Abstracts

Sandra Britton and Jenny Henderson

University of Sydney, Australia

[email protected] [email protected]

Student Expectation and Usage of ICT in First Year Undergraduate

Mathematics Courses

This paper investigates the perceptions and expectations of students with respect to integrated web-based formative assessment offered as part of undergraduate mathematics and statistics courses. In particular, we report on student opinion and usage of interactive web quizzes which are integrated into the course material provided for five different first year courses. Data on usage has been obtained by counting the number of times the quizzes have been accessed on a daily basis throughout semester. Student opinions have been canvassed via email surveys, to which over 200 students responded. The following questions are addressed:

• do students use the material in the way that academics expect? 

• do students find the material useful to their learning?

· what factors inhibit student usage of web-based mathematical material? 

• what differences are there in student perceptions and usage of multiple choice questions as opposed to questions requiring student input of numerical answers? 

Guadalupe Carmona & Angeles Dominguez

The University of Texas at Austin, USA & Tecnológico de Monterrey, Mexico

[email protected] [email protected]

Designing learning environments with network-based capabilities for the

Calculus classroom

The purpose of this study is to present how the use of network-based technologies, with an appropriate activity design and focused content, can create a learning environment that favors student participation, assessment, and learning. In this study, the work of Stroup and others (Stroup, Ares & Hurford, 2005; Stroup, Hurford, Ares, & Lesh, 2007) on the design of generative learning environments is used as a framework to design an activity for students in a Calculus course to approach modeling and function approximation. More particularly, in this paper, a case study will be discussed in which the teachers and students were engaged in a learning environment designed with the use of a network-based system with wireless capabilities (TI-Navigator) which supported the design of a generative activity (Stroup, Ares & Hurford, 2005; Stroup, Carmona & Davis, 2005; Stroup, Hurford, Ares, & Lesh, 2007) to hold a lesson on modeling by interpolation and function approximation in a Calculus classroom. Through this learning environment, the 79 students who attended class were able to participate, and the teacher and students were able to constantly assess the knowledge generated by each student, and by the whole group. Students were able to learn in a qualitatively different way that would not be possible without the technology and the appropriate design of the learning environment. In addition, this modeling activity served as a preamble for students to approach other relevant topics (e.g., integration by parts to find volume, continuity of a function, among others) in their Calculus course in a meaningful way for the whole group. The mathematical content addressed in this lesson involves modeling by interpolation and function approximation, which has not been very much explored in the field of mathematics education.  

Anne D’Arcy-Warmington

Curtin University of Technology Western Australia

[email protected]

Look Who’s Talking-Incorporating oral presentations into mathematics

“By learning you will teach, by teaching you will learn.” – Latin Proverb

The essence of this proverb can be used to illustrate the educational benefits of oral presentations in tertiary level foundation mathematic units.  Currently most educators will explore a variety of mediums to teach mathematical concepts, though only use written assessments to test students’ understanding.   A common form of written assessment is the traditional test, which evaluates a student’s comprehension of a specific component relating to a mathematical concept, whereas the oral presentation assesses a student’s understanding of an entire concept, beyond rote-learning and applying formulae.  This paper will examine the unique elements of oral presentations including; two-way communication, general understanding, and incorporation of mathematics into the chosen field of study.  The importance of oral presentations is primarily found with students of non-mathematical majors who require broad knowledge rather than a deep theoretical comprehension of mathematical curriculum. 

Gilda de La Rocque Palis

Pontifícia Universidade Católica do Rio de Janeiro, Brazil

[email protected]

Introduction to Calculus:  Integrating Maple in regular classes and examinations

This paper gives an overview of our Research & Development Project: Introduction to Calculus: Integrating Maple in regular classes and examinations. The investigation carried out aims at a better understanding of the potentialities and difficulties of this technology integration, in particular its impact on student learning and assessment issues. The Maple software is totally integrated in the discipline as it is used for concept development, problem resolutions and examinations.

Viviane Durand-Guerrier

Université de Lyon, France

[email protected]

About logic, language and reasoning

The CI2U is a national commission in France in which tertiary and secondary teachers from various IREM in France interested in “teaching and learning mathematics” at the beginning of University, taking in account questions related with transition, work together. Among our interests are the difficulties met by students concerning logic, language, reasoning, and proving in their mathematical activity. Our contribution will rely on the one hand on various situations and innovations discussed, analysed and experimented in the group for several years; on the other hand, about the results obtained through a questionnaire that was proposed in September 2006 in more than seven universities in France, in order to recover information about students ‘competencies in the areas of sequences, functions, and logic (mainly about implication, negation and quantification). We will support the thesis that the complexity of theses logical notions that are at the very core of mathematical activities, is generally underestimated by teachers, as well at secondary level as at tertiary level, especially concerning the articulation between natural language and formalised language. Our argumentation relies on epistemological considerations on the one hand, and some empirical results on the other hand.

Barbara Edwards

Oregon State University, USA

[email protected]

Revitalising College Algebra: A tale of change initiative 

College Algebra is a title given to a course taught to approximately one million students in the United States each year. Its content varies but originally it was a course designed to meet the needs of college students with an inadequate background for studying calculus. Today approximately 50% of the students taking College Algebra in the United States each year fail to pass with a grade of C or better; and of those who pass fewer than 10% actually go on to take a rigorous calculus course. This paper describes an effort by the Mathematics Association of America to address issues of content, goals and pedagogy in College Algebra at eleven institutions in the United States and the lessons learned about such change initiatives.

Ansie Harding  & Johann Engelbrecht

University of Pretoria, South Africa

[email protected] [email protected]

New perspectives on zeroes of functions

This paper offers an answer to the frequently asked question: "So what cuts at the imaginary roots of a parabola?" We expand on an idea that appeared in literature in the 1950’s to show that a parabola, for instance, is not a single curve but has a “sibling” curve  existing in a perpendicular plane. In other words, the well-known curves in the real plane only depict part of a bigger whole. These sibling curves are obtained by restricting the domain of functions to those complex numbers that map onto real numbers. The existence of these sibling curves explains the existence of “imaginary” roots for these functions visually. Our suggestion is that this new approach be introduced to students by imparting the visual presentation as exposed in the paper to offer a richer teaching and learning approach to the topic. Furthermore this provides a new way of employing technology to visualise concepts and curves that were previously not noticed.

Ana Henriques

Naval Academy, Portugal

[email protected]

Exploring Investigative Activities in Numerical Analysis

This paper reports on a teaching experiment using investigation activities in a numerical analysis course. The main aim of this study is to understand the mathematical processes used by university students when exploring investigation activities and the teaching and learning implications of this kind of activity. The study stands on a qualitative and interpretative methodology based on case studies of groups of students. The participants were the numerical analysis students of the 2^nd year of the Naval School. The results suggest that the introduction of investigation activities has several potentialities for students’ learning and is adequate to be used as a teaching and learning approach in university mathematics courses.

Belinda Huntley, Johann Engelbrecht & Ansie Harding

University of Witwatersrand, South Africa , University of Pretoria, South Africa

[email protected] [email protected] [email protected]

A model for measuring a good question

In this study we develop a model for measuring how good a mathematics question is, which we call the Quality Index (QI) model.  Based on the literature on mathematics assessment, we firstly developed a theoretical framework, with respect to three measuring criteria: discrimination index, confidence index and expert opinion.  The theoretical framework forms the foundation against which we form an opinion of the qualities of a good mathematics question.  We then formulate the QI that gives a quantitative value to the quality of a question. We also give a visual representation of the quality of a question in terms of a radar chart. We illustrate use of the QI model by applying the measure to question examples, given in each of two formats – provided response questions (PRQs) and constructed response questions (CRQs). A greater knowledge of the quality of mathematics questions can assist mathematics educators and assessors to improve their assessment programmes and enhance student learning in mathematics.

S.O. King, A.C. Croft, L. Davis, C.L. Robinson and J.P. Ward

Loughborough University, UK

[email protected]

Staff Perceptions of the One-Tablet Mathematics Classroom

 Much has been written about the explosion in the use of electronic/interactive whiteboards in British primary and secondary schools. However, the research literature is pointedly vacuous when it comes to interactive whiteboard use or penetration at the university level. This study was therefore designed to fill this knowledge gap by providing information on the use of interactive whiteboards in Higher Education. This study is based on the use of interactive or electronic whiteboard-enabling devices such as Tablet PCs (tablets) and Promethean Boards for Mathematics teaching by staff from the Mathematics Education Centre (MEC) at Loughborough University. Consequently, the paper focuses on the perceptions of staff about the impact the use of tablets, based on the one-tablet mode of instruction, have had on teaching and learning. The results show that tablets are a very useful medium for resource archiving and real time annotation of teaching material. However, staff expressed doubts about the overall potential of tablets to substantially enhance student learning and teaching.

Moneoang Leshota

University of Leshoto, Lesotho

[email protected]

Obstacles in the Usage of Technologies in Teaching Mathematics at the National University of Leshoto

Today most educators of mathematics recognize ICTs as essential for teaching and learning mathematics. Whereas the industrialised nations are currently exchanging ideas on how best ICTs can be used in teaching mathematics, many developing countries are still battling with merely, how to get started. Socio-economic factors and issues of access to ICTs have been identified as major hurdles which have to be overcome at the National University of Lesotho in order for the ICTs to be incorporated in the teaching of  mathematics.

Fabrice Vanderbrouck presented by Viviane Durand-Guerrier

Université de Lyon, France

[email protected]

Functions at the transition between French upper secondary school and University

A questionnaire was proposed in more than seven universities in France to detect students’ skills in the fields of sequences, functions and general reasoning. The communication shows some results in the domain of functions. We introduce four levels of students’ conceptions of a function at the beginning of the university: punctual, global, local and subglobal level. The results of the questionnaire confirm some older works about the teaching at the secondary school which has more or less banished the local level and has also contributed the dissociation of punctual and global levels. The analysis of university exercises sheets and curricula also stresses that university teaching has not taken sufficient responsibility for the transition towards the expected local level.

Zhongdan Huan

Beijing Normal University , China

[email protected]

How Mathematics Major Students should be taught 

Beijing Normal University has adopted a reform on teaching methodology of mathematics since 1999. The purpose of the reform is to encourage students to be actively involved in the learning process. The reform was motivated by students’ exam-orientated learning behavior.  Students try to obtain high scores by memorizing types of problems instead of ideas. Such orientation let students mistakenly believe that mathematics is made of various types of methods to be memorized. We initiated a three-semester mathematical analysis course as the first step of the reform. The course includes three parts: lectures, mathematics software labs, and seminars. Our revised textbook consistent with the reform will systematically enlarge the basic knowledge of real number that students learned from high school, emphasize on multi-variable calculus, vector and matrix, and focus on Lebesgue integral in integral calculus. The result of reform is encouraging. A lot of students start to think mathematics scientifically and become more interested and persisted, though we still face many challenges.