**Abstracts**

**Sandra
Britton and Jenny Henderson**

sandrab@maths.usyd.edu.au jennyh@maths.usyd.edu.au

**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

lcarmona@mail.utexas.edu
angeles.dominguez@itesm.mx

**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

**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

gildalarocque@gmail.com

**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**

vdurand@univ-lyon1.fr

**About logic, language and reasoning**

The CI2U is a national
commission in

**Barbara
Edwards**

edwards@math.oregonstate.edu

**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

**Ansie Harding
& Johann Engelbrecht**

**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

anaclaudiahenriques@hotmail.com

**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

**Belinda
Huntley, Johann Engelbrecht & Ansie Harding**

Belinda.Huntley@wits.ac.za

**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**

S.O.King@lboro.ac.uk

**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

**Moneoang**** Leshota**

mj.makoele@nul.ls

**Obstacles in the Usage of Technologies in Teaching
Mathematics at the **

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**

vandebro@math.jussieu.fr

**Functions at the transition between French upper
secondary school and University**

A questionnaire
was proposed in more than seven universities in

**Zhongdan**** Huan**

zdhuan@bnu.edu.cn

**How Mathematics Major Students should be
taught **