Painting a Portrait of Mathematics: A Case Study of Secondary Students' Assessment Portfolios

Abstract

This study analyses the effect of introducing student portfolios as a means of assessing the learning of mathematics. It examines the intended and the unforeseen outcomes in terms of the students, the caregivers, and the teachers involved, using quantitative data to match classroom environments with the response to the innovation. A major focus of the qualitative aspect of the study is the decisionmaking process that was associated with the implementation of change. For this study, all the junior students in a New Zealand secondary school were asked to compile portfolios of their mathematical work. The portfolios were graded by the teachers, the marks contributing to the students' assessments for the year's work. At the outset, the plan was to survey the 510 students involved to determine their attitude towards mathematics, survey them again once the innovation was in place to quantify the classroom environment, then repeat the first survey. Analysis was expected to reveal whether classroom environments that approximated a "portfolio culture" (Duschl & Gitomer, 1991) contributed to an improved attitude towards mathematics. This quantitative approach was supplemented with taped interviews of students and teachers, ongoing records of less formal interactions, review of examination marks and school reports, and questionnaires mailed to the homes of a sample of the students. As the study progressed, it emerged that the major impact was on the teachers, and the focus shifted to them. For four years, follow-up surveys were conducted with teachers, including those who had transferred to other schools. The study found that all students can benefit from portfolios, both in terms of skills and attitude towards mathematics.Portfolios legitimated the involvement of caregivers, a positive change that provided greater links between classroom activity and the world of employment. The professional practice of teachers was affected by portfolios, prompting development of new classroom resources and techniques, increased collegial cooperation, and well-informed reflection on teaching and assessment. Teachers maintain great influence on classroom culture, and for many of those involved in the study, portfolios prompted a renewed interest in the process undertaken by students as they develop mathematical ideas, and a change in the relationship between teacher and students. The "portfolio culture" resulted in students improving in their appreciation of mathematics, and a changed role for the student within the social environment of the classroom.