Learning to Teach and Assess Mathematics Using Multimedia: A Teacher Development Project

ANTHONY HERRINGTON, JAN HERRINGTON, LEN SPARROW andRON OLIVER

LEARNING TO TEACH AND ASSESS MATHEMATICS USINGMULTIMEDIA: A TEACHER DEVELOPMENT PROJECT

ABSTRACT. The current reform agenda in mathematics education promotes the view thatmathematics should be taught and assessed in a variety of meaningful and authentic ways.However, recent international research indicates that more limited, traditional approachesstill dominate.

The difficulty in expanding teachers’ practices may result from a lack of personalexperiences with these new approaches. This article describes an interactive multimediaresource designed to provide experiences to develop preservice teachers’ knowledge andpractices for teaching and assessing mathematics in K-12 classrooms. The resource consistsof two CD-ROM disks and written materials that enable student teachers to view video clipsof strategies occurring in real classrooms, to hear the views of teachers and students in theseclassrooms, and to read advice from novice teachers and expert mathematics educators.

A description is given on how these materials were used with elementary and secondarypreservice teachers enrolled in teacher education courses, as well as evidence on theinfluence of the resource on preservice teachers’ school practice.

INTRODUCTION

Despite the variety of innovative and effective strategies to teaching andassessment, the recent Third International Mathematics and Science Studyindicated that teachers generally continue to limit their approaches to tradi-tional methods (Lokan, Ford & Greenwood, 1996). Traditional classroomapproaches reflect a view of mathematics as a set of discrete, hierarchicallyarranged facts and skills; a view of learning mathematics as replication andrepetition; a view of teaching mathematics as exposition and practice; anda view of assessing mathematics as paper-and-pencil testing for the solepurpose of grading and ranking (Niss, 1993; Stephens, 1992).

Today’s society has moved from an industrial to an information-basedsociety with changes in the way equity and justice are perceived, and witha greater reliance on technological understanding and application. This hasnecessitated a new focus on how classroom mathematics should be viewedas exemplified in curriculum documents across the world. Rather than factsand skills, mathematics is seen more in terms of general processes or ways

Journal of Mathematics Teacher Education 1: 89–112, 1998.c 1998 Kluwer Academic Publishers. Printed in the Netherlands.

90 ANTHONY HERRINGTON ET AL.

of thinking, such as communication (Department of Education and Science(DES), 1982), methods of investigating and reasoning (National Councilof Teachers of Mathematics (NCTM), 1989) and a science of patterns(Australian Education Council (AEC), 1991). Learning mathematics isseen as students’ constructing ideas based on active, challenging experi-ences. These ideas reflect an understanding of mathematics that is idio-syncratic as opposed to a replication of ideas found in the textbook or theteacher’s mind (von Glasersfeld, 1995).

None of the recent reports on mathematics education promotes a defin-itive style, a particular method or teaching strategy that should be usedto teach mathematics. Instead, teaching mathematics is broadened fromexpository approaches and practice, to include investigations, problemsolving, practical work, discussion (DES, 1982), projects, group work aswell as individual tasks (NCTM, 1989), and the use of technology (AEC,1991). In a similar fashion, alternative approaches have been suggested toassess mathematics (NCTM, 1995).

These new visions of mathematics teaching and assessment appear tobe widely accepted by the community and government agencies as one thatshould be implemented in schools. The difficulty faced by novice teachers,practicing teachers, and teacher educators is that many of the teachingand assessment strategies that underpin the new vision are seldom partof teachers’ personal experiences and for this reason alone, they may beresistant to change. As McIntosh (1977) pointed out, the principles forimprovement in learning and school mathematics, gleaned from over onehundred years of reports, advice and documents, are still largely unheededin modern classrooms.

Of course, teacher education courses attempt to provide these realexperiences when preservice teachers undertake school practice. For thefortunate ones, school experience may involve classroom situations whichreflect the reform vision, displaying a range of teaching and assessmentprocedures. For many, however, school experience is often a reaffirmationof the traditional approaches that are already ingrained from their ownschooling. For those students who do observe and engage with teachersusing current approaches, the extent and range of approaches seen is limitedto a few – the ones with which their supervising teachers are familiar andcomfortable implementing.

In an attempt to overcome this problem, the theoretical framework ofsituated cognition or situated learning has been used to produce an inter-active multimedia resource that allows preservice teachers to experienceapproaches that are appropriate for teaching and assessing the range of out-comes that are valued in the K-12 mathematics curriculum. The resource

LEARNING TO TEACH AND ASSESS MATHEMATICS USING MULTIMEDIA 91

enables users to encounter the authentic use of a full range of strategies andto view and reflect upon their interpretations from multiple perspectivesgained from practicing teachers, preservice teachers, school children andtertiary educators.

SITUATED LEARNING

The resource has been developed to reflect current notions of learning, inparticular, the theory of situated learning. Collins (1988) defines situatedlearning as “the notion of learning knowledge and skills in contexts thatreflect the way the knowledge will be useful in real life” (p. 2). One of theprincipal effects claimed for situated learning is that it facilitates transfer oflearning to new situations (Young, 1993; Cognition and Technology Groupat Vanderbilt, 1993). As awareness of different teaching and assessmentstrategies and their future application to classrooms are the primary goalsof the resource, the characteristics of situated learning appear to be anappropriate framework to adopt.

A critical reading of the principal theorists (and critics) of situatedlearning reveals a number of important characteristics which have addedto the evolving theory of situated learning, and an attempt has been madeto distinguish those features (Herrington & Oliver, 1995). The criticalcharacteristics that designers of situated learning environments need tomake are to:

1. Provide authentic contexts that reflect the way the knowledge will beused in real-life.

2. Provide authentic activities.3. Provide access to expert performances and the modelling of processes.4. Provide multiple roles and perspectives.5. Support collaborative construction of knowledge.6. Promote reflection to enable abstractions to be formed.7. Promote articulation to enable tacit knowledge to be made explicit.8. Provide coaching and scaffolding at critical times.9. Provide for integrated assessment of learning within the tasks.

Teacher education courses generally are concerned with developingknowledge and skills that will need to be transferred to classroom situa-tions. However, the medium through which these skills are provided, forexample, through lectures and tutorials with an emphasis on abstract,academic analysis, is often quite distinct from authentic classroom activitywhere a myriad of contextual factors need to be taken into account.The practicalities of providing experiences for preservice teachers that


acknowledge the importance of the context in which the teaching takesplace initially appear insurmountable. However, recent advances incomputer technology do seem to provide a means by which more concretelinks can be made to real practice.

MULTIMEDIA RESOURCES

Multimedia has been the basis for a number of recent developments forboth students learning mathematics and teachers learning about mathe-matics education. Multimedia simply means a combination of media, suchas text, video, graphics, sound and animation in a computer-based learn-ing environment which enables users to interact with a wide variety ofresources and activities. An example of an early application of multi-media in mathematics education is described by Lampert & Ball (1990).Their approach was to use hypermedia to enable students to access teacheractions in two classrooms videotaped over one year, encompassing a broadrange of pedagogical issues.

CD-ROM technology has been utilised by developers from VanderbiltUniversity to produce Investigations in Teaching Geometry (Barron &Goldman, 1996). This resource focuses on a major strand of the mathe-matics curriculum and uses written vignettes, classroom video segments,teacher journal segments, and descriptions of critical incidents. Thesebecome cases for preservice teachers to investigate and discuss. Thepreliminary results indicate that “use of multimedia materials helpedpreservice teachers develop instructional practices and views of teach-ing that are compatible with recent recommendations” (p. 1). They alsonoted that students began to challenge their current beliefs and attemptedto apply these reflections to their teaching.

Recently from Australia there has been the development of a generalresource for teaching, set in a context of an elementary mathematicsclassroom: Learning about Teaching (Sullivan & Mousley, 1996). ThisCD-ROM resource includes a video recording of a whole mathematicslesson, interviews with the teacher, lesson transcripts and notes, readingsand graphic representations of the classroom interactions. The programenables the user to investigate in depth the more general aspects and prin-ciples of quality teaching and learning within a single lesson.

Goals for all these teacher education projects include the improve-ment of mathematics preservice education through the use of multimediaresources. All the projects attempted to situate the material in real contextsas a method for achieving effective learning.


DESCRIPTION OF THE PROJECT

The project described here differs from the teacher education projectsabove in that the resource is developed for teachers to engage in authentictasks that span a number of different mathematics lessons which include arange of mathematical content areas, a range of teaching and assessmentstrategies, and a range of year levels (K-12). As well, the resource wasdesigned to account for all the critical characteristics of situated learningdescribed above.

As designers of the learning environment, we wanted to providepreservice teachers with the experience of observing expert teachers usingdifferent types of assessment and teaching in classrooms. We also wantedthe preservice teachers to be able to hear teachers talk about why andunder what conditions they used each particular strategy and to be able tohear students talk about their feelings. It was important to have access toinformed comment by experts and to the thoughts of other learners withvarying degrees of expertise (Collins, Brown & Newman, 1989).

One method would have been to take groups of preservice teachers toa large number of schools and to have them observe many expert teachersin their classes (in addition to their professional practice). They couldinterview the teachers and their students after the class. This scenariowould have provided an excellent representation of the situated learningmodel, although Spiro, Feltovich, Jacobson & Coulson (1991) contend thatlearning a complex concept from “erratic exposures to complex instanceswith long periods of time separating each encounter, as in natural learningfrom experience, is not very efficient” (p. 30). The logistics of organisingthe preservice teachers was also highly problematic in that they would needto observe a large number of classes. The imposition such an arrangementwould make on normal classroom practice, together with the difficulty inlocating a sufficient number of teachers who could model the range ofstrategies, made it a totally impractical option.

However, McLellan (1993) points out two other contexts which areacceptable for situated learning: a virtual surrogate of the actual workenvironment (such as aircraft simulators) or anchoring contexts (such asvideos or computer programs). The virtual surrogate of the work environ-ment was also ruled out very quickly on the basis of prohibitive costs ofdevelopment, and lack of resources within the university for use of thefinished resource. The situated learning environment had to be useable bya large number of students simultaneously, and in a relatively accessibleplatform.

It was decided to use computer-based interactive multimedia as thevehicle for the situated learning environment. There is agreement that


computer-based representations and microworlds provide a powerful andacceptable vehicle for the critical characteristics of the traditional appren-ticeship to be located in the teaching-learning environment. For example,Collins (1988) and Harley (1993) support the potential of educationaltechnology to bring situated learning within the reach of the student inthe classroom, particularly through developments in virtual reality andhypermedia. Reeves (1993) considers that one of the major benefits of awell designed interactive multimedia environment is its ability to include“opportunities for simulated apprenticeships as well as a wealth of learningsupport activities” (p. 107).

Technology and computer-based systems per se do not have the abilityto create a situated learning environment for a student in a classroom. Thosecritical elements, which define the situated learning model as it has evolved,need to be deliberately planned and incorporated into the design. However,interactive multimedia, within the constraints described had enormouspotential to provide exemplary and effective situated learning opportunitieswithin classrooms:

The more educational technology is constrained to “essentials” and “individuals,” themore it resembles a nugatory “delivery system” : : : A preferable goal : : : is to designtechnology that provides an underconstrained “window” onto practice, allowing studentsto look through as much of actual practice as it can reveal, to see increasingly greaterdepths, and to collaborate in exploration. (Brown & Duguid, 1993, p. 14)

Preservice teachers using the program to investigate assessment andteaching strategies would need to be able to observe experienced teachersin the field demonstrating a range of strategies and techniques, and to thenreflect on the most appropriate strategy to use in a particular situation.

Video clips of classroom scenes and interviews appeared to be an appro-priate means to provide such opportunities to the students who would usethe program. Bransford, Vye, Kinzer & Risko (1990) advocate that the useof video clips have a number of advantages over printed media and thegraphics and animation of computer-based programs because they providea much richer source of information. Gestures, affective elements, scenesand music accompanying the dialogue mean that there is much more tonotice, and it is possible to find relevant issues which are embedded withinthe real-life context which might otherwise go unnoticed.

Other important requirements of the program were that the contextwould need to be situated in a real or simulated classroom, and authenticactivities could require students to address realistic problems associatedwith teaching and assessment. The elements of the framework which needto be provided by the learner, such as articulation and collaboration, couldalso be adequately catered for in the use of the interactive multimedia in the


learning environment. Drawing upon these considerations, the characteris-tics of a situated learning environment, and the requirements of the contentarea of teaching and assessment, the resource was designed to comprisetwo CD-ROMs, one on the issue of assessment and the other on teachingstrategies in mathematics education, each incorporating:

(a) video clips of teachers using various assessment or teaching strategieswithin their classrooms;

(b) video clips of teachers reflecting and discussing the strengths andweaknesses of the approach;

(c) video clips of children discussing their feelings and thoughts;(d) interviews with experts in the field providing theoretical perspectives;(e) reflections by preservice teachers on the assessment or teaching

approach;(f) text descriptions of each approach;(g) teacher and student work samples;(h) a problem-based notebook providing a variety of tasks within which

to examine the resource;(i) a manual for users and facilitators on how to implement the resource,

which also provides advice on the situated learning elements whichare not enabled by the resource itself (such as collaboration and artic-ulation).

In conducting a review of the literature on teaching and assessment,and from the reading of current issues in the field, 28 teaching strategiesand 23 categories of assessment were selected as relevant to both primaryand secondary mathematics classrooms (see Table I). This was done withthe assistance of two visiting scholars, one with experience in multimediadevelopment in mathematics education, the other knowledgeable in thearea of assessment in mathematics.

Videos

By clicking on the video cassette objects under the television screen,preservice teachers can view a short video sequence of either the scenein the classroom where the teacher demonstrates the use of the technique(Scenario), the teacher’s comments on the use of the technique (Teacher),or a student’s comment (Student). The controls under the television imageallow the students to control the progress of the video clip. They can usethe sliding switch to move the scene along or to replay phrases or sectionsof the scene. They can also rewind, fast forward and pause the video. Aspeaker allows students to control the volume of the audio.


TABLE I

Teaching and assessment strategies

Teaching strategies Assessment strategies

Drill and practice Open-ended tasks Checklists Pencil and paper

Homework Exposition Anecdotal Multiple choice

Textbooks Beginning a lesson Higher-order Problem solving

Worksheets Team teaching questioning Attitude

Group work Involving others Factual questioning Oral

Role play Puzzles Open-ended Written

Explaining Modelling questioning Portfolio

Peer tutoring Applications Structured Investigation

Manipulatives Themes interviewing Modelling

Game playing Problem solving Open interviewing Journals

Outdoors Problem posing Parent interviewing Reflective prompts

Mathematics Calculators Diagnosis Self-questioning

centres Graphic calculators Performance-based Peer assessment

Guided discovery Computers

Projects

Figure 1. The main interface of the teaching strategies program.

Filing Cabinet Resources

Each of the filing cabinet drawers contains a written resource whichstudents can examine. With the exception of the Samples drawer, segments


Figure 2. Description of the assessment category (First drawer of filing cabinet).

of the documents can be copied and pasted into the students’ electronicnotebook which sits on the desk. The strategy of Reflective prompts fromthe assessment CD-ROM is used as an example to illustrate each drawerof the cabinet.

Descriptions. By clicking on the top filing cabinet drawer, students canread a description of the strategy which includes advice on how to imple-ment the strategy effectively in the classroom (see Figure 2). There arethree buttons at the bottom of this screen which students can use eitherto return to the main interface after reading the information, or to copysentences or paragraphs to put into their notebooks.

Samples. By clicking on the second drawer students can examine samplesof school children’s work or teachers’ records (Figure 3). These sampleswere collected from the schools at the time of filming the segments andthen scanned and imported into the program.

Reflections. The third drawer of the filing cabinet contains advice givenby a preservice teacher, on his or her experience of using the strategy onprofessional practice in schools (see Figure 4). Responses were edited, butonly to correct spelling mistakes, repetitions and major grammatical errors.


Figure 3. Work samples of the assessment category (Second drawer of filing cabinet).

It was important to retain the terminology and idiom of a young person,only slightly more experienced and knowledgeable than the intended usersof the program. An important consideration in the design of the programwas that learners have the opportunity to observe not only accomplishedteachers and experts but also other learners with varying degrees of skill(Collins, et al., 1989).

Interview. Clicking on the bottom drawer of the filing cabinet gives studentsaccess to an expert commentary on the use of the strategy (Figure 5). Thedesign of the interface simulates a features page of a newspaper to empha-sise the fact that the document is based on an interview with the expert,rather than a scholarly piece of writing. Apart from providing valuableadvice on methods of implementing the strategies in the classroom, theexpert’s comment is important because it allows students to compare theirown level of thinking on the issue with the expert’s. This is critical to thekind of reflection students might engage in as they use the program.

Notebook

Clicking on the notebook on the table allows students to use the elec-tronic notepad and also gives them access to the authentic activities of


Figure 4. Preservice teacher’s advice on the assessment category (Third drawer of filingcabinet).

Figure 5. Expert comment (Fourth drawer of filing cabinet).


the program. The first tab, the notes, enables students to write their ownreflections and ideas as they explore the various elements provided, andalso to cut and paste text from three of the resources provided in the filingcabinet drawers: the description of the strategy, the preservice teacher’sadvice, and the expert’s comment. At the end of a work session, studentscan save copies of their notes to their own disks, then format them usingtheir regular word-processing program.

Clicking on the Problem Solving tab gives students access to shortproblems which are more narrowly focused and require less time tosolve. For example, one of the problems presented in this section is givenbelow:

Make a list of different items that could be included in a student’smathematics portfolio. Explain how and why you would use aportfolio for assessment purposes.

Such problems do not necessarily conform to the situated learningmodel proposed for the program, but were included to allow facilitatorsa broader range of approaches and to add versatility to the resource as amarketable item. It means that educators are not excluded from using thepackage with their students if they cannot commit a large proportion oftheir course time to the topic. The problems could be attempted in a singlework session rather than the extended period of time recommended for theinvestigations.

The last tab on the notebook, Investigations, takes students to a seriesof authentic activities which replicate the kind of task a school teachermight be faced with in real life. The tasks are presented to the studentrealistically, such as in a memo or letter, rather than simply a list ofpossible activities, and they include genuine constraints such as deadlinesand time allowances. Activities assume that students will be working inpairs or small groups, and require them to examine the resource from avariety of perspectives (see Figure 6 for an example of an investigation).

The Manual

The manual provides educators and students with a list of optimum imple-mentation conditions which are all based on the situated learning modelused for the development of the program, and acknowledges the positionthat not all the critical elements of this model can be incorporated into theprogram itself. Some of necessity must be provided by the educator, andsome by the students themselves. This list of optimum conditions is givenin Table II below.


Figure 6. An investigation from the assessment program.

TABLE II

Optimum conditions for use of interactive multimedia program

Users will gain the most from the program if it is used under the following conditions:

Focus of investigation: The resource is best examined in depth, from a number ofdifferent perspectives

Length of time: Best used over a sustained period of 2–3 weeks rather thanfor a single session

Number of students: Students working in pairs or small groups around each com-puter, rather than individually

Educator support: Facilitator present during use to provide “scaffolding” andsupport, rather than as an independent study activity

Setting the task: Teacher demonstrates the resource by thinking-aloud as aninvestigation is modelled. Students then choose an investi-gation from those provided, or their own choice.

The manual also provides educators and students with a description ofthe theoretical framework on which the program was based, summaries ofeach of the strategies and ways in which educators can assess students’ useof the resource.


IMPLEMENTATION OF THE RESOURCE

The resource has been used with elementary and secondary preserviceteachers enrolled in a Bachelor of Education degree and also a GraduateDiploma in Education. Typically the students spent about three weeks orone quarter of their unit investigating either the teaching or the assessmentstrategies disc. This usually involved the equivalent of three hours classtime per week as well as independent study time. The final third week wasspent in class for the group presentations. Two approaches have been usedwith the students: lecturer present and lecturer free. In both approaches wefound it useful to begin with demonstrating the features of the software bybriefly modelling a search strategy, and then providing time for students towork on an investigation. At this time initial questions could be answeredand students could start to plan an approach with their colleagues. For adescription of the set investigations see the earlier outline and Figure 6.

The students had been presented with a task which contained manyinnovative features for them and for many this was an initial barrier toprogress. Students had to accommodate using new technology, a nonlinearand loosely structured assignment, and working in a collaborative way.The assignment had moved from a familiar surface to a deep learningemphasis. The modelling helped allay students’ fears about at least thefirst two of the new features of the situation.

Generally, students appeared to value working in small groups, espe-cially when they were able to select their partners and the task they wishedto investigate. Whenever possible, however, we tried to achieve a range ofinvestigations so that the presentations and hence the variety of perspec-tives experienced by the class as a whole was maximised. Five presenta-tions of the same problem could become tedious and lessen the impact ofthe insights offered by each group.

In one trial implementation, students worked in small groups in acomputer laboratory for the first two weeks of class time with the lecturerpresent. This set time and lecturer-present format was useful, in the sensethat the form was one with which the students were familiar. This methodallowed for immediate assistance. Nevertheless, the majority of time wasspent on answering procedural difficulties with the computer system – littleclarification was sought, or needed, on the content of the resource.

Part of the initial impetus to design the resource was a growing require-ment to incorporate worthwhile student learning activities which neededless lecturer presence and more independent work by students. Difficul-ties encountered with booking computer laboratories at the required time,along with the search for flexibility of delivery, meant that other ways touse the resource were sought.


The lecturer-free method used the initial modelling of the CD-ROMresource and the search strategy as described with the lecturer-presentmodel. From this point on, the student groups were given time in which tocomplete the investigation, either the scheduled lecture times or mutuallyconvenient times. The software had been deliberately designed to run onboth Macintosh and Windows environments, thus allowing students to usetheir own computers – subject to having a CD-ROM capability. Studygroups and students with other commitments, for example, parents withyoung children or people with part-time jobs, found this flexibility oftime and place beneficial. While lecturers were, in theory, available and“on call,” they could not always provide immediate responses to studentqueries and this placed greater responsibility for scaffolding on the othergroup members.

The collaborative nature of the investigations also meant that allstudents had a part to play. Some groups approached the task by parti-tioning it, and then assigning distinct roles to individuals who then workedalone – cooperation rather than collaboration (Katz & Lesgold, 1993). Thisapproach generally resulted in a lower quality of outcome. The majorityof groups, however, approached the task in a collaborative way and inthese cases the results appeared to be more polished, professional andmeaningful.

For assessment purposes students were required to prepare a writtenreport and a class presentation. This presentation was assessed by thestudents’ peers using the following checklist of criteria shown in Figure 7.

The checklist for evaluation was disseminated at the time of the assign-ment briefing and was discussed with the student groups to inform theirthinking and allow for a more critical response to the task. Typically, thegrade for the assignment was a compilation of a score for the presentationand a score for the written report. The presentation score was the averagemark allocated by the other students in the class, while the written reportwas graded by the lecturer. The same grade was awarded to all membersof a particular group.

Refinements to this process, based on student comment and lecturerreflection, have seen some minor changes and additions. Many of thestudents were unskilled in assessing presentations critically and being ableto justify their decisions and mark. Before the presentations were givenin the third week, time was taken to help students to identify specificevidence for their mark. In pairs, students listed exactly what features theywould hope to see in a good presentation for each of the categories onthe peer evaluation form (see Figure 7). These features were shared withthe whole class. Students then used the features to comment against the


Evaluation Form

Your name:

Group no.

Presenters’ names:

Criteria: Score out of

� Effectiveness of argument /5

How persuasive was the group’s

proposal? Were you convinced of

the value of the suggestions?

� Proposal’s practicality /5

Were the suggestions practical and

able to be implemented? How

convinced were you that the

suggestions would work?

� Argument well-supported /5

Was there sufficient evidence to

support the proposal? Did you feel

they had researched the problem well?

� Presentation skills /5

How well did the group present

the report? Did the presentation

hold your attention?

Figure 7. Peer evaluation forms for student presentations.

criteria on the peer evaluation form in support of their mark. A section wasalso added to the form which asked students to nominate one feature ofthe presentation which they thought was good and to offer a thought as tohow the presentation might have been improved.

After each presentation, restricted to ten minutes, another five minuteswas given for individuals in the non-presenting groups to decide and justifytheir marks. The evaluation forms were then collected by the lecturer to be


used in the formulation of the overall grade. Peer evaluation forms werenot given to the presenting group and remained privy only to the lecturer toguard against any bad feeling that might have occurred among the groups.The lecturer used specific anonymous comments from the forms as part ofthe final feedback on the assignment.

The class presentation was an anxious time for many students. Onestudent, however, noted that the capacity of their peers to respond andquestion their findings meant that the presenters had to have a clear under-standing of the topic. This was a very different way of learning for manystudents who, in the past, have relied primarily on rehearsal of their lecturenotes.

Quality of presentations varied but as lecturers became more experi-enced with the format, presentations of lower quality became rarer. At theinitial briefing for the assignment, examples of good and poor responseswere outlined. This technique reduced the number of presentations whichwere composed of lists of the various teaching or assessment strategies– a regurgitation of the CD-ROM without critical comment or argument.Examples of better, more worthwhile presentations involved students react-ing to the specific context of the investigation, taking the opportunity tobe creative, and developing the role play aspects. Staff meetings, completewith coffee and cakes, were conducted; parent evenings with concernedparent interjections took place; a Queen-of-Hearts-type calculator appearedand delivered a soulful plea to be used more often in classrooms. Quality ofthe presentations were usually high with many groups using presentationsoftware and video.

The result of a challenging and realistic activity, approached and artic-ulated in a collaborative way, appeared to be significant awareness ofapproaches to teaching and assessing mathematics. An evaluation of thetransfer of this knowledge to teaching practice is explored in the nextsection.

EVALUATION

As well as the formative evaluation of the resource during the developmentof the project, ongoing research is continuing to evaluate both the accept-ability of the resource and its effects on preservice teachers’ learning aboutmathematics teaching and assessment. The aspect of evaluation reportedhere investigated the extent of the preservice teachers’ use of the differentassessment techniques featured in the interactive multimedia program, intheir professional practice in schools. The participants were six preserviceteachers in the second year of a three-year Bachelor of Education course


studying mathematics method for secondary schools, and six teachers whosupervised the students in their professional practice in schools.

Approximately five weeks after the conclusion of the use of the assess-ment multimedia package in their mathematics method course, the six stu-dents completed a two-week professional practice in six different metropol-itan schools. All the students were required to teach mathematics classesin this practice, and it was expected that they would have the opportu-nity to implement different assessment strategies at this time. In order toassess whether students used a variety of assessment strategies during theirmathematics classes on professional practice, both the students and theirsupervising teachers in the schools were interviewed and the commentswere analysed.

Within three weeks of their completion of professional practice, eachstudent was interviewed for approximately 30 minutes, using an inter-view protocol based on the Prediction Technique suggested by Miles &Huberman (1994). This technique requires the researcher to predict studentperformance in the area of assessment. Students are later shown the predic-tion and asked to comment on their experience and whether or not it match-ed the prediction. They are then asked to provide further specific data onsupporting and negating factors associated with their use of the assessmenttechniques.

The prediction was made by the authors that the students would usea variety of assessment techniques in their mathematics classes duringteaching practice, and this was true of all six students. In spite of thefact that one student reported the prediction to be untrue and anotherwas unsure, all the students did use a variety of strategies. Evidence tosupport this conclusion was provided by the students on their own reportin the interviews, and this was generally corroborated by their supervisingteachers.

A situated-learning view of transfer is not one that suggests that a personcan acquire a set of skills which can be lifted and applied in a totally novelsituation. The view of transfer adopted by the proponents of situated learn-ing, and used here, is that knowledge is more likely to be transferred tonovel situations when it is learnt in the context of use and becomes “acentral or integral part of one’s cognitive structure” (Prawat, 1992, p. 375).It appeared from analysis of the comments made by students in the studythat assessment issues had been incorporated into students’ cognitive struc-tures. They spoke openly and knowledgeably about assessment issues aftertheir teaching practice, in a manner which substantiated Brown, Collins &Duguid’s (1989) claim that new situations enable knowledge to be recast“in a new more densely textured form” (p. 33). The students acknowl-


edged the complexity of the area but were well acquainted with the typesof assessment which might be suitable in the mathematics classroom, andthey used appropriate language with familiarity and ease.

The students were also aware of the usefulness of assessment inperforming more functions than the summative appraisal of students’understanding. Writers in the mathematics education area (e.g., Burton,1992; Clarke, 1988; NCTM, 1995) have listed many additional purposesof assessment such as: to make decisions about the content and methods ofinstruction; to improve the teaching of the child; to make decisions aboutthe classroom climate; to help in communicating what is important; and toinform parents of their child’s progress. The various roles of assessmentwere not explicitly listed in the interactive multimedia program but wereintrinsic to much of the comment by experts and teachers, and demonstratedin many of the scenarios. Comments by the majority of students indicatedthat they were aware of many important roles for assessment, and that itcould be used, as noted by Jonassen (1991) as “less of a reinforcementor behaviour control tool and more of a self-analysis and metacognitivetool” (p. 32). For example, one of the students commented on “formal”and “informal” assessment when asked whether assessment was necessaryon short professional practice:

It depends what you mean by assessment. Like when we used the multimedia, they lookedat questioning and monitoring as part of assessment and some people don’t think that isassessment. So I think maybe formal assessments like maybe long investigations where alot of work is done, maybe that’s not necessary, but I think the informal like questioningand monitoring is. (Interview with Louise)

Rowan also pointed out that assessment has a critical role in helpinghim to monitor his own performance as a teacher:

As a teacher, you need to know where [the students] are at and the objectives you’re settingyourself to start off with. I think it’s quite important really because you have a feel for howyou’re doing, especially if you can see that they’re learning something, it actually allowsyou to assess your own teaching. (Interview with Rowan)

The fact that the students used a variety of assessment strategies mayor may not have been due to the influence of the interactive multimediaprogram on assessment. There is no firm evidence to assume a causal rela-tionship between the two. It is possible, however, to assess students’ ownbeliefs about the program and its impact on their teaching performance.

The majority of students believed that their use of the interactive multi-media program on assessment was a direct and important influence on theiruse of assessment strategies during their professional teaching practice.One student was the exception by stating that the program had no effecton his teaching and was irrelevant to his choice of assessment strategies.


The remaining students all attributed the interactive multimedia programas an influence in their adoption of assessment strategies, albeit to varyingdegrees. One student believed that the program was a very importantinfluence:

I think it influenced me greatly, I really took it to heart. So I basically did implement a lotof the assessment types that were identified in the multimedia. I think it was a really bighelp in that part. (Interview with Evie)

Another student pointed out how the program influenced his thinkingas he prepared his lesson plans:

It made me think about assessment a lot more, each time I was writing up a lesson plan.Each time I came to assessment, I thought about it a lot more. It was a case of, “Well Iwouldn’t want to end up doing a pencil and paper test, so how am I going to structureassessment while I’m here doing this series of lessons?” I was a lot more conscious of it.(Interview with Rowan)

Like Rowan, other students also referred to consciously reflecting onassessment as a result of using the assessment program. For example, Zoemade the following comment which also reflects her concern about theexcessive use of pencil and paper tests by her supervising teacher:

It’s opened my eyes a lot more, like on the pencil and paper tests and also watching myteacher and really disagreeing with a lot of the assessment strategies he’d use. He only usedpencil and paper assessment strategies. Of course I didn’t say anything, but I’d sit therethinking “Oh remember what we learnt.” (Interview with Zoe)

Interestingly, some of the students spoke about using the assessmentstrategies from the interactive multimedia program almost unconsciously.For example, Carlo admitted that he may have been influenced to usestrategies without consciously knowing it. Similarly, Louise commentedthat her use of the strategies was unconscious but then went on to describea very thoughtful and reflective response to children’s concerns aboutassessment:

It probably wasn’t conscious, I was doing it unconsciously. I was trying to use a variety ofthings like the questioning and the observing and things like that rather than say “If youdidn’t get that correct, that’s wrong!” Rather I’d say “What if you did it this way?” I’d try touse the assessment strategies that made the students feel more comfortable and so knowingwhich ones were less threatening, other than pencil and paper, made me think about whatI wanted to do, and helped me to find out if there was a particular thing that the studentscould do. I thought about which method would be the best for finding that out. (Interviewwith Louise)

Several students expressed the view that in their future practice asqualified teachers they would be able to exercise greater discretion in theiruse of assessment strategies. For example, the following comment wastypical of five students’ views:


There were only limited types of assessment that I could use, but hopefully in the futureI’ll be able to use a wider range of the ones that were on the multimedia. Hopefully I’ll beable to : : : start journals and things like that. (Interview with Evie)

An important issue relating to transfer was raised by one student whohad a double major and was studying both mathematics and languagemethod. She pointed out that it was possible for her to transfer her learningabout assessment strategies to other subject domains:

It’s based on maths, the multimedia one was, but I would probably think that it could beapplied to anything. It’s more general. I found myself using some of these techniques inmy other classes, like English. I thought they helped if you look at them in a general view,not just for maths. (Interview with Louise)

According to the beliefs of the students themselves, the multimediaprogram on assessment appeared to influence the types of strategies theyemployed and their thinking about assessment as they taught mathematicsand other classes during their professional practice in schools.

Analysis of the data showed that all the students could speak knowledge-ably and confidently about assessment, and all the students used a varietyof techniques to assess children’s understanding. The students appearedto be influenced very strongly in their use of assessment strategies by thesupervising teacher. However, even when assessments had been plannedin advance, all students used techniques that they were able to use withoutthe contribution or agreement of the supervising teacher. Five of the sixstudents attributed their use of assessment techniques to the interactivemultimedia program.

Resnick (1996) has recently been critical of one aspect of the situatedlearning model which she perceives as problematic: the disappearance ofthe individual. According to Resnick, “Individual knowledge and skill– characteristics of individuals that can be carried with them from onesituation to another – are replaced by emergent cognition that belongs tono one and disappears when the moment of emergence has passed” (p. 41).The findings of this study, within the parameters of transfer given here,refute this assertion. The students had clearly internalised the assessmentissues investigated within the situated learning environment, and wereable to use them competently in situations where they had the discretionto do so.

CONCLUSION

The benefits of using multimedia resources that incorporate characteristicsof a situated learning environment appear to hold promise for preservice


teachers learning about mathematics teaching and assessment. Teacherswho use these materials are motivated to explore challenging and authentictasks in collaborative settings that include multiple perspectives denied intraditional forms of course delivery. In relation to the assessment strategiesprogram, it appears that student teachers can gain and apply importantpedagogical knowledge, however, this needs to be further researched usingthe teaching strategies program.

As these materials were developed within a particular cultural setting,further research is necessary to determine the benefits of the resourceacross cultures. While positive outcomes have been found for preserviceteachers, the benefits for inservice teachers need to be determined. Theauthentic tasks provided in the package are the result of the developers’concerns about teaching and assessing school mathematics. It would beuseful to investigate how teachers, given access to this resource, may useit to identify and seek solutions to their own problems.

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Edith Cowan University

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Learning to Teach and Assess Mathematics Using Multimedia: A Teacher Development Project

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