In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict…

The goal of learning analytics is to optimize learning and the environments in which it occurs. Since 2011, when learning analytics was defined as a separate and distinct area of academic inquiry, the literature has identified a need for research that presents evidence of effective learning analytics, as well as, learning analytics research that…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

Theorising STEM Education in the 21st Century is a book that captures the essence of Science, Technology, Engineering and Mathematics and the intricacies of STEM education in the contemporary society. It explores STEM as an interdisciplinary field as well as the individual disciplines that make up STEM. This ensures the field of STEM as a whole is…

This study utilized an innovative data analysis approach to examine how engineering undergraduates engaged in mathematical modelling. Individual modelling routes were constructed via modelling activity diagrams and were used to critically examine the theoretical framework. Implications for the theoretical model are offered along with implications…

The "gender gap" on various physics conceptual evaluations has been extensively studied. Men's average pretest scores on the Force Concept Inventory and Force and Motion Conceptual Evaluation are 13% higher than women's, and post-test scores are on average 12% higher than women's. This study analyzed the gender differences within the…

This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Social cognitive research has linked students' perceived academic capabilities, or self-efficacy, to academic choices, self-regulation, and performance in diverse contexts from reading comprehension to mathematical problem solving. This study addressed a need to investigate the interactions among prior achievement, self-efficacy, calibration (the…

In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

These conference proceedings include two invited lectures, three working group reports, three topic group reports, two Ad Hoc group reports, a round table report, a list of participants, and a list of previous proceedings. The invited lectures were: "Values in Mathematics Education" (Ubiratan D'Ambrosio) and "Remarks on…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…