ICMI Study On the Teaching and Learning of Mathematics at University Level.

 

Assessing Student Project Work

 

Christopher R Haines (c.r.haines@city.ac.uk) City University, London.

S Kenneth Houston (sk.houston@ulst.ac.uk) University of Ulster.

 

Abstract

This paper is a response to the Discussion Document published in ICMI Bulletin, 43, December 1997. It introduces and reviews the work of a UK Assessment Research Group (ARG) which, during the last seven years has conducted research into the assessment of student project work. The paper will give a history of the work of the group, explain its methodology and assess its implications for future research and practice. One additional purpose of this paper is to disseminate this work to a wider audience through the ICMI Study.

 

History of the Assessment Research Group

While this group mainly comprised British academics it also had an international dimension through one if its members and through its participation in international conferences. ARG met annually from 1991 to 1994 for workshops, two in Exeter, one in Ulster and one in Birmingham. It also made presentations at the 6th and 7th International Conferences on the Teaching of Mathematical Modelling and Applications in 1993 and 1995. It has published four reports and several conference papers (Berry and Haines, 1991, Haines et.al. 1993, Houston et.al. 1994, Burton and Izard, 1995, Haines and Izard, 1995, Izard 1997, Houston 1997). The group also made a major contribution to a UK government funded project "Mathematics Learning and Assessment - Sharing Innovative Practices" (Haines and Dunthorne, 1996)

 

Context

Mathematics projects in higher education are extended tasks at which students work over a period of weeks. They may be mini projects which can be completed in a short period, say three or four weeks, or major projects which take one or two semesters. Students may work in groups on a common project, or they may work alone. Usually they will communicate details of their activity in a written report which they may or may not be required to defend at an oral examination, and they may be required to give a formal seminar presentation or present their work in a poster, and to answer questions.

 

Methodology

Draft assessment criteria were written by "experts" following initial discussion. These were tested in practice by the experts on examples of work such as project reports written by students, posters created by students or video recordings of student oral seminar presentations. The assessment strategies were based on item response modelling and the results were analysed using FACETS (Linacre and Wright, 1994). This analysis determined how stringent each assessor was, how well each student or group performed and how effective each criterion descriptor was. Subsequent discussion and reflection helped inform revisions of the criteria so that the assessors began to have a shared meaning of the criteria and a uniform judgement of standards of performance.

 

Outcomes

ARG have created and tested assessment criteria for the following types of project work :- Communication Skills (Oral), Communication Skills (Written), Poster Presentation, Mathematical Modelling Projects, Pure mathematics Projects, Statistics Projects and General Projects which might include projects involving History of Mathematics or Mathematics Education. The Written Communication Skills assessment sheet is appended to this paper as an example.

Several lessons were learned from the exercises and the analyses and thus the people concerned were in a better position to improve their assessment of project work in the future. The methodology separated candidate achievement from examiner performance from worth of the particular assessment item. It is useful for dealing with the problems that arise with multiple judges. It highlights judges who are inconsistent or who are markedly harder or easier than the others. It emphasised the need for training and practice, particularly for students who were to engage in peer assessment. This highlights the need, when teaching students, to link teaching with assessment so that students learn to be effective self assessors.

From these experiences and analyses we are driven to ask:

 

References

 

Berry J and Haines CR, 1991, "Criteria and Assessment procedures for Projects in

Mathematics", University of Plymouth.

 

Burton L and Izard J, 1995, "Using FACETS to Investigate Innovative Mathematical

Assessments", University of Birmingham.

 

Haines CR and Dunthorne S, 1996, "Mathematics Teaching and Learning - Sharing

Innovative Practices", London : Arnold.

 

Haines CR and Izard J, 1995, "Assessment in Context for Mathematical Modelling", in

Sloyer C, Blum W and Huntley I, editors, Advances and Perspectives in the

Teaching of Mathematical Modelling and Applications, Yorklyn Delaware :

Water Street Mathematics, 131-159.

 

Haines CR, Izard J and Berry J, 1993, "Rewarding Student Achievement in

Mathematics Projects", London : City University.

 

Houston SK, 1997, "Evaluating Rating Scales for the Assessment of Posters", in

Houston SK, Blum W, Huntley I and Neill NT, Teaching and Learning

Mathematical Modelling, Chichester : Albion Publishing (now Horwood

Publishing Ltd), 135-148.

 

Houston SK, Haines CR and Kitchen A, 1994, "Developing Rating Scales for

Undergraduate Mathematics Projects", University of Ulster.

 

Izard J, 1997, "Assessment of Complex Behaviour as Expected in Mathematics

Projects and Investigations", ", in Houston SK, Blum W, Huntley I and Neill

NT, Teaching and Learning Mathematical Modelling, Chichester : Albion

Publishing (now Horwood Publishing Ltd), 95-107.

 

Linacre JM and Wright BD, 1994, FACETS - Many Facet Rasch Analysis, Chicago Il :

MESA Press.

 

Appendix

Communication Skills (Written)

 

Communication Skills (Written)

   

High

    

Low

Not shown

Not applicable
W1 Gives a free standing abstract or summary

Includes a statement of the problem which may need redefinition, states the methodology used and gives specific conclusions. This section is free standing, brief and precedes the report itself.

 

o

o

o

o

o

o

W2 Gives an introduction to the report

States the problem, gives the background to the problem, sets it in context, explains the strategy.

 

o

o

o

o

o

o

W3 Structures the report logically

Connects main points logically, gives supporting evidence succinctly and concisely.

 

o

o

o

o

o

o

W4 Makes the structure of the report verbally explicit

Explains relative importance, emphasises important points (Can see what is there without digging). Makes clear the logical function of constituent parts, uses good and consistent internal referencing (labelling).

 

o

o

o

o

o

o

W5 Demonstrates a command of the appropriate written language

Uses good spelling and grammar. Uses an appropriate style (technical and linguistic).

 

o

o

o

o

o

o

W6 Complements logical structure with visual presentation and layout

Draws clear tables and diagrams, spaces report so it is easy to read. Makes it aesthetically pleasing, gives a contents list if needed.

 

o

o

o

o

o

o

W7 Makes appropriate use of references and appendices

Has a good external referencing system, lists references, uses clearly labelled appendices for secondary data, gives bibliography if appropriate.

 

o

o

o

o

o

o

W8 Gives concluding section in the main report

Appears near the end of the report, makes a summary of the important points which have been logically derived, conclusions represent an adequate solution to the problem, (does not introduce any new information at this point).

 

o

o

o

o

o

o

W9 Gives a well reasonable evaluation

This could appear before the end. Considers limitations of the solution, discusses possible extensions and makes recommendations for appropriate action.

o

o

o

o

o

o