**Abstract**

*This paper brings
together data from two research projects concerned with assessment in school
mathematics. It is an attempt to combine data and analysis focusing on
the selection of pupils for certain mathematical experiences within school
classrooms and their subsequent test entry levels. Highlighting the teacher,
connections are made between the external system of national testing and
internal formative assessment in continual process during schooling. Data
from a recent ESRC is used to examine different school practices for pupil
test entry. Behind the resulting official statistics of examination performance
- the public, lie the everyday practices in the maths classroom - the private.
Insights from an ethnographic study of secondary school mathematics classes
are used to elucidate some aspects of this private life. In bringing these
two elements together this paper highlights both the overt and covert influence
that teachers still have on the test results of their pupils.*

**Introduction**

The historical context of the two research studies in this paper is a period in which a conservative agenda, initially sponsored by the New Right was set up to gradually displace liberal progressive educational ideology (Ball, 1990; 1994). The emphasis behind this effort to reconstitute state educational provision has continued into the late 90’s despite a change of national government. The incremental establishment of this conservative educational agenda has been effected by changes in the detail and emphases of teachers’ work, a changing balance of activities and priorities (Brown, 1992) supported by the introduction of a different educational discourse around the problematics of everyday life in schools (Dunne, 1994). The pressures on teachers to make the transition from progressive to conservative are both coercive and obvious in terms of particular innovations and legislation eg the National Curriculum (NC) or the Teachers Pay and Conditions Act 1986, but they are also pervasive and subtle.

The National Curriculum (NC) and Key Stage (KS) Assessment at ages 7, 11, 14 and 16 were introduced through the Education Act 1988. This has led to the establishment of annual national testing of pupils at each of these four Key Stages. School and teacher accountability measures, other features of the educational reform, have given rise to enormous interest in school effectiveness. The publication of school league tables is an important element in the government efforts to raise standards and make schools more effective. With the emphasis on measurable school outcomes, these tables report the relevant KS test results for all state schools. As the teachers in our research studies observed, this focus on the national paper and pen test results has affected their pedagogy and teacher assessment practices. In relation to the latter, the teachers noted a diminished contribution of teacher assessed attainment levels to each pupils final KS result.

In this context, in
which teachers appear more distanced from the formal processes of pupil
assessment, this paper is concerned with the ways in which teachers still
have overt and covert influence on their pupils’ test results. Constraints
of space permit only a glossing of some of the most significant elements
of this argument which otherwise might be more elaborated and developed.
After a brief overview of the two research projects informing this paper,
I first look at the implications of particular school practices for pupil
entry to the different NC mathematics test levels at KS3. Following this,
I examine the ways in which teachers describe their formative assessment
practices taking place continually during mathematics classes with their
pupils. The focus here will be an analysis of mathematics teachers’ explanations
of the processes by which certain pupils are selected for particular classroom
experiences and ultimately particular levels of the National Curriculum
tests*. *The final picture that emerges shows how, despite major educational
reforms, teachers still have a highly significant influence on the public
grading of mathematics performance of their pupils.

**Research overview**

The data used in the next section derives from an ESRC study concerned with pupil interpretation and performance on KS2&3 NC tests in mathematics (Cooper and Dunne, 1997). At the KS3 level we collected three Nelson Cognitive Ability test scores (CATs) and the 1996 Mathematics National Curriculum test scores of 473 Year 9 children from three secondary schools. We also interviewed 15 teachers, concentrating on the school’s approach to mathematics and on teachers’ perspectives on the NC assessment and their pupils in their schools. The selection of schools was based upon providing a cross social class sample of children and a willingness of the school and mathematics teachers to be involved in the research project.

The second research
project was an ethnographic study undertaken from between 1991 - 1994 in
four state secondary schools. The data and analysis presented here were
obtained from a year of intensive school-based field work, followed by
continual periodic contact with four mathematics teachers from each school.
The use of formal and informal interviews were central to the data collection.
In the larger study a wide variety of data collection methods were employed.
The data presented and analysed in this paper derive predominantly from
the individual and group interviews with four mathematics teachers. Transcriptions
of each of these interviews were circulated to the teachers for comment.
The selection of the participating schools was based upon providing a broad
range of school contexts, in terms of social class and ethnic mix. All
school were co-educational to provide a gender mix. The final selection
was made to maximise the representation of different sex and ethnic groups
among the teachers. Both the schools and the teachers were volunteers.

**Public performance**

The tables and figures presented below are derived from a section of a recently completed ESRC project on mathematics assessment (Cooper and Dunne, 1997). In this paper I want to draw attention to school practices in relation to pupil KS3 mathematics test level entry. Decisions about examination entry are informed by mathematics teachers’ assessment of their pupils’ abilities which in turn are mediated by the mathematics department and/or school policy (whether formal or informal) in this regard. There are several factors above and beyond a concern for the individual child that might influence school policy regarding pupil entry. School examination results have implications for school / teacher accountability, the position of the school in the league tables and in the educational market place. Given that a pupils’ NC level is capped at the top of each test’s level range a school’s attitude to risk as well as its expectations of children will affect test entry decisions. Whatever the practice within each context, decisions on test level entry are underpinned and rationalized by teacher assessments of their pupils’ mathematical abilities relevant to the test.

It was evident from
this research that schools had different practices in relation to these
pupil entry decisions. Taking measured ability as an heuristic baseline,
schools differ in their allocation of children with given ability scores
to levels of the May 1996 tests. The example of non-verbal ability is shown
in Table 1 where it can be seen that the first school ‘requires’ a higher
CAT score for entry to the three major test levels than the other two.

SAT
3-5 taken |
SAT
4-6 taken |
SAT
5-7 taken |
SAT
6-8 taken |
|||||

Mean NV CAT score | Count | Mean NV CAT score | Count | Mean NV CAT score | Count | Mean NV CAT score | Count | |

School |
||||||||

D | 94.74 | 84 | 106.70 | 110 | 113.65 | 51 | 120.67 | 10 |

E | 85.46 | 39 | 99.60 | 50 | 109.09 | 11 | 126.50 | 2 |

F | 89.30 | 54 | 98.31 | 35 | 107.25 | 28 | n/a | 0 |

The higher ratios in
the first column bear out the tendency of School D to ‘under-enter’ children
relative to the others in our sample.

School
D |
School
E |
School
F |
||||

All
pupils |
Ratio | Count | Ratio | Count | Ratio | Count |

1.03 | 255 | 0.85 | 102 | 0.93 | 117 |

It is possible to push this analysis further through an exploration of the considerable overlap of scores on baskets of common items across neighbouring levels (e.g. 3-5, 4-6) of the May 1996 tests. As an illustration, the distribution of marks on the 61 common items are shown for the two groups entered for 3-5 and 4-6 in Figures 7 and 8. Ten children appear at the right of Figure 7 who were entered for the 3-5 test but who score better than the mean achieved by children entered for the 4-6 test (52.1). . This difficult area of level placement, critical to both school and pupil profiles, raises a threat to valid assessment inherent in the testing arrangements for KS3

Although they can hardly be expected to get selection for test levels ‘just right’, teacher judgements are key to the limits of their pupils’ possible KS level attainment. It should be noted, however, that these judgements are circumscribed by structures for the national testing from which, on the whole, mathematics teachers are distanced. Mediation at the institutional level, through school and mathematics department policy/practices are processes in which mathematics teachers have more direct but variable influence. Nevertheless, at the fundamental level, in the classroom, teachers clearly have an overt and pivotal role in the entry of their pupils to specific test levels.

Having touched upon
some of the problematics of the public life of test entry, I now move,
in the next section, to consider the private life of the classroom as the
context within which pupils are framed in terms of their mathematical ability
and teachers have a more covert role in their pupils’ NC test level entry.

**The private life
of teacher assessment**

An element of the educational reforms was the introduction of systems of school accountability, one net effect of which has been to highlight examination results as a measure of school effectiveness. Interviews with teachers from both projects elicited descriptions of resultant changes in pedagogy and assessment. The overwhelming majority of these teachers reported increased tendency to teach whole class lessons in a formal style, give tests and continually to reinforce basic mathematical operations. They also noted the diminished importance and independence of the Teacher Assessment level recorded for each pupil in the official NC test results. Despite these latter observations concerning the greater circumscription of teachers’ control over the mathematics curriculum and its assessment, there are still significant ways in which teachers make crucial decisions about the school mathematics experiences of individual pupils and the limits of their achievement level in public examinations. The previous section considered this influence in terms of the apparent school policy for examination entry. The rest of this paper will look at the processes of teacher assessment through a preliminary exploration of the social relations of the classroom. At issue here is an attempt to understand how teachers explain their part in grading their pupils. It is important to note here that this not a claim that mathematical ability is only constructed within the confines of the classroom or to suggest that there are no extra-situational components at work in the shaping of individual mathematical achievement.

In the initial phases
of this research with teachers it became evident that despite the divergence
in their responses to the changing material and ideological conditions
of their work, brought on by the educational reforms, there were also implicit
continuities. Hidden sets of social relations, part of the covert curriculum,
structure the teaching and learning context. The local conditions that
frame school teaching and learning settings are assumed across different
educational ideologies and often remain unproblematic. As such they represent
certain continuities underlying ideological conflicts emergent at different
junctures in educational debate. This basic argument is made succinctly
by Davies et al (1990) in reference to the most recent educational reforms.

"The broad dichotomy between traditional and progressive education can serve to hide the variability which exists within the framework of progressive education. Forms of progressive education can be class, race and gender biased and depress the performance of working class children, blacks and girls. These biasses intrude from a range of sources - the middle class assumptions upon which schooling itself is predicated, teacher expectations, the impact of hidden curriculum - which operate in both traditional and progressive educational environments. " (Davies et al, 1990: 26)

The evident poor achievement and participation in mathematics of the same particular social groups (Apple, 1992; Dowling, 1991; Ernest, 1991; Dubberley, 1988) despite educational and pedagogical reform lends support to the assertion of fundamental continuities. The assumptions teachers make about pupils and schools are more part of the hidden agenda than the official rhetoric of an educational or political party line. Importantly, these assumptions directly influence the assessments teachers’ make of individual pupils’ mathematical abilities.

In efforts to understand
the process of teacher assessment, this study began by exploring how teachers
described the ways they made judgements about their pupils’ mathematical
capacities. The initial discussions revealed the teachers shared confidence
around the way they assess the 'ability' of pupils.

*R: . . . we're going
to have setting within two streams - an A and B stream. For maths a top,
middle and lower group in both streams. . . .*

*MD: Do you already
envisage where people in this class will be?*

*R: If I went through
a list I think I'd get 90% right without looking at marks. I haven't given
it any thought. But I'd probably be able to say what group they'd be in.
. . .* *I've always felt I've known kids. I've known them well enough
and a lot of my assessment is mental, stored in my braincells and not down
on paper.*

*MD: As you don't
teach them what gives you that impression?*

*R: I would have
said if we weren't talking about this, that they are the less able kids
within the group.*

*MD: How do you know?*

*R: Their written
work is not very good, they are not the quickest at thinking if you ask
them questions. Making decisions, not very quick at making decisions, not
always the best decision. The comments I hear from other staff.*

*MD: One pupil I
talked to felt she could never be good at maths because she was shy.*

*R: Well, I mean
certainly that would be true of somebody whose left my group. You would
think that he was very able because he'd talk a lot.*

Through critical reflection
attempts were made to make explicit those factors that informed teacher
assessments.

*H: Because you get
away with it and there's no one else around to say that that's not acceptable.
It's only when you get an adverse response from the pupils that you know
that you've done something particularly wrong.*

*MD: I wonder with
people like Sofna for example, if she were a boy, how different would the
school or teachers response be to her?*

*A: Yeah, because
she's very demanding yet. . . . If it was a boy I wouldn't let them nag
me so much, I'd just say go away. I say go away enough to Sofna, but I'd
say it more to a boy.*

*MD: In a way, talking
about her being very demanding, she's actually always on task.*

*A: Yeah, she's always
trying, she tries but yeah, I mean she is always on task. That is amazing,
she never really strays off. . .*

The deeply personal
effect of what is a routine teacher task is clearly described by two Year
9 pupils talking about being moved down a mathematics set:

*Andrea: I was really
angry. So was Daniella. Well she was in there before so it's worse for
her. That means she hasn't done no good during the year, so it's worse.
At first I said I wasn't gonna come to school. When I just found out I
told Miss, 'How come I'm in that class.' and she didn't say nothing. I
don't feel like going to maths anymore. I used to love maths when I used
to go to the other group.*

*Harvinder: I don't
know. I mean I was doing really okay in Miss Stanton's class. I thought
I was really good and I was proud that I'm okay and then when I just went
down there, I just felt ashamed of myself and didn't want to live any more.
. . . When I found out. Disappointed. . . . Felt stupid. I feel dumb..
. . It's just that the work that we do now we're supposed to* *do
it in the first year. And that's what really disappoints me.*

**Conclusion**

This paper has attempted
to highlight the various ways in which the daily work of mathematics teachers
is fundamental to the limits and possibilities of their pupils mathematics
education experiences. The increase of external regulation on the teaching
profession has coincided with the institution of national testing arrangements
that contradictorily, depend upon the teachers’ professional attitude to
their work. Indeed, the validity of national KS testing rests on assumptions
of such teacher attitudes. Despite the displacement of teacher assessment
in favour of national paper and pen tests it is evident that teachers retain
powerful influence over the processes integral to national assessment.
This influence is overt in the public sphere through pupil test entry and
more covert, in the private context of the mathematics classroom. Teachers
connect and mediate between the local arena of classroom mathematics and
the department, school and national results. Interests in the school outcomes
and effectiveness have tended to focus on the public part of these processes
of assessment. More research on the hidden structuring of teacher decisions
about the mathematical capabilities of their pupils would undoubtedly provide
greater understandings of the social relations of the classroom and the
assessment process. Such developments would clearly contribute also to
associated issues concerned with social justice in education

**Acknowledgements**

I would like to thank
the teachers and children in the ten schools within which these two research
projects were located. The data and analysis in the first research project
was mainly funded by the ESRC (Project: R000235863, 1995 - 1997). Thanks
go to my co-researchers Nicola Rodgers and Dr Barry Cooper. For the demanding
task of interview transcription, thanks also go to Iestyn Williams, Sally
Jeacock, Beryl Clough, Hayley Kirby and Julia Martin-Woodbridge

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