This article describes how mathematics may be experienced in widely different ways across mathematics and physics courses and highlights some unexpected constraints in a trigonometry curriculum. The examples and discussion are based on a study (Mateas 2020) that compares how trigonometry is portrayed in representative physics (i.e., "Holt…

Trigonometry is an important part of secondary school mathematics, but it is usually challenging for students to understand and learn. Since trigonometry is learned and used at a university level in many fields, like physics or geodesy, it is important to have an insight into students' trigonometry knowledge before the beginning of the university…

Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of…

This study was conducted to compare two grade-ten mathematics textbooks according to Bloom's Taxonomies. In the Arabic version, 37 out of 70 periods (55.29%) were given to plane geometry and trigonometry, whereas 29 out of 70 periods (41.41%) were allocated for geometry and trigonometry. Also, 12 periods (17.14%) were allocated for algebra in the…

"University of Chicago School Mathematics Project" ("UCSMP") is a core mathematics curriculum that emphasizes problem solving, real-world applications, and the use of technology. The curriculum is based on a student-centered approach with a focus on active learning that incorporates reading and uses a flexible lesson…

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the…

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…

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…

In the deconstruction of the California state standards for trigonometry, linear algebra and mathematical analysis for the Cal-PASS (California Partnership for Achieving Student Success) Content Standards Deconstruction projects, it became apparent that terms were used for which no definition was given. The San Diego Central Cal-PASS Math…

A portion of all students in introductory or developmental undergraduate mathematics courses find themselves at an unfortunate tipping point: the border between passing and failing. These high-stakes courses often come with high enrollments, and a recurring problem: high failure rates. The measure of success used at the author's institution, the…

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at…

The purpose of this study was to: (a) investigate the effects of email to enhance learners' use of self-regulation strategies; (b) examine different effects between email list and individually addressed notes on the enhancement of self-regulation; (c) observe and record changes in self-regulation and self-efficacy; and (d) explore the…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

A process for eliminating the xy term in a quadratic equation in two variables is presented. The author feels this process will be within the reach of more high school students than more commonly used methods. (MK)