Monitoring and Assessment in Mathematics in Classroom

2. Formative Assessment

Zhou (2017), in his study, said that early education requires a quality monitoring system, and mathematics is the key content for the early assessment and development evaluation of children. Further, he mentioned that formative assessment and evaluation of its results reflect children’s problem-solving ability and promote diversity in the learning methods of children. According to Wanner (2018), in higher education, the central aspects of the processes of student-centred assessment are self and peer assessment. He further mentioned that both assessment types are essential in developing key capabilities among students, such as better understanding and more responsibility towards the subject. Both assessment forms develop critical reflection skills among students by evaluating one's learning skills. Further, he argued that developing this effective tool requires careful design for giving feedback to the developed capabilities.

However, another research by Thomas, Martin, and Pleasants (2011) mentioned that peer assessment is a deeper reflection of an individual’s learning, also called autonomous assessment. It is related partially to self-assessment and partially to other’s performances, such as classmates, when students reflect on their selves. On the other hand, Pachler et al. (2010) stated that the core factor in formative assessment is the learner’s self-regulation, which is directly linked with emotional and motivational factors that affect learners’ engagement in learning. Furthermore, a study has evaluated that formative assessment is effective in assessing mathematics learning abilities for students specifically; this study reviewed that in algebra interventions, instructional effectiveness is critical, and the best measure of instructional effectiveness is provided by a formative assessment, which also promotes professional development (Accardo and Kuder, 2017; Hošpesová, 2018). In addition, Lambert, Algozzine, and McGee (2014) stated that in formative assessment, progress monitoring assesses students’ performance individually in mathematics with the technology named accelerated math (AM) from grades 1-12 (Suurtamm et al., 2016).

3. Summative Assessment

An assessment in which the evaluator identifies what has been learned by an individual or group of students is known as a summative assessment (Hošpesová, 2018).  However, Ofsted critically emphasised ‘teaching to the test’ and stated that “it prepares students to gain qualifications but not in equipping them well enough mathematically for their future”. He argued the fact that achieving good grades is not necessarily examined by ‘teaching to the test’. It means that teachers should adopt interesting and engaging approaches to teaching mathematics such that students feel confident in applying their knowledge to practical situations (Marley, 2008). Summative classroom assessments are often performed for formative purposes, as summative results are used to understand students' misconceptions for large-scale instructional purposes (Suurtamm et al., 2016).  Furthermore, as stated in the study of Schoenfeld (2015), summative assessments in mathematics are performance opportunities or examinations where the primary purpose is to assess the knowledge gained at the end of the course, such as SATs, stakes assessments, etc. However, another research by Marinho, Leite, and Fernandes (2017) on mathematics summative assessment practices presented that summative assessment emphasized competition and beliefs, which is problematic as it only tells about what a student can do and what he cannot do, nothing about where they should improve themselves.