The purpose of this study was to investigate the errors experienced by students learning with REACT strategy and traditional learning in solving problems of mathematical representation ability. This study used quasi experimental pattern with static-group comparison design. The subjects of this study were 47 eighth grade students of junior high…

The exponential increase in the number of cases and number of affected countries of the novel coronavirus disease 2019 (COVID-19) brought significant change in the mode of instruction from face-to-face to distance learning among the different levels of education around the world. This descriptive-developmental method of study adopted the ADDIE…

A visual proof that sin x/x is monotonically increasing on (0, pi/2). For tan x/x, see p. 420 (EJ1017686).

A visual proof that tan x/x is monotonically increasing on (0, pi/2). For sin x/x, see p. 408 (EJ1017684).

A "k"-out-of-"n" system functions as long as at least "k" of its "n" components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting…

A number of papers find the velocity that minimizes the wetness of a traveler caught in the rain. In this capsule we determine, in addition, the necessary amount of forward bend (slouching) so that the traveler stays as dry as possible.

We count the number of group homomorphisms between any two dihedral groups using elementary group theory only.

Combining D'Alembert's ratio test and Cauchy's condensation test, we present a new ratio test for any positive monotone series.

In the popular television show "Survivor", the winner of a million-dollar prize is determined in a final election, where the votes are read aloud as the winner is announced. We hypothesize that the show's producers purposely alter the order of the ballots in order to build audience suspense. We test our hypothesis using the Poisson binomial…

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

The Common Core State Standards for Mathematical Practice (CCSSI 2010) elevate the ways of thinking used to create mathematical results to the same level of importance as the results themselves. These mathematical habits of mind (MHoM), or "specialized ways of approaching mathematical problems and thinking about mathematical concepts that…

Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

The technique of "group-averaging" produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being well-known in typical courses on algebra or geometry. The material makes an excellent discovery project, especially for students with some background in…

In this paper, we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a theorem, emphasizing that a definition was just an arbitrary assumption, a student rejected the…