Primary Teacher Trainees’ Mathematics Subject knowledge and Classroom Performance

**Tim Rowland, Sarah Martyn, Patti Barber,
Caroline Heal**

Institute of Education, University of London

Paper presented at the British Educational Research Association Annual Conference, University of Sussex at Brighton, September 2-5 1999

UK government agencies have recently set in train requirements to ‘crack down’ on primary [elementary] school teacher trainees whose own knowledge of mathematics is weak. The responsibility to identify and support (or fail) them currently rests with training providers (mainly university schools of education). We describe one approach to this process and some findings concerning what trainees find difficult and how their knowledge is related to their teaching competence. We flesh out these findings with a case study of a mathematically-strong trainee whose path to qualification was less than smooth.

Recent changes in the curriculum for Initial Teacher Training incorporate a stronger
focus on trainees’ subject knowledge (DfEE, 1997). Some evidence would seem to
support this shift of emphasis. In the US, Kennedy’s research (1991) suggested that
teachers’ mathematical understanding is frequently limited, whilst in the UK
Alexander *et al.* (1992) called for improvement of the knowledge base of teachers in
order to improve the teaching of mathematics. Inspection evidence identifies
teachers’ lack of subject knowledge and confidence in mathematics as being a
contributory factor in low standards of mathematics attainment of pupils (Ofsted, 1994).

Circular 10/97 (DfEE, 1997)(1) sets out what is considered to be the "knowledge and understanding of mathematics that trainees need in order to underpin effective teaching of mathematics at primary level". Since September 1998, audit and remediation of students’ subject knowledge has been statutory.

All providers of ITT must audit trainees’ knowledge and understanding of the mathematics contained in the National Curriculum programmes of study for mathematics at KS1 and KS2, and that specified in paragraph 13 of this document. Where gaps in trainees’ subject knowledge are identified, providers of ITT must make arrangements to ensure that trainees gain that knowledge during the course …(DfEE, 1997, p. 27)

At the Institute of Education, we piloted the new ITT curriculum one year ahead of time. In this paper, we describe our approach to the audit of the mathematics subject knowledge of a cohort of 154 trainees following a one-year primary PGCE course. We present some findings related to a number of different aspects of our research.

APPROACH AND TIMING

The structure of the primary PGCE at the Institute of Education is perhaps unusual, in that the methods course for each core curriculum subject is taught in three intensive 5- or 6-day blocks, one in each term. The blocks for mathematics are timetabled first in each term, so that by the middle of January, with fully six months of the course remaining, the main content areas - number concepts and operations, data handling, mathematical processes, shape and space, measures, algebra, probability - have been ‘covered’ in lectures and workshops. This therefore seemed to us to be the optimum moment for an audit of subject knowledge, giving the trainees maximum opportunity and professional motivation to recall those topics they had forgotten (for lack of use) since they did mathematics at school.

A 11/2 hour written assessment consisting of 16 test items in mathematics was therefore administered at this point of the course. Trainees had been given notice of the ‘test’ and a revision syllabus some six weeks earlier. Their response to each question included a self-assessment of their ability to complete it successfully. The scripts were marked and the response to each question coded either: secure, possibly secure, not secure. The middle category was created in recognition of the difficulty (resolved later) of making confident inferences from some of the written responses. Corresponding scores of 2, 1 and 0 respectively were recorded for each question and each student. In mid-February, an individual audit feedback sheet was returned to each student, with guidance (where appropriate) for further study.

39 students (about 25% of the cohort) who had been found to be secure in 15 or more of the 16 topics audited were invited to become mathematics peer tutors. Following training for this task, they conducted one-to-one peer tutoring sessions with all other students (on average, three per peer tutor) in April, writing a feedback sheet on each of their tutees.

TRAINEES’ MATHEMATICAL THINKING

One dimension of our research is to identify what mathematics (within the remit of Circular 10/97) primary trainees find difficult, and the nature of their errors and misconceptions in these areas. Facilities in the four ‘easiest’ and ‘hardest’ of the 16 items audited were as follows:

HIGHEST FACILITY |
LOWEST FACILITY |
|||||||

% secure |
Mean score |
TOPIC | % secure |
Mean score |
TOPIC | |||

94 |
1.92 |
Ordering decimals | 63 |
1.46 |
Generalisation | |||

94 |
1.92 |
Inverse operations | 60 |
1.40 |
Pythagoras, area | |||

90 |
1.86 |
Divide 4-digit number by 2-digit | 43 |
1.17 |
Reasoning, argument | |||

89 |
1.85 |
Order fractions | 40 |
0.95 |
Scale factors, percentage increase |