This study investigated students' procedural and conceptual knowledge of the definite integral. Twenty-five students enrolled in one section of an undergraduate Calculus II class participated in this study. Data were collected from a test that was conducted during the fourth week of the semester. The test aimed at collecting information about the…

Most readers would be familiar with the standard domino set which is played with rectangular domino tiles. The domino set, sometimes called a deck or pack, consists of 28 dominoes, colloquially nicknamed bones, cards, tiles, stones, or spinners. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games…

The concept of functional thinking as a foundational idea associated with algebraic thinking is explored by Tracey Muir, Leicha Bragg and Sharyn Livy. They provide ideas for using children's literature as a context to promote functional thinking

Contributing to a growing body of research addressing secondary students' quantitative and covariational reasoning, the multiple case study reported in this article investigated secondary students' quantification of ratio and rate. This article reports results from a study investigating students' quantification of rate and ratio as…

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

Color addition and subtraction apps in HTML5 have been developed for students as an online hands-on experience so that they can more easily master principles introduced through traditional classroom demonstrations. The evolution of the additive RGB color model is traced through the early IBM color adapters so that students can proceed step by step…

Using the work of philosopher Henri Bergson (1859-1941) to examine the nature of movement and memory, this article contributes to recent research on the role of the body in learning mathematics. Our aim in this paper is to introduce the ideas of Bergson and to show how these ideas shed light on mathematics classroom activity. Bergson's monist…

The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

Students enrolled in a middle school prealgebra or algebra course often struggle to conceptualize and understand the meaning of radical notation when it is introduced. For example, although it is important for students to approximate the decimal value of a number such as [square root of] 30 and estimate the value of a square root in the form of…

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an…

This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…

This study explored first-semester calculus students' understanding of tangent lines as well as how students used tangent lines within the context of Newton's method. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and…

This essay reflects on the challenges of thinking about scale--of making sense of phenomena such as continuous professional development (CPD) at the system level, while holding on to detail at the finer grain size(s) of implementation. The stimuli for my reflections are three diverse studies of attempts at scale--an attempt to use ideas related to…

Proportional reasoning is key to students' acquisition and application of complex mathematics and science topics. Research is needed regarding how students' progress towards and come to demonstrate key developmental understandings within proportional reasoning. To this end we created and administered assessment items to 297 middle grades students.…

The multiplication principle is a fundamental principle in enumerative combinatorics. It underpins many of the counting formulas students learn, and it provides much-needed justification for why counting works as it does. However, given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we document…