This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes's method of exhaustion in order to compute the number p. Working in a computer environment, students inscribe and…

The Aboriginal English spoken by Indigenous children in remote communities in the Northern Territory of Australia is influenced by the home languages spoken by themselves and their families. This affects uses of spatial terms used in mathematics such as "in front" and "behind." Speakers of the endangered Indigenous Australian…

Knowledge that teachers bring to the teaching context is of interest to key stakeholders in improving levels of numeracy attained by learners. In this regard, the centrality of, and the need to investigate, the quality of teachers' mathematical knowledge for teaching mathematics has been gaining momentum in recent years. There is a general…

This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to…

Examples and explanations are inherent elements of mathematics learning and teaching. This study explores the relationship between examples and explanations given for the same concept. Results indicated that for the concept of parity, fifth grade students offer different explanations for different examples. However, for the concept of equivalent…

There are essential connections between the isoperimetric theory and information theoretic inequalities. In general, the Brunn-Minkowski inequality and the entropy power inequality, as well as the classical isoperimetric inequality and the classical entropy-moment inequality, turn out to be equivalent in some certain sense, respectively. Based on…

Mathematical fallacies have an embedded sense of awe and mystery that can be used effectively in a classroom to inspire students to tackle a fallacy and find the "hidden" violation. In doing so, the student may discover the consequence of a rule violation in a stimulating manner, thus making a lasting impact of the rule as well as providing the…

We present the quotient rule version of integration by parts and demonstrate its use.

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

This paper introduces a new matrix tool for the sowing game Tchoukaillon, which establishes a relationship between board vectors and move vectors that does not depend on actually playing the game. This allows for simpler proofs than currently appear in the literature for two key theorems, as well as a new method for constructing move vectors.We…

A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for…

Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

Characterizing how quantities change (or vary) in tandem has been an important historical focus in mathematics that extends into the current teaching of mathematics. Thus, how students conceptualize quantities that change in tandem becomes critical to their mathematical development. In this paper, we propose two images of change: chunky and…

The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…