REVIEW OF RELATED LITERATURE
2.2 Classroom assessment in mathematics education
Assessment is an essential issue in the teaching and learning of mathematics and requires careful consideration by mathematics educators. Reform in mathematics education has captured the attention of policy makers and educational practitioners. Topical among the issues which have emanated from the reform were how to assess students’ attainment and how to assess improvement that may result from curricular and instructional reforms (Silver, 1992). Assessment has been defined by some academics as an administrative process in which information regarding students’
academic progress is provided (Hove & Hlastshwayo, 2015). Others have regarded assessment
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more as a tool for supporting students’ learning, rather than an administrative process (Bell &
Cowie, 2001; McMillan, 1997). However, the NCTM (2000, p. 3) reported as follows:
Assessment should be more than merely a test at the end of instruction to see how students perform under special conditions; rather, it should be an integral part of mathematics instruction that informs and guides teachers as they make instructional decisions. They also point that assessments should not merely be done to students; rather, it should also be done for students, to guide and enhance their learning.
This implies that assessment should be understood as a tool for learning mathematics. This position was supported by Kilpatrick (1993), who advocated for a change of assessment practice in mathematics education. He noted that “the challenge for the 21st century as far as mathematics educators are concerned, is to produce an assessment practices which does more than measuring a person’s mind and assign a mind treatment” (p. 44). This view changes the focus of assessment from a practice meant to measure some endpoint status, such as the competency of an individual (Boulet, 2008), or making a judgement in accordance with specific standards (Taras, 2009), to an assessment practice which has the potential to improve students’ learning outcomes (Heritage, 2011).
According to Oduro (2015) assessment in mathematics should elicit, assess and respond to students’ mathematical understanding and problem-solving skills. The NCTM (2014) mooted that assessment should provide evidence of proficiency with important mathematics content and practices, include a variety of strategies and data sources, and provide feedback for students, instructional decisions and programme improvement. The NCTM (2014, p.89 ?) posited that assessment should serve four distinct functions in school mathematics, and should provide evidence to enable educators to:
(1) Monitor students’ progress to promote students’ learning; (2) Make instructional decisions to modify instruction to facilitate students’ teaching; (3) Evaluate students’
achievement to summarize and reports understanding at a specific time; (4) Evaluating programs to make decisions about the instructional programme.
In the Principles and Standard for School Mathematics (2000, p. 2), the NCTM noted that assessment should “support the learning of important mathematics and furnish useful information
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to both teachers and students”. The goal of assessment is to evaluate mathematical programmes to assess their quality and to determine students’ mathematical achievement (Wiliam, 2007b).
Similarly, Burkhardt and Swan (2012) held that assessment in mathematics should reflect the mathematics which is important to students and valued.
It is therefore important to note that the methods or tools adopted by mathematics educators in their modules are essential to understand teacher educators’ assessment practices in mathematics.
The literature has shown that assessment in mathematics education in most schools around the world involves testing and grading (Bezuk et al., 2001; Lissitz & Schafer, 2002; Van De Walle, 2001). In addition, Dandis (2013) and Susuwele-Banda (2005) indicated that mathematics educators mainly use written examinations (tests) and quizzes to assess their students in mathematics. Senk, Beckmann, and Thompson (1997) explored the assessment and grading practices of 19 high school mathematics teachers and also found that tests and quizzes were the most frequently used assessment tools. On this premise, the Department of Education and Science of England (1982, as cited in Niss (2013), expounded as follows:
Examinations in mathematics which consist only of timed written papers cannot, by their nature, assess ability to undertake practical and investigational work or ability to carry out work of an extended nature. They cannot assess skills of mental computation or ability to discuss mathematics nor, other than in very limited ways, qualities of perseverance and inventiveness. Work and qualities of this kind can only be assessed in the classroom and such assessment needs to be made over an extended period.
Therefore, there is a need for multiple assessment techniques that assess what students know and what they do not know.
Birgin (2011) recommended that alternative assessment tools, such as portfolios, students’
journals, self-assessment, and peer and group assessment are useful in determine what students know and where they are in their learning. McMillan (2007a) also averred that there are different forms of assessment practices that are used by mathematics educators, such as observation, interview, projects and many more. Wiliam (2007b) opined that students’ mathematical understanding and mathematical thinking can be enhanced via observation, interview, self- assessment, reflective journals, portfolios, performance tasks and projects. This indicates that
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students’ mathematics thinking cannot be assessed through one short test. This point suggests that mathematics educators should adopt multiple assessment techniques and carefully consider assessment which focuses on students’ learning and has the potential to improve students’
mathematics thinking and understanding.
Although various studies advocate for different forms of assessment due to its importance in the process of learning, little is known as to whether, how or which type of assessment is being implemented. Teacher educators, as the people responsible for training pre-service teachers, are those who need to lead by example. Therefore, the aim of this study is to explore teacher educators’
knowledge and practices of FA in mathematics modules.