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…

Many teachers of intermediate algebra or precalculus use an activity where balls are dropped from known heights and the heights of the bounces are recorded. The "bounce height" will be a roughly constant fraction of the "drop height." Then one can plot each bounce height against its bounce number, an exponential function can…

This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…

Precalculus and calculus are considered gatekeeper courses because of their academic challenge and status as requirements for STEM (science, technology, engineering, and mathematics) and non-STEM majors alike. Despite college mathematics often being seen as a neutral space, the field has identified ways that expectations, interactions, and…

Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school…

For quite some time, research on the use of the History of Mathematics in the classroom has confirmed a lot of academic benefits for students. However, the History of Mathematics can also be used as an inclusion tool in classrooms where there are foreign students because it allows working with the specific contexts of other cultures. This article…

The purpose of this quantitative, quasi-experimental study was to determine if, and to what extent, technology-enhanced problem-based formative assessment instruction would have an impact on college students' algebra learning and development of critical thinking skills, when compared to traditional classroom instruction in a first-year college…