Formative assessment feedback on the mathematical competence of students

Abstract

The aim of the study reported on in this dissertation is to develop a formative feedback instrument on the mathematical competence (competence instrument) of students and to examine students’ experiences of the use of such an instrument. The study was conducted among first-year students of the University of Pretoria enrolled for a Finite Mathematics module. A quantitative approach in the form of a non-experimental research design, together with questionnaires completed by the students, was used in the study. A mathematical competence assessment instrument was developed in terms of a five-point radial chart, each radial related to a mathematical competency. The five fundamental competencies (or skills) were identified from literature (Kilpatrick, 2001; Kilpatrick et al., 2001; Niss, 2003; OECD, 2003; Sáenz, 2008; Schoenfeld, 2007) for constituting mathematical ability or competence. A rubric was designed to assess formative tests written by students and the five-point radial chart was used to report the mathematical competence of the students as assessed by using the rubric. Students completed questionnaires on their experience of the competence instrument at the end of the study. Student performance in formative assessments where the competence instrument was used correlated well with the performance in the examination. The competence instrument proved to be valid in assessing the mathematical ability of students. Students found the instrument helpful in identifying their lack of mathematical skills, but did not know how to improve on all the mathematical skills or competencies. When conducting formative assessment, the importance of providing students with performance standards is essential, but students need to be informed on how to close the gap between their actual performance and the expected performance (Nicol and Macfarlane-Dick, 2006; Black & Wiliam, 1998). The mathematical competence instrument has potential in realising the objectives of formative assessment, but more research needs to be done on the implementation of the instrument in guiding students to improved performance. Future research based on the study, can take the form of the utilisation of the competence instrument in the assessment of students in other mathematics modules.