Background: Many students solving quantitative problems in science struggle to apply mathematical instruction they have received to novel problems. The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon. Understanding the sensemaking opportunities…

The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…

Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

This paper conceptualizes children's mathematical thinking from a materialist perspective on language and mathematics. This perspective considers human and non-human bodies as ontologically equivalent; that is, as both being agentive, vibrant, and animated, thus resisting static representations. This conceptualization is an alternative to the…

Natural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that…

With mathematics education dominated by practices of standardized test alignment, the quest for mathematical understanding is adrift despite so much talk about the importance of STEM subject matters. To add to the confusion there has long been worries among educators about any curricular programs or instructional practices that can be labeled…

This is the fifth in a series of statistical articles for mathematics teachers. In this article the authors discuss graphs for exploring relationships between one categorical variable and one numerical variable using stemplots and boxplots and between two numerical variables, using scatterplots and time series plots. [For "The Data Files 4:…

Parents and caregivers can use the activities in this report to help youth learn to solve algebra problems using different strategies. Knowing different strategies for solving algebra problems may help your child approach algebra problems with confidence. Children could apply the most appropriate strategy for a particular problem or could try a…

To solve an unfamiliar mathematics problem, students of the subject must know more than the appropriate prerequisite content knowledge. They must also know how best to strategically apply their knowledge, how to monitor and gauge the effectiveness of their work, and how to respond (both cognitively and emotionally) to unanticipated results.…

Evaluation has become a common, and even an expected, practice across undergraduate mathematics tutoring centres in the USA, UK and other countries. However, these evaluation efforts could benefit greatly from leveraging organizational theory research. In this study, we situate mathematics tutoring centres as non-profit organizations (NPOs) to…

The study investigated the effect of self-regulated learning (SRL) on mathematics performance among learners in Kenya. The study employed Solomon four research design. A sample size of 408 grade 11 learners from four schools was obtained using stratified and simple random sampling techniques. Validity of the instruments was ensured with assistance…

Prior research has shown that brief motivation interventions, such as interventions targeting students' perceptions concerning relevance of the learning material, can have long-lasting effects on students' motivation and performance. However, the educational contexts in which these interventions have been implemented have their own motivational…

We present evidence of a secondary school teacher's Knowledge of Mathematics Teaching when she teaches linear equations in a word problem setting. We focus on analyzing the examples and mathematics support that she provides her students with during two classes. When faced with contingencies, she takes decisions whereby she adapts or creates…