A framework towards improved instruction of probability to grade seven students : a case of South African schools in Mpumalanga province

Abstract

This empirical phenomenological study explored teachers’ conceptual understanding of probability to gain insights into how this understanding enhanced their instructional classroom practice. The study was motivated by the fact that many teachers did not receive training on this topic during their pre-service training, and their students often demonstrate below average performance in this topic. Studies have found that primary school mathematics teachers require specific training to enhance students’ understanding of probability. Scholars advocate the implementation of intervention programmes to ensure effective practices in probability and mathematics education in general. In this study the researcher used purposive sampling to select nine participants. These individuals included five qualified teachers; the snowballing method was then used to select another teacher, two subject advisors and one mathematics coordinator. Participants’ experience in the field of mathematics teaching ranged from 10 to 25 years. Open-ended questionnaires, semi-structured interviews, lesson observations and focus group discussions were used to collect data. An initial needs analysis phase was conducted to determine what intervention strategies could be used to empower primary mathematics teachers and subject advisors. These intervention strategies were implemented following a lesson study model first used in Japan. The data collection instruments were developed from the conceptual tools of Kilpatrick, Swafford and Findell’s (2001) model. The items in the open-ended questionnaire were adapted from school textbooks and national and international assessments. The findings from the first phase of the study revealed that teachers had limited conceptual understanding of probability. The analysis of the data collected during the second phase of the study (the intervention) revealed the following: • There was an improvement in participants’ understanding of probability in relation to teaching, and how teachers’ classroom instructional practices could be enhanced. • Teachers and subject advisors acknowledged that readily available common lesson plans provided by the Department of Education would not have a significant impact on their classroom practices unless they were modified. • Greater collaboration between teachers and higher education institutions was required to enhance teachers’ professional development. • A platform for subject advisors and teachers to share their experiences and provide support should be created. • The use of a lesson study process as an accelerant promotes collaborative learning and enhances teachers’ instructional practices. In this study, teachers were encouraged to share their practices with others and to implement what they had learnt at school level (Lipscombe, Buckley-Walker & McNamara, 2020). The study found that the absence of policy on the support and mentoring of teachers has resulted in a lack of confidence when teaching the concept of probability. The unsystematic way in which issues of mentoring and teacher support are dealt with does not serve teachers well. This seems to suggest that mentorship and teacher support programmes require regulation by policy. Likewise, subject advisors need training if they are to provide proper support to mathematics teachers. These recommendations were translated into specifications to empower teachers and subject advisors. These specifications form the basis of the RIRAD (Review, Identify, Reconsider, Adapt and Develop) framework conceptualised in this study. The framework was conceptualised within the conceptual tools of Kilpatrick et al.’s (2001) model and strengthened by the findings that emerged from data. This framework has a dual integrated purpose, aimed at enriching teachers’ conceptual understanding of probability and empowering them to enhance their classroom instructional practices. Secondly, the framework empowers subject advisors to offer appropriate support to teachers. Based on findings from the literature review and empirical inquiry, more recommendations for the improvement of practice were made.