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…

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

We study the following family of integral-valued alternating sums, where -infinity equal to or less than m equal to or less than infinity and n equal to or greater than 0 are integers [equation omitted]. We first consider h[subscript m](n) for m and n non-negative integers and show that it is of the form 2[superscript n + 2m] - P[subscript m](n),…

This article focuses on four-parameter logistic (4PL) model as an extension of the usual three-parameter logistic (3PL) model with an upper asymptote possibly different from 1. For a given item with fixed item parameters, Lord derived the value of the latent ability level that maximizes the item information function under the 3PL model. The…

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…

There are many studies with a focus on examining and developing individuals' Technological Pedagogical Content Knowledge (TPACK). When examining these studies, one can recognize that these studies are usually conducted with preservice teachers. Nevertheless, examining teachers' preparation processes of classroom activities constitutes an important…

This quantitative study was designed to investigate the differences between the traditional high school and the Early College High School (ECHS) in a school district in southeast Texas. The purpose of this study is to determine the effect that participation in an early college high school program has on student attendance and achievement in…

This study examined the effectiveness of the iPad app Mathspace on high school students' algebra computation and skill maintenance. The participants in this study were four ninth grade students enrolled in beginning algebra at a large, urban high school. All four students were struggling to obtain grade-level algebra skills and were reported by…

The increasing amount of available subjective text data in internet such as product reviews, movie critiques and social media comments provides golden opportunities for information retrieval researchers to extract useful information out of such datasets. Topic modeling and sentiment analysis are two widely researched fields that separately try to…

This report presents key lessons from the third year of the Better Math Teaching Network (BMTN), a networked improvement community aimed at improving student-centered instructional practices. As a networked improvement community, BMTN educators use a collaborative work approach and quick-cycle testing to refine instructional routines, adjusting…