This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

The researchers conducted a microanalysis of two purposefully sampled sessions of a tutor working with a student with a learning disability (LD) engaging with multi-step equations with and without fractions. During the tutoring sessions, the student experienced quick, independent success on equations without fractions, but struggled considerably…

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…

Improving the algebraic concepts and skills of secondary school students with learning disabilities is critical for their success in college and in the job market. This research reviewed 12 studies to examine interventions for students with learning disabilities in relation to algebraic notions and competencies. The results indicate that in regard…

The design of the Cognitive Tutor Algebra I (CTA1) intelligent tutoring system assumes that students work through sections of material following a pre-specified order, and only move on from one section to the next after mastering the first section's skills. However, the software gives teachers the flexibility to override that structure, by…

Use of online credit recovery is a growing trend across the country, with the hope that expanding credit recovery options through online courses will help students get back on track toward graduation (e.g., Atkins, Brown, & Hammond, 2007; Gemin, Pape, Vashaw, & Watson, 2015). But expanded use of online credit recovery for high school…

This case study investigated the phenomenon of the black white test score gap by seeking to determine if there was a difference in the academic performance of African American students and their White peers. The determination of student academic performance was made using scores from second semester Algebra II classes at two high schools in the…

This research presents the analysis of image of the popular program packages: CAS (Computer Algebra Systems) Matlab, Mathcad, Mathematica, and the spreadsheet 'Microsoft Excel' among students of engineering specializations studying in Bauman Moscow State Technical University (BMSTU). The research has explored perception of program packages by all…

This study sought to answer if a relationship existed between required corequisite support and success in gateway College Algebra courses. Complete College America and Complete College Georgia initiatives over the last ten years have sought ways to increase access to higher education with high progression and completion rates. Efforts such as the…

The aim of this study is to question freshmen's conceptual knowledge on function. In this context, after the teaching of the function, students' skills of defining the concept of function, interpreting the definition and multirepresentation for the function were examined. In the study, qualitative research approach was adopted and was an example…

Prompted by the evidence of international tests of achievement that Swedish students have poor equation solving skills, this paper presents an interview study of upper secondary students' understanding of the topic. Students, from both vocational and academic tracks in two typical suburban upper secondary schools were invited to explain how a…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

The issue of early algebraic thinking is of great importance for the school life of young students. In this paper, the Father Woodland, a puzzle-like environment, is presented aiming to facilitate the use of algebraic thinking in early schooling. Seventy grade 3 students participated and their work was examined within Radford's (2011, 2014)…