In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

This study contributes to the call for influencing practice by increasing attention to how learning environments can be designed to support learning in statistical inference. We report on a design experiment in secondary school (students 14-16 years old), that resulted in a set of lessons with the learning goal of teaching students how to apply…

This paper presents research into closed orbits parallel to quadrilaterals inscribed in various geometric shapes that can be represented by mathematical functions: straight lines, circles, ellipses, parabolas, and hyperbolas. Mathematical proofs have been given for the existence of an infinite number of parallel orbits for each of these shapes.…

The paper addresses concept formation processes of a student in the field of geometry. More precisely, the paper deals with the question of how to assist a student in a mathematical concept formation process -- in the context of area calculations in triangles -- with a specially designed learning environment based on the usage of 3D printed…

The benefits of technological and theoretical scaffolding were observed when pre-service teachers aiming to teach upper elementary grades were given three learning-based geometrical inquiry tasks involving inscribed circles. They were asked to collaboratively examine the accompanying geometrical illustration and data for some new or interesting…

To test the hypothesis that a higher tendency to "s"pontaneously "f"ocus "o"n "m"ultiplicative "r"elations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional quantities, we presented sixth graders (n = 112) with fraction number line estimations and a…

Cognitive load theory (CLT) uses working memory resources depletion to explain the superiority of spaced learning, predicting that working memory resources will be less taxed if there are resting/spacing periods inserted between learning tasks, in comparison to learning from the same tasks in a single session. This article uses the working memory…

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a "target…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Currently, the number of science, technology, engineering, and mathematics (STEM) jobs are expanding faster than the U.S. labor market; yet many individuals with STEM degrees choose to work in other fields. The present study uses social cognitive career theory as a framework for researching the impact of several variables on future expectations to…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

This study sets out to investigate the attitude KS3 pupils have towards mathematics and the factors that influence this attitude. A case study approach was used as the pupils were a unit of the school under study and a survey method was chosen to provide scope to the study. Purposeful sampling was employed for the selection of 200 pupils from…

This study assessed the demographic characteristics of students' performance in Mathematics in senior secondary Certificate Examination in Delta Central Senatorial District of Delta State. The purpose of the study is to assess the relationship between gender, location, socio-economic status and students' performance in Mathematics in Senior…