Most research on Cognitive Load Theory (Sweller, 1988) has uncovered many instructional design considerations for learning complex tasks. Additionally, the Community of Inquiry (Garrison, Anderson, & Archer, 2000) framework describes many of the learning experiences in online education. A gap existed in the literature for investigating…

The aim of this study is to characterise students' understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding…

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

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…

This contribution focuses on a scheme developed to characterize the level of difficulty of an examination in the course "Linear Algebra for Engineers" and on the transfer of the underlying idea to a similar scheme for examinations in the course "Analysis I for Engineers". Using these schemes, it is possible to define standards…

Although the simulation of an oxidation/reduction titration curve is an important exercise in an undergraduate course in quantitative analysis, that exercise is frequently simplified to accommodate computational limitations. With the use of readily available computer algebra systems, however, such curves for complicated systems can be generated…

In this paper we present a case study of an individual student who consistently used semantic reasoning to construct proofs in calculus but infrequently used semantic reasoning to produce proofs in linear algebra. We hypothesize that the differences in these reasoning styles can be partially attributed to this student's familiarity with the…

The Tennessee Department of Education explored course enrollment patterns in an effort to better understand in which courses students are enrolling and whether course enrollment policies and procedures are promoting students' interests. This report focuses on math course enrollment patterns throughout high school by following the 2013-14 twelfth…

Many researchers argue that a deep understanding of fractions is important for a successful transition to algebra. Teaching, especially in the middle years, needs to focus specifically on those areas of fraction knowledge and operations that support subsequent solution processes for algebraic equations. This paper focuses on the results of Year 6…

Researchers of mathematics education have been paying attention to the affective aspect of learning mathematics for more than one decade. Different theoretical frameworks have been suggested to analyze this aspect, where we utilize in the present research the discursive framework of Evans, Morgan and Tsatsaroni. This framework enables to link…

Many studies in mathematics education research occur with a nonrepresentative sample and are never replicated. To challenge this paradigm, I designed a large-scale study evaluating student conceptions in group theory that surveyed a national, representative sample of students. By replicating questions previously used to build theory around student…

The purpose of this study was to analyze the high school curriculum and instruction per pupil allocation and the effect on the Algebra I and English I State Assessment of Academic Readiness (STAAR) End of Course (EOC) scores. A mixed Analysis of Variance (ANOVA) was used to find if the high school curriculum and instruction per pupil allocation…

Over the last several years, iPads have become increasingly popular in the classroom. The number of available apps that could be used in the mathematics classroom are countless, but some make better mathematical learning tools than others. This research presents a set of sixteen criteria that can be used to evaluate the potential of an iPad app to…

Context personalization--the incorporation of students' out-of-school interests into learning tasks--has recently been shown to positively affect students' situational interest and their performance and learning in mathematics. However, few studies have shown effects on both interest and achievement, drawing into question whether context…

In response to students' difficulties with algebra, many have advocated for algebraic thinking in elementary schools as a route to algebra. However, many studies show students' difficulties with algebraic thinking and teachers' challenges with creating a context that supports reasoning. This article presents a constructivist-grounded theory of…