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.

Matematik Öğretmeni Adaylarının Dörtgenleri Sınıflandırma Becerilerinin İncelenmesi

This study aimed to explore prospective teachers’ performance on recognizing quadrilaterals with their special cases and constructing a hierarchical classification of them. The participants consisted of 44 freshmen studying at a public university’s elementary school mathematics education department. Data was collected with a question form containing two questions at the first day of the geometry course taught in the second term of the first year. For quantifying the data of the first question, while students who identify the prototypes of quadrilaterals and their special cases were given 1 and 2 points for each correct answer respectively, -1 point was given for each incorrect answer. The similarity index was employed to quantify students’ concept maps. We investigated that students could detect the prototypes of the quadrilaterals but not their special cases. Additionally, the similarity index between majority of freshmen’ concept maps and the referent map was found as low or moderate.

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.

Impact of a play-based curriculum in the first two years of primary school: literacy and numeracy outcomes over seven years

In 2000–2002 an innovative early years curriculum, the Enriched Curriculum (EC), was introduced
into 120 volunteer schools across Northern Ireland, replacing a traditional curriculum similar to
others across the UK at that time. It was intended by the designers to be developmentally appropriate
and play-based with the primary goal of preventing the experience of persistent early failure in
children. The EC was not intended to be a literacy and numeracy intervention, yet it did considerably
alter pedagogy in these domains, particularly the age at which formal reading and mathematics
instruction began. As part of a multi-method evaluation running from 2000–2008, the research
team followed the primary school careers of the first two successive cohorts of EC children, comparing
them with year-ahead controls attending the same 24 schools. Compared to the year-ahead control
group, the findings show that the EC children’s reading and mathematics scores fell behind in
the first two years but the majority of EC children caught up by the end of their fourth year. Thereafter,
the performance of the first EC cohort fell away slightly, while that of the second continued to
match that of controls. Overall, the play-based curriculum had no statistically significant positive
effects on reading and mathematics in the medium term. At best, the EC children’s scores matched
those of controls.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

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.

Measuring math anxiety in Italian college and high school students: Validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS)

Given that the ability to manage numbers is essential in a modern society, mathematics anxiety – which has been demonstrated to have unfortunate consequences in terms of mastery of math – has become a subject of increasing interest, and the need to accurately measure it has arisen. One of the widely employed scales to measure math anxiety is the Abbreviated Math Anxiety Scale (AMAS) (Hopko, Mahadevan, Bare & Hunt, 2003). The first aim of the present paper was to confirm the factor structure of the AMAS when administered to Italian high school and college students, and to test the invariance of the scale across educational levels. Additionally, we assessed the reliability and validity of the Italian version of the scale. Finally, we tested the invariance of the AMAS across genders. The overall findings provide evidence for the validity and reliability of the AMAS when administered to Italian students.

Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

Cross-age tutoring in kindergarten and elementary school settings: a systmeatic review and meta-analysis

Background: Qualified teaching staffs are neither available nor affordable to provide large numbers of children with individual attention. One solution to providing individual tuition has been the development of tutoring programs that are delivered by nonprofessional tutors, such as classmates, older children and community volunteers. Objectives: We have conducted a systematic review of cross-age tutoring interventions delivered by non-professional tutors to children between 5 and 11 years old. Only randomized controlled trials with reliable measures of academic outcomes, and continuing for at least 12 weeks, compared to instruction as usual, were included. Results: Searches of electronic databases and previous reviews, and contacts with researchers yielded 11,564 titles; after screening, 15 studies were included in the analysis. Cross-age tutoring showed small significant effects for tutees on the composite measure of reading (g=0.18, 95% CI: 0.08, 0.27, N=8251), decoding skills (g=0.29, 95% CI: 0.13, 0.44, N=7081), and reading comprehension (g=0.11, 95% CI: 0.01, 0.21, N=6945). No significant effects were detected for other reading sub-skills or for mathematics. The quality of evidence is decreased by study limitations and high heterogeneity of effects. Conclusions: The benefits for tutees of non-professional peer and cross-age tutoring can be given a positive but weak recommendation, considering the low quality of evidence and lack of cost information. Subgroup analyses suggested that highly-structured reading programs may be more useful than loosely-structured programs. Large-scale replication trials using factorial design, process evaluations, reliable outcome measures and logic models are needed to better understand under what conditions, and for whom, cross-age non-professional tutoring may be effective.

Cross-age tutoring in kindergarten and elementary school settings: A systematic review and meta-analysis

This systematic review summarizes effects of peer tutoring delivered to children between 5 and 11 years old by non-professional tutors, such as classmates, older children and adult community peer volunteers. Inclusion criteria for the review included tutoring studies with a randomized controlled trial design, reliable measures of academic outcomes, and duration of at least 12 weeks. Searches of electronic databases, previous reviews, and contacts with researchers yielded 11,564 titles. After screening, 15 studies were included in the analysis. Cross-age tutoring showed small significant effects for tutees on the composite measure of reading (g = 0.18, 95% CI: 0.08, 0.27, N = 8251), decoding skills (g = 0.29, 95% CI: 0.13, 0.44, N = 7081), and reading comprehension (g = 0.11, 95% CI: 0.01, 0.21, N = 6945). No significant effects were detected for other reading sub-skills or for mathematics. The benefits to tutees of non-professional cross-age peer tutoring can be given a positive, but weak recommendation. Effect Sizes were modest and in the range −0.02 to 0.29. Questions regarding study limitations, lack of cost information, heterogeneity of effects, and the relatively small number of studies that have used a randomized controlled trial design means that the evidence base is not as strong as it could be. Subgroup analyses of included studies indicated that highly-structured reading programmes were of more benefit than those that were loosely-structured. Large-scale replication trials using factorial designs, reliable outcome measures, process evaluations and logic models are needed to better understand under what conditions, and for whom, cross-age non-professional peer tutoring may be most effective.