Researchers have reported that preservice mathematics teachers' (PMTs') conceptions for radian angle measure are dominated by conceptions of degrees, memorization, and calculational strategies, and are always expressed in terms on [pi]. In this report, I unpack the mathematical meanings of a PMT, Henry (pseudonym), as he engaged in three…

This study examined the opportunity to learn function transformations afforded by the GeoGebra applets available on the GeoGebra website. Our analysis focused on the functions and their representations through which function transformations are explored in these GeoGebra applets, the effects and components of transformations that the GeoGebra…

This research explores two methods through which ten preservice math teachers develop an understanding of trigonometric values. Using the unit circle, preservice math teachers engage in knowledge-building activities such as paper folding and GeoGebra application. Grounded in Altman and Kidron's 2016 didactical design research, this study examines…

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

Trigonometry is one of the fundamental topics taught in high school and university curricula, but it is considered as one of the most challenging subjects for teaching and learning. In the current study Mason's theory of attention has been used to examine undergraduate student's perception of the transformation of sinusoidal functions. Two types…

In this research we discuss relating the description of certain harmonic phenomena, with models that represent them, with the goal of promoting the understanding of the period, the frequency, and the amplitude of the trigonometric functions, particularly referring to sinusoidal functions; in this way the frontier between sinusoidal functions and…

This study uses APOS Theory to study students' construction of the sine and cosine functions and their inverses. The conjecture of the constructions students would need to do in order to attain a process conception of these functions is tested by using semi-structured interviews with a group of 11 undergraduate students. Analysis of the interviews…

Precalculus and Discrete Mathematics (PDM) is the sixth and final course in the secondary mathematics curriculum developed by the University of Chicago (Illinois) School Mathematics Project. During the 1989-90 academic year, a formative evaluation of the third field-trial edition of PDM was conducted among a volunteer sample of 9 high schools with…

We examine a prospective high school teacher's instructional representations of rate of change and right triangle trigonometry to investigate his interpretation and understanding in relation to the development of proportional reasoning. Despite a constant effort by the subject to resort to "real life" examples in order to give meaning to his…