Computer programming in the UK undergraduate mathematics curriculum

This paper reports a study which investigated the extent to which undergraduatemathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016 programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first year coursesthan a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination)

The development of students’ algebraic proficiency

Students’ algebraic proficiency is debated worldwide. To investigate the development of algebraic proficiency in Dutch secondary education, we set up a study, in which 1020 students in grades 8 – 12 took four algebra tests over a period of one year. Rasch analysis of the results shows that the students do make progress throughout the assessment, but that this progress is small. A qualitative analysis of test items that invite structure sense reveals that students’ lack of structure sense may explain the results: the majority of the students were not able to deal flexibly with the mathematical structure of expressions and equations. More attention to structure sense in algebra education is recommended

Promoting insight into algebraic formulas through graphing by hand

Teaching and Teacher Learning (ICLON

The relation between graphing formulas by hand and students' symbol sense

Abstract Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense come to play. In a previous study, we showed how graphing formulas by hand could be learned. The aim of the study we present here is to explore the relationship between students’ graphing abilities and their symbol sense abilities while solving non-routine algebra tasks. A symbol sense test was administered to a group of 114 grade 12 students. The test consisted of eight graphing tasks and twelve non-routine algebra tasks, which could be solved by graphing and reasoning. Six students were asked to think aloud during the test. The findings show a strong positive correlation between the scores on the graphing tasks and the scores on the algebra tasks and the symbol sense used while solving these tasks. The thinking-aloud protocols suggest that the students who scored high on the graphing tasks used similar aspects of symbol sense in both the graphing and algebra tasks, that is, using combinations of recognizing function families and key features, and qualitative reasoning. As an implication for teaching practice, learning to graph formulas by hand might be an approach to promote students’ symbol sense

Tool use and the development of the function concept : from repeated calculations to functional thinking

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of departure and the notions of emergent modeling and instrumentation as design heuristics, a potentially rich technology-intensive learning arrangement for grade 8 students was designed and field-tested. The results suggest that the relationship between tool use and conceptual development benefits from preliminary activities, from tools offering representations that allow for progressively increasing levels of reasoning, and from intertwinement with paper-and-pencil work