Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

This paper reports the factors that three Year 11 mathematics students identified as influencing their choice to use a Computer Algebra System (CAS) for solving selected problems, some of which were expected to be outside their pen-and-paper (p&p) range. In individual interviews, the students were presented with eleven algebra problems and…

The purpose of this study was to determine if the size of a public school district or the amount allocated per-pupil in the state of Texas made a difference in student academic outcomes for special education students. The data evaluated in the study were the State of Texas Assessments of Academic Readiness (STAAR) Algebra I score and the Public…

Teachers' negative experiences can be detrimental to how they teach math because their beliefs about mathematics affect how they see themselves, their instructional practices, and the level of appropriate mathematics activities offered in their classrooms. Research has shown that there are many classrooms where appropriate activities are happening…

The literature shows that the integration of technological tools, like "GeoGebra," has the potential to improve the teaching and learning of mathematics. The aim of this study was to see whether "GeoGebra" could be used to address identified, systematic misconceptions that National Certificate Vocational (NCV) students hold…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

We present a design study developed in an Italian school. Taking inspiration from the work of the Russian psychologist V. V. Davydov, we have reformulated some activities of his curriculum for the first grade, in order to adapt them to a didactic project for a fifth grade class. In the paper we firstly expose our theoretical assumptions and the…

I propose that students pay more attention to the approximations that lead to integral formulas when they study applications of the definite integral. The goal is to focus students on the underlying concepts and the definition of the definite integral--and to steer them away from memorizing formulas. To address this goal, I have written some…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

In this article, Jason Taff shares an approach that he presented to advanced seventh-grade prealgebra students. He begins by summarizing some of the shortcomings of equating the order of operations concept with the PEMDAS (often rendered mnemonically as "Please Excuse My Dear Aunt Sally") procedure with the hope of helping teachers at…

This study focuses on how students in different postsecondary mathematics courses perform on domain and range tasks regarding graphs of functions. Students often seem to focus on notable aspects of a graph and fail to see the graph in its entirety. Many students struggled with piecewise functions, especially those involving horizontal segments.…

Informed by Gagne's belief in the necessity of prerequisite knowledge for new learning, and Bruner's Spiral Curriculum Theory, the objective of this case study was to explore the postsecondary pathway from remedial mathematics, through one gateway mathematics course, and into the quantitative literacy requirements of various non-STEM programs of…

In the United States, as the Hispanic population continues to grow, persistently low mathematics achievement among Mexican Americans continues to exist, particularly among girls. Low mathematics achievement places this group in a disadvantaged position. As such, a multistage mixed method study was implemented to investigate possible factors…

English schoolchildren do not fare well in international comparisons of mathematical, particularly algebraic, ability. I believe that this is at least partly due to algebra being traditionally taught using only symbols, ignoring the enactive-iconic-symbolic trajectory described by Jerome Bruner, which says that experiencing the way in which…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…