using e‐learning to support primary trainee teachers’ development of mathematical subject...

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Using e‐learning to support primarytrainee teachers’ development ofmathematical subject knowledge: Ananalysis of learning and the impact onconfidenceHilary Burgess a & Ann Shelton Mayes ba Centre for Research in Education and Educational Technology(CREET), Faculty of Education and Language Studies , The OpenUniversity , Milton Keynes, UKb School of Education , The University of Northampton ,Northampton, UKPublished online: 01 May 2008.

To cite this article: Hilary Burgess & Ann Shelton Mayes (2008) Using e‐learning to support primarytrainee teachers’ development of mathematical subject knowledge: An analysis of learning andthe impact on confidence, Teacher Development: An international journal of teachers' professionaldevelopment, 12:1, 37-55, DOI: 10.1080/13664530701827731

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Teacher DevelopmentVol. 12, No. 1, February 2008, 37–55

ISSN 1366-4530 print/ISSN 1747-5120 online© 2008 Teacher DevelopmentDOI: 10.1080/13664530701827731http://www.informaworld.com

RESEARCH ARTICLE

Using e-learning to support primary trainee teachers’ development of mathematical subject knowledge: An analysis of learning and the impacton confidence

Hilary Burgessa* and Ann Shelton Mayesb

aCentre for Research in Education and Educational Technology (CREET), Faculty of Education and Language Studies, The Open University, Milton Keynes, UK; bSchool of Education, The University of Northampton, Northampton, UKTaylor and FrancisRTDE_A_282888.sgm10.1080/13664530701827731(Received 8 December 2004; final version received 19 November 2007)

Teacher Development1366-4530 (print)/1747-5120 (online)Original Article2008Taylor & Francis121000000February 2008Dr [email protected] This article explores the effectiveness of a mathematics subject knowledge developmentmodel that integrates conventional text-based distance learning with an e-learning coachingand peer group conferencing environment. The effectiveness of the model in supporting 194trainee primary (pupil’s aged 5–11 years) teachers achievement of the subject knowledgestandards required for qualified teacher status is evaluated and the impact of the model ontrainee confidence is explored. Features of the model that trainees, tutors and post-qualifiyingteachers identify as critical factors for success are outlined and the relevance of the model forteacher professional development is discussed.

Keywords: primary teaching; mathematics subject knowledge; trainee teachers; e-learning; distance learning; coaching

1. Context

In the UK, the period 1998–2002 saw an unprecedented rise in national regulations (DfEE1998a) governing initial teacher training programmes, including an extensively prescribed,subject knowledge curriculum that each trainee was to be assessed against. This was a responseto the perceived decline in mathematical performance by English school pupils when viewed ina comparative international context (Second International Mathematics Study [SIMS] 1993;Third International Mathematics and Science Study [TIMSS] 1996). Whilst the DfEE subjectknowledge standards remain controversial in terms of content, level and relevance to primarymathematics teaching, nevertheless it established a national set of subject knowledge standardsthat all initial teacher training providers were required to measure. Whilst acknowledging thecontested nature of the subject knowledge standards they define a legitimate framework for thisresearch.

For practising teachers, this was paralleled by the introduction of the National NumeracyStrategy (NNS) in England (DfEE 1998b; DfEE 1999) which has involved all primary schoolsin training activities to improve the teaching skills and subject knowledge of teachers and setkey objectives for the progression of pupil learning. The National Numeracy Strategy (NNS)was introduced during September 1999 and later incorporated into the Primary Strategy in2003. Evaluation reports on the introduction of these national strategies (OISE/UT 2003) indi-cate some improvements in the teaching of mathematics. However, variation across teachers

*Corresponding author. Email: [email protected]

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38 H. Burgess and A. Shelton Mayes

and schools, alongside the task of sustaining these improvements, suggests that continuedprofessional development input will be required, particularly in the areas of subject knowledgedevelopment and teaching skills. Proposals for accredited teacher postgraduate professionaldevelopment (TTA 2004a) and the reform of mathematics teaching (DfES 2004), confirmsthat the development of teacher subject knowledge remains a key national priority. Thissuggests that the range of government strategies introduced since the 1990s, including thenewly qualified teacher standards (DfEE 1998a) and the National Numeracy Strategy, havenot resolved the issue of teacher subject knowledge. Research by Basit (2003) suggests thatimproving subject knowledge is a particular issue for newly qualified teachers entering theprofession. In her study, some trainees felt that they were able to ‘get away’ with knowingless subject knowledge because of the prescriptive nature of the NNS. It would appear thateffective teaching involves much more than a teacher being mathematically competent(Cooney 1999) and mathematical knowledge alone does not translate into better teaching.Aubrey (1996) found that teachers of mathematics for the early years were influenced by theirown feeling and beliefs, disciplinary knowledge and assumptions about teaching and learning.While Edwards and Ogden (1998) argue that the challenge lies in the situated nature of teach-ers professional knowledge and the extent to which it is evidenced in action rather than inexplanation.

Concern about the improvement of teachers subject knowledge and the quality of mathemat-ics teaching is an international issue and breaking the cycle of conventional mathematics teachingpractice emerges as a common theme in the literature. In the US, Ball (1988) has argued that alack of attention to what teachers bring with them to learning to teach may account for the reasonwhy teachers tend to teach mathematics as they were taught themselves. In Australia, Hill (2000)has explored why mathematics education programmes appear to have only a limited effect ontrainee teachers capacity and willingness to learn and teach mathematics for relationalunderstanding – knowing both what to do and why – (Skemp 1989), reverting to the instrumentalmethods they learnt in school.

These issues present a major challenge to those designing subject knowledge developmentprogrammes for teachers, suggesting the need to incorporate an open exploration of their personalexperience of mathematics learning in schools in order to provide a vehicle for longer termpedagogical development.

The subject development model explored here represents a distance learning response tothe initial teacher training regulations relating to the mathematical subject knowledgerequired for qualified teacher status (DfEE 1998a). However, the rapid expansion of e-learn-ing (Laurillard 1993, Salmon 2003) to support trainee and teacher professional develop-ment in the past decade, suggests an analysis of the successful features of this model mayhave relevance for a wider audience, including those planning professional developmentopportunities for teachers. The key characteristics, for example, of the cohort that drove thedevelopment of this subject knowledge development model, are shared by qualified teach-ers generally and, specifically, by the growing number of flexible routes into initial teachertraining (TTA 2004b). That the teachers/trainees are: (i) geographically dispersed; (ii)require flexible modes of study patterns to align with personal and professional timedemands; and (iii) have variable levels of prior achievement/qualifications in mathematics,requires a differentiated approach that allows individuals to focus on and develop, inspecific identified mathematical areas, in relation to personal need. The logistical demandsof providing individualised training, support, assessment and monitoring for a high volume,geographically dispersed teacher population are challenging (Banks and Shelton Mayes1998). In this context, distance-learning, with programme specific text materials and an e-conferencing environment, presents an appropriate teaching and learning model because it

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Teacher Development 39

combines the opportunity for individualised training with access to a community of supportfrom tutors and peers.

2. Research study

This research relates to a cohort of 194 trainee primary teachers on the Open University’s Post-graduate Certificate in Education programme (1998–2001), who were among the first trainees inthe UK to undertake the formal process of subject knowledge development in mathematics forqualified teacher status through an integrated e-learning and text-based distance learningmedium. The graduates from this programme entered teaching during the introductory phase ofthe National Numeracy Strategy and were in a unique position to reflect on their training experi-ence in the context of the requirements of the strategy. The study considered these questions:

Was the subject knowledge development model successful supporting trainees in achieving themathematical subject knowledge standards for qualified teacher status?

What features of the model did trainees, tutors and, in particular, qualified teachers attribute to theirsuccessful achievement of the subject knowledge standards?

What relevance does the model have for planning teacher professional development?

The research evidence was drawn in part from a larger study (Burgess and Shelton Mayes 2001),undertaken to analyse the developing subject knowledge of the primary trainee teacher cohort.Data were also drawn from a follow up questionnaire sent to this cohort in their third year ofteaching as part of an ongoing longitudinal study in 2004. This follow-up survey was critical indetermining whether successful features of the model identified by trainees and tutors wereconfirmed by the cohort from their perspective of qualified teachers. The following sources ofdata were particularly useful in assessing the effectiveness of the subject knowledge developmentmodel, in terms of trainee achievement of nationally set standards and exploring which featurescontributed to effective learning:

● E-conferencing involved 194 (1998–2001 part-time cohort) primary trainees, producingdata consisting of 1403 messages relating to mathematics subject knowledge (Burgess andShelton Mayes 2003).

● Entry and exit mathematical subject knowledge trainee outcomes as measured in mathe-matics tests were compared as the basis for judging the success of the subject knowledgedevelopment model.

● Interviews with the mathematics subject knowledge tutors.● Programme questionnaires.● A follow-up questionnaire sent to the 194 graduates in post as qualified teachers in 2003–

2004 (Respondents N=63, approximately 33% return) (see Tables 1–7).

In addition to the specific data sources identified above, the programme was set up to generateongoing data for evaluative and improvement purposes (Banks and Shelton Mayes 1998).Programme specific quality assurance procedures provided sources of evidence includingtrainee monitoring and observation records and, reports from tutors and school-based mentors.Benigno and Trentin (2000) identify questionnaires for online course evaluations as a valuablesource of research data and information from course questionnaires, completed by the trainees,was therefore included. In addition, the requirement by OfSTED to provide information ontrainee progress led to the development of detailed trainee case studies and quantitative dataon trainee outcomes in terms of subject knowledge competence. Research evidence, therefore,was taken from a variety of sources and provided both quantitative and qualitative data. Theuse of different research methods and detailed analysis of evidence allowed for triangulation

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of data and provided verifiable research outcomes (Wilcox 1993; Burgess and Shelton Mayes2003).

3. The subject knowledge development model

The mathematics subject knowledge development model was conceptualised as a three-stageprocess:

(1) identification: trainee awareness of subject knowledge requirements and self-auditing toidentify personal subject knowledge areas for development. The identified areas fordevelopment were confirmed by tutor assessment.

(2) personal development: trainee self-study of Passport to Mathematics (CME 1998). Apurpose-designed mathematics subject knowledge self-study text with e-conferencesupport leading to a formal diagnostic assessment (carried out under examination condi-tions) to confirm subject knowledge achievement and areas still to be developed.

(3) directed support: three levels of support were provided depending on extent of subjectknowledge development required. Individual trainee teachers directed to specialistsubject knowledge e-conferences for coaching and support and, if required, face-to-facesessions. Training continued until trainee ‘signed off’ through tutor assessment.

All trainees undertook the self-auditing process and diagnostic assessment and the results wereanalysed to produce an individual trainee teacher profile in relation to specific areas of mathemat-ics: Number and Measure; Statistics and Measuring; Number and Algebra; Geometry andAlgebra; Chance and Reasoning; and Proof and Reasoning. The profile formed the basis for iden-tifying specific areas for further development for each trainee teacher through directed personalstudy, individual coaching via e-conferencing and, group and individual tutorial sessions. SeeFigure 1 for an outline of the model.Figure 1. OU PGCE primary mathematical subject knowledge.Alongside the conventional distance-learning self-study text (CME 1998) and face-to-faceworkshops, the e-environment was organised as a series of conferences for specific teaching andlearning purposes, such as mentoring, peer support and coaching, and to reflect a mathematicssubject culture. E-conferencing provided the integrative dimension in this model, functioningthroughout the course as the primary mode of communication and support as well as, at differentpoints, a direct teaching medium and a monitoring tool for quality assurance purposes (Burgessand Shelton Mayes 2003). The overall e-environment design therefore was set up as a hierarchyof conferences for specific teaching and learning purposes (see Figure 2).Figure 2. OU PGCE primary e-conference environment.The PGCE on-line community was organised around subject conferences or ‘rooms’ andeach was distinctive, reflecting the different subject cultures. In stage 1, there were three peda-gogy rooms based on the core National Curriculum subjects of English, mathematics andscience. In these environments, the trainees shared ideas relating to their pedagogic subjectknowledge and supported each other in their planning and evaluation of their teaching experi-ences. In stage 2, two subject knowledge rooms in English and mathematics were set up wheretrainees could develop their subject knowledge, specifically required by Circular 4/98 (DfEE1998a), by asking questions and responding to tasks that had been set by tutors. In this learningenvironment both peer and mathematics tutor specialist support was strongly in evidence,facilitating the discussion and suggesting ways of finding solutions to queries. In stage 3, themathematics subject knowledge conference was developed to form a series of six specialistsub-conferences focusing on specific mathematical areas, in order to support direct trainee-tutor coaching. Trainees also had access to their own personal mailbox for private communica-tion and, importantly, this was the medium for communicating individual assessment outcomesand SK targets.

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Figure 1. OU PGCE primary mathematical subject knowledge.

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The development of this staged e-conference environment represented the programme team’sevolving response to external regulations on trainee subject knowledge training and assessment.In the context of a distance learning course with a highly dispersed trainee population, thisevolution of e-conferencing could be seen as a pragmatic response. However, the design of eachconference reflected the pedagogical and curriculum views of the programme team, as well as aresponse to external demands.

The philosophy underpinning the model was premised on minimising negative emotionalresponses to mathematics as a subject; promoting connections between subject content knowl-edge and school pedagogical knowledge; and, providing opportunities for collaborative working,peer and tutor support and direct coaching. The emphasis was on developing the trainee mathe-matics teacher as a ‘thinking professional’ (Edwards and Collinson 1996), requiring more thanreflection on practice with opportunities for the consideration of wider professional issues, suchas working collaboratively, for understanding subject matter and relating this to the pedagogy ofmathematics.

The role of emotion in the dynamic of learning and teaching is widely acknowledged (Hogdenand Askew 2007). Elbaz (1983) has suggested that the images that teachers have of themselves(self), their role in the school (professional self) and their academic and personal criteria, all haveconsiderable influence on how they use and present knowledge to their pupils. Images of the selfand professional self are inextricably bound together (Nias 1989) and, therefore, how traineeteachers construe their developing understanding of mathematics teaching and learning needs tobe understood in the context of personal belief about mathematics teaching and emotionalresponse to the subject.

Figure 2. OU PGCE primary e-conference environment.

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Schuck (1998) argues that one of the reasons for the lack of success in challenging traineeteachers’ views of mathematics and mathematics teaching, is that the engagement betweentrainee and teacher educator is an engagement with an inappropriate ‘self’ of the trainee. Sheproposes that trainees engage in different ways with their mathematics education courses throughthe perspective of three ‘selves’: ‘student-learning-to-teach’; ‘primary-school-student’; and‘teacher’.

Brown et al. (1999) argue that for primary teachers, the initial transition from school learnerof mathematics to trainee teacher of mathematics is an important part of the complex process oflearning to teach. If the transition is to be successful, it involves for many ‘a considerable degreeof “unlearning” and discarding of mathematical baggage, both in terms of subject misconceptionsand attitude problems’ (Brown et al. 1999, 301). This is also evident in Meredith’s work (1993),whose research suggests that there is a need to clarify the relationship between prior learning andattitudes towards pedagogical content knowledge.

Other research on affective issues in mathematics education has focused on high levels ofanxiety (Newstead 1998) and protection of self-worth (Thompson 1993). Such emotionalresponses to knowing and doing mathematics have also been recognised by Bibby (2002) whoargues that shame is a reaction to other people’s criticisms.

Drawing on this work, it was essential that this model of subject knowledge development builtpersonal confidence in the trainees as learners first and, then, as teachers and did not increasenegative responses to mathematics as a subject.

4. Developing subject knowledge with trainee teachers

Evidence of developing subject knowledge is drawn from conversational strands, a facilitysupported by FirstClass, within the e-conferencing environment. This facility made it possible totrack strands of trainee subject knowledge development on particular mathematical topics and atthe same time provided evidence of the trainee’s emotional and professional development inmathematics. The 1403 messages allowed strands of subject knowledge development to be drawnup across each of the six mathematics topic areas (see Figures 1 and 2) and, the two reported hereare representative of typical strands where trainees supported each other and demonstrate the roleplayed by tutors.

Trainee teachers were encouraged to share experiences with their peers and messagescommonly contain vivid descriptions that combine reflections on their developing subjectknowledge and practical teaching skills alongside an openness to revealing their personal feel-ings. The tutor’s role in the electronic environment was to encourage the trainees to bespecific and analytical about activities in the numeracy lessons. Often, the conversationalstrands were initiated by tutors who would encourage the trainees to focus on a particularaspect of numeracy. In the first example below, a tutor has set up the strand by providingtrainees with a list of mental strategies, taken from the National Numeracy Strategy, to beintroduced year by year. The trainees were asked to draw on their school experience to focuson methods of developing mental strategies with their pupils, and to identify their problems aswell as their successes.

Trainee 1.

…after one or two days practice at using the cards, we could maintain a fast pace during thesesessions, due to the enthusiasm of the class and a clear introduction to the sessions, so that all knewwhat they were to do. I have since had some positive feedback from the Head (my mentor) who feltthat these mental maths sessions appeared to be both very beneficial as well as being fun. This hasspurred me on no end, particularly as I have never considered maths to be one of my strongersubjects!!

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Trainee 2.

I was interested to read your comments on using cards with Year 1 classes. I tried with my Year 2class and found it very difficult. The children were not used to using this type of resource and it tooksome of them a long while to find the correct cards – then they often reversed the numbers when theyheld them up. While waiting for all the class to find the correct cards others became restless andstarted chatting, however if I moved on too quickly then the lower attainers became bored as theycouldn’t keep up. I thought a solution to this may be to differentiate questions between tables, but thistoo became confusing, as they were then unsure of which questions to answer. Can anyone suggesthow this system worked for them?

Trainee 3.

I have used Number Cards in the past and found that the first thing I had to do was take away theelastic bands! After this I had the same problem but I got the children who had the answer to put onehand on their head so I knew they had the answer and with the other hand use their pencil and writedown the answer to doubling it tripling it etc. Perhaps you could just ask your Year 2 to add orsubtract?

This short strand identifies the experienced teacher’s role in providing feedback as in the case ofTrainee 1, who was greatly encouraged by the positive response from the Head teacher. Thetrainee identified mathematics as one of her weaker subjects and yet was ‘spurred on’ to developand extend her knowledge and teaching skills. Trainee 2 had attempted a similar activity with herYear 2 class and found her numeracy lesson to be far more problematic. She had issues linked tomanagement of the activity, yet to be resolved successfully and, maintaining the interest andenthusiasm of the children was also problematic. Unable to solve the problems herself, the traineesought help from her peers and tutors in the electronic environment. The response came from oneof her peers, Trainee 3, who had noted the despair in the message and began by trying to lift herspirits by making a joke about elastic bands. The advice that followed was both practical interms of managing the pupils while at the same time gently suggesting that her peer simplify theactivity.

In this second strand, a trainee instigates a subject knowledge conversation by asking aspecific question.

Trainee 1: Can anyone explain why number lines generally seem to be written with the smallernumbers to the left

e.g. 0 1 2 3 4 5 6 7 8 9 10

whereas when we teach place value we teach th h t u 1/10’s 1/100’s ?

Trainee 2: Because it’s the same direction in which you write and the same way your ruler is marked?

Trainee 3: Because in the West we are used to reading from left to right, and when we count naturalnumbers, we begin with 1 and count on from there. It seems intuitive to represent them from left toright.

whereas when we teach place value we teach th h t u 1/10’s 1/100’s ?

Because no matter which number you consider be it 9, 99, 199, the units figure is always the one onthe right, the tens is one place to the left of it, etc.

The question you are really asking, I think, is, “Why are numbers not written beginning with the unitsdigit?” It is because we want to read the most significant digit first. If numbers were written the otherway around, and indeed pronounced verbally the other way around, it would mean having to waituntil the end of the number to get any idea of magnitude. The conventional method gives the mostsignificant figure first, so that right from the start of hearing a number spoken, you should have someidea of magnitude.

Trainee 4: I have always assumed that this was to facilitate children’s ‘counting on’ and ‘countingback’ for early addition and subtraction.

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Tutor: Well asked! This is the kind of question that has an answer in culture and history. Theorientation of the number line is a matter of convention. These things often emerged as a consensusin a similar way to the new meaning of the word “cool”.

Also:

Why are the English numbers from 13 to 19 spoken the other way around to numbers beyond 20 e.g.nineteen not tentynine

For primary teachers it is well worth knowing how other cultures write/wrote their numbers e.g.Mayans in base 20, Babylonians base 60 (hence 60 seconds in a minute, 60 minutes in an hour). TheSMILE centre produce a collection of jigsaws with various number scripts see also for example“Crest of the Peacock” by George G. Joseph [see Joseph 2000] – a lovely introduction to history ofmaths.

This second strand demonstrates how the trainees worked collaboratively in their electronic envi-ronment to seek the answer to a problem that an individual trainee had in relation to numbers. Acouple of the trainees were unsure and so gave a response phrased as a question. Trainee threeresponds confidently with a longer message and even rephrases the question which the firsttrainee asked. At the end of the strand, the tutor joins in and responds and develops the knowledgeof all the trainees by taking account of the issues they raise and linking her answer to both historyand culture, with clear examples of different ways of counting supported by a recommendedreading. Morrone et al.’s (2004) research suggests that where discourse patterns encouragetrainee teachers through emphasising understanding and autonomy, while de-emphasising evalu-ation of contribution and explicit instruction on how to arrive at a correct answer, then traineesare more likely to achieve mastery of mathematical problems.

The electronic environment enabled trainees to extend their knowledge, teaching strategiesand classroom management issues in a supportive environment by allowing them to ask questionsabout different aspects of mathematics and, comment on their feelings and the experiences oftheir teaching placements. Emotional responses to teaching were accepted as valid commentsalongside pedagogical and mathematical issues. The recognition of trainees as individuals whoneed emotional support and understanding, as well as practical knowledge and intellectual inspi-ration, helped to engage the trainees as active participants in their own developing professionalpractice in mathematics teaching. The comments from trainees demonstrate the emotional benefitgained from their peers and the tutor’s role in shaping the electronic environment. In addition,there is strong evidence that the model was very effective in terms of developing mathematicssubject knowledge for distance learning trainees because it allowed continual interaction betweentrainees and tutors, whilst on placement, using e-conferencing. The e-conferences were specifi-cally framed by the tutor to focus on different elements of subject knowledge in the context oftheir emerging classroom practice.

The effectiveness of the subject knowledge development model in supporting primarytrainees to achieve the prescribed national standards in mathematics subject knowledge, isevident from an analysis of their degree background and subject knowledge outcomes at the endof the programme.

The 194 trainee primary teachers were all postgraduates with a diverse range of first degreesubject specialisms. Ninety trainee teachers had a degree specialism in a mathematics/science/design and technology area, however more than 50% had only the minimum entry level ofmathematics (Grade C GCSE or equivalent). This represented a significant challenge, for themajority of trainees, who had an average age of 35 and had achieved the basic entry mathematicalqualification at age 16. Nevertheless, by the end of the programme, 99% of all trainees hadachieved the required standard for mathematical subject knowledge, with 76% awarded theOfSTED grade ‘good’. This successful outcome was confirmed through an external independentinspection (OfSTED 2001) by the award of a Grade 2 (good) on a four-point scale for trainee

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mathematical subject knowledge. The criteria for this grade stated that all trainees who pass thecourse, must achieve the standards for mathematical subject knowledge and, that more than 70%of the cohort must achieve a ‘good’ subject knowledge outcome (OfSTED/TTA 1998). WhileOfSTED inspections are controversial in terms of their methodology and judgements (Hackettand Dean 1999), nevertheless this was an additional source of external evidence confirming thatthis subject knowledge model met the requirements of the ITT national curriculum. An analysisof the final subject knowledge OfSTED grades showed that 57.6% of those trainees originallyidentified as requiring the highest level support (that is, achieving the lowest diagnostic assess-ment scores – 29.6% of the cohort), had achieved an OfSTED ‘good’ subject knowledgeoutcome. This suggested that the programme was able to provide a ‘value-added’ dimensionwhere trainees performed better than might be expected based on their entry level of subjectknowledge.

5. Subject knowledge development as qualified teachers

The views of this cohort as practising, qualified teachers were sought during their third year ofteaching in relation to specific questions (see Tables 1–7). Many respondents (77.8%) rated thesubject knowledge development model as useful or better in developing their personal subjectknowledge (see Table 1), with 14.3% rating it at the highest level. When asked to rate the model’simpact on their self-confidence to teach mathematics in their first teaching post (see Table 2), theresponses were more positive with 85.6% rating the model as helpful, with 19.0% rating it at thehighest level. A typical response from the survey was:

it reinforced that I did know and understand what I thought I did. Some of it was quite ‘meaty’ anddidn’t need to use it in my teaching but you do need to know where your pupils are going with thatknowledge.

Those who rated it least useful (9.5%) (Table 1) were those who identified a high level of personalmathematics subject knowledge on entry, for example, a prior degree with a mathematics orscience specialism. Some of this group commented on the de-motivating aspect of the govern-ment requirement to demonstrate their mathematical subject knowledge competence duringinitial teacher training and, one likened the process of auditing and testing as ‘being forcedthrough hoops’. Despite the subject knowledge model specifically embedding the subjectknowledge testing requirements within a pedagogical framework, this has remained a deeply feltissue by a small minority of the surveyed teachers.

Interviews with tutors during initial teacher training revealed that a lack of confidence was amajor issue for many trainees (Burgess and Shelton Mayes 2003), confirming research under-taken by Bibby (2002) and Thompson (1993). MacNab and Payne (2003) have researched thebeliefs and practices of Scottish primary school mathematics teachers and found that their

Table 1. Percentage respondents rating usefulness of the mathematics subject knowledge training in developing the mathematical subject knowledge required to teach mathematics for first teaching post.

Usefulness of the mathematics subject knowledge training: developing subject knowledge

Not very useful1 2

Useful3 4

Very useful5

% (no. of respondents) 9.5 (6) 12.7 (8) 28.6 (18) 34.9 (22) 14.3 (9)

Note: Respondents N=63.

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trainees felt more confident teaching the more structured aspects of mathematics, such as mathe-matical facts: for example, multiplication tables and mental methods of calculation. They wereleast confident, argue MacNab and Payne, using problem solving strategies and mathematicalprocedures, such as conversion of fractions to percentages. It has also been argued by Stipek et al.(2001) that those who have greater self-confidence in their mathematical ability are more likelyto use inquiry-oriented methods in their teaching of mathematics. This is supported by the major-ity of the qualified teachers in our research who commented favourably that the methods used tosupport their subject knowledge development in mathematics helped with solving problems,maintained their motivation and enabled a transition to using new methods to understand andteach mathematics that they had not previously used.

I felt that I was very much responsible for my own learning and was very self-motivated.

It provided an excellent transition between the ‘old’ maths I learnt at school and the ‘new’ mathstaught now.

This link between self-confidence and perception of competence is corroborated by theresponses of the qualified teachers, indeed the majority of comments related specifically to theissue of confidence. Their responses resonate with the work of Stipek et al. who suggest thatgreater confidence as a learner of mathematics leads to teachers who are more likely to beconfident of their teaching ability in the classroom. The supportive approach adopted by tutorsand peers in the e-conferences was identified as helpful for avoiding adverse responses toteaching the subject.

I felt most confident when working through subject knowledge with my peers/fellow students (e-conferencing) and when supported face-to-face – I need interactive learning.

Developing confidence in my own ability, my growing enjoyment of the subject and seeing children’sknowledge grow and ‘fear’ of maths disappear.

I battled with self-doubt because I had such poor maths tuition as a schoolchild myself’. (…) Studyingmaths was an eye-opener for me (…) I had only ever ‘done’ maths in one certain way – it was almostscary to suddenly de-construct numbers and mix up strategies – it helped take away that debilitatingfear of ‘getting it wrong’ and maths became enjoyable at last.

A small number of the qualified teachers commented that they believed that their self-confidencewas linked to the practical application or delivery of the subject, rather than the prior developmentof personal subject knowledge. Others were critical of national standards that required a separateassessment of trainee personal subject knowledge (DfEE 1998a), from that demonstrated throughtheir practical teaching. Despite the unanimous acknowledgement in the survey (100%) that goodpersonal subject knowledge is important to the effective teaching of primary mathematics, therewere some negative comments.

Table 2. Percentage respondents rating usefulness of mathematics subject knowledge training in developing confidence to teach mathematics for first teaching post.

Usefulness of the mathematics subject knowledge training: developing confidence

Not very useful1 2

Useful3 4

Very useful5



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KS1 (teaching 5–7 years) does not lend itself to improving subject knowledge – only methodology.

Some aspects (of mathematical subject knowledge standards) were above the level which is appro-priate.

While we may not agree with these statements, they reveal the frustration of some teachers whobelieved that the national standards required greater levels of personal mathematics subjectknowledge than was necessary for the demands of teaching in primary schools.

This is further illustrated by the difference between Key Stage 1 (KS1) (5–7 age range) andKey Stage 2 (KS2) (8–11 age range) teachers’ responses. Seventy per cent of KS1 teachers(N=30) reported that the subject development model was useful or better in developing theirpersonal subject knowledge for teaching, rising to 84.8% for teachers working in KS2 (N=33).Similarly, 80% KS1 teachers reported that the model was helpful or better at developing theirconfidence for teaching, rising to 90% for KS2 teachers. This suggested that neither the govern-ment standards, nor indeed this specific subject knowledge development model, had beensuccessful in persuading all trainees and teachers of the importance of developing personalsubject knowledge which extends directly beyond that required to teach a specific age-group. Theexplicit separation of pedagogy and subject knowledge in the national standards for qualifiedteacher status (DfEE 1998a) was likely to have exacerbated this perception. It is interesting tonote that the revised national standards (DfES 2002) removed the prescriptive atomised subjectknowledge curriculum and, replaced it with a standard that requires only qualified teachers tohave appropriate subject knowledge to teach specific age-groups. This may go some way toaddressing the negative responses of some teachers in relation to identifying what is perceived asappropriate subject knowledge requirements.

Alongside confidence-building, the comments from tutors and trainees suggest other featuresthat were successful in supporting trainees learning. First, the process of self-auditing anddiagnostic auditing inherent in the model, allowed tutors to focus on specific trainees and targettheir coaching to individual need. This was likely to be a factor in the support of those traineeswho entered the programme with low levels of subject knowledge. Specific case studies on theprogress of some trainees in this category suggested that this was a successful strategy.

Second, the high levels of peer and tutor support, provided for trainees, was identified as afactor that helped to make it effective. Teachers rated levels of peer support (68.3%) comparableto the tutor support in e-conferences (71.4%) (see Table 3). Coaching was one of the supportivestrategies used by tutors which can be tracked through the e-conferences. In this strategy, thetrainee worked directly one-to-one with a tutor. It was both intensive and supportive. Research,by Oldroyd and Hall (1991), has demonstrated that coaching is likely to have a greater impact onpractice than simply a presentation of the theory. The key word was ‘doing’, being engaged in theactivity of working through a problem. In many respects, this is similar to mentoring and sharessome of the positive and negative features of this activity. One of the essential differences is thata mentor will counsel and listen, but not necessarily tell a trainee what to do; while in directcoaching the tutor is directing the trainee, through their interventions, towards a particularoutcome. Direct coaching was a common strategy in the e-conferences where trainees wererequired to prepare answers to questions set by tutors in specific mathematics areas linked to theoutcomes of the diagnostic assessment and, directed towards a deeper understanding throughdetailed feedback provided by the tutor.

Third, in using and developing strategies of peer support and collaborative working, thetrainees were committed to helping each other achieve success in their mathematics subjectknowledge and assignments. They shared the common goal of improving their mathematicsknowledge in order to improve the quality of their teaching. Swafford (1998) has argued that peercoaching is non-evaluative and non-judgmental, encouraging a community of learning where

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teachers can investigate and explore alternatives, implement new strategies and explore again.Swafford’s research suggests that such strategies build confidence in trainee teachers and, there-fore, can have a positive impact on the outcome of mathematics subject knowledge development.Though not rated as highly as some other features of the model, peer support was valued as usefulor better by 68.3% (see Table 4) and, it is interesting to note that 60.3% (see Table 7) were stillin contact with their peers three years into their teaching career. This suggests that even thoughthe trainees were on a distance learning course and rarely met, the electronic environment as acommunity of learning was a medium with enduring consequences for peer support. A typicalcomment from the survey was:

you can’t beat talking with people who are experiencing the same things as yourself and want thesame end result. It became a habit of communicating I have been hooked on ever since.

Fourth, all the modes of learning and support operated within a common mathematics subjectknowledge framework. Six mathematical areas, based on the National Curriculum subject knowl-edge requirements for teaching primary mathematics, provided the common structure for thesubject knowledge learning and support model through the self-study text, the e-conference envi-ronment and face-to-face teaching sessions. An individualised subject knowledge developmentplan was created from a diagnostic profile. Trainees were able to move easily between differentmodes of learning and support and make connections. Of the various components of the OpenUniversity (OU) subject knowledge development model (see Table 4), the cohort rated the Pass-port to Mathematics as most useful (87.3%), followed by face-to face support (79.4%), which wasoffered primarily to those trainees who required additional support but, was available andaccessed by most of the cohort. All other forms of support received an overall positive responsewith mentor support gaining the lowest positive response (61.9%). This supports national initialteacher training inspection reports (OfSTED 1999, 2003) which have suggested that school-basedmentors play a less significant role in subject knowledge training.

Fifth, high levels of tracking and quality assurance were built into the model with the progressof all trainees monitored in the e-environment. Additional face-to-face support was provided fortrainees who did not appear to be making sufficient progress in the development of their subject

Table 3. Percentage respondents rating different aspects of the mathematics subject knowledge model useful or better.

Mathematics subject knowledge model aspects % (no. of respondents)

Distance learning text (self-study) 87.3 (55)Face-to-face workshops 79.4 (50)E-conferences 71.4 (45)Peer support 68.3 (43)School-based mentor support 61.9 (39)

Table 4. Percentage respondents rating personal subject knowledge improvement post qualifying.

Personal subject knowledge improvement: post qualification

No improvement1 2

Improved3 4

Very good5



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knowledge. The cohort rated this strategy highly (79.4%) (see Table 4) in terms of positivesupport for their subject knowledge development.

The questionnaire responses taken with comments from tutors, trainees and teacherssuggested that it was likely to be a combination of the above features that supported the cohort’ssuccessful development of subject knowledge.

6. Teacher professional development in early career

Overall, this research has suggested that trainees’ perceptions of mathematics, their emotionalresponses to the subject and to the e-environment in which they learned and extended their subjectknowledge, all appeared to play a part in a successful outcome. The challenge beyond qualifyingis for teachers to maintain their confidence in their mathematics subject knowledge, extend thatknowledge and continue to enhance their teaching skills and professional practice.

The responses of the cohort as qualified teachers in the third year of their teaching careerraises some interesting points for those planning teacher professional development.

Of the cohort, 87.4 % (see Table 4) reported improvements in their subject knowledge duringthe first years of teaching and identified number and algebra, geometry and algebra and, statisticsand measure as the strongest areas. Given the emphasis in the national curriculum on theseaspects of mathematics this was not surprising and, indeed, there appears to have been little shiftfrom their areas of mathematical strength at the end of their training. Teachers also identified arange of strategies undertaken during their early years of teaching to improve their understanding(see Table 7), illustrating a commitment to ongoing professional development in this area. Thisperiod also coincided with a period of training for the introduction of the National NumeracyStrategy which would account for the high levels of external and school-based INSET linkedtraining reported by the teachers.

Conventional modes of teacher professional development, such as school-based and externalin-service training and published materials, remained the most commonly accessed strategies byteachers in post (93.7%, 87.3% and 85.7% respectively) and received the highest ratings in termsof usefulness (95.2%, 96.8% and 98.4%) (see Tables 7 and 8). Given this cohort’s positive expe-rience of e-learning as trainees, there was little indication that this was a preferred professionaldevelopment strategy in the first teaching years, with only 57.1% reporting use of teacher specifice-environments and 47.6% rating it as useful. Given the features rated most strongly in terms ofthis model, including peer and tutor support and structured support for individualised progress,this response may be a comment on the design and purpose of current teacher websites. Over half,60.3% of the cohort, continued to use their initial teacher training materials to support their ongo-ing professional development, which suggested these continued to be viewed as a useful resource.

Table 5. Percentage respondents rating confidence in personal mathematics subject knowledge to informally support other teachers in teaching mathematics?

Confidence in personal subject knowledge to support other teachers in teaching matters

Not very confident

1 2Confident

3 4Very confident

5

% (no. of respondents) 3.2 (2) 0 (0) 28.6 (18) 41.3 (26) 27.0 (17)


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Maintaining and developing subject knowledge as a practising teacher was not universallyrecognised by the qualified teachers in this study, as their teaching roles were not seen as demand-ing in this respect. Here, there was a difference between Key Stage 1 and Key Stage 2 teachers.The former were less inclined to value a breadth of personal subject knowledge extending beyondthat directly relevant to teaching their specific 5–7 age range. However, it was revealing to notethat 96.9% of teachers felt confident informally supporting other teachers in teaching mathemat-ics and 81.0% felt confident to undertake more formal support, for example through leadingschool-based training (see Tables 5 and 6). This may have implications for the future of school-based initial teacher training, where these teachers might be able to play a stronger role than iscurrently expected of mentors in subject knowledge training. It also suggests there is a developingreservoir of teachers who feel confident to engage in supporting the professional development ofcolleagues, though presumably only in the specific context of KS1 or KS2 content as specified in

Table 7. Percentage respondents using identified strategies to develop personal mathematics SK post qualifying.

Strategies used to develop personal subject knowledge (mathematics) % (no. of respondents)

School-based INSET 93.7 (59)Published material 87.3 (55)External INSET 85.7 (54)OU PGCE materials 60.3 (38)OU PGCE Peer support 60.3 (38)E-conferences for teachers 57.1 (36)OU PGCE alumni e-conference 54.0 (34)

Table 6. Percentage respondents rating confidence in personal mathematics subject knowledge to formally support other teachers in teaching mathematics (e.g. leading school-based training)?

Confidence in personal subject knowledge to support other teachers in teaching mathematics

Not very confident1 2

Confident3 4

Very confident5


Table 8. Percentage respondents rating usefulness of strategies in developing personal mathematics subject knowledge post qualifying.

Usefulness of strategies in developing personal subject knowledge (mathematics) % (no. of respondents)

Published material 98.4 (62)External INSET 96.8 (61)School-based INSET 95.2 (60)OU PGCE training materials 50.8 (32)OU PGCE Peer support 50.8(32)E-conferences for teachers 47.6 (30)OU PGCE alumni e-conference 17.5 (11)

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the national curriculum. This would seem to accord with the national proposals (TTA 2004a) toprioritise the collaborative nature of teacher professional development.

7. Conclusion

This study makes a significant contribution to the debate on teacher education pedagogy(Edwards and Ogden 1998). In the context of a continuing national and international emphasison mathematics subject knowledge for primary teachers, the study has identified the combina-tion of features of a subject knowledge development model, including focused tutor and peersupport in an e-environment that successfully supported teacher trainees, including those withlow entry levels of personal subject knowledge, to achieve the national subject knowledgestandards required for qualified teacher status (DfEE 1998a). Specifically, we would identifythe focused tutor support, the coaching with individual students and peer support as elementsof the model that were particularly valuable. In addition, the philosophy upon which themodel was based, to build personal confidence in the trainees as learners first and, then, asteachers was key to determining successful outcomes in mathematical subject knowledgedevelopment.

The research indicated that the teachers preferred model of learning involves an integrationof subject knowledge training, with classroom pedagogy and this was particularly evident in theresponses from teachers of the 5–7 age range. These teachers considered that some of the subjectknowledge they had been required to learn, in response to the requirements of national standards,was not relevant to their teaching of very young children.

Our analysis of the subject knowledge development model in the context of other researchsuggests significant features that can support trainee learning, particularly through enhancingself-confidence in mathematics. A key feature in the learning processes in the electronic environ-ment was the support, advice and knowledge gained and shared between trainees. The majorityof teachers in this study continued to use these e-learning conferences, after they had completedthe programme, to remain in contact with each other for the purposes of mutual professionalsupport. Though not directly attributable to the model, it is noted that the majority of teachers inthis study demonstrated the self-confidence to take on a professional development role, in orderto support their colleagues in schools.

Peer support, tutor mentoring and coaching can be successfully embedded in e-learning envi-ronments and, as part of a future national strategy for teacher professional development, mightenhance continuous learning for practising teachers. However, the analysis showed that moreteachers had continued their professional development through conventional face-to-face trainingthan e-learning.

Finally, it should be noted that this study has shown that trainees with a broad range of entryqualifications can achieve equally good subject knowledge outcomes. The evidence from thequalified teachers in this study indicates that such trainees do maintain high levels of confidencein their subject teaching in the early years of their teaching careers. This has implications forgovernment policies on setting entry requirements to teacher training programmes and futureprofessional development for practising teachers.

This article makes a significant contribution to the debate on recruitment to initialteacher training programmes, where contrary to the current emphasis on selecting candi-dates based on good entry qualifications, our research suggests that applicants with weakentry qualifications can achieve equally good subject knowledge outcomes. It also suggestsa way forward for those involved in developing mathematics subject knowledge both withtrainees and practising teachers and one which, at the same time, enhances personal confi-dence in mathematics teaching. The underpinning philosophy of the model was based on

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encouraging confidence in both learning and teaching mathematics. The model allowedtrainees to develop their subject knowledge at their own pace and addressed specificrequirements drawn from a personal audit. The e-learning environment proved to besupportive to the trainees during the programme and, afterwards, when they were teachersas many continued to share ideas with their peers. It is evident that professional develop-ment programmes would benefit from including an e-environment of structured support forboth trainees and practising teachers, thus leading to more confident learners and teachers ofprimary mathematics.

Notes on Contributors

Dr Hilary Burgess is Director for Postgraduate Studies in the Centre for Research in Education and Educa-tional Technology (CREET), at the Open University. Her research and publications are in the areas ofprimary school teaching and teacher professional development and mentoring in primary and secondaryschools. She joined The Open University in 1993 and initially worked as a PGCE Staff Tutor in the SouthRegion. Previously, she was a Senior Lecturer at Westhill College in Birmingham and has taught in primaryschools in Coventry and Inner London.

Professor Ann Shelton Mayes is Dean of School of Education, The University of Northampton. She wasformerly a deputy head in a secondary comprehensive school and Director of Initial Teacher TrainingProgrammes at the Open University. Her career in higher education has focused on teacher professionaldevelopment – pre-service and postgraduate – and she has published in the area of distance education ande-learning, mentoring, professional standards, initial teacher training and the wider school workforce. Shehas been involved in international projects in Africa and USA developing distance learning approaches forteacher education.

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