it and pupils' achievement in school mathematics

IT and Pupils' Achievement in School MathematicsAuthor(s): David C. JohnsonSource: Mathematics in School, Vol. 23, No. 2 (Mar., 1994), pp. 39-42Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215099 .

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IT and

pupils' levemen

n school

thema by David C. Johnson, Centre for Educational Studies, King's College London

The theme of "Mathematics and IT", Mathematics in School, November 1993, presents many exciting ideas, not the least being the potential for taking advantage of micros in the home even with the limitations noted by the authors.' Databases,2 spreadsheets3 and programming4,5,6 are all noted for their potential and one need only peruse some of the special themes in past issues of Micromath for further ideas on what might be accomplished with these tools (e.g., Autumn 1989, Data Bases; Spring 1990, Numerator; Autumn 1990, Spreadsheets; Summer 1991, Graphics Calculators; Autumn 1991, Handling Data; and Summer 1992, Cabri Geometry).

I have had the opportunity to discuss these and other developments with IT at the recent BCME conference in Leeds. My talk also noted developments in, for example, telematics, CD Rom, Video disk, and hypermedia. However, I then took the opportunity in the talk to look at the reality of the classroom and school - what is really happening? My remarks were based on the results from a major rigorous research evaluation study commissioned by the Department for Education - the ImpacT study. This was the largest major study on the impact of IT on teaching and learning undertaken anywhere in the world.

Introduction The ImpacT study, "An evaluation of the impact of Information Technology on children's achievements in primary and secondary schools"' was carried out by a team of researchers in the Centre for Educational Studies, King's College London. The focus of the work was on pupils' learning and classroom activity involving IT in four school subject areas - mathematics, science, geography, and English - at three age levels - 8-10, 12-14, and 14-16, designated here in terms of the initial year, i.e., year 4 (Y4), year 8 (Y8) and year 10 (Y10). Each age cohort, with some exceptions, was followed for two years.

The work was designed to extend our understanding from earlier research to include longitudinal effects within school subjects, cross-subject considerations of general aspects of classroom use of IT, and the provision and use of hardware and software resources. These were integrated to address a range of issues encompassing learning, pedagogy, and school organisation. The ImpacT results from the main component parts were linked to enable the research team to address three main questions:

0 Pupils' Learning: did IT make a contribution? 0 Pedagogy and Practice: what can we say about the

planning and practice of teaching to incorporate IT? 0 Schools' Organization: what were the demands of IT on

the schools?

My intent here is to focus on an aspect of the first question: the impact of IT on mathematics learning, although findings from the second equation will be used in the discussion relative to how we might move forward. [Full details on all aspects of the ImpacT study are given in the main report [op cit]].

The Research The study included data collected from over 2300 pupils from 87 classes in 19 LEAs, distributed throughout England and Wales. The classes were chosen as matched pairs, all classes being nominated for their good teaching and curriculum delivery, but one of each pair made regular use of IT (HiIT), while the other (LoIT) did not. Three kinds of data were collected:

0 An assessment of pupils' achievement of specific learning tasks and skills, through two administrations of specially designed subject- focussed assessments to the matched pairs of classes. The assessments were administered as post-tests twice during the study, once during the first year and again near the end of the second year. Additionally, some of the pairs, and some of the HiIT classes were the focus of eight topic-specific mini-studies, and all pupils took a final test for IT concepts and skills. Soon after the classes had been chosen, all pupils also took a general reasoning test; to be used as a pretest in the research and to provide a check on how well matched the two classes in each pair were.

a Five in-depth longitudinal case studies in HiIT classes focused on classroom processes and pupil interactions. Classrooms were observed, pupils and teachers were interviewed and docu- mentary evidence was gathered to illuminate classroom realities. Qualitative analysis was based on those themes and issues that emerged from the data across the five studies.

* IT resourcing and use was monitored throughout by the regular returns of questionnaires and data sheets from the teachers and pupils in each class. Hardware and software provision, pupils' IT use in ImpacT subjects and across all subjects, and pupils' extra-mural use of IT were analysed descriptively by classes, age- cohorts and subjects. [There are some interes- ting contrasts here with the results reported by Robertson and Green. ]

Thus, in the case of mathematics the "assessment of achievement" and "IT resourcing and use" data were from matched pairs of classes in each of the three age groups - six classes (i.e. three matched pairs) in the Y4 group, and eight classes (i.e. four matched pairs) in each of the Y8

Mathematics in School, March 1994 39



and Y10 groups, although only seven of the eight took the mathematics reasoning test a second time. In addition a comparative HiIT-LoIT mini-study was conducted with one of the Y8 matched pairs - this involved the role of LOGO programming in the study of angles (the learning activities taking place during the summer term in the 1989/90 school year).

As indicated above, the case studies were treated as a whole with the focus on general themes across the five studies (one of which was a secondary school mathematics classroom).

The mathematics subject-reasoning assessments (tests) were developed from a set of items taken from the Wisconsin Centre for Education Research "mathematical problem-solving super items". A "super-item", as defined for the Wisconsin research, is an item which, on the basis of one stem problem, asks questions at a number of levels of difficulty - in this case four. In principle, such an item may be given to pupils of widely differing age and attainment, since there is always something that any pupil can understand and usually something that the most able find challenging. The levels used here are derived from the SOLO taxonomy8'9 and are described as uni-structural (single step to a solution), multi-structural (several steps to a solution), relational (some generalisation) and extended abstract (transfer of generalisation).

The first administration of the mathematics test, designated MR1, was in the spring or summer term of 1990 and the second administration, MR2, in the spring (Y10) and summer (Y4 and Y8) terms of the following year (pupils in each cohort now one year older). Two versions of the general reasoning test were used, one, denoted AH1, for the Y4 cohort the other, denoted AH2, for both Y8 and Y10. As indicated earlier, the AH tests were administered once at the beginning of the research.

Discussion of selected results The following has been extracted from chapters 4-7 in the ImpacT Report.'

Pupils' Learning 1. Within the limitations of the study, the answer to the first research question is yes, IT did make a contribution to the learning of mathematics, but the contribution was not consistent across age bands or classes within an age band.

Group data for each age cohort are given in Table 1. When the results were adjusted for the differences in ability of the classes (on the basis of the AH tests - the details are in the main report), the Y4 and Y10 HiIT classes scored significantly better (p<0.05) on both administrations of the mathematics assessments.

While the results on the mathematics reasoning assessment for the Y8 cohort indicated no significant differences, the "Angles" mini-study conducted with two classes in this age-group did yield highly significant differences on both an immediate "angles" posttest and a retention test given eight months later. On the immediate posttest the main difference was in the subscale "application", while on the delayed posttest the HiIT class was significantly better on the subscales of "knowledge", "estimation", and "application". With certain qualifications these results provide strong support for the inclusion of LOGO turtle geometry programming, both during the study of angles and angle relationships and as an on-going activity in school mathematics at this level. 2. However the general better performance of the HiIT groups masks considerable variation between the groups, and the main proportion of the increase in scores came from a small number of the HiIT classes. Access and use

Table 1 Lo- and HilT group performance: AH1, MR1 and MR2

Y4 AH1 MR1

Group na mean sd mean sd

HilT 70 24.41 8.21 8.20 3.29 LolT 93 26.33 7.69 7.51 3.45

MR2

HilT 59 24.61 8.57 10.39 4.00 LolT 69 26.35 7.85 9.26 4.00

Y8 AH2 MR1

Group n mean sd mean sd

HilT 90 63.18 13.40 18.46 6.20 LolT 95 58.85 12.47 16.87 5.20

MR2

HilT 62 64.10 12.89 23.10 6.09 LolT 60 57.98 13.14 21.50 5.98

Y10 AH2 MR1

Group n mean sd mean sd

HilT 86 62.12 11.48 19.33 4.59 LolT 69 58.39 9.40 15.45 3.52

MR2

HilT 68 63.28 11.63 21.75 4.56 LolT 42 58.79 8.91 19.55 4.11

aPupils with both AH pretest and a corresponding MR1 or MR2 posttest score.

in these classes suggested there may well be some minimum threshold of IT use for any detectable impact on mathematics attainment. This was particularly noticeable in the Y8 Hi- and LoIT matched pair involved in the angles mini- study (this HiIT class also out-performed all other classes in the cohort on MR2, but this performance was offset by the lower performance of the other HiIT classes in the cohort).

Table 2 below provides an indication of frequency of access of pupils in each of the ImpacT mathematics classes. For the ImpacT sample across all four subjects and age groups, very few class median scores for IT use in subject for any one term, on a scale of 0-4, were 3 or higher, where 3 represented pupil use of the computer in the main subject at a frequency on average of once each week, and 2, for example, represented use between three and five times per

Table 2 Median scores" for class IT use in mathematics; Y4, Y8 and Y10

LolT HilT

Class Number 2 4 6 1 3b 5 7

Y4 Max. 3 0 0 3 2 2 Min. O 0 0 0 1 0

Y8 Max. 0 0 0 3 3 3 1 Min. 0 0 0 0 1 3 1

Y10 Max. 0 0 0 3 2 3 1 Min. 0 0 0 0 0 1 1

aThe IT use entry is on a scale of 0-4 with 3 being once per week on average. Maximum and minimum are for school terms with the highest and lowest median values. bThere were six classes included in the analyses for Y4.

40 Mathematics in School, March 1994



term. Returns from 70 classes were included in the analysis, and of these, nine attained a median score of 3 or above for at least one term - these comprised seven from mathematics and two from English. From these data it would appear that the notion of frequent use of IT in ImpacT classes throughout the country during the period of the research was still far from being achieved. [And the issue here is are we really coming close to what might be required?]

With few exceptions, the results reported in Table 2 confirmed the designations of Hi- and LoIT, but note is again made of the wide variations in use, even in those classes designated as HiIT.

Information was also collected on the software used in subject. Software reported as used in the mathematics classes identified as among the highest or most consistent users of IT for each age cohort included:

Y4 Class 5: Teacher programs, Junior Find, Star Seeker, Spaceship Earth, Revelation on A3000, Bounce, Taxman, Dart, Branch, Space Walk, Writer, Turtle. Y8 Class 5: LOGO, SMILE software, Mathemagic Land. Y10 Class 5: AVP computing, AVP computing revision, AVP arithmetic revision, LOGO, Micros in Maths ITMA.

It seems reasonable to conclude here that the IT activity in these classes, along with aspects of school resource and teaching style, made a significant contribution to the pupils' achievements. Further, as indicated previously, the results suggested that there may well be some minimal threshold of access, both frequency and over time, and type of classroom activity for such a contribution to become apparent within the assessment schemes now utilised in classrooms, or even nationally.

3. The main focus of the case study research was on classroom processes. The case study aspect of the research must be qualified in terms of the approach and method in that while the data collection was rigorous and detailed, the analyses were designed to provide exemplification rather than generalisations. Selected observations from the case study classes suggested some important considerations for pupil use of IT which tended to support and extend results from the other assessments, for example:

0 computers were found to be good motivators which heightened pupils' interest and enjoy- ment and were also seen to have a positive effect upon the status of the subject; computers aided concentration by focusing pupils' attention on the work in hand and as a result some pupils and teachers believed that the standard of work produced was of a higher quality than it would have been otherwise; opportunities to work in an open-ended way enabled pupils to become involved in more complex and challenging learning situations beyond that typically experienced.

Further, some of the failures to detect any contributions through the use of IT may be attributed to some of the problems encountered by pupils in the case study classes:

difficulties in using a particular software package; inability to work effectively in a collaborative environment.

Pedagogy and Practice 1. The answer to the question regarding the planning and practice of teachers mainly involved a consideration of classroom management and organisation and teaching styles along with aspects of hardware and software availability and use. The results from the case studies and

other aspects of the field study indicated quite clearly that any contribution was dependent upon a range of factors, the most important being that of the role of the teacher.

2. Teachers' responsibilities were found to demand careful attention to organisation and management, in particular the effective use of collaborative or group work. Further, effective use of IT represented substantial demands in terms of knowledge and understanding of, and familiarisation with, a variety of software in order to integrate the activity, in philosophical and pedagogical terms, within a large scheme of work.

3. The use of more general purpose software, e.g. spreadsheets, databases, and programming, placed additional demands on the teacher, beyond that of becoming familiar with the use of the more complex software, to include more reflection on the nature of the subject and the potential role of such software in enhancing processes and understanding.

Epilogue The ImpacT research has provided evidence of a significant contribution of IT to pupils' learning of mathematics. However, the issues and problems regarding changes in the educational system are complex and multi-faceted. Enhancing educational opportunity through IT is no different, in that any strategy must take into account a range of needs and issues and the fact that achieving the goals will take time. The research showed that in spite of a number of commendable efforts and a sustained national strategy to support the implementation of IT in education, people at all levels still need more help in formulating clear policies and strategies; this should go beyond focussing on particular aspects of issues and problems and provide a comprehensive and long term view to take full advantage of the potential impact of IT on pupils' learning.

Not the least of the issues is the need for "easy access", e.g. Acorn Computers "One per Child, OPC"" and what I would like to put forward as the real need, SCHOOLS, AS IN BUSINESS AND INDUSTRY, SHOULD HAVE MORE COMPUTERS THAN PEOPLE, along with the advisory support to facilitate the implementation of a range of activities across the curriculum. The potential for the impact of IT has actually been demonstrated, both at the practitioner level and through research and evaluation; there are substantial implications for financial and personnel resources at all levels if this potential is to be achieved in schools throughout the country. M

References 1. Robertson, K., and Green, D. (1993), Micro computers in the home

and at school, Mathematics in School, 22, 5. 2-6. As above, papers by Miller, D., pp. 6-7; English, R., pp. 38-40;

Bzowski, M. J., and Sieron, R., pp. 12-13; Buck, S., p. 33; and Fletcher, T., pp. 36-37.

7. Watson, D. M., Ed. (1993), The ImpacT Report: An evaluation of the impact of information technology on children's achievements in primary and secondary schools, King's College London (for the Department for Education, DFE).

8. Biggs, J. B., and Collis, K. F. (1982), Evaluating the quality of learning: The SOLO taxonomy (structure of observed learning outcomes), New York: Academic Press.

9. Collis, K. F., and Romberg, T. A. (1992), Collis-Romberg Mathematical problem solving profiles, Hawthorn Victoria: Australian Council for Educational Research.

10. Johnson, D. C. (1993). "Chapter 6. Secondary pupils' achievements using IT", pp. 115-150 of the ImpacT Report.

11. Acorn Computers (1993), One per child?, Arc, Issue No. 3, Autumn 1993, p. 18.

[Note: Information on the availability of the full ImpacT report (182 pages) or the summary (19 pages), can be obtained by writing the ImpacT project, Centre for Educational Studies, King's College London, Cornwall House Annex, Waterloo Road, London SE1 8TX.]




Strategies for using one micro in a

maths classroom

by Richard English, School of Education, University of Hull

"The increasing availability of microcomputers in schools offers considerable opportunity to teachers of mathematics both to enhance their existing practice and also to work in ways which have not hitherto been possible ... Nevertheless ... these possibilities ... are at the present time being exploited by a very small number of teachers."

You could be forgiven for thinking that this is a fairly recent comment on the use of microcomputers in mathematics but it is in fact a quote from the Cockcroft Report (HMSO, 1982) which has already celebrated its eleventh birthday. During these eleven years there has been a massive increase in the number of microcomputers in schools but it would seem that this growth has not been matched by an increase in pupil accessibility to microcomputers in mathematics. One source (The Mathematical Association, 1987) refers to a survey suggesting that nearly three-quarters of secondary mathematics teachers use computers in their classrooms either very rarely or never. There are many possible reasons for this but I will mention just two. Firstly, many staff are not sufficiently aware of how a microcomputer can be used effectively in mathematics. Much time and money needs to be spent raising levels of awareness, confidence and competence amongst teachers. Secondly, in many secondary schools all of the microcomputers are gathered in one room and so access is often a problem. All curriculum areas have legitimate claims on these facilities, although some tend to be more demanding than others, notably computer studies, and so use by mathematics classes is usually restricted to one or two sessions each week. This is a long way from the ideal situation of having at least one microcomputer in every maths classroom so that it is a resource that is available at all times to be used as and when necessary, rather than being a novelty item that is only used very occasionally for "special" work. A recent report by Her Majesty's Inspectorate (HMSO, 1991) says, referring to secondary schools,

"In many mathematics departments pupils did not have sufficient access to microcomputers. Schools need to review the overall number of microcomputers and their distribution in departments and central areas to ensure that they meet the requirements of the National Curriculum."

My own experiences in secondary schools are not dissimilar to those of the HMI. Very few maths classrooms that I have visited are equipped with a microcomputer or have easy access to one, but I have detected a change over the last twelve months or so. An increasing number of mathematics departments are trying to equip their classrooms with a microcomputer or are providing a few shared, mobile machines that can be wheeled quite easily from one classroom to another. This change has come about partly because the BBC microcomputers in the computer rooms are being replaced by, for example, RM Nimbus machines, thus freeing the former for departmental use, and partly because heads of department can now put forward a much stronger case to senior management for having microcomputers in their mathematics classrooms due to the specific references to information technology in the Mathematics National Curriculum.

So I have detected a slight improvement in the accessibility problem but what about the raising of teacher awareness, confidence and competence? I have been trying to address this during the last two years by way of inservice training for teachers and I would like to share with you some of the ideas that I have used on such occasions. For convenience I have divided the possible situations in which you might want to make use of the microcomputer into two categories.

1. A pupil or small groups of pupils at the keyboard This, by the very nature of the situation, implies that those pupils not using the microcomputer (i.e. the vast majority) need to be engaged in some other activity. I have seen this strategy widely used in primary classrooms where a flexible approach allows pupils to be enjoying a wide variety of activities often from a range of curriculum areas. While the rest of the class are busy doing art, science, geography, reading and so on, two or three pupils can be using the microcomputer for mathematics. The primary classroom lends itself to this sort of approach but there is no reason why it cannot also be used in the secondary mathematics classroom. Many mathematics departments use an "individualised" scheme of work, for example the SMP 11-16 booklets, whereby pupils progress along their own unique pathway through mathematics. In such a situation there is a wide variety of mathematical activities going on at any one time and the microcomputer can be looked upon as a resource in the same way as the fraction strips, multilink cubes, angle measurers, polydron etc., that is, it is used as and when appropriate. Particular pieces of software could be used to reinforce, consolidate and in some cases even replace the materials in such published schemes. For example the program ANGLE90 (ILECC, 1984) could be used by pupils working on the SMP 11-16 booklets "Angle 1" and "Angle 2". Some schools that I have visited have created their own booklets to add to the SMP 11-16 series. These booklets are designed specifically to make use of the microcomputer in the classroom and provide pupils with an introduction to topics such as LOGO.

Another strategy is to allow pupils to use the microcomputer on a rota basis. For example, when doing work on data handling, I allow each pupil to enter his or her own information onto the database in turn while the rest of the




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