Around the world, in many countries, teacher educators, researchers and policymakers are interested in the mathematical knowledge needed to teach effectively. This dissertation used a nationally representative sample to investigate Irish primary teachers' knowledge of mathematics using an instrument based on the construct of mathematical knowledge for teaching (MKT). Because MKT was based on studies of teaching practice in the United States, the study included an examination of the equivalence of the construct and the validity of the instrument for use in Ireland.

To establish the usability of the instrument, 501 teachers from a representative sample of Irish schools completed a teacher knowledge survey; ten additional teachers who completed the survey were videotaped teaching four lessons each. Ten Irish lessons were analyzed to examine construct equivalence between the mathematical demands of teaching in this sample of Irish practice and the mathematical demands of the teaching studied by U.S. researchers to develop the construct of MKT. Multiple-group factor analysis complemented the lesson analysis. Validity was examined by coding forty Irish lessons for the mathematical quality of the instruction; these codes were correlated with teachers' MKT scores. Factor analyses of teachers' responses, and comparison of tasks identified in Irish lessons with tasks that formed the basis of MKT, suggested that the constructs were sufficiently similar to use the measures in Ireland.

Results showed that Irish teachers' scores on MKT measures were moderately correlated with the mathematical quality of their instruction, suggesting that items were measuring knowledge used in instruction. Although MKT varied among teachers, performance on algebra items was strong and teachers were skillful at identifying and classifying student errors. Teachers demonstrated good knowledge of fractional representations. Applying properties and definitions of shapes, numbers and operations, and attending to student explanations and evaluating student understanding were more difficult.

This study suggests that measures based on the construct of MKT as conceptualized in the United States are valid for use in at least one setting outside the United States. Methods of establishing conceptual equivalence are identified; future research should refine further cross-cultural measurement of teachers' mathematical knowledge for teaching.