Beginning computer-based modelling in primary schools

Compurers Educ. Vol. 22, No. l/2, pp. 129-144, 1994 Printed in Great Britain. All rights reserved

BEGINNING

Copyright 0

COMPUTER-BASED MODELLING PRIMARY SCHOOLS MARY

Advisory

Unit for Microtechnology

in Education, Wheathampstead

0360-1315/94 $6.00 + 0.00 1994 Pergamon Press Ltd

IN

E. WEBB Wheathampstead Education AL4 8PY, England

Centre,

Butterfield

Road,

Abstract-This paper describes an investigation of how children in primary schools can start to build their own models on a computer and what skills are inherent in this modelling process. The study focused on qualitative modelling using a rule-based expert system shell, Expert Builder, which made the knowledge structure and inference mechanism clearly visible to and manipulable by the user through a graphical user interface. The study was conducted within typical classroom contexts where pupils worked in groups on various activities. Towards the end of the study some of the pupils were able to structure and develop models without any help. An analysis of the pupils’ activities was carried out using elements of learning taxonomies developed by Ennis, Kyllonen and Shute and Sternberg. A combination of the approaches of these three taxonomies enabled the clarification of specific modelling skills and general learning skills involved in modelling activities and provides one way of comparing modelling activities in terms of their component skills although it takes no account of the social interactions that also played an important part in the activities in this study. The national curriculum attainment target suggests that being able to build models on a computer is at attainment level 6 or 7 that is only likely to be reached by pupils over the age of 11. This study has shown that computer-based qualitative modelling can be successfully undertaken as collaborative group work by children aged 8-1 I.

INTRODUCTION

Computer-based modelling is beginning to take place in schools particularly now that the national curriculum in England and Wales specifies that: “pupils should be able to use information technology to design, develop, explore and evaluate models of real and imaginary situations”. The Modus Project, a collaboration between the Advisory Unit for Microtechnology in Education and King’s College London set out in 1987 to research how computer-based modelling could be developed across the curriculum and to provide appropriate software and resources. A study of teachers’ perceptions of the types of modelling activities that they felt could be usefully undertaken by children suggested that a range of different types of modelling activity is desirable[l]. Many of the modelling tasks, suggested by teachers, fall in the category of qualitative models of logical reasoning. These models are based on heuristics rather than precise mathematical relationships and are concerned with relationships between concepts such as causality and dependence. Models of this type can be constructed to guide decision making, diagnose a problem, make predictions and classify objects. Many teachers wanted tools to aid pupils in structuring and ordering ideas and relationships in this way. These investigations led to the development of Expert Builder (see Appendix) as a prototype to explore the opportunities for rule-based modelling[2]. This paper is based on a detailed investigation conducted in primary schools. Primary schools were chosen because children of 9-l 1 years are probably at the lower limit of the age range of children who are likely to possess the cognitive skills required to undertake computer-based modelling tasks successfully and it has also been suggested that qualitative modelling tasks may be particularly beneficial for stimulating thinking for children who are moving between the concrete and formal operational Piagetian stages [3]. OUTLINE

OF

THE

STUDY

The study was conducted in three primary schools within typical classroom contexts where pupils worked in groups on various activities, each class having access to one computer that groups of 129

130

MARY E. WEBB

pupils used in turn. The study took place over one academic year so as to provide sufficient opportunities for pupils to develop some expertise with the software. Selected groups were observed and recorded. The teachers involved in two of the schools had worked on a pilot study so they were fairly familiar with the features of Expert Builder. In school A, year 6 pupils, aged 9 and IO participated in the work with Expert Builder. The teacher regarded this group as ranging from a little above average to fairly well below average in ability. It was intended that modelling with Expert Builder should be a normal part of the classroom work and the computer was also used for other activities such as word processing and graphics work. The teacher made use of Expert Builder when he felt that an aspect of the topic on which they were currently working was appropriate for modelling with Expert Builder. During the first part of the autumn term the class was working on a topic about holidays as part of a study of the Far East. The teacher showed the class Expert Builder and introduced them to its features by working with small groups of pupils to construct a model about where to go for a holiday. Two or three groups of pupils went on to build a further model about selecting a hotel. During the second part of the autumn term the class topic was energy and several groups built models on conserving energy in the home. During the early part of the spring term the class was studying developments of technologies and the teacher used Connections: a History qf Technology by James Burke as stimulus material. The class used Expert Builder to develop a model based on this book. In school B the class contained both year 5 and year 6 pupils, aged 9-11. Seven of the year 6 and four of the year 5 pupils took part in the study. The teacher regarded the pupils as ranging in ability from well above to fairly well below average. The teacher organized use of the computer in a similar way to school A so that pupils took turns to use it for particular purposes whenever its use was appropriate for their work. During part of the autumn term the class was working on a topic about communications and two groups of pupils built models about selecting a method of communication. Expert Builder was not used during the spring term as the teacher and the class had other commitments but in the summer term, when the class were working on a topic about the skeleton and bones, two groups built models about identifying bones. In each case, the teacher decided the structure for the model and introduced a small group of pupils to the software by showing them some examples of models and how they worked and then started them off with their models by working with them to produce the first few rules. The pupils then carried on building the model, following a similar pattern and the teacher gave them help from time to time as he went around checking on the progress of each group. In school C, the class was working on a topic about rock formation, volcanoes and earthquakes and the pupils who worked with Expert Builder built models to identify rocks. During a further day pupils were given the opportunity, on a voluntary basis, to build models of their own choice.

OBSERVATIONS Selecting modelling tasks Expert Builder is suitable for certain types of models; those which can be expressed as heuristic rules so task selection is important. When students become reasonably competent modellers, they can be expected to select a suitable modelling environment for a modelling task but this is only expected at levels 9-10 in the national curriculum and so generally this would only be achieved by more able 14-16 yr-olds. In the early stages it is obviously necessary for teachers to match the modelling environment and task. The teachers had no difficulty in identifying tasks that were well suited to rule-based modelling that they felt could be of value to their pupils and fitted well within the topic on which they were working. Where the pupils selected their own tasks, more than half of them were able to identify suitable tasks. Several pupils were able to suggest suitable modelling tasks after only a brief 20 min demonstration of the software. These pupils were considering knowledge with which they were very familiar and thinking about how they might use the software to produce a model that would be useful in an area that interested them. The models that they built were very simple, for example, the one shown in Fig. 1, which advises on selecting football boots, makes use of the logical rule structure and the pupils were able to tackle this with little help.

Modelling

Manipulating

in primary

schools

131

the software

The pupils learnt to manipulate the modelling interface rapidly and this presented no barrier to their progress. Towards the end of the study some of the pupils were able to structure and develop models without any help. They must therefore have been using adequate mental models of at least some aspects of the modelling metaphor. Most groups used rule structures that they had been shown but some experimented and found other structures. Cooperative

working

Expert Builder was not designed specifically to facilitate cooperative working although it was expected that pupils would work on a modelling task in groups and it was assumed that the pupils would cooperate by discussing their ideas. The task of building a mode1 as a diagram in this environment means that the activity is split almost equally between manipulating the mouse and typing text. During the study pupils worked in groups of 2 or 3 and one group member manipulated the mouse while another used the keyboard. Expert Builder seemed to encourage cooperative working since one of the members was positioning and linking boxes and the other typing the text. Where there were three members of the group, the personality of the third person was important in determining whether he or she took an active part in the work. In some groups the member who was not operating the equipment took a significant role in directing the others or thinking of ideas whereas in other groups the third member made little contribution and his/her attention wandered from the work. In all the groups the pupils organized themselves to swap round at intervals. In most of the groups there was relatively little detailed explaining of their ideas but the emerging structure of their diagram helped each of them to understand others’ intentions. It also encouraged the pupils to communicate and try to understand others’ ideas. Teacher intervention Expert Builder can give some feedback to pupils about whether their mode1 is working as they intended. However help is sometimes needed in interpreting the feedback and in particular, when the mode1 does not behave as expected the pupil often needs to be introduced to further features of the system. Pupils were able to discover some of these features for themselves but made faster progress if they could ask how to do something. The appropriate level and type of teacher intervention is very difficult to achieve but probably no more so than in other learning situations. In this case the particular problem on which the pupils are focusing is clearly visible on the screen and this enabled the teacher to assess the situation quickly. Teacher intervention can be examined in relation to three aspects of the modelling activities: l l l

manipulating the software structuring the mode1 selecting and structuring knowledge.

1

moulded football

screw in football studs

grass

surface

rubber screw in football studs

studs

astroturf football

metal boots

hard surface

Fig. 1. A simple model

identified,

designed

and constructed

by a pupil.

football

MARY E. WEBB

132 Identify

Define

an area of interest

the problem

Evaluate

the model

Fig. 2. The modeiling

--+

Direction of process

---w

Flow of information

process.

Intervention concerned with manipulating the software, e.g. which tool to use, generally involved immediate correction or instruction. If the teacher observed a pupil using the software ine~ciently the pupil was immediately told a better way of working or at least an alternative way of working was suggested. Teachers were slightly more tentative in their intervention concerning inappropriate structuring of the model, e.g. if the pupil had created a rule upside down or failed to connect an advice box. They usually intervened by asking the pupils to examine the part of the diagram carefully or asked them to look for a mistake. The nature of the intervention concerned with selecting and structuring knowledge depended on the nature of the task and the objectives of the teacher. Where the teacher was concerned that the students would consolidate particular aspects of their knowledge he used directed questions to aid students in selecting their knowledge.

THE MODELLING

PROCESS

There are risks associated with modelling in that it is relatively easy to miss important factors by drawing the boundaries too narrowly or tackling a complex situation in a fragmentary, uncoordinated way. It follows that there is a need to define a modelling process that minimizes these risks and optimizes the chances of success as well as providing a framework for learning how to model. Attempts have been made to define the modelling process in the context of mathematical modelling, e.g. the seven-box diagram 141.The Modus project has outlined a modelling process that may be of more general application and this is shown in Fig. 2. Step I. IdentifVing an area of interest This is analogous to the first stage of Checkland’ methodology for systems design]51 in which he was concerned with developing a rich picture of the environment. This first step in the modelling process may arise from any normal learning situation where the learner identifies an area where (s)he has an incomplete understanding or a complex situation that needs clarifying. This step is viewed as part of the modelling process because this places the process in a context just as Checkland’s early stages establish the environment for systems analysis.

Modelling in primary schools

Step 2. Dejining

133

the problem

In this step a specific problem is identified from the area of incomplete understanding and some consideration is given to what needs to be known in order to solve this problem or to achieve greater understanding. A decision is taken as to whether there may be any benefit from constructing an external model. This will depend on the tools available, the learners’ skills in using the tools and the learners knowledge of the scope and benefits of modelling. Step 3. Deciding

the scope, boundaries

and purpose

of the model

In this step the nature of the model is outlined. It is important to be clear about the purpose of the model and how it is expected to be used. It may be intended to provide answers to “what if” questions or the intention may simply be to clarify a particular problem, in which case there may be no requirement to complete a usable model. It is also necessary to identify a suitable environment in which to create the model. Step 4. Building the model Most successful models are built in stages. The task is split into sub-tasks before proceeding.

and each part is tested

Step 5. Testing the model The model or partly built model is tested with a range of different sets of data. If the model is considered to be fairly complete the process continues with step 6 but this would normally be after steps 4 and 5 had been repeated a number of times. Step 6. Evaluating

the model

The model is evaluated by testing with real data and comparing its performance purpose. At the higher attainment levels in the national curriculum students are expected stages in the modelling process, for example at level 10 pupils are expected to: “decide how to model a system, and design, implement choice made.”

and test it; justify

with its stated to carry out all

methods

used and

In different learning environments teachers may involve learners in only parts of the modelling process, in order to pursue specific learning outcomes. Is it possible to identify the skills and abilities required for modelling and thereby to clarify the intellectual requirements for undertaking the modelling process? It may then be possible to determine which of these skills and processes are evident in the children modelling in this study. This may shed some light on the learning opportunities offered through modelling activities and also how to enable people to become successful modellers.

SKILLS

AND

ABILITIES

IN COMPUTER-BASED

MODELLING

What types of skills and abilities are involved in computer-based modelling? Clearly, when the model is actually being constructed and tested on the computer a number of practical and manipulative skills are involved but throughout the earlier stages as well as at the construction stage, a variety of cognitive and metacognitive skills are in use as well as communications skills. The development and application of frameworks for analysing and classifying computer-based learning environments is still in its infancy but some progress has been made by Kyllonen and Shute[6]. This taxonomy was developed to analyse activities with adult learners so it is open to question as to whether it can be applied to young children. However, Carey[7] presents a compelling case against the existence of any fundamental difference in the thinking of children and

MARY E. WEBB

134

adults. She discusses studies that dispute some of the conclusions of earlier Piagetian-based work and suggest that the only difference between children and adults is in domain specific knowledge. Kyllonen and Shute’s taxonomy was applied to one of the modelling activities recorded in the classroom to see whether it might help to define the types of learning skills within the modelling activity and to identify additional factors that might need to be incorporated in order to characterize a modelling activity. They suggest that in applying their taxonomy the researcher should initially categorize the instructional programs in their domain space (Fig. 3), which illustrates how computer-based modelling might be positioned in a two-dimensional space. The researcher then makes use of a matrix of instructional environment and knowledge type (see Figs 5 and 6). Finally the observations should be examined for encouragement of particular learning styles. Of their three intelligent tutoring systems, the environment that was most similar to the modelling situation was Smithtown: Discovery World for Economic Principles, which aims to enhance students’ general problem-solving and inductive-learning skills. Smithtown is highly interactive. The student generates problems and hypotheses such as “Does increasing the price of coffee affect the supply or demand of tea?” and then the student tests it by executing a series of actions, such as changing the values of two variables and obtaining a bivariate plot. Kyllonen and Shute produced two scores, one for the time spent engaging the learning skill and the other on testing for the learning skill. Smithtown constantly monitors student actions, looking for evidence of good and poor behaviour, then coaching students to become more effective problem-solvers, making use of the student model that it constructs. The activity chosen was the development of a model to identify bones, carried out in school B by two 9-yr old boys. This activity was chosen for analysis because it was felt by the teacher and the author to be a fairly successful attempt at modelling which had been followed through to a reasonably complete model. In addition a fairly detailed record had been made of most of the activity. The analysis was applied to the complete activity that involved interaction between the students, the students and the computer and the students and the teacher. This analysis is only intended to give a rough indication of the time spent exercising various skills. A more rigorous analysis could produce a precise breakdown of the time spent exercising and testing various learning skills. There was no formal testing built into the “bones” modelling activity; instead the students exercise their skills through building the model so that their actions and talk give evidence of their learning but it is only possible to give one score, i.e. that for the time spent engaging the learning skill.

Fast processing (Quick de&ions)

0 Air Vattic controller

Non-quantitative

/

0 Administrator

Quantitative

I

technical

non-technical l Smithtown

0 Computer programmer

0 Journalist 0-a

Computer b,I&

modelling -0

Slow processing (Quality decisions) Fig. 3. Domain

space proposed

by Kyllenon

and Shute[6],

with examples

located

within

it.

Modelling in primary schools

135

Analysis of classroom activities

In the modelling activity the explicit and implicit learning goals in this activity were quite varied and included: extending and consolidating knowledge of the arrangement and function of bones and skeletons developing modelling skills l developing skills in using this particular software l developing more general computer skills l developing problem solving ability through tackling an unfamiliar task l developing information retrieval skills involving extracting relevant info~ation from written material o developing ability to interpret diagrammatic representations and to relate them to concrete structures o developing cooperative learning skills-for this exercise the teacher had deliberately paired these two boys together because they learnt well together. One of the boys was under pe~o~ing because he made little effort in conventional learning situations.

l

l

The initial instruction given by the teacher showed pupils how to manipulate the Expert Builder interface and use the tools and gave them one way of structuring rules although they were free to experiment and try out their own ideas within the overall task of developing a working model that would identify a bone. The teacher also instructed the pupils in obtaining the information needed to construct the model. This involved examining samples of bones, and a scale model of the skeleton looking up the names of the bones on diagrams of the skeleton. They were also encouraged to deduce the functions of the bones. Several books were used to find additional information. The pupils were expected to discuss their ideas and collaborate in producing the model. This learning environment is more varied and complex than the instructional programs to which Kyllenon and Shute applied their taxonomy. The instructional environment started as didactic but the teacher gradually gave control to the pupils so that they were learning to manipulate the modelling environment by practice. The pupils structured their model by mapping from parts of the model already built to new structures. This was categorized as learning by analogy, using Kyllenon and Shute’s categories, rather than from examples because the process was predominantly mapping from one knowledge structure to another similar one and there was no requirement to attempt a generalization. The pupils were also able to discover rules about using the environment. The teacher provided help when requested and sometimes intervened to provide instruction on a particular point. During the next session the pair continued to build the model, learning by practising what they had learnt from the instruction session, by analogy and by observation and discovery. In a subsequent session they went on to improve their model and overcome some of the problems thay had encountered. This involved some didactic instruction followed by practice in applying rules and pupils asked questions so learnt from examples. They then spent a further two sessions, working predominantly on their own, using practice, analogy and discovery. It was possible to identify the employment of declarative knowledge of the subject matter since the pupils built this into their model. The knowledge was about the structural arrangement of bones and their functions and so consisted of propositions about the names and positions of bones and schema concerning how to identify a particular bone with precision and the functions of bones. Procedural knowledge included manipulating the modelling environment and structuring the model, as well as obtaining information from the secondary sources. There are specific rules about how and when to use each tool and when a number of these are employed to construct a section of diagram this becomes a skill. Since this exercise involved building only one model on one subject area, the rules and skills are only demonstrated in this specific context but pupils may have learnt their generality across a range of models and across other problem solving tasks. Automatic skills, as when a pupil constructs a section of diagram while discussing the content of the model, were not observed during this activity. During the exercise pupils may have developed mental models of how to construct a qualitative model and subsequent work suggested this to be the case. Scoring the amount of time

136

MARY E. W~etl

Expert

2

0

File

Edit

use

View

Builder

Diagram

Window

Options

v

- [BONES21

A A

Help

4 ADVICE

ADVICE

The bone could be the lower jaw bone.

The bone could be the upper jaw bone.

The bone could be the humerus. .

The bone could be the ulna. . The bone could be the clavicle.

AND

’

1 iii&Gio

Fig. 4. Part of the “bones”

the/

model.

spent on learning a mental model is difficult because it may develop gradually as the schema and rules are assimilated, or, once a certain critical mass of schema and skills have been learnt, a mental model may be instantly generated. This would only become evident when pupils applied it to new situations. Although pupils may have been developing mental models, it was not possible to score this in the analysis. Figure 5 shows an informal analysis of the skills that are being exercised in the activity using the same grid as that used by Kyllenon and Shute. This grid includes only the knowledge type and

i

Fig. 5. Learning

activities

profile for the “bones”

i i

exercise.

I

Modelling in primary schools

137

instructional environment dimensions. The skills have been roughly quantified based on timings taken from notes made during observations and transcriptions of the tapes (one square represents approx. 5 min). DISCUSSION The profile for the modelling exercise reveals a fairly balanced mix of instructional environments. This contrasts with the published profiles for BIP: The BASIC Instruction Program, which teaches students how to program in BASIC, and Anderson’s LISP Tutor where the instructional environments were mainly didactic and practice. The profile is more similar to that for Smithtown where the predominant instructional environment was discovery and this reflects the more student-centred nature of the tasks in Smithtown and the modelling activity. Analogy is more important in this modelling activity than in any of the intelligent tutoring systems. This may be due to a difference in interpretation but probably reflects an important modelling technique in which structures that have worked previously are selected again to represent similar knowledge structures or processes. The application of Kyllenon and Shute’s analysis of domain space and instructional environment provides a partial characterization of the modelling activity in terms of the learning skills that are developed. It is not capturing all the important aspects of the process because there is no consideration of the social context and limited attention to higher order thinking skills. In addition although they identified learning style as an important factor they did not analyse it in their discussion of the three programs mentioned above. They suggested the inclusion of impulsivity-reflectivity, holistic versus serial processing, activity level, systematicity and exploratoriness, theory-driven versus data-driven approaches, spatial versus verbal representation, superficial versus deep processing and low versus high motivation. Observation of the “bones” modelling activity suggested that the following aspects of learning styles were being encouraged: l

l

l l l

A systematic approach-the pupils were working step-by-step through the bones in the skeleton Spatial representation-the pupils were working with a diagrammatic representation of the logic in the decision-making process as well as with a three-dimensional model and diagrams of the skeleton Deep processing Active involvement High internal motivation-the pupils followed the exercise through to completion, including voluntary lunch-time work.

Pask[8] distinguishes learning styles from learning strategies and suggests that holistic versus serial processing is an example of different learning strategies. He devised categories for learning styles where some students were “disposed to act” like holists, others like serialists and others were categorized as versatile since they were able to act in either way depending on the subject matter. This idea of learners being “disposed to act in particular ways” is also used by Ennis [9] who defined a taxonomy of 14 critical thinking dispositions and abilities. All of them seem to be useful for modelling but some can be adapted to make them more specific to the modelling process as defined earlier, e.g.: l l

Keep in mind the original purpose of the mode1 Seek as much precision as the subject permits and the purpose

In addition, l l l l l

the following

four dispositions

Seek a clear understanding of the modelling Expect models to be imperfect Be prepared to experiment Look for inconsistencies Look for similarities with other problems.

seem to be important metaphor

of the model implies. for modelling:

as it applies in the situation

being modelled

138

MARY E. WEBB

It is unlikely to be easy carrying out modelling in their modelling tasks on the “bones” exercise

to find a way of measuring the occurrence of these dispositions in students tasks but observations suggested that those students who were successful showed some evidence of these dispositions. The two students who worked certainly displayed some of them, e.g.:

l Use and mention credible sources-they referred to several books o Take into account the total situation-they kept referring to the model skeleton to see where the bone fitted and how it could be identified l Keep in mind the original purpose of the model-throughout the activity they were focusing on advice to help people identify a bone l Seek as much precision as the subject permits and the purpose of the model implies-they made great effort to distinguish between all the different bones and to ensure that their rules led to precise identification o Deal in an orderly manner with the parts of a complex whole-they started at the top of the body and worked down systematically and the arrangement of their model on the screen was also systematic although arranged horizontally l Be prepared to experiment-they tried out various ways of structuring the model l Look for inconsistencies--they kept testing the model to see whether it worked in the way they expected l Look for similarities with other problems-within this particular model they were looking for similar rule structures, e.g. some bones could be identified by the bones at each end, others could be identified by position and function.

Students who were less successful in modelling sometimes could be said to be failing to show some of these dispositions. In particular, those who became confused about how to structure the model and make use of the modelling metaphor usually did not: seek a clear statement of the thesis or question; look for inconsistencies; or seek a clear understanding of the modelling metaphor as it applies in the situation being modelled. Failing to seek a clear understanding of the problem and the modelling metaphor may reflect a quite fundamental difference between students’ learning styles where some students do not expect to understand, perhaps as a result of continued failures in the past. There is a temptation to regard this simply as a reflection of students’ general ability but during these studies at least two students who were identified as achieving significant success in modelling and who demonstrated some of these dispositions were considered by their teachers to be of relatively low general ability. If it is possible to define specific dispositions that are important or even essential for modelling and to find ways of encouraging these dispositions it may be possible to improve modelling ability. The list identified here is at least a first step in this process. A method of analysis that focuses on higher order thinking skills is Sternberg’s componential analysis[lO]. Sternberg’s componential sub-theory specifies the mechanisms underlying intelligent performance. Sternberg uses the information-processing component as the basic unit of analysis and defines a component as: “an elementary

process

that operates

upon

internal

representations

of objects

The component may translate a sensory input into a conceptual representation, conceptual representation into another, or translate a conceptual representation output. Three kinds of components are identified by function:

or symbols.” transform one into a motor

Metacomponents are higher order executive processes used in planning, monitoring and decision making in task performance l Performance components are processes used in the execution of a task l Knowledge acquisition components are processes used in learning new information. l

When analysing the modelling process, the most important ponents since Sternberg[lO, p. 1071 stated that:

components

are likely to be metacom-

“performance components are potential sources of intellectual development and individual differences, but a joint analysis of their role with that of metacomponents leads me to believe that metacomponential processes are more fundamental sources of consequential individual

Modelling in primary schools

139

and developmental differences. Changes in metacomponential functioning lead almost inevitably to changes on the functioning of performance components, but one can understand the latter changes only by looking for their metacomponential sources”. The stages in the modelling process were analysed in order to identify the metacomponents and then the classroom activities were examined for evidence of these. During the classroom work in school A most of the modelling process was carried out by the teacher who involved the pupils to some extent by class discussions. This was particularly true in the first two exercises--“where to go on holiday” and “selecting a hotel” so that in these exercises pupils were peripherally involved with the modelling process and there is no clear evidence of whether they were using any particular metacomponents. In the third exercise concerned with conserving energy the pupils did tackle parts of step 4 with little help and some showed evidence of the following metacomponents in that they successfully created appropriate rule structures: identifying the main conclusions or advice statements identifying the main factors which will affect the conclusions *identifying the need for a particular logical operator in a relationship. l l

Figure 6 shows one of the models concerned with conserving energy. The students had identified a number of factors that were important in saving energy. They built the model by considering each in turn and specifying either advice or a premise, which would become a question, by considering how the system would appear to the user. They achieved this by testing each rule carefully. The process of structuring the model was partly trial and error where they tested each rule and sometimes found a need to change the structure because it did not behave in the way that they wanted it to but they clearly had some idea of how the model would work so they must have identified a mental representation of the inference mechanism even if it was not completely accurate. The model consists of a number of separate rule structures arranged across the page. Each is fairly similar and works in a similar way so that once the group had identified one successful way of structuring the rules, they made use of the same basic structure so it is likely that in considering a new part of the model they were identifying mental representation of other similar structures in this model or perhaps in others. In order to do this they would have had to make some mental comparisons of structures they were intending to build with mental or physical representations of other similar structures. In school B the teacher decided the problem and the scope and purpose of the model but the pupils were encouraged to investigate ways of structuring the model following only a brief demonstration of Expert Builder. They were then given some help when they needed it but to a large extent pupils tackled steps 4 and 5 of the modelling process themselves and to some extent step 6. Owing to their limited experiences of modelling pupils were working with a fairly narrow view of the modeliing environment as well as the subject matter to be modelled. They therefore had to focus on a particular task that they hoped would help them to move towards achieving their goal of creating an appropriate working model. For example, one group chose to create a series of advice boxes and factors affecting them (see Fig. 7) although they had no clear mental representation of how these might be linked. These pupils were employing the following metacomponents: l l

identifying the main conclusions or advice statements identifying the main factors which affect the conclusions.

After being given some help they were able to arrange the boxes to structure their model and at this stage they were using the following metacomponents: identifying the need for a particular logical operator in a relationship *identifying a mental representation of the inference mechanism.

l

Other groups having been given some help in structuring their models appeared to be employing the metacomponents listed above as well as:

lidentifying similarities to mental representation of other similar models or parts of models

More advice is

and windows

d

energy

*

\

AND

JL

c Draught proof your doors and windows. There is more advice available

with conserving

I have told you what to do. Shutting doors etc. is free. There is more advice if you want it 1

Fig. 6. One of the pupil’s models concerned

more advice

You are still

‘I Put at least 1OcI-n of lagging in your loft

Modelling in primary schools Expert Builder Diagram - message 1

a

File

141

Edit

Use

View

Print

KsY

yelp

@ox Site 4

Fig. 7. The first stage in building a model on communications for one group.

o comparing the physical representation ships

to the mental representation

of components and relation-

because they went on to create functioning models in which similar structures were repeated. One group, who built the “bones” model described earlier, did test their model on several occasions. From the transcript of their conversation, the students appear to be using the following metacomponents: Identifying/creating a mental representation of a scenario in which the model might be used Identifying sets of data as answers. They had to decide how to answer the questions given that they were testing whether the system would identify a particular bone o Selecting a mental representation of the expected output of the model. In this case this was very simple as the model was intended to identify the bone.

l

l

In school C the original instructional plan had been for pupils to construct their own simple models on selecting clothes following a brief demonstration of Expert Builder. This would enable them to gain familiarity with the software and they would then go on to construct models on the topic that they were currently studying. This plan was revised when pupils asked to build models on subjects of their own choosing. This modelling activity, although brief, was quite successful; students tackled steps, 1, 2, 3, 4 and 5 of the modelling process. It had been felt that steps 1 and 2 were particularly difficult, requiring a diverse range of complex metacomponents, but this experience suggests that they are very context dependent. In particular, pupils can undertake steps 1 and 2 in areas in which they are already interested and knowledgeable. The four pairs of pupils who successfully chose a problem to model and started to construct it must have used all the metacomponents identified for steps 1 and 2, i.e.: 8 reflecting on what you know knowing the limits of your knowledge

l

142

MARY E. WEBB

l identifying gaps in your knowledge e constructing mental representations e identifying mental representations l selecting a specific problem l deciding on the nature of the problem e deciding whether a problem is susceptible to modelling l identifying mental representations of other similar problems

which have been modelled.

At this stage they needed help in structuring their models but later when they were given a subsequent opportunity to choose a modelling problem some pupils were able to undertake the whole modelling task with very limited help. It therefore appears that some pupils are able to employ the metacomponents identified in the modelling process provided that they are interested in and knowledgeable about the subject matter. Those groups who were successful in their chosen tasks during the first stage of this work were more successful in structuring their rock identification models. In this activity a basic structure for the model was taught but some groups, on testing their models, decided that they required slightly different functionality and experimented with the structure to try to achieve this with some success.

CONCLUSIONS

Towards a curriculum for computer-based modelling There is not yet sufficient evidence to define a complete taxonomy of computer-based modelling but the application of existing methods of analysis has suggested that aspects of learning which should be considered are the domain space, instructional environments, dispositions and metacomponents. It is possible for some students at 9 years old to successfully undertake the modelling process, as outlined here, provided that they are working with subject matter with which they are familiar and knowledgeable. This is in accordance with a number of studies cited by Donaldson[l l] which she uses to support the view that children are capable of inference at a much younger age than would be expected according to Piagetian stage theory but that the nature of the subject matter is of critical importance. The importance of context in cognitive development has also been shown by other recent work, e.g.[7,12}. This suggests that the development of modelling ability is heavily context dependent so that if learners are able to undertake successfully the modelling process in one domain they will not necessarily be able to do so in another. However, even with excellent knowledge of the subject matter modellers are unlikely to be very successful unless they have appropriate dispositions and can deploy relevant metacomponents and can follow through the modelling process. Computer-based modelling capability then is unlikely to show a linear progression through levels of modelling skills. Children can be expected to show competent modelling ability when tackling some modelling tasks but require a great deal of help in others. The modelling curriculum should develop modelling ability as well as allowing for the learning of other subject matter through modelling. Activities based on subject matter with which students are familiar and knowledgeable may be good starting points for developing modelling skills and dispositions and for encouraging students to follow through the modelling process including the evaluation of their models. Students who have acquired some basic understanding of the modelling process, in this way, and developed some modelling skills and dispositions, may then be able to tackle a modelling task based on less familiar subject matter where an important aim of the task is to develop understanding of the topic. Another approach, favoured by the teachers in this study, is to embark on a modelling task involving subject matter with which the pupils are unfamiliar and to structure the task so that the students undertake only parts of the modelling process and the teacher takes them through the more difficult aspects particularly the early stages of the process. Both of these approaches ensure that students’ early encounters with computer-based modelling involve building parts of the model. This contrasts with the starting point for computer-based

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modelling contained in the national curriculum, which states that pupils working towards level 4 should be taught to: “analyse the patterns and relationships in a computer model to establish how its rules operate; change the rules and predict the effect.” It is probable that this starting point was arrived at because it was considered too difficult for students aged 7-l 1 to undertake to build their own models and this was probably true until recently because there was no suitable software. However it would be easier for students to understand the patterns and relationships in a computer model if this were one that they had been involved in designing and building rather than trying to guess the basis of a model that is built into a simulation program by examining the output under different circumstances, as this statement from the national curriculum suggests. At the same time as learning to build simple models the students could also be learning about the modelling process and the nature of models. The modelling curriculum should therefore introduce the process of model building at a fairly early stage and initially pupils will need help, particularly with the early steps in the process. Progression in this curriculum will involve students tackling more steps of the process alone and modelling more complex situations. Teacher intervention is important when students are undertaking computer-based modelling activities, In this study there was a significant amount of teacher intervention. In schools A and B the teachers appeared to spend approximately the same amount of time with the group working on the modelling activity as with groups involved in other activities. Eraut and Hoyles[ 131report that generally teachers do not intervene when pupils are working at a computer, because they work on them for long periods without any signs of boredom or disturbance and this frees the teacher to attend to other pupils. This approach is inappropriate where the computer is being used in an emancipatory way as with collaborative writing or computer-based modelling. In the early stages students need help with using the software. This should take the form of regular checks to see that students are working reasonably efficiently within the environment. If such monitoring is not done students may make frustrating and time-consuming mistakes. A balance needs to be achieved between allowing students to experiment and diverting them from fruitless efforts. This type of intervention is relatively easy and can be achieved by a quick glance at the screen at intervals and short periods of instruction, provided that the teacher is fairly familiar with the software environment. The second type of intervention is concerned with promoting modelling abilities and dispositions and is more time-consuming. The teacher can gain significant insight into the strategies the group is adopting from looking at the screen but will probably need to observe and question the students to determine what their intentions are and whether they are employing appropriate abilities and dispositions. Deciding what intervention is necessary presents the same complex dilemma as with any other open-ended learning activity although the teacher may have slightly more information available in this situation in that the visual representation of the model on the screen can reveal more about the students thinking than the products of most other group activities. Acknowledgements-The work reported here was carried out as part of the Modus Project which is supported by British Gas, D.F.E., Hertfordshire County Council, King’s College London and Research Machines Limited. Thanks are also due to my supervisor Dr Eileen Scanlon of the Open University, Institute of Educational Technology.

REFERENCES I. Webb M. E. and Hassell D., Opportunities for computer based modelling and simulation in secondary education. In Computers in Educarion (Edited by Lovis F. and Tagg E. D.). Elsevier, Amsterdam (1988). 2. Webb M. E., Learning by building rules based models. Computers Educ. 18, 899100 (1992).

3. Galpin B., Expert systems in primary schools. British Library Research paper 73, British Library Research and Development Department (1989). 4. Open University. MST204 Project Guide for Mathematical Modelling and Methods. Open University, Milton Keynes (1981). 5. Checkland P. B., Systems T~j~kj~g, Systems Practice. Wiley, Chichester (1981). 6. Kyllonen P. C. and Shute V. J., A taxonomy of learning skills. In Learning and Individual Dzfirences: Advances in Theory and Research (Edited by Ackerman P. L., Sternberg R. J. and Glaser R.), pp. 117-163. Freeman, San Francisco, Calif. (1989). I. Carey S., Are children fundamentally different kinds of thinkers than adults? In Thinking and Learning Skills, Vol. 2 Research and Open Questions (Edited by Chipman S. F., Segal J. W. and Glaser R.), pp. 485-517. Lawrence Erlbaum, Hillsdale, N.J. (1985).

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8. Pask G., Styles and strategies of learning. Br. J. Educ. Psycho/. 46, 128-148 (1976). 9. Ennis R. H., A taxonomy of critical thinking dispositions and abilities. In Teaching Thinking Ski//s (Edited by Baron J. B. and Sternberg R. J.), pp. 9-26. Freeman, San Francisco, Calif. (1987). 10. Sternberg R. J., Beyond IQ. CUP (1985). 1I. Donaldson M., Children’s Minds. Croom Helm (1978). 12. Keil F. C., On the structure-dependent nature of stages of cognitive development. In Sfage and Structure: Reopening the Debate (Edited by Levin I.), pp. 144163. Ablex, N.J. (1986). 13. Eraut M. and Hoyles C., Groupwork with computers. Occasional paper: InTER/3/88 ESRC, University of Lancaster (1988). APPENDIX

Expert

Builder

Expert Builder is a rule-based expert system shell, which makes the knowledge structure and inference mechanism clearly visible to and manipulable by the user through a graphical user interface. The program works in a similar way to commercially available rule-based expert system shells used in business, the major difference being the graphical user interface that makes the execution of the model transparent and easy for children to use. Using Expert Builder. a model is constructed by building a logical diagrammatic structure on the screen using mouse-controlled tools. The diagram consists of boxes containing textual clauses, connected together into a logical construction using the logical operators, AND, OR and NOT. The prototype version of Expert Builder was tested extensively in a range of educational institutions. A revised version has now been published by the Advisory Unit for Microtechnology in Education.