Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

Desmos Battleship is an engaging activity in which students can improve their visualisation skills, and deepen their understanding of linear functions and circles by making connections between algebraic and graphical representations. The Desmos Battleship activity was used in a Saturday STEM (Science, Technology, Engineering, and Mathematics)…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

Multiple reports highlight the increasingly quantitative nature of biological research and the need to innovate means to ensure that students acquire quantitative skills. We present a tool to support such innovation. The Biological Science Quantitative Reasoning Exam (BioSQuaRE) is an assessment instrument designed to measure the quantitative…

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of…

In Canada, as in other Western countries, solving word problems has comprised an important part of mathematics curricula. Traditionally, arithmetic thinking has largely been privileged as the main strategy for solving word problems at the elementary level, thus postponing the introduction of algebraic thinking to the secondary school. Drawing on…

At a time of persistent unemployment, especially among the less skilled, many wonder whether our schools are adequately preparing students for the 21st-century global economy. Despite above average employment rates, firms are experiencing shortages of educated workers, outsourcing professional-level work to workers abroad, and competing for the…

The purpose of this study was to examine the relationship between scheduling and first-year-high-school students' exam scores on the South Carolina Algebra I End-of-Course (EOC) assessment. The study compared existing empirical data from two southeastern high schools from the same school district using 4 X 4 block schedules from 2011-2014 and…

Too many students do not learn algebra and therefore do not graduate from high school. This basic qualitative study conducted in a large suburban public school district explored the perspectives of high school seniors who were at least 18 years old and at risk for not graduating from high school because they had not demonstrated an adequate…

In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two…

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

This paper is based on a study which sought to examine the various errors and misconceptions committed by students in algebra with the view to exposing the nature and origin of the errors and misconceptions in secondary schools in Machakos district. Teachers' knowledge on students' errors was investigated together with strategies for remedial…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

This paper reports on a case study that aimed to evaluate the perceptions of 73 student teachers at Mukuba University on the nature and purpose of mathematical proof. They were presented with a mathematical reasoning and proof arguments assessment tool followed by a 10-member focus group interview. Algebraic tasks presented to them involved (i)…