Classroom assessment as an essential aspect of effective teaching

Recent years have seen increased research on classroom assessment as an essential aspect of effective teaching and learning (Bryant and Driscoll, 1998; McMillan, Myran and Workman, 2002; Stiggins, 2002). It is becoming more and more evident that classroom assessment is an integral component of the teaching and learning process (Gipps, 1990; Black and Wiliam, 1998). The National Council of Teachers of Mathematics [NCTM](2000) regard assessment as a tool for learning mathematics. The NCTM contends that effective mathematics teaching requires understanding what students know and need to know. According to Roberts, Gerace, Mestra and Leanard (2000) assessment informs the teacher about what students think and about how they think. Classroom assessment helps teachers to establish what students already know and what they need to learn. Ampiah, Hart, Nkhata and Nyirenda (2003) contend that a teacher needs to know what children are able to do or not if he/she is to plan effectively.

Research has revealed that most students perceive mathematics as a difficult subject, which has no meaning in  real life (Countryman, 1992; Sobel & Maletsky, 1999; Van de Walle, 2001). This perception begins to develop at the elementary school where students find the subject very abstract and heavily relying on algorithm, which the students fail to understand. This trend continues up to middle, high school and college. By the time students get to high school they have lost interest in mathematics and they cannot explain some of the operations (Countryman, 1992). According to Countryman (1992), the rules and  procedures for school mathematics make little or no sense to many students. They memorize examples, they follow instructions, they do their homework, and they take tests, but they cannot say what their answers mean. Most research studies in both education and cognitive psychology have reported weaknesses in the way mathematics is taught. The most serious weakness is the psychological assumption about how mathematics is learned, which is based on the “stimulus-response” theory (Althouse, 1994; Cathcart, Pothier, Vance & Bezuk, 2001; Sheffield & Cruikshank, 2000). The “stimulus-response” theory states that learning occurs when a “bond” is established between some stimulus and a person’s response to it (Cathcart, Pothier, Vance & Bezuk, 2001). 

Cathcart et al.(2001) went further to say that, in the above scenario, drill becomes a major component in the instructional process because the more often a correct response is made to stimulus, the more established the bond becomes. Under this theory children are given lengthy and often complex problems, particularly computations with the belief that the exercises will strengthen the mind. Schools and teachers need to realize

that great philosophers, psychologists, scientists, mathematicians and many others created knowledge through investigation and experimentation (Baroody & Coslick, 1998; Phillips, 2000). They understood cause and effect through curiosity and investigation. They were free to study nature and phenomenon, as they existed. Today, learning mathematics seems to suggest repeating operations that were already done by other people and examinations that seek to fulfill the same pattern (Brooks & Brooks, 1999).

The constructivist view is different from the positivist view and, therefore, calls for different  teaching approaches (Baroody & Coslick, 1998; Cathcart, et al., 2001; von Glasersfeld, 1995). The constructivist view takes the position that children construct their own understanding of mathematical ideas by means of mental activities or through interaction with the physical world (Cathcart, et al., 2001). The assertion that children should construct their own mathematical knowledge is not to suggest that mathematics teachers should sit back and wait for this to happen. Rather, teachers must create the learning environment for students and then actively monitor the students through various classroom assessment methods as they engage in an investigation. The other role of the teacher should be to provide the students with experiences that will enable them to establish links and relationships. Teachers can only do this if they are able to monitor the learning process and are able to know what sort of support the learners need at a particular point.

The main hypothesis of constructivism is that knowledge is not passively received from an outside source but is actively constructed by the individual learner (Brooks and Brooks, 1999; von Glasersfeld, 1995). Within this hypothesis lies the crucial role of the teacher. Today many psychologists and educators believe that children construct their own knowledge as they interact with their environment (Brooks and Brooks, 1999; Cathcart, et al., 2001; Hatfield, Edwards, Bitter & Morrow, 2000; von Glasersfeld, 1995). Unfortunately, classrooms do not seem to reflect this thinking. Some teachers still continue to teach in the way perhaps they themselves were taught because human beings naturally look back and claim that the past offered the best. If children construct knowledge rather than passively receive it, they must be offered the  opportunities to act on their environment, physically and mentally, to use methods of learning that are meaningful to them, and to become aware of and solve their own problems (Althouse, 1994). Althouse is in agreement with Baroody and Coslick (1998) who suggest that teaching mathematics is essentially a process of translating mathematics into a form children can comprehend. Teaching mathematics is providing experiences that will enable children to discover relationships and construct meaning. Students should be assisted to see the importance of mathematics not by rote learning but by investigating and relating to real-life situations. Giving students dozens and dozens of problems to solve does not help them to understand mathematics, if anything it frustrates them even more. The more they do things they cannot understand or explain, the more they get

frustrated.

The way teachers perceive assessment may influence the way they teach and assess their students (Assessment Reform Group, 1999; Fennema and Romberg, 1999). To investigate teachers’ perceptions of classroom assessment in mathematics and their current classroom assessment practices. Specifically, the study sought to understand the methods and tools teachers use to assess their students. The researcher studied closely how classroom assessment was being carried out in the classroom by focusing on the strategies and tools the teachers used to assess the learners. 

Classroom assessment is one of the tools teachers can use to inform their teaching and the learning of their students. Unfortunately, the purpose of classroom assessment in most schools seems to be confused and, therefore, not supporting learning (Ainscow, 1988; Stiggins, 2002; Swan, 1993). The term assessment in some schools means testing and grading (Stiggins, 2002).

Researchers have attempted to investigate teachers’ perceptions of assessment in many different ways (Chester & Quilter, 1998). Chester and Quilter believed that studying teachers’ perceptions of assessment is important in the sense that it provides an indication of how different forms of assessment are being used or misused and what could be done to improve the situation. More critical also is the fact that perceptions affect behavior (Atweh, Bleicker & Cooper, 1998; Calderhead,1996; Cillessen & Lafontana, 2002) A study conducted by Chester and Quilter (1998) on inservice teachers’ perceptions of classroom assessment, standardized testing, and alternative methods concluded that teachers’ perceptions of classroom assessment affected their assessment classroom practices. Teachers that attached less value to classroom assessment used standardized tests most of the times in their classrooms.

Chester and Quilter went further to say that teachers with negative experiences in classroom assessment and

standardized testing are least likely to see the value in various forms of assessment for their classroom. They

recommended, therefore, that in-service training should focus on helping teachers see the value of assessment

methods rather than “how to” do assessment. A study conducted by Green (1992) on pre-service teachers with measurement training revealed that the pre-service teachers tended to believe that standardized tests address important educational outcomes and believed that classroom tests are less useful. In the same study inservice teachers believed that standardized tests are important, but not to the degree that pre-service teachers did. A case study of one science teacher conducted by Bielenberg (1993) showed that the teacher’s beliefs about science defined how she conducted her science classes.

Diene (1993) conducted a study to understand teacher change. The study considered the classroom practices and beliefs of four teachers. Findings suggest that teachers’ beliefs and practices were embedded within and tied to broader contexts, which include personal, social and previous ideas about a particular aspect.