulties faced by the students during the transition from school to university mathematics? To what extent has high school mathematics prepared students for undergraduate mathematics?

11. Method The study involved mathematics majors and mathematics education students from two universities in Zimbabwe. Sampling was purposive: 29 CPD mathematics education students, 40 mathematics majors: 16 first and 24 second year students. Qualitative data were gathered that consisted of students’ written responses

12. Data analysis Students’ written responses were mapped onto the theoretical constructs discussed (Varghese, 2009). However we do not claim that there was a one to one correspondence between the constructs and students expressions of their perceptions about the nature of university mathematics and the kinds of transitional challenges In recognition of the possibility of the emergency of categories not covered by literature, summative content analysis technique (Berg, 2009). Manifest elements blended with latent meanings

13. Results The dominant student perception about the nature of university mathematics is that it involves logical reasoning (9 out of 36) for university A and (6 out of 16) for university B. It is worrisome to note that a significant of informants ( 8 out of 36) from University A and (4 out of 16) from university B and expressed that mathematics learning involves doing calculations, a view consistent with high school mathematics (Tall, 2008, p.5). This is indicative of a robust synthetic model, negative met-befores which make negotiation of transitional phase difficult

14. Results “Mathematics requires reasoning and logic while with other subjects its just memorizing…” (T26) “ … a lot of calculations are involved” (T23) “Mathematics involve calculations and there exact solutions to a problem” (T8)

15. Results Content related sources of difficulties were dominant among participants from both universities. The results are very much consistent with our findings from research question 1 where most students perceived mathematics as a discipline involving calculations, a view not compatible with university mathematics (Tall, 2008). “… failing to understand limits.” (T8) “… the use of many variables” (T6) Once again pointing to a robust synthetic model where negative met-befores from informal intuitive discourse interferes with axiomatic formalism dominant at undergraduate level (poor classification and recognition skills in Beinstein’s terms)

16. Results Research question 3 was addressed by analyzing students’ responses to the item: Do you think school mathematics prepared you well for university mathematics? Explain your answer most students expressed that high school mathematics has a link with undergraduate mathematics. Very few students suggested that high school and undergraduate mathematics are disjointed knowledge systems, pointing to weak knowledge classification skills. Such students probably had not developed recognition rules to distinguish between the highly intuitive school mathematics involving numerous calculations and the highly specialized axiomatic formalism in tertiary mathematic

17. Results “ Most of the material found in the first courses Linear maths 1 and Calculus 1 are covered at A level except that some of the methods were were being discarded in Linear Maths” (T11) “Most complex concepts we meet at this level actually build from school mathematics” (T9) Responses classified as partial include: “for other courses school mathematics is used at the university but for other courses completely new courses are learnt.” (T18)

18. Concluding remarks and looking ahead Overall, students’ responses revealed: Prevalence of negative met-befores and dominance of synthetic model of definitions. Inconsistencies lack classification and recognition skills needed to negotiate the transitional phase Delayed gratification Low self-attribution factor among undergraduate

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