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In mathematics education, researchers often contrast conceptual and procedural teaching approaches, although labels and conceptualizations often vary across studies. Prior research has extensively examined empirical relationships between the two teaching approaches and mathematics achievement. In our study, we aimed to extend this research by exploring whether one teaching approach moderates the relationship between the other teaching approach and algebra achievement. Specifically, we investigated whether the relationship between one teaching approach and algebra achievement differs depending on the degree to which the other teaching approach is implemented. We used data from the High School Longitudinal Study (HSLS:2009) that was conducted in the USA. In our study, procedural teaching was measured as the amount of emphasis that teachers placed on objectives related to procedures and computational skills, whereas conceptual teaching was measured as the amount of emphasis that teachers placed on objectives related to understanding, application, and motivation. Hierarchical linear modeling (HLM) was used to analyze the data, thus accounting for clustering of students within classes and classes within teachers. We found a statistically non-significant interaction effect. This result suggests that the association between one teaching approach and algebra achievement is similar across the degrees of the other teaching approach. Furthermore, we found a statistically significant association between conceptual teaching and algebra achievement. Specifically, conceptual teaching was positively related to algebra achievement. For procedural teaching, we found a statistically non-significant association. Hence, we did not find evidence that procedural teaching is related to algebra achievement.

Mathematics specialists support the teaching and learning of K-12 mathematics and attend to school-based responsibilities and needs. This study examined the shifts in responsibilities of mathematics specialists during the COVID −19 pandemic to better-understand their current and potential future influence on mathematics teaching. An online survey was administered nationally to reveal how school-based mathematics specialists adapted their responsibilities in response to the changing school conditions. Responses from school-based mathematics specialists were analyzed using a mixed methods approach to capture self-reported shifts in responsibilities, as well as challenges and opportunities. Findings indicate that the school-based mathematics specialists were able to rapidly reprioritize their responsibilities in response to both teachers' professional learning and instructional needs. These findings illuminate the importance of mathematics specialists as school-based leaders who must continually navigate relationships and apply leadership knowledge and skills in novel ways to support shifts in mathematics teaching and learning. [ABSTRACT FROM AUTHOR]