Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

The rules of indices, e.g. a[superscript n] b[superscript n] = (ab)[superscript n], are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered…

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First,…

Growth in two subscales, Informal and Formal Mathematics Skills, of the "Test of Early Mathematics Abilitity-3" (TEMA-3) was explored in a sample of 281 children. Children were identified as either typically developing (TYP; n = 205) or having mathematics difficulties (MD; n = 76) based on their total TEMA-3 score at the end of…

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from "R"[superscript 2] to "R" at a point "P"[subscript 0] focusing on the formal definitions. Alternative definitions and other…

We analyze the process of constructing a definition within the theoretical framework of "Abstraction in Context." Pairs of students were engaged in a task designed to engender a need for a definition of a tangent to a graph at a given point, and lead to constructing a definition following that need. The results of our analysis point to…

How students' rigid perceptions of mathematics persist over years has been a conundrum. Students not only think that only one solution exists for a mathematical task (Schoenfeld 1985) but also rigidly fuse mathematical concepts with specific tasks. Students deserve to learn a variety of mathematical strategies to flexibly deploy at will. Teaching…

The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In…

Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by: (1) using a teacher as the implementer; (2) providing teacher flexibility in intervention…

In many educational systems, textbooks are a leading factor for daily instructional practices, and consequently may affect educational outcomes. Whereas in many countries textbook assessment is a common practice in light of evaluating and improving educational effectiveness, in other countries these practices are absent, mainly under the realm of…

Although it is common for researchers to assess implementation fidelity (IF) within the context of math intervention, IF assessments are often restricted to intervention adherence. Further, the degree to which IF influences observed outcomes is commonly ignored. The current study examined the relationship between three aspects of IF and the math…

Many school psychologists work in schools that have low proficiency rates on the year-end test of mathematics, which is concerning because math proficiency is a powerful indicator of long-term academic success. Addressing math instructional problems is not easy work. One reason the authors examine is that the work is so challenging for school…

One of the most intransigent problems in mathematics education is the culturally-influenced divide between classroom practice and educational research. This paper describes our explicit attempt to bridge that divide by translating research on instructional practices linked to improving students' mathematics achievement into a brief guide outlining…

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.…

This action research study examined the effects of review games using Kahoot! on students' quiz scores as well as student engagement. The study was conducted in a high school geometry classroom at Tiyan High School (THS) in Barrigada, Guam. This study consisted of a sample size of 42 students in the 10th through the 12th grade. The data collected…