Clemency Montelle

From lessons to lectures: NCEA mathematics results and first-year mathematics performance

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study.

“We definitely wouldn't be able to solve it all by ourselves, but together…”: group synergy in tertiary students' problem-solving practices

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students working in groups to identify what strategies they employed and how, including what encouraged the opportunities to invoke them. The study revealed behaviours not included in the original taxonomy, including one that we termed ‘group synergy’. We propose extensions to Carlson and Blooms original taxonomy to encompass group behaviour and identify the importance of these behaviours in developing problem-solving skills. Finally, we suggest improvements for future problem-solving session iterations, with the goal of promoting opportunity for more expert performance.

Meeting the Needs of Our Best and Brightest: Curriculum Acceleration in Tertiary Mathematics

For many years, it has been a common practice to recognize students with high potential by according them targeted privileges and opportunities. This includes the practice of allowing students to accelerate their high school programme and, in the case of New Zealand students, to take university courses during their final school years. This work assesses the wisdom of this practice of acceleration in mathematics both for the student and the tertiary institution.

The Candrārkī of Dinakara: A Text Related to Solar and Lunar Tables

A set of tables devoted to the sun and the moon, titled the Candrārkī (“Related to the moon and sun”), was compiled in Sanskrit by Indian astronomer Dinakara along with a short accompanying text, intended to give guidance on how to construct a calendar (pañcāṅga) for any desired year and geographical circumstances. The epoch of this table-text is 9 April 1578. We present here an edition of the text, a literal translation, and detailed technical commentary.

The Karaṇakesari of Bhāskara: a 17th-century Table Text for Computing Eclipses

Critical edition, translation and commentary for the verse instructions accompanying a late seventeenth-century set of eclipse tables in Sanskrit by Bhāskara of Saudāmikā (fl. 1681).