In recent years, there has been an increasing interest in utilising videos as a tool for enhancing the professional noticing skills of prospective mathematics teachers (PMTs). Several studies have shown the effectiveness of video-based approaches for the professional development of PMTs. However, limited research has been conducted on the impact of PMTs’ mathematical knowledge for teaching on their professional noticing skills in the context of video-based lessons, particularly in relation to specific mathematical topics. This study aimed to address this gap by proposing a video-based lesson analysis framework to investigate the possible effects of PMTs’ mathematical knowledge for teaching on their professional noticing skills. We then utilised this framework to explore Vietnamese PMTs’ knowledge required for teaching the application of the derivative in economic contexts, with a focus on their situation-specific abilities such as perception, interpretation, and decision-making. Our findings indicated that various components of PMTs’ knowledge exerted different influences on their noticing abilities. Additionally, our study revealed that there are limited connections between PMTs’ mathematical knowledge for teaching and their professional noticing skills. Finally, the study demonstrated the effectiveness of the proposed lesson analysis framework for evaluating PMTs’ video-based professional noticing skills.
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