Numeracy

Numeracy teaching via the web

Introduction

The purpose of this preliminary report is to identify resources and delivery methods for the numeracy module of the key skills training package. It is not intended to give any more than a cursory description or evaluation of those resources found. Recommendations are given at the end of the report.

In the first section the advantages of using the web to deliver numeracy education are considered followed by an indication of some of the general research into numeracy teaching in order to provide possible frameworks for evaluating a system. The section after that proposes both an outline syllabus and a model for delivery. The succeeding sections provide references to material that is already available both in paper-based and electronic forms.

The bibliography provides details of references and further reading.

Advantages of web-based delivery

Web based delivery allows adaptable, accurate and anonymous delivery of material. Since the material is essentially only kept in one place it is easy to adapt and update. Since the evaluation of the students' efforts in various tests can be computerised, the accuracy can be ensured. The anonymity has specific advantages in a subject that can be seen as carrying a stigma. Essentially we are teaching remedial mathematics and students are reluctant to admit to weaknesses in basic skills. Allowing material to be absorbed without having to ask for assistance from academic staff or fellow students may increase the uptake.

The hypertext nature of the web is ideal for the student led learning approach which allows the user to follow up paths (for example, definitions, examples, quizzes, further explanation, recommended reading) as and when desired.

The graphical and interactive nature of the web is ideal for the visual presentation and manipulation of objects, which is so important in helping to understand the material being presented.

Thirdly, the popular appeal of this technology should not be overlooked as a selling point for the appeal of the package to the intended users.

Current research in numeracy

There are two areas to be considered in the determination of the content of a numeracy module: strategy and syllabus. In (Ginsburg, 1996) 13 instructional strategies for teaching adult numeracy skills are identified. These provide both a framework for any in-house development of a numeracy package, and a benchmark for evaluation of any ready-made package.

(Kopp, 1997) surveyed employers in the UK to determine the relative importance of different aspects of numeracy.

It would seem that there is no standard definition of numeracy, however (Chakrapani, 1985) defines it to be 'the ability of an individual to understand numbers in terms of observation, measurement, evaluation and verification.'
 

Proposed coverage

A list of skills addressed by the numeracy package should be identified. This would indicate the syllabus of the package and should be explicitly stated at the outset of the package to ensure the student was aware of the expected outcomes.

For example (adapted from (Mottershead, 1996)):

• To be able to handle numbers
• To be able to understand basic statistical methods
• To be able to analyse and manipulate data
• To be able to formalise and solve numeric problems
• To be able to evaluate outcomes of computations

Appendix A gives a proposed list of topics.

Since the package should ideally be self-contained the following model would appear to be the most appropriate:

Currently available resources

i) Printed instructional material

There are many books on the subject of acquiring numeracy skills with various approaches. The adult learning style taken by (Hopkins, 1992), (Mason, 1988) and (McDonald, 1989) provides many examples and apply them to everyday experiences.

The strategic mathematical approach taken by (Polya, 1957) provides a conceptual approach to problem solving.

The workbook approach taken by (Page, 1996), (Greer, 1993), (Graham, 1981), (Appling, 1994), (Poole, 1994), and (Streeter, 1998) provides a guided programme of work of academic study. Additionally, for (Streeter, 1998) a multimedia tutorial is apparently available on CD.

ii) Computer based resources.

In the following guide, names of packages in brackets refer to web addresses given in the bibliography.

(SATMath) is an American web based service that coaches high school students for the SAT tests undertaken in that country. It provides all the aspects of the model detailed in the section above and demonstrates well the strong points of the web as a delivery method. The package is available on individual subscription and therefor may not be suitable for our purposes. The cultural dependent aspects would also have to be changed.

(TRANSMATH) is a PC based product, which delivers modules in certain areas. It is likely that these topics are too high level for the purposes of a numeracy course. The software is not networked though it may be possible to do so. A licence for 50 students costs £500. A demonstration copy is available by anonymous ftp from the address given in the bibliography.

(CALMAT) provides a tutorial and test approach from the model described above. Again many modules are available at two levels. The CoreCALMAT provide the numeracy modules, which along with the more advanced topics are tutored and assessed in the CALMAT package. TASMAT offers yet more advanced modules. A demonstration is again available from the address given in the bibliography.

The following packages offer parts of the model illustrated in the above section.

(MathPrac) is an example of a basic question and answer approach. It is again aimed at the US K-12 level of education.

(WebTest) provides web based assessment tools, including those for maths. However it does not provide the tutorial part of the model above.

(Diagnosys) again provides diagnostic assessment for mathematics (and other subjects).

(Qmark) is a commercial product that allows the construction of tests and quizzes and surveys. It has been used to construct diagnostic tests in mathematics.

(MinusPlus) is a project in Liverpool to help improve the numeracy of school leavers. Their web page includes an evaluation of software available. The individual packages have not been included here, but it is recommended that they are reviewed to see if any might be applicable.
 

Recommendations

It is recommended that the material described above be evaluated to see if any of them can be used or adapted for the purposes of the proposed module, or whether it is necessary to implement our own system.

A locally produced prototype demonstrates a basic approach to the conceept which could be developed further if a local option was seen as prefereable to a bought in package.
 

Bibliography

Appling, J.R., 1994. Math survival guide : tips for science students. Chichester : Wiley.

Bullock, J.O., 1994. Literacy in the language of mathematics. American Mathematical Monthly, 101(8), pp. 735-743.

CALMAT. http://sword.gcal.ac.uk/calmat/

Chackrapani, C., 1985. Numeracy. In: Kotz, S., Johnson, N.L. Encyclopedia of statistical sciences. Volume 6.
    New York : Wiley, 1985, pp. 377-383.

Diangnosys. http://www.ncl.ac.uk/~ntltp/

Kopp, E., Higgins, D., 1997. http://www.hull.ac.uk/mathskills/newsletters/issue3/page13.htm

Ginsburg, L., Gal, I.,1996. Instructional strategies for teaching adult numeracy skills. Philadelphia, PA. : National Center on
    Adult Literacy. Sponsored by Office of Educational Research and Improvement, Washington, DC. NCAL-TR-96-02.

Graham, L., Sargent, D., 1981. Countdown to mathematics. Volumes 1 and 2. Wokingham : Addison-Wesley.

Greer, A., 1993. A complete GCSE mathematics : general course. 3^rd ed. Cheltenham : Stanley Thornes.

Hopkins, N.J., Mayne, J.W., Hudson, J.R., 1992. Go figure! : the numbers you need for everyday life. Visible Ink.

Houston, K. (ed), 1994. Innovations in mathematics teaching. Birmingham : Staff and Educational Development Association.
    SEDA Paper 87.

Mottershead, D., Suggitt, S., 1996. Developing transferable skills : some examples from geomorphology teaching.
    Journal of Geography in Higher Education. 20(1), pp. 75-82.

Mason, J.H., 1988. Learning and doing mathematics. Milton Keynes : Open University.

MathPrac. http://www.lerc.nasa.gov/Other_Groups/K-12/p_test/math_pro1.html

McDonald, I., MacLellan, R., 1989. Now try this…: a progressive mathematics course for students. Unwin Hyman.

MinusPlus. http://www.merseyworld.com/minusplus/eval.html

Page, S.G., Berry, J. Hampson, H., 1996. Mathematics : a second start. 2^nd ed. London : Prentice Hall.

Polya, G., 1957. How to solve it : a new aspect of mathematical method. 2^nd ed. Harmondsworth : Penguin.

Poole, B., 1994. Basic mathematics. London : Prentice-Hall.

Qmark. http://www.qmark.com/

SATMath. http://www.satmath.com/

Streeter, J., Hutchison, D., Hoelzle, L., 1998. Basic mathematical skills : with geometry. 4^th ed. Boston : McGraw-Hill.

TRANSMATH. ftp://caliban.leeds.ac.uk/

WebTest. http://flex-learn.ma.hw.ac.uk/
 
 

Appendix A