This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was…

Feedback indicating how well students are performing during a learning task can be very stimulating. In this study with a pre- and post-test design, the effects of two types of performance feedback on learning results were compared: feedback during a learning task was either stated in terms of how well the students were performing relative to…

Trigonometry is an important section in mathematics that links algebraic, geometric and graphical reasoning. Many secondary school learners are not familiar with these types of reasoning; thus, trigonometry presents a challenge for these learners. The traditional 'chalk and talk' method of teaching trigonometry is used by many teachers; however,…

Using a simple trigonometric limit, we provide an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix.

This study combines the Japanese lesson study approach and mathematics teachers' professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of…

This dissertation reports the results of a qualitative research project that aimed to develop a research-based perspective on the purpose of trigonometry in the modern sciences. The investigation was guided by three objectives. First, the study sought to identify the purpose of trigonometry as described by educators and high school textbooks.…

Topics in trigonometry have not been well-studied, especially with college-level students. Thus, despite providing a venue for important concepts such as notions of proof and algebraic skill, the process of verifying trigonometric identities, or VTI, has not been thoroughly explored. This study attempts to remedy this gap in the literature by…

One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

Many types of visual representations are used in math textbooks but not all of them contain mathematically relevant information. Little research directly addresses the effects of different types of representations on mathematics performance. Theories offer differing perspectives about how visual representations such as illustrations influence…

The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument…

Students from small rural schools (class 1A, 2A, and 3A) historically have not had access to dual credit courses for several reasons including distance from a college campus, affordability, and district teaching strength. In an effort to address these problems and to begin the college experience sooner, a new program was developed by the…

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student…

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being…

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…