Design and Validation of an Instrument to Assess Didactic-Mathematical Knowledge in School Algebra Diseño y validación de un instrumento para evaluar el conocimiento didáctico-matemático en álgebra escolar

Abstract

This study outlines the design, development, and validation process of an instrument aimed at assessing primary school teachers' knowledge of school algebra, based on the Didactic-Mathematical Knowledge and Competencies (DMKC). We developed a preliminary version of the instrument, which was validated by ten international experts in mathematics, mathematics education, and algebra education. Their detailed feedback enabled us to make necessary adjustments and refine the instrument. The revised version was then tested with eight primary school teachers in Chile, allowing us to enhance the initial tool and ensure its alignment with the DMKC model for evaluating teachers' mathematical teaching knowledge in the context of school algebra. These steps led to the creation of the final version of the questionnaire, which will assess primary school teachers' mathematical teaching knowledge in practice. The pilot testing revealed that teachers' mathematical teaching knowledge is insufficient. However, further application of the instrument to a larger number of educators is necessary to gain a more comprehensive and conclusive understanding of primary school teachers' mathematical teaching knowledge, particularly in the area of school algebra. Additional results will provide a more complete view of teachers' competencies and help identify key areas for improvement.