The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

This article discusses results from interviews with two undergraduate students in an introductory proofs course. The researcher assessed the participants' general proof schemes and built models of the participants' conception of probabilistic independence and mutual exclusivity. The participants were then tasked with asserting a relationship…

The likelihood-to-act (LtA) survey measures impulsive and analytic dispositions in solving mathematics problems. The current version has 16 impulsive and 16 analytic items. Its validity was assessed using a sample of 27 in-service and 92 pre-service teachers. Both the impulsive and analytic subscales were found to have internal consistency…

This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience…