Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

e-Math Workshops : a forum for exchanging experiences of mathematics e-learning at university level

We report here about a series of international workshops on e-learning of mathematics at university level, which have been jointly organized by the three publicly funded open universities in the Iberian Peninsula and which have taken place annually since 2009. The history, achievements and prospects for the future of this initiative will be addressed.

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.

Bad Medicine: Homework or Headache? Responsibility and Accountability for Middle Level Mathematics Students

In this action research study of my 5th grade mathematics class, I investigated the issue of homework and its relationship with students and parents. I made some interesting observations and discovered that the majority of students and parents felt that the math homework that was given was fairly easy, yet issues of incomplete assignments and failing homework quizzes were notorious for some individuals. Comments were also made to make homework even easier and have shortened assignments despite the already indicated ease of the work. As a result of this research, I plan to look more closely at the history and development of homework, as well as the psychological implications and “hereditary” issues involving homework, which I believe are passed from one generation of learners to the next. My intent is to continue to study this phenomenon in future school years, trying to develop methods of instilling successful, intrinsic motivational skills to aid students in their homework endeavors. Finally, I will take a close inventory of my own beliefs and understandings toward homework: What is the purpose of having students do work away from the classroom, and how can homework serve as a proactive service for all who are involved?

Affordances of ICTs: an environmental study of a French language unit offered at university level

This project investigates the integration of Information Communication Technologies (ICTs) into educational settings by closely looking at the uptake of the perceived affordances offered by ICTs by students enrolled in a French language course at Queensland University of Technology. This cross-disciplinary research uses the theoretical concepts of: Ecological Psychology (Gibson, 1979; Good, 2007; Reed, 1996); Ecological Linguistics (Greeno, 1994; Leather & van Dam, 2003; van Lier 2000, 2003, 2004a, 2004b); Design (Norman, 1988, 1999); Software Design/ Human-Computer Interaction (Hartson, 2003; McGrenere & Ho, 2000); Learning Design (Conole & Dyke, 2004a, 2004b; Laurillard et al. 2000;); Education (Kirschner, 2002; Salomon, 1993; Wijekumar et al., 2006) and Educational Psychology (Greeno, 1994). In order to investigate this subject, the following research questions, rooted in the theoretical foundations of the thesis, were formulated: (1) What are the learners’ attitudes towards the ICT tools used in the project?; (2) What are the affordances offered by ICTs used in a specific French language course at university level from the perspective of the teacher and from the perspective of language learners?; (3) What affordances offered by ICT tools used by the teacher within the specific teaching and learning environment have been taken up by learners?; and (4) What factors influence the uptake by learners of the affordances created by ICT tools used by the teacher within the specific teaching and learning environment? The teaching phase of this project, conducted between 2006 and 2008, used Action Research procedures (Hopkins, 2002; McNiff & Whitehead, 2002; van Lier 1994) as a research framework. The data were collected using the following combination of qualitative and quantitative methods: (1) questionnaires administered to students (Hopkins, 2002; McNiff & Whitehead, 2002) using Likert-scale questions, open questions, yes/no questions; (2) partnership classroom observations of research participants conducted by Research Participant Advocates (Hopkins, 2002; McNiff & Whitehead, 2002); and (3) a focus group with volunteering students who participated in the unit (semi-structured interview) (Hopkins, 2002; McNiff & Whitehead, 2002). The data analysis confirms the importance of a careful examination of the teaching and learning environment and reveals differences in the ways in which the opportunities for an action offered by the ICTs were perceived by teacher and students, which impacted on the uptake of affordances. The author applied the model of affordance, as described by Good (2007), to explain these differences and to investigate their consequences. In conclusion, the teacher-researcher considers that the discrepancies in perceiving the affordances result from the disparities between the frames of reference and the functional contexts of the teacher-researcher and students. Based on the results of the data analysis, a series of recommendations is formulated supporting calls for careful analysis of frames of reference and the functional contexts of all participants in the learning and teaching process. The author also suggests a modified model of affordance, outlining the important characteristics of its constituents.

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.

A model for a successful organization of a university-level English Phonetics course. 'Un modelo para una organización acertada de un curso de fonética de inglés a nivel de universidad'.

Resumen tomado del autor. Artículo escrito en inglés. Resumen también en inglés

Higher level mathematics : developed specifically for the IB diploma.

Texto que cubre el curso completo para el programa del diploma en Matemáticas del Bachillerato Internacional. También ayuda a preparar a fondo y de forma metódica los exámenes. Dentro de cada capítulo, hay ejercicios numerados para poder practicar y aplicar los conocimientos adquiridos y ayudan al alumno a evaluar su progreso. A veces, hay ejemplos que muestran cómo abordar las preguntas particularmente difíciles. El material para las cuatro opciones figura en la pagina web de la editorial del libro de texto y esta protegida con contraseña. El profesor debe indicar cuál de los cuatro temas de opción va a estudiar el alumno. Tiene las soluciones a las preguntas y a las prácticas de los capítulos.

Standard level Mathematics: worked solutions CD developed for the IB Diploma.

Este práctico CD-ROM de ejercicios cubre las necesidades básicas para conseguir el Diploma de Bachillerato Internacional en estudios de matemáticas. Los temas de los ejercicios del CD-ROM son: álgebra y números (ecuaciones de segundo grado), lógica y probabilidad, funciones (funciones exponenciales y gráficos), geometría y trigonometría (la regla del seno y el área de un triángulo, la regla del coseno), estadísticas (clasificación de datos, tablas de frecuencia y polígonos), cálculo diferencial (ecuaciones de línea tangentes), matemáticas financieras.