Alfinio Flores

Conceptions and practices of extraordinary mathematics teachers

Abstract Four teachers were identified as “extraordinary“ teachers of mathematics. Data gathered from interviews, tests on content knowledge, discussions during a series of seminars, and one observation in each teachers classroom were used in summarizing characteristics of these teachers under three headings: (a) their mathematical preparation and their content knowledge of mathematics: (b) their conceptions about mathematics, about learning, about teaching, about the roles of teachers and of students, and about the assessment of learning; and (c) their teaching practices. Within each of these three areas, many commonalities were found among these teachers. This article will describe these commonalities and make inferences about the conditions and support necessary for teachers to begin to adopt beliefs and practices necessary to sustain reform of school mathematics.

A History of Mathematics Course to Develop Prospective Secondary Mathematics Teachers' Knowledge for Teaching

Abstract The authors describe ways in which a history of mathematics course can help prospective teachers of mathematics develop knowledge they will need for teaching. The types of knowledge include content knowledge of mathematics, knowledge of mathematics for teaching, and pedagogical knowledge.

Using student-made games to learn mathematics.

Abstract First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses.

GEOMETRY OF NUMERIC ITERATIONS

ABSTRACT Simple numeric iterations can be represented by interesting geometrical patterns. Iterating different functions such as x → x 2(modp), and x → 2x(modp − 1) surprisingly generate essentially the same figures if p is prime. The fact that two cyclic groups have the same structure is used to explain why the two diagrams have the same shape.

Rowing competitions and perspective

This paper is about integrating the use of graphing technology (specifically, GeoGebra) with principles of motion, principles of perspective, and the concept of vanishing points to model a dynamic event. Students were asked to analyse video images of a rowing competition filmed with a single camera positioned perpendicular to the race. The fixed position of the camera in such races makes it difficult to determine whether a scull closer to the camera is actually overtaking another, more distant scull. The paper illustrates how students in their first year at the university can integrate the use of technology, science, mathematics, and writing to solve a real world problem involving motion.

Fermat's point from five perspectives

The Fermat point of a triangle is the point such that minimizes the sum of the distances from that point to the three vertices. Five approaches to study the Fermat point of a triangle are presented in this article. First, students use a mechanical device using masses, strings and pulleys to study the Fermat point as the one that minimizes the potential energy of the system. Second, students use soap films between parallel planes connecting three pegs. The tension on the film will be minimal when the sum of distances is minimal. Third, students use an empirical approach, measuring distances in an interactive GeoGebra page. Fourth, students use Euclidean geometry arguments for two proofs based on the Torricelli configuration, and one using Vivianis Theorem. And fifth, the kinematic method is used to gain additional insight on the size of the angles between the segments joining the Fermat point with the vertices.

Integrating Computers, Science, and Mathematics

A course for prospective secondary mathematics teachers was developed at the University of Delaware, based on professional recommendations to integrate science, technology, engineering, and mathematics in the preparation of teachers of mathematics. Students used GeoGebra, Cabri3D, and Mathematica to model phenomena in the physical, natural and social sciences. They used motion sensors and graphing calculators to study motion. They wrote Python programs to simulate random phenomena. They built a robot and controlled it with a computer program, and made explicit the mathematical and scientific concepts involved in the functioning of the robot. Several forms of formative and summative assessment were conducted during the course. Teachers learned alternative ways of looking at mathematical concepts, and established connections in mathematics and with other areas.

The mean as the balance point: thought experiments with measuring sticks

This article presents activities to help students establish a connection between the mean and the balance point of a lever. The lever and its law are discussed briefly. Thought experiments with a meterstick are presented to emphasize different properties of the mean and weighted averages.

History of mathematics and problem solving: a teaching suggestion

This note presents a teaching suggestion, using the history of mathematics, to give students from middle school and high school the possibility of facing problems found in old mathematics books and comparing their solutions with those given in those books.

Student-Made Games to Learn the History of Mathematics.

Abstract Prospective secondary mathematics teachers design their own adaptations of popular board and computer games to learn the history of mathematics.