Does flexibility in secondary level mathematics curriculum affect degree performance?

The authors have much experience in developing mathematics skills of first-year engineering students and attempting to ensure a smooth transition from secondary school to university. Concerns exist due to there being flexibility in the choice of modules needed to obtain a secondary level (A-level) mathematics qualification. This qualification is based on some core (pure maths) modules and a selection from mechanics and statistics modules. A survey of aerospace and mechanical engineering students in Queen’s University Belfast revealed that a combination of both mechanics and statistics (the basic module in both) was by far the most popular choice and therefore only about one quarter of this cohort had studied mechanics beyond the basic module within school maths. Those students who studied the extra mechanics and who achieved top grades at school subsequently did better in two core, first-year engineering courses. However, students with a lower grade from school did not seem to gain any significant advantage in the first-year engineering courses despite having the extra mechanics background. This investigation ties in with ongoing and wider concerns with secondary level mathematics provision in the UK.

A-level Mathematics Module Choice and Subsequent Performance in First Year of an Engineering Degree

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules. The flexibility in choice of applied modules has led to concerns that many students would proceed to study engineering at university with little background in mechanics. A survey of aerospace and mechanical engineering students in our university revealed that a combination of mechanics and statistics (the basic module in both) was by far the most popular choice of optional modules in A-level Mathematics, meaning that only about one-quarter of the class had studied mechanics beyond the basic module within school mathematics. Investigation of student performance in two core, first-year engineering courses, which build on a mechanics foundation, indicated that any benefits for students who studied the extra mechanics at school were small. These results give concern about the depth of understanding in mechanics gained during A-level Mathematics.

Interpreting A-level Mathematics grades – as easy as A, B, C?

Many concerns have been expressed that students’ basic mathematical skills have deteriorated during the 1990s and there has been disquiet that current A-level grading does not distinguish adequately between the more able students. This study reports the author’s experiences of teaching maths to large classes of first-year engineering students and aims to enhance understanding of levels of mathematical competence in more recent years. Over the last four years, the classes have consisted of a very large proportion of highly qualified students – about 91% of them had at least grade B in A-level Mathematics. With a small group of students having followed a non-traditional route to university (no A-level maths) and another group having benefitted through taking A-level Further Mathematics at school, the classes have contained a very wide range of mathematical backgrounds. Despite the introductory maths course at university involving mainly repetition of A-level material, students’ marks were spread over a very wide range – for example, A-level Mathematics grade B students have scored across the range 16 – 97%. Analytical integration is the topic which produced the largest variation in performance across the class but, in contrast, the A-level students generally performed well in differentiation. Initial analysis suggests some stability in recent years in the mathematical proficiency of students with a particular A-level Mathematics grade. Allowing choice of applied maths modules as part of the A-level maths qualification increases the variety of students’ mathematical backgrounds and their selection from mechanics, statistics or decision maths is not clear from the final qualification.

A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Assistive software tools for secondary-level students with literacy difficulties.

Study conducted to evaluate the effectiveness of four assistive technology (AT) tools on literacy: (1) speech synthesis, (2) spellchecker, (3) homophone tool, and (4) dictionary. All four of these programs are featured in TextHelp’s Read&Write Gold software package. A total of 93 secondary-level students with reading disabilities participated in the study. The participants completed a number of computer-based literacy tests after being assigned to a Read&Write group or a control group that utilized Microsoft Word. The results indicated that improvements in the following areas for the Read&Write group: (1) reading comprehension, (2) homophone error detection, (3) spelling error detection, and (4) word meanings. The Microsoft Word group also improved in the areas of word meanings and error detection, though performed worse on homophone error detection. The authors contend that these results indicate that speech synthesis, spell checkers, homophone tools, and dictionary programs have a positive effect on literacy among students with reading disabilities. This study was conducted by researchers at the Queen’s University in Belfast, Ireland.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

Peacebuilding at the Local Level: Refugee Return to Prijedor'

During the 1992-95 war, Prijedor was synonymous with mass killing, ethnic cleansing and detention camps. A decade after the end of the war, international agencies consider this town to be an example of successful foreign intervention. Thousands of Muslim displaced persons (DPs) returned to their pre-war homes, mosques have been rebuilt, and hard-line Serb nationalists have lost much influence. How could Prijedor turn from a hopeless case of ethnic violence to an example of successful intervention? This essay argues that Prijedor's (relative) success is due more to the determination of Muslim DPs than to the international peacebuilding strategy. The initial post-Dayton international intervention exacerbated the problem of internal displacement, raised ethnic tensions and left Prijedor in the hands of the same indicted war criminals responsible for the war. Against the advice of international agencies, which feared a backlash among the Bosnian Serbs, in 1998 Muslim DPs began returning home. Eventually, large-scale return improved ethnic relations and helped marginalize Bosnian Serb extremists. The essay concludes by highlighting the lessons from Prijedor, and identifies the domestic and international contribution to Prijedor's post-settlement success.

A precisely-dated lake-level rise marked by diatomite formation in northeastern Ireland

The intercorrelation of palaeoclimate events from various studies is often hindered by a lack of precise chronological control. Tephra isochrons can overcome this problem by providing direct site linkages. This paper outlines a study of Holocene peat and diatomite deposits that accumulated within the floodplain of Lough Neagh, Northern Ireland. The Icelandic Hekla 4 tephra has been identified at the base of diatomite deposits at a number of sites and provides firm dating evidence for a widespread flooding event in the area at ca. 2300 BC. The evidence is consistent with other studies in Ireland and elsewhere for increased wetness at this time. The results demonstrate that the terrestrial deposits around Lough Neagh contain an important record of Holocene lake-level change. Dendrochronological evidence from the Lough Neagh area provides additional information about lake-level fluctuations over the past two millennia.