REVIEW OF RELATED LITERATURE
2.3 Perspectives on formative assessment
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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.
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Black and Wiliam (2009) note that both teacher and students are involved in generating information to help in determining the next steps of instruction. Similarly, Popham (2008) posits that both teachers and students can derive instructional changes from FA; specifically, “assessment elicited evidence of students is used by teachers to adjust their instructional procedures or can be used by students’ to adjust their current tactics of learning” (p. 6). According to McMillan (2007b), the goal of FA is to improve students’ motivation and learning, which can be attained through some continuous circular processes involving: 1) evaluations of students’ work, 2) provision of feedback to students, and 3) instructional correctives. It is worth noting that the ultimate goal of FA is to gauge students’ learning, diagnose weaknesses and adjust instruction as and when needed.
In addition, Coffey et al. (2011) mentioned that the aim of FA is to help teachers to address their students’ thinking during instruction. Through FA gaps in students’ learning are identified, which gives the teacher an opportunity to modify or make adjustments to the instruction with the primary aim of supporting teaching and learning. Shermis and DiVesta (2011) assert that FA is premised on the inference that assessment is not an end in itself, but can be used constructively to identify where and when to improve instruction by teachers. This assertion means that teachers can change their approach to instruction but maintain the strategy that yields positive results during instruction and learning.
FA can be categorised as informal or formal, and the distinction can be made on the basis of the way the information is gathered, how it is perceived and the purposes of the assessment (Shermis
& DiVesta, 2011). This gives credence to the point that the rationale for assessing and the belief held by the teacher in relation to assessment will inform him/her the form of assessment to be adopted in the classroom. For York (2003) informal and formal FA are distinguished by context.
According to Cowie and Bell (1999) FA can be planned or interactive and the two forms are classified based on the processes employed in each. These two major forms of FA are discussed in the following sections.
27 2.3.1 Formal formative assessment
According to Shermis and DiVesta (2011) formal FA is carried out deliberately to provide feedback on curriculum matters; for example, feedback on students’ readiness, diagnosis, remediation, and placement. This simply means that formal FA requires: (a) deliberate and planned gathering of information, (b) interpreting the information on the basis of the assessment goal, and (c) acting upon the information to modify or restructure the instruction, curriculum or system (Shermis & DiVesta, 2011). Formal FA is also known as planned FA (Bell & Cowie, 2001).
According to Bell and Cowie (2001) planned FA is used to generate permanent evidence of students’ thinking and can be organised at the beginning or at the end of a topic. Cowie and Bell (1999) produced a model of planned FA (Figure 2.1).
Figure 2.1: Planned formative assessment (adapted from Cowie and Bell, 1999, p. 103).
According to them eliciting of information, interpreting it, and acting upon the information denote the process of planned FA. In the planned FA the information collected, interpreted and acted upon are determined by the purpose of the assessment (Cowie & Bell, 1999). This suggests that there should be a purpose for assessing students, since the information obtained enables the teacher to plan how best to support subsequent learning of the students. Similarly, McMillan (1997) argues that formal FA is a planned activity in which students’ knowledge and understanding are assessed, and the evidence generated is used in providing feedback and planning of instruction by the teacher (p. 120). He reiterated that there is always some measure of time between the assemblage of data
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and the interpretation, that permits the instructor to reflect and determine the next most appropriate instructional activities. Based on the different perspectives of FA, it can be construed that FA is more than just a method to assess students’ knowledge of a particular concept, but also to capacitate both the instructor and the students for further learning.
2.3.2 Informal formative assessment
This form of FA takes place during an interaction between the instructor and the students. Cauley and McMillan (2010) referred to informal FA as an ongoing assessment conducted primarily through informal observation and oral questions posed to students when content has been delivered or reviewed. Eisenkraft (2004), as cited in Ruiz-Primo (2011), conceived that everyday learning activities are potentially informal FA, which provides evidence of students’ learning in a different mode. According to Ruiz-Primo (2011) evidence from learning activities can be accumulated within a class and information can involve one or two sources of evidence. Some of the evidence which informal FA uses comes from everyday activities such as “students’ questions, students’
oral responses, students’ written responses in a handout, student-to-student conversation and observation of students conducting practicals” (Ruiz-Primo, 2011, p. 15). Nineteen years ago Bell and Cowie (2001) termed this interactive FA and described it as incidental ongoing FA which arises out of learning and cannot be anticipated; its aim is to improve learning by intervening or mediating in the students’ learning. The process involved in interactive informal FA is described in Figure 2.2.
Figure 2.2: Interactive formative assessment (adapted from Cowie and Bell, 1999, p. 104).
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Cowie and Bell (1999) observed that instructors might plan or prepare to carry out an interactive informal FA, but they cannot plan or determine exactly what they and their students will be doing and the time such an activity will occur. As presented in Figure 2.2, these authors explained that the interactive FA process involves teachers noticing, recognising and responding to students’
thinking, and this process is teacher–student-driven rather than curriculum-driven. For example, as an instructor you must notice whether students appear disengaged or enthusiastic about the topic, recognise their difficulty and respond by looking at the best way of getting each student to the place they need to be.
Similarly, Ruiz‐Primo and Furtak (2007) describe informal FA as “ESRU” cycles: the teacher elicits a question; the student responds; the teacher recognises the student’s response; and then uses the information collected to support students’ learning. According Ruiz‐Primo and Furtak (2007), an incorrect response by a student or an unexpected question can inform the teacher about students’ misunderstanding of classroom activity and can trigger an assessment event. What can be noticed from Cowie and Bell’s (1999) definition and that of Ruiz-Primo and Furtak (2007) is that informal FA happens concurrently during instruction. This suggest that while an instructor is teaching, he or she will be assessing at the same time, because noticing and recognising students’
difficulties or problems happens in the process of teaching, and within that process one needs to respond to the issues. In addition, Yorke (2003) defined informal FA as a form of assessment which takes place in the course of an event and is not specifically stipulated in the curriculum design. Informal FA is therefore not curriculum-specific, and materialises as a result of classroom interaction between the teacher and students. Therefore, it worth noting that informal FA does not happen in a vacuum; rather, it is an ongoing process and takes place during instruction because of interaction between teachers and students.