2.8 Error analysis in assessment
2.8.1 Assessment
The national CAPS (DBE, 2012, p. 154) document explains assessment as follows:
Assessment is a continuous planned process of identifying, gathering and interpreting information regarding the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this
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evidence; recording the findings and using this information to understand and thereby assist the learner’s development in order to improve the process of learning and teaching. Assessment should be both informal and formal. In both cases regular feedback should be provided to learners to enhance their learning experience. This will assist the learner to achieve the minimum performance level of 40% to 49% required in Mathematics for promotion purposes.
This means that assessment can be simply defined as a day-to-day activity, process, that is an ongoing, integral part of teaching and learning. The CAPS (DBE, 2012, p 154) document further divides assessment into four types: baseline assessment, diagnostic assessment, formative assessment, and summative assessment.
Baseline assessment is defined as a type of assessment for mathematics teachers who might want to establish whether their learners meet the basic skills and knowledge levels required to learn a specific mathematics topic. Knowing learners’ level of proficiency in a mathematics topic enables the teacher to plan her/his mathematics lesson appropriately, and to pitch it at the appropriate level. Baseline assessment, as the name suggests, should therefore be administered prior to teaching a mathematics topic.
Diagnostic assessment is not intended for promotion purposes but to inform the teacher about the learner’s problem areas in mathematics that have the potential to hinder performance. Two broad areas form the basis of diagnostic assessment: content-related challenges, where learners find certain topics difficult to comprehend, and psychosocial factors such as negative attitudes, mathematics anxiety, poor study habits, poor problem-solving behaviour, etc. Appropriate interventions should be implemented to assist learners in overcoming these challenges early in their school careers.
Formative assessment is used to aid the teaching and learning processes, and hence is assessment for learning. It is the most commonly used type of assessment because it can be used in different forms at any time during a mathematics lesson (for example, short class work during or at the end of each lesson, and verbal questioning during the lesson). It is mainly informal and should not be used for promotion purposes. The fundamental distinguishing characteristic of formative assessment is constant feedback to learners, particularly with regard to their learning processes. The information provided by formative assessment can also be used by teachers to inform their methods of teaching.
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Summative assessment is carried out after the completion of a mathematics topic or a cluster of related topics. It is therefore referred to as assessment of learning, according to CAPS (DBE,2012) since it focuses mainly on the products of learning. The results of summative assessment are recorded and used for promotion purposes. It is mainly formal by nature, comprising school-based assessment (SBA) and the end of year examination in South Africa.
The forms of assessment presented in Table 2.1 are examples of summative assessment according to CAPS (DBE, 2012).
Table 2.1: minimum requirement for formative assessment at the senior phase mathematics
Drawing From the above definitions, the researcher holds the view that teachers can use diagnostic assessment and formative assessment when engaging with learners’ errors in the teaching and assessment of mathematics. Classroom assessments are concepts and applications that explore how assessment is a key component of all aspects of the teaching and learning process, including organising and creating a classroom principle or rules, planning lessons, carrying out teaching, and assessing how students have understood concepts as a result of teaching.
The researcher in this study supports the explanation of assessment given by Airasian and Russel (2001), that assessment is an ongoing integral part of teaching which occurs on daily basis and adds that assessment is one of the key functional duties of teachers. Considering this, the researcher has defined assessment as a tool that is used to measure teaching and learning.
This means that teachers always measure teaching and learning through assessment. Not far
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removed from the above views of assessment, Keeley (2015) believes that assessment can also be defined as a useful tool to inform teaching and learning as well as for measuring and documenting students’ achievements.
Recently, other researchers who have written about assessment, such as Lund and Kirk (2019), defined assessment as part of the teaching process and stated that assessment results are critical for teachers to have a deeper reflection of what students have learned and what they still need to know. They believe that “good teaching is inseparable from good assessment” (Lund & Kirk, 2019, p. 19). This means that assessment and teaching go hand in hand, and whenever there is teaching there must be assessment. As teaching informs assessment and vice versa, this means it is not only teaching that impacts on learning, assessment also impacts on learning; therefore, errors manifest either during the teaching process or during the assessment process. Teachers therefore need to be able to diagnose errors during teaching and assessment and to formulate strategies to address them.
In contrast, Kalajahi and Abdullah (2016, p. 233) defined assessment as “the systematic process that provides an opportunity for teachers to meaningfully reflect on how learning is best delivered, collect respective evidences, and then use that information to improve their teaching”. Recognising the above explanation of assessment, the researcher in this study agrees with the views given above by other researchers, but for the purposes of this study is more convinced by the definition given by Kalajahi and Abdullah that assessment gives teachers information about learners, and that the teachers use assessment to improve their teaching.
When the assessment practices of teachers are improved, this might help them to engage with learners’ errors in mathematics effectively and help learners to reduce or minimise the errors they make in mathematics.
Earl (2012) grouped assessment into three categories: assessment for learning (formative assessment), assessment of learning (summative assessment), and assessment as learning (peer assessment). For the purposes of this study, the researcher will not deal with these three categories of assessment much, but will rather pay attention to formative assessment, because
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in the teaching and learning process formative assessment provides immediate feedback on learners’ work to teachers, in order for proper turn around strategies to be used to help improve learners’ understanding. Considering the topic of this study, ‘Exploring Grade 9 mathematics teachers’ engagement with learners’ errors in the teaching and assessment of mathematics’, the researcher believes that formative assessment will be the most appropriate and effective assessment type to discuss.