finding out more about teacher candidates' prior knowledge: implications for teacher educators
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Finding out more about teachercandidates' prior knowledge:implications for teacher educatorsFiona Ell a , Mary Hill a & Lexie Grudnoff aa University of Auckland , Auckland , New ZealandPublished online: 24 Jan 2012.
To cite this article: Fiona Ell , Mary Hill & Lexie Grudnoff (2012) Finding out more about teachercandidates' prior knowledge: implications for teacher educators, Asia-Pacific Journal of TeacherEducation, 40:1, 55-65, DOI: 10.1080/1359866X.2011.643760
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Asia-Pacific Journal of Teacher EducationVol. 40, No. 1, February 2012, 55–65
Finding out more about teacher candidates’ prior knowledge:implications for teacher educators
Fiona Ell*, Mary Hill and Lexie Grudnoff
University of Auckland, Auckland, New Zealand
(Received 25 July 2010; final version received 4 October 2011)
While it is recognised that prior knowledge is a key factor in determining futurelearning, its influence on learning to teach is less well known. This study investigatestwo cohorts of teacher candidates studying for a one-year, graduate qualification forprimary teaching, who completed two tasks at entry to their initial teacher educationprogramme: a task in writing and a task in mathematics. The tasks focused on teachercandidates’ ability to recognise the key features of a piece of student work. The teachercandidates’ responses to the tasks highlighted the diverse nature of the prior knowledgethat underpinned their responses. The study raises questions about the pedagogy ofinitial teacher education, particularly in relation to the assumptions teachers educatorsmake about the candidates they teach. The findings suggest that the prior knowledgethat students bring to initial teacher education is both a resource and a challenge forteacher educators.
Keywords: formative assessment; teacher knowledge; initial teacher education
Theoretical framework and rationale
This study considers the role of teacher candidate prior knowledge in performing two teach-ing tasks, one in each of two subject contexts – mathematics and writing. We had two keypremises in undertaking this study: firstly, that prior knowledge has a significant role to playin learning, and therefore in learning to teach, and secondly, that being able to recognisekey features of student work is an important task for teachers who want to enable learningin their classrooms.
Prior knowledge and learning to teach
We focused on prior knowledge because of its established role in influencing learning(Bransford, Brown, & Cocking, 2000). Teacher candidates come to teacher education asadults, with their own history as learners, as well as the subject matter knowledge they havegained through their education. In-depth study of the nature of subject matter knowledgefor teaching has shown that it differs from the subject matter knowledge held by teachercandidates that have studied particular subjects as learners (Ball, Thames, & Phelps, 2008;Hill et al., 2008). Prior knowledge may be helpful in this process, or it may hinder the devel-opment of understanding subject content from a learner’s perspective (Ball & Bass, 2000).In a similar way, the idea that past experience of the education system as a learner is anunhelpful ‘apprenticeship of observation’ (Lortie, 1975) is pervasive. Teacher candidates
*Corresponding author. Email: [email protected]
ISSN 1359-866X print/ISSN 1469-2945 online© 2012 Australian Teacher Education Associationhttp://dx.doi.org/10.1080/1359866X.2011.643760http://www.tandfonline.com
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are seen as likely to reproduce in their practice what they experienced themselves as learn-ers. The nature of teacher candidates’ prior knowledge about teaching and learning couldbe an important influence on what they learn in teacher education.
The influence of teacher candidates’ prior knowledge and preconceptions has beenexamined by some researchers. These studies tend to look at attitudes, beliefs, and dispo-sitions (Hollingsworth, 1989; Wubbels, 1992). Wideen, Mayer-Smith, and Moon’s (1998)review of this literature suggests that teacher candidates’ preconceptions are hugely vari-able and hugely powerful. Studies that examine teacher candidates’ knowledge or skills areinfrequent. Stofflet and Stoddart (1994) investigated teacher candidates’ science knowledgeand its influence on acquiring conceptual change pedagogy – a way of teaching sciencethat was in contrast with their learning experiences. The teacher candidates were found tohave weak understandings at entry, but those who experienced science instruction throughconceptual change pedagogy were more likely to adopt it in their own lesson planning.
In this study we wanted to look beyond subject matter knowledge to investigate whetherteacher candidates held prior knowledge about teaching and learning. This prior knowledgemight contain facts, experiences, expectations and preconceptions, and be held as knowl-edge, skills or beliefs about teaching and learning. In particular we wanted to find outwhether prior knowledge of teaching and learning would be evidenced through completinga task that teachers frequently engage in – recognising the key features of student work.
Assessment practices as key tools in effective teaching
Formative assessment practices are frequently hailed as high-leverage practices that canimpact student achievement (Alton-Lee, 2003; Black & Wiliam, 1998; Hattie, 2009).This is echoed in calls for teacher education to concentrate on establishing such practices(Shepard, Hammerness, Darling-Hammond, & Rust, 2005). Formative assessment practicescall on a range of knowledge and skills that can be characterised as particular to teaching(Bell & Cowie, 2002).
Cowie and Bell (1999) introduced a model for understanding teachers’ role in for-mative assessment. Their analyses of teacher practices yielded two analogous cycles –one for planned assessment events and one for unplanned or ‘interactive’ assessmentevents. Interactive assessment occurs as part of ongoing learning activities that studentsare involved in. In this cycle teachers must first notice that something is occurring, thenrecognise its significance, and then respond appropriately. Recognising is about identify-ing the key features of the students’ work or actions and seeing them as an example ofsomething that has significance for their learning.
The focus of this study
This study focuses on one small part of the complex skills and understandings that teachersneed in order to assess formatively in their classrooms: recognising the key features of stu-dent work. Bell and Cowie’s (2002) respondents highlighted that recognising is a teacherskill, informed by knowledge and experience particular to teaching. For this reason theinferences that a teacher might draw from something that a child does in writing or math-ematics are likely to differ from those that a layperson might draw. We hypothesised thatthe teacher candidates would not have the knowledge or skill to recognise what teacherswould recognise in the student work. We expected them to respond as laypeople, bring-ing common-sense understandings to the task, rather than the knowledge that a teacherwould bring. Work on the importance of prior knowledge (Bransford et al., 2000) suggests
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that this could be a significant influence on what the teacher candidates gained from theirsubsequent teacher education.
Method
Participants
The participants in this study were teacher candidates, enrolled in a one-year professionalpreparation course for those who already hold degrees and wish to teach in Year 0–8 class-rooms. All teacher candidates enrolled in the course in 2007 and 2008 were invited toparticipate (N = 230). In 2007, 59 of 120 teacher candidates completed both the mathe-matics and writing tasks. In 2008, 44 of 110 teacher candidates completed both tasks. Thetwo obtained samples’ performance on the recognising task were not significantly different(for mathematics: c2 = (1, n = 103) = 0.1, p = 0.949; for writing: c2 = (1, n = 103) = 0.9,p = 0.635), so the results for the two cohorts were combined.
This study was approved by the Human Participants Ethics Committee of ourUniversity, and all participants gave informed, written consent for participation.
Materials
The participants completed two tasks designed to assess their ability to recognise key fea-tures of student work. They represented the results of genuine teaching tasks that teachercandidates could respond to in written form. The teacher candidates were asked to iden-tify what they thought was significant or important about each student’s performance.In terms of Bell and Cowie’s (2002) model, we were interested to know whether theteacher candidates could recognise the significance of each child’s performance on eachtask. We anticipated that both tasks might have a ‘layperson’ response and an ‘expertteacher’ response. For an expert teacher’s response in the mathematics task, teacher can-didates needed to realise that more than the ‘right answer’ was needed, and that the waysstudents came to their answers mattered. In writing, the teacher candidates needed to realisethat the deep features of the student’s writing were very significant for the next teachingsteps in the selected sample. It was anticipated that teacher candidates would initially focuson the surface characteristics of the sample, without recognising these deep features.
Mathematics
The mathematics recognition task presented the teacher candidates with a snapshot of stu-dents’ oral responses to a simple addition question. The students’ responses were presentedas a cartoon (see Figure 1 below). All the students in the cartoon gave the correct answerto the equation, but the responses differed in important ways that would be evident to anexpert teacher of mathematics. The students used different strategies which revealed theirconceptual understanding of addition. Recognising the nature and efficacy of the strategiesstudents use is an important starting point for determining their next learning (Fraivillig,Murphy, & Fuson, 1999).
The three strategies these three students used are clearly linked to the New ZealandCurriculum’s (Ministry of Education, 2007) description of progress in mathematical think-ing. Each strategy is importantly different and has instructional implications (Fraivilliget al., 1999). Thus teacher candidates who recognised that the difference betweenthe strategies was important were responding like teachers who had this knowledge.Recognising the difference between strategies was thus termed ‘expert’.
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Three children in a group that you are teaching are working out the answer to 8 +7. They all get the right answer.
When you ask them how they did it, they say:
I counted in myhead:1, 2, 3, 4, 5, 6,7, 8,and then 9, 10, 11,12, 13, 14, 15.
I know that 8 and 8are 16, so eight andseven must be oneless – 15.
Does it matter that they did it different ways if they all got the right answer? Why /why not?
I started with 8 becausethat’s first and I counted9, 10, 11, 12, 13, 14, 15.
Figure 1. The mathematics task.
The teacher candidates’ responses were coded as either recognising or not recognisingthe difference between the strategies. The reliability of this distinction was estimated by tworaters judging participants’ responses that are not included in this study (those who onlycompleted the mathematics task, n = 29). The structure of the task meant that this codingwas straightforward, and high inter-rater agreement was established (over 95%). There werefew difficult-to-code responses in the data set, and these were coded by consensus betweenthe two raters.
Writing
The writing task was based on an exemplar of children’s work sourced from the NewZealand Ministry of Education’s exemplar project (‘Table Manners, Poetic Writing:Character and Personal Experience’, Ministry of Education, 2008). The sample of writing,in the child’s handwriting, was given to the teacher candidates with the prompt: ‘Describewhat you think are the most important features of this child’s writing.’
To establish what a knowledgeable teacher response to this task would be, the teachercandidates’ responses were compared with the Ministry of Education’s summary ‘Whatthe Work Shows’ that accompanies the exemplar (http://www.tki.org.nz/r/assessment/exemplars/eng/personal/wpp_2a_e.php). The exemplars and their summaries were writtenby a team of experts, and are resources that are used throughout New Zealand for bench-marking children’s writing. Therefore, the ‘What the Work Shows’ summary was deemedto be an example of what knowledgeable teachers would note about the writing, and thedegree of match between the teacher candidates’ responses and the exemplar statementwould give a measure of the teacher candidates’ ability to recognise key features of thewriting as a knowledgeable teacher would.
The teacher candidates’ responses to the task were coded by assigning them tocategories used by the Ministry of Education in its advice to teachers, assessment tools and
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resources (http://www.tki.org.nz/r/assessment/exemplars/eng/matrices/matrx_pi_about_e.php). These categories were spelling, grammar and punctuation (surface features) andimpact, voice, ideas, sentences, structure, vocabulary, and language features (deepfeatures).
To estimate the reliability of these coding decisions, two raters coded the answers ofparticipants who completed only the writing task and were therefore not included in thisstudy (n = 31). The percentage of agreement across the ratings was 86%. Therefore theresponses of participants in this study were coded by one of the raters, with any hard-to-code responses being considered by both raters and agreement reached. A three-pointrubric was used to categorise the responses. Participants who gave no response were coded0. Participants who only recognised surface features were coded 1 and participants whorecognised the deep features highlighted by the exemplar description (and who may havealso recognised surface features) were coded 2. This coding is summarised in the rubricgiven in Table 1. Recognising relevant deep features as well as surface features (2) wastermed ‘expert’ for this task.
Procedure
The teacher candidates completed the two tasks on the first day of their programme of study,before they had received any explicit instruction from the university.
Results
The results of this study are presented in two sections. The first section considers the ques-tion: Do teacher candidates have prior knowledge of subjects, students and learning thatallows them to recognise the key features of the student work before they begin initialteacher education? The second section describes in some depth the responses they gave tothe performance of each task.
Teacher candidates’ ability to recognise at entry to initial teacher education
This study conjectured that, because of the teacher knowledge required to recognise the keyfeatures of student work as an expert would, teacher candidates at entry to teacher educationwould produce few expert responses. In fact, in both mathematics and writing around halfthe teacher candidates recognised the key features outlined by the experts. Table 2 showsthe number and percentage of participants who gave expert and non-expert responses to themathematics task, and Table 3 shows the same information for writing.
Table 1. Coding rubric for responses to the writing task.
Score Criteria
0 No response1 Response focuses on surface features only, or on irrelevant features such as neatness,
putting a date or cursive handwriting.2 Response mentions deep features as well as surface features. Includes mention of one
of: audience, humour, voice, personal significance of ideas, sentencing or structure.
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Table 2. The number and percentage of teacher candidates who, at entry to teachereducation, gave expert and non-expert responses to the mathematics recognition task.
Response type Response n %
EXPERT Recognised strategy significance 50 47%NON-EXPERT Did not recognise strategy significance 57 53%
Table 3. The number and percentage of teacher candidates who, at entry to teachereducation, gave expert and non-expert responses to the writing recognition task.
Response type Response n %
EXPERT Deep and surface features 56 55%NON-EXPERT Surface/irrelevant response/NR 45 45%
Teacher candidates’ responses to the recognising tasks
The range of responses given by teacher candidates to the recognising tasks gives a pic-ture of the prior knowledge about learning and teaching they are bringing to their teachereducation programme. Key themes from the teacher candidates’ responses are now exem-plified to show how particular types of prior knowledge exist which might impact learningto teach.
Responses to the mathematics exemplar
All the participants responded to the mathematics task. Teacher candidates who did notfeel there was an important difference between the strategies commonly invoked the ideaof ‘learning styles’ as an explanation:
No, each individual has different learning styles – the main thing is that they got the rightanswer using a method that works. (PN 29)
No, there are lots of different learning styles. (PN 45)
No it doesn’t matter, they learn different ways but all had the correct outcome. (PN 48)
Not at all. All people have different learning styles. (PN13)
This explanation is potentially problematic as it has been found to limit teachers’ expec-tations of students and could lead to not intervening if students continue to use inefficientstrategies (Alton-Lee, 2003). An implication of the ‘learning styles’ view is that nothingshould be done to change the way the student tackles the problem.
Some students identified that the strategies were importantly different, using speed andthe problems of larger numbers as justification:
It would be good if the child could work out the answer using a quick method rather thancounting on. (PN 15)
Yes it does matter because the two that are counting will take much longer and it will not helpthem if they are adding up bigger numbers. (PN 34)
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They would have problems starting with bigger numbers – longer to do if they counted in theirheads. (PN 133)
As teachers we can help simplify and quicken the thinking process to help children think likethe child that is adding. (PN 126).
These responses show an understanding that the counting strategies are not very effi-cient, and will eventually result in overload if larger numbers are used. This is a useful wayto think about the strategies in the task, as it identifies that there is a need for teaching.In the view of these teacher candidates, something can and should be done.
A further group of teacher candidates went beyond the utility of faster and more effi-cient strategies to seeing the children’s responses as indicative of depth of mathematicalthinking:
It indicates different levels of mathematical thinking. (PN 107)
It proves that there are processes of figuring out solutions. Children have the ability and capac-ity of deeper and more complex methods of problem solving so to leave the counting studentsat their present level of problem solving would be a problem. Ideally all the children would beable to answer the question the way that the third student did. (PN 82)
The strategies that are used in getting to the answer vary in complexity, speed and depth ofunderstanding of the mathematical concepts. (PN 98)
These responses show a more sophisticated understanding of the strategies than weexpected in our teacher candidates before they began their courses. These three teachercandidates recognise that the strategies are more than just a superficial problem solvingstrategy; they are indicative of the children’s mathematical thinking.
The two justifications outlined above – speed/efficiency and depth of mathematicalthinking – will both be aligned with the content that the teacher candidates will be taughtin their mathematics education courses, potentially advantaging these teacher candidateswhen their courses start. There were some more problematic justifications given, however,that will need to be addressed in teacher education. Two examples of this are:
A teacher may have a method or rule that can be applied to other maths problems. If they alllearn this rule maths may be easier for them in the future. (PN 86)
If you have taught them a certain way you would hope that they would get the answer in the waythat you taught them. It shows that the teaching that you have taught has not been understood.(PN 72)
Both of these justifications focus on the need to follow rules and do it the way theteacher says in mathematics. Teacher candidates who see mathematics as a series of rulesto be acquired will find themselves at odds with the intention of the New Zealand curricu-lum and the orientation of their mathematics education courses, whereas teacher candidateswho see the differences as indicative of depth of thinking may not experience thisdissonance.
Responses to the writing exemplar
Teacher candidates found the writing exemplar more difficult to respond to than the math-ematics task. Nineteen per cent of the participants wrote ‘I don’t know’ or left the question
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blank. Most of the teacher candidates who recognised the deep features of the writingpicked up on the importance of the child’s voice, and the depth of description that the childprovided. Their first instinct was to acknowledge the message that the writing conveyed.This is exemplified by these responses:
I think an important feature of the child’s writing is their ability to describe and explain thestory in complete sentences in a clear and coherent way. (PN 124)
They can describe an event and something that is real to them. (PN 33)
That the story flows and makes sense. The child is describing in detail what it is like to visittheir grandparents. (PN 23)
Their thoughts and the message are very clear. They also express a sense of humour. (PN 130)
The writer has a wonderful chatty voice. (PN 98)
In contrast, the teacher candidates who did not recognise the deep features felt thatsurface features were the most important aspect of the writing:
The writing is neat and tidy and there are spaces left for the teacher to correct spelling andgrammar. (PN 133)
Spelling is incorrect. (PN 29)
They repeat a lot of spelling errors. (PN 46)
Nice writing. Largely correct. (PN 4)
Legible. Spelling and grammar need work. (PN 132)
These contrasting sets of comments illustrate how the prior knowledge of the teachercandidates could influence their learning to teach. The teacher candidates who show aware-ness of the importance of deep features are already aligned with the literacy teachereducation they will receive. Those who could not respond or are focused on surface featuresmay have more to learn about how to evaluate children’s writing.
Two further comments from teacher candidates focused on the lack of imagination inthe piece of writing. These recognition comments suggest that the teacher candidates feelthat children’s writing should be imaginative. This prior knowledge has implications fortheir learning to teach a curriculum that values a range of genre.
Able to tell the events but not using imaginative writing about the events. (PN 127)
The child’s writing is very formal and shows a strong desire to get it right. The strictness of thechild’s background (as possibly indicated by the content – table manners, serviettes) inhibitsimaginative expression. (PN 24)
The second response is also interesting because assumptions about the child and his orher background have also been made from this small writing sample.
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Discussion
Our initial hypothesis about teacher candidates’ ability to recognise the key features of stu-dent work was that they would not be able to do so in the same way as a teacher. We expectedthe teacher candidates to respond as ‘non-experts’. Our findings show that we were par-tially incorrect. In both the mathematics and writing tasks, approximately half the teachercandidates were more competent than we expected.
The study is limited by several factors. Only half the teacher candidates from eachcohort participated in the study, and this may have affected the results. More confident orknowledgeable teacher candidates may have volunteered to participate, inflating the propor-tion of students who appeared to have prior knowledge in the task areas. Furthermore, thetasks themselves are limited in scope. While they stimulated interesting and unexpectedresponses, they represent only a tiny part of the formative assessment process. In futurestudies it would be helpful to give participants a range of tasks that could be triangulated toform a more robust picture of the teacher candidates’ prior knowledge. This could includeitems about teacher candidates’ attitudes to assessment and demographic information abouttheir prior studies and experience with children.
The concept of formative assessment as a set of skills, knowledge and dispositionsneeds further attention. This paper argues that if teacher candidates could recognise thekey features of the student work samples at entry to teacher education, then they might bebetter placed to learn to use formative assessment practices, with all their attendant skillsand dispositions. Further investigation is needed to find out if this is the case. Of particularinterest is the link between knowing the educational importance of something a studentdoes, and reacting to it in a way that causes learning. This study only begins to raise ques-tions about teacher candidates’ prior knowledge in order to promote a richer view of ourteacher candidates and what they bring to their teacher education.
The importance of prior knowledge to the learning process of children is widelyaccepted (Bransford et al., 2000). Common sense suggests that it will be an even moresignificant influence on adult learning, as adults have more prior experience to bring tolearning situations. In tertiary institutions, however, the ‘one size fits all’ approach to attain-ing a teaching qualification assumes that teacher candidates know little or nothing aboutteaching. Bransford et al.’s (2000) principles of learning emphasise the attainment of deepfactual knowledge that is conceptually organised. For teacher candidates this needs to beknowledge of teaching and learning as well as knowledge of subject matter. The findingsof this study suggest that some teacher candidates come to teacher education with helpfulprior knowledge about teaching and learning, not just with conservative views based ontheir own experiences (Lortie, 1975; Stofflet & Stoddart, 1994).
The examples of the teacher candidates’ responses to the tasks reveal a wide range ofprior knowledge. For example, some teacher candidates in mathematics are already focusedon depth of mathematical thinking; some believe it is all right for students to use whatevermethods they like. As teacher educators we saw that these groups have different needs.Without this information about the teacher candidates we were assuming that they wereunaware of the importance of strategies in children’s mathematical development. We haveteacher candidates who could extend their thinking beyond our current expectations whilesome may require extra help and different experiences. There may also be key miscon-ceptions, such as the importance of rules in mathematics, which need specific challenge(Korthagen & Kessels, 1999).
This study revealed that our assumptions about our teacher candidates were problem-atic. These assumptions have important consequences for what and how we teach. The
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content of our courses requires consideration, and our pedagogical approaches require con-sideration. Using the prior knowledge of our teacher candidates to enhance their learningin the university classroom requires both course content that will engage their knowledgeand allow them to apply it, and opportunities to share knowledge through discussion andcooperative group work. For example, knowing more about the range of prior knowledgethat we have in our cohorts allows us to group teacher candidates to learn from each other,as well as from faculty staff, creating a learning community that better utilises the expertiseof the group. When we design courses we need to consider both extending thinking andscaffolding teacher candidates’ learning. University courses tend to have defined contentand assessments that assume the material is new to all students. This poses a challengefor teacher educators who want to be responsive to the prior knowledge of their teachercandidates. Utilising a team-based learning model (Michaelsen, Knight, & Fink, 2002), ortaking an inquiry approach to their subject matter (Aitken & Sinnema, 2008) may enableteacher educators to make more use of teacher candidate expertise.
Teacher candidates come to teacher education with prior knowledge that can help orhinder their development as teachers (Bransford et al., 2000). Teacher education has ambi-tious goals. Teacher candidates’ prior knowledge is a resource that can be harnessed in theservice of these goals. The findings of this study suggest that teacher educators, and there-fore teacher education, could benefit from understanding more about teacher candidateprior knowledge.
AcknowledgementsWe would like to acknowledge the contributions of Associate Professor Graeme Aitken and Dr DeidreLe Fevre to this work.
Notes on contributorsFiona Ell is a lecturer in the Faculty of Education at the University of Auckland. Her research focuseson initial teacher education, often in the context of mathematics education.
Mary Hill is Associate Professor in the Faculty of Education, University of Auckland, where sheteaches educational assessment and investigates teacher learning in assessment.
Lexie Grudnoff is Director of Teacher Education at the University of Auckland. Her research interestsfocus on initial teacher education and beginning teacher learning and development.
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