| Issue 62 (WAIS 2) Contents
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Future Science - Starting in
Schools:
The Case of Mathematics
Gilah C Leder
Institute for Advanced Study
La Trobe University – Bundoora
Introduction
Mathematics, gender, and equity issues have attracted considerable attention in recent decades. Substantial funds and energy have also been spent on intervention programs aimed at changing the gender composition of educational and occupational fields in which females are under represented. During the 1970s and 1980s, much effort was directed at documenting gender differences in mathematics participation and performance. These comparisons typically assumed that the achievements, experiences, behaviours, and beliefs of males should be accepted as the norm. Measured against these standards, females were frequently found wanting (1). The removal of perceived barriers and, if necessary, the resocialisation of females were seen as the paths to equity. Over time, the growth of feminist research increasingly challenged these earlier assumptions. Explanatory models put forward to account for the gender differences observed have much in common. Typically they emphasize the importance of the social environment; the influence of other significant people in that environment; individuals’ reactions to the cultural and more immediate context in which learning takes place; the cultural and personal values placed on that learning; and the inclusion of learner-related affective, as well as cognitive, variables. In the next section I discuss an educational intervention which challenged perceptions of gender differences in mathematics education. Briefly, data from a large, state-wide examination are used to illustrate not only how achievement in mathematics can be influenced by the method of assessment used but also to indicate the subtle disadvantage experienced by girls in traditional methods of assessment.
Making a difference
The Victorian Certificate of Education (VCE), an innovative curriculum and assessment system, was introduced into all Victorian schools in the early 1990s (2). From its inception, the VCE was envisaged as a two year course which spanned grades 11 and 12, served as a common credential for completing secondary school, and was designed to replace the collection of alternate certificates which had evolved over time to cater for students with diverse aspirations and abilities. Two of the VCE’s fundamental aims were to encourage innovative teaching practices through a diversification of assessment tasks, and to provide a broad curriculum to allow all students, not just those intending to go on to tertiary education, an opportunity to remain within the mainstream school and examination structure. Its assessment format symbolized and reinforced real structural changes in the delivery of post-compulsory education in Victoria. Entrance to tertiary institutions and courses is based on performance on Common Assessment Tasks (CATs), described in more detail below. Since its introduction, the assessment structure of the VCE has attracted much attention, praise, and criticism. Over the years various changes have been made to the mathematics subjects (also known as studies): in nomenclature, in the grouping of the subjects, and in the number of CATs set. Details of these changes are beyond the scope of this paper.
The VCE in 1992
In 1992, the first year of the full implementation of the VCE, there were six mathematics subjects or studies. These were Space and Number (S&N) - concerned with the study of algebra, geometry, and trigonometry, Change and Approximation (C&A) - dealing with calculus and polynomials, Reasoning and Data (R&D) - which focussed on probability and statistics, and Extension blocks for each of these to allow specialised study and more in-depth treatment of work covered in the three basic blocks. C&A Extension (Ext) was recognised as the most demanding of the six mathematics subject. Each of these studies had four CATs, all worth one-quarter of a subject’s marks:
CAT 1 - Investigative project: a written report (of 1500 words) based on an independent mathematical investigation. Devised centrally, the total time spent on the task was expected to be between 15 and 20 hours - some in class, the bulk outside school hours. However, determined to do well, many students exceeded this suggested time.
CAT 2 - Challenging problem: a problem selected from four set centrally. This task required students to undertake a problem-solving or modelling activity and to submit a report of their work which contained details of the methods and procedures used, as well as of the solution obtained. In an attempt to maximise their marks, many students again exceeded the six to eight hours recommended for this CAT.
CAT 3 - Facts and skills task: a set of 49 multiple choice questions, completed under test conditions in school and designed to assess mathematical concepts and skills in standard ways.
CAT 4 - Analysis task: a traditionally administered, strictly timed, examination of four to six questions of increasing complexity, designed to test interpretive and analytical skills. There were several important differences, it can be seen, between CATs 1 and 2 and CATs 3 and 4. The former were longer term projects, were attempted inside as well as outside mathematics classes, initial solution attempts were expected to be redrafted after some teacher input, and considerable explanations were required of the methods used to reach a solution. The latter were traditional, timed tests, done under timed examination conditions.
The results for the 1992 examination are shown in Table 1.
The group differences shown are striking as a group, males and females performed differently on inherently different assessment tasks, yet all were high stake and given in the same academic year. Males appeared to do better on the traditional assessment tasks. More innovative but still demanding assessment tasks with a focus on the solution process as well as on the answer, which required sustained and independent efforts over a longer period of time, and which had a stronger verbal component seemed to favor females. The data illustrate how the mode and requirements of assessment tasks can influence a student’s performance in mathematics, often equated with mathematical ability.
Some implications
The selection of educational and career pathways, it has been argued, is influenced not only by reality but also by perceptions of that reality: Attitudes involve what people think about, feel about, and how they would like to behave toward an attitude object. Behavior is not only deter-mined by what people would like to do but also by what they think they should do, that is social norms, by what they have usually done, that is, habits, and the expected consequences of behavior. (Triandis, 1971, p. 14, ref 3) The widespread identification of mathematics and related fields and occupations as male domains, perpetuated by results on traditional assessment tasks, is challenged by the 1992 VCE assessment data (as well as by data from subsequent years). Anecdotal and research data indicate that males rather than females are now often seen as the educationally disadvantaged group. For example, in a recent Victorian study which involved some 1600 students from a diverse set of schools, students considered that boys more often than girls: distracted others in class, teased peers if they are good at mathematics, found mathematics more difficult, and gave up when a problem proved difficult. Girls, on the other hand, were believed more likely to get on with their work in class, considered it important to understand the work, found mathematics interesting, cared about doing well, and were thought by their mathematics teachers likely to do well. The attributes in italics can be interpreted as a change in traditional student perceptions of mathematics from a “male” to a “female” domain.
What next?
Several Australian reports, published during the 1990s, began to highlight concerns about boys’ performance and behaviours (4). Boys: Getting it right. Report on the inquiry into the education of boys (5) not only drew further attention to the difficulties faced by boys but also stimulated wide-spread community debate. Listed among the disadvantages experienced by boys were: lower measures of early literacy achievement; lower rates of school; lower results in most subjects at Years 10 and 12; lower levels of admissions to higher education; as well as other indicators such as suspensions and expulsions which involve many more boys than girls. Without simplistically attributing boys’ educational disadvantage to a single cause, the writers of the report noted that “there are indications that because of changing assessment methods, boys with relatively poor literacy skills are disadvantaged across much of the curriculum.” At the same time in educational and employment domains considered high status in Australia, males continue to dominate and prosper. The most recent Census data confirm that there is a high disparity in earnings favouring males, with females on average often earning only 80%-85% of the amount earned by males in the same occupation.
The emphasis in the paper to date on gender differences has ignored another pressing problem which requires urgent attention (and is discussed in more detail in other papers in this collection). Throughout the professional communities of scientists and mathematicians in Australia, increasing alarm is expressed about the declining numbers of school students, graduate and post-graduate students engaged in the physical sciences and rigorous mathematics options. Dire predictions are made about an increasing shortage of appropriately qualified mathematics and science teachers. The lack of employment opportunities for young researchers, many of whom instead grasp lucrative employment opportunities offered overseas, is also noted with great concern. Our challenge, then, is not to advance strategies which favour one group at the expense of another, but rather to convince a larger (student) body of the excitement and satisfaction to be obtained from persistent efforts in the fields of mathematics and science and to make studies in those areas relevant and attractive.
1. Representative reports published during that time include Girls, Schools and Society (1975) Report by a Study Group to the Schools Commission; Women’s Advisory Committee to the Prime Minister (1977) Australian Government Publishing Service; Report to the premier of Victoria (1977) Victorian Committee on equal opportunity in schools; Girls and Tomorrow: The Challenge for Schools National Policy for the Education of Girls in Australian Schools (1987) Australian Education Council + annual follow up reports; Girls in Schools 1-4 Department of Employment, Education and Training
2. Assessment changes similar to those described in the VCE were introduced in other Australian states. Space constraints allow no more than a reference to these other state initiatives.
3. Triandis, H. (1971) Attitude and attitude change. New York: Wiley
4. These included: Who Wins at School? Boys and Girls in Australian Secondary Education (1995) Commonwealth of Australia; and Inquiry into boys’ education 1994. Challenges & opportunities: A discussion paper (Stephen O’Doherty). NSW: Ministry of Education, Training and Youth Affairs
5. House of Representative Standing Committee on Education and Training (2002, October) Boys: Getting it right. Report on the inquiry into the education of boys. Canberra: Commonwealth of Australia