A validation study of the use of mathematical knowledge for teaching measures in Ireland

Researchers who study mathematical knowledge for teaching (MKT) are interested in how teachers deploy their mathematical knowledge in the classroom to enhance instruction and student learning. However, little data exists on how teachers’ scores on the US-developed measures relate to classroom instruction in other countries. This article documents a validation study of Irish teachers’ scores on measures of MKT that were adapted for use in Ireland. A validity argument is made identifying elemental, structural and ecological assumptions. The argument is evaluated using qualitative and quantitative data to analyse inferences related to the three assumptions. The data confirmed the elemental assumption but confirming the structural and ecological assumptions was more difficult. Only a weak association was found between teachers’ MKT scores and the mathematical quality of instruction. Possible reasons for this are outlined and challenges in validating the use of measures are identified.