Computer Aided Assessment of Mathematics for Undergraduates with Specific Learning Difficulties – Issues of Inclusion in Policy and Practice

Glynis Perkin, Nigel Beacham and Anthony Croft

Mathematics Education Centre, Loughborough University, UK.
g.perkin@lboro.ac.uk   n.beacham@lboro.ac.u;   A.C.Croft@lboro.ac.uk

This paper opens up a debate about policy and practice in computer-assisted assessment (CAA) of mathematics for undergraduates with specific learning difficulties e.g. dyslexia.  Guidelines for designing assessments for such students are emerging and some may be transferable to CAA.  Whether mathematics brings with it particular issues is unclear.  With the growth in CAA and an increase in the number of students who have learning difficulties, the issue of disadvantage poses real challenges if universities are to adopt good practice in designing and implementing accessible systems.  This paper analyses some of the available data on computer-based mathematics testing of dyslexic students and describes an exploratory study of the effects of media combinations.  It raises issues which suggest that larger-scale research is necessary before satisfactory guidelines can be drawn up concerning good practice in the provision of mathematics CAA for students with specific learning difficulties.  It closes with an invitation to engage in a dialogue about improving policy and practice.

 

Procedural Knowledge in the Presence of a Computer Algebra System (CAS):  Rating the Drawbacks Using a Multi-factorial Evaluation Approach

Lazim M. Abdullah

University of Malaysia, Terengganu, Malaysia.
lazim_m@umt.edu.my

Computer algebra systems (CASs) have been used by thousands of teachers and students for teaching and learning algebra. They have the ability to perform efficiently almost all of the algebraic expansions and simplifications.  Nevertheless, the traditional approach of using paper and pencil in acquiring procedural knowledge is still widely practised. It was hypothesised that developing symbolic manipulation through procedural knowledge is not always favoured by students.  This paper investigates this hypothesis and gives a rating of several drawbacks of procedural knowledge using the fuzzy set theory decision making processes.  The study involved a survey which consists of four factors for the purpose of giving a rating. A multi-factorial fuzzy evaluation approach was used to analyse the data collected from one hundred and sixty four students sampled from a secondary school in Terengganu, Malaysia.  The students were taught the technique of the completing the square method for quadratic functions using both a CAS and a traditional procedural approach.  The evaluation indicated that students felt that there were disadvantages with the procedural approach in the presence of a CAS.  This rating gives rise to concerns about the relevance of procedural knowledge in the age of computerised mathematics technology.

 

Introducing Mathematics Teaching and Learning to Technological Changes: Introducing Algorithmic Problems into Elementary School Mathematics

Ronit Hoffman and Ronith Klein

Kibbutzim College of Education, Tel Aviv, Israel
ronithof@macam.ac.il ronit_kle@smkb.ac.il

This paper reports on a study that examined if it is possible to start teaching algorithmic problem solving as early as elementary school, given the condition that studying mathematics is augmented by suitable use of computer technology.  Three pre-service teachers, enrolled on a course on algorithmic problem solving in mathematics and who were already teaching in elementary schools, participated in the study.  By analysing the results of teaching a unit of work to 9 and 11 year-old pupils, the results show that the topic of algorithmic problem solving can be modified to suit elementary school pupils.  The data show that pupils exhibited better number sense and better ability to make mathematical generalizations.  Most pupils were able to write an adequate algorithm to a given problem and to ‘run’ it on a computer using a spreadsheet.

 

The Use of Webquest to Enhance the Mathematical Problem-Posing Skills of Pre-Service Teachers

Reda Abu Elwan

College of Education, Sultan Qaboos University, Sultanate of Oman
abuelwan@squ.edu.om

The advent of the World Wide Web is affecting many aspects of education, with claims that its use can transform the way students learn and are taught. WebQuest, the name given to an inquiry-oriented activity in which most or all of the information used by learners is drawn from the Web, is being suggested as a means of enhancing learning.  This paper investigates how WebQuests might be effective in developing the problem-posing skills of pre-service mathematics teachers.  Fifty pre-service teachers from a College of Education took part in this research and, with data from both an achievement test in mathematics problem-posing and a mathematics problem-posing beliefs scale, the effectiveness of using WebQuests in learning problem-posing was measured.  The results show significant differences between those pre-service teachers who experienced WebQuests and those who did not; illustrating that it is possible to change the beliefs of pre-service teachers toward the role of problem-posing in mathematics education

 

Affective Pointers in Mathematics Online Help

Dragana Martinovic

Faculty of Education, University of Windsor, Ontario, Canada
dragana@uwindsor.ca

This report is focused on the use of affective pointers (acknowledgements and hedges) detected in exchanges between learners and tutors on asynchronous mathematics online help sites.  In this environment, both students and tutors use feedback in form of acknowledgements to control communication and assess its success.  Hedges, or insecurities, point to difficulties in obtaining shared meaning between interlocutors in this type of tutoring.  Three purposely selected sites with open access and asynchronous, text-based communication were investigated here.  The results show that expert tutors use affective pointers differently than peer tutors.  Detailed descriptions of acknowledgements and hedges are provided accompanied with conclusions related to their interpretation in attempt to raise sensitivity not only to cognitive but to affective states of participants in these forums.

 

Computor Tutorials to Visualise Symmetry in Introduction Group Theory
         
Darren Wick

Department of Mathematics and Computer Science, Ashland University, Ashland, Ohio 44805. USA
dwick@ashland.edu

The author has developed five interactive computer tutorials that introduce the basic ideas of group theory within the context of symmetry groups.  The tutorials are interactive and employ moving images that describe the motions of various geometric figures.  The user is asked questions designed to connect these concrete visualizations to the more abstract notions of group theory.  The author has employed the tutorials in a course for gifted high school students and in one-semester introductory abstract algebra courses.

 

Assessment, Blending and Creativity:  The ABC of Technology in Mathematics Teaching

Michael Mccabe

Department of Mathematics, University of Portsmouth, UK
michael.mccabe@port.ac.uk

Recent papers at ICTMT conferences have highlighted different aspects of technology in mathematics teaching: computer based learning with computer algebra (1997), on-line assessment (1999), computer assisted assessment for higher level learning (2001) and interactive classrooms (2003).  Blended learning and creative assessment have become increasingly important throughout this period.  This paper explains how a virtual learning environment (WebCT) has been used to support the blending of established and newly created learning resources for selected university level 1 and 2 mathematics units.  It will focus on the role of technology in the development of student assessment: from face-to-face questioning with interactive classrooms (formative) to objective computer marked tests (formative and summative), from computer algebra to learning diaries (formative and summative).  The basic components ABC:  Assessment – Blending – Creativity are identified as driving the learning of mathematics.

 

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