We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…

Three mathematics teacher educators who were assigned to teach fundamental concepts of algebra course in a teacher education college, as well as their prospective elementary mathematics teachers who took the course, took part in a job embedded, context-specific, and content-based comprehensive professional development (PD) program on assessment…

The overarching aim of this article is to exemplify and analyse how some algebraic aspects of equations can be theoretically explored and reflected upon by young students in collaboration with their teacher. The article is based upon an empirical example from a case study in a grade 1 in a primary school. The chosen lesson is framed by the…

This study presents a novel video recommendation system for an algebra virtual learning environment (VLE) that leverages ideas and methods from engagement measurement, item response theory, and reinforcement learning. Following Vygotsky's Zone of Proximal Development (ZPD) theory, but considering low affect and high affect students separately, we…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

In this dissertation in practice, the background of middle grades mathematics acceleration detailed why the organization benefited from a program analysis. Middle grades mathematics acceleration encourages students to take high school Algebra I in eighth grade so they can earn college-level math credits for free in high school. Often acceleration…

The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal…

NP-complete problems such as the traveling salesman problem (TSP) play a prominent role in most advanced undergrad/graduate courses in discrete optimization modeling. Teaching such an important topic from a purely mathematical perspective without discussing specific applications may result in reduced student interest and motivation. The DeLand…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion…

Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom's and its relationship to algebraic thinking and reasoning. The data sources include classroom observations, field notes,…

One does not have to teach for very long to see students applying the wrong formula in the wrong situation (e.g., Kirshner and Awtry 2004; Tan-Sisman and Aksu 2016). Students can become overreliant on the power of the formula instead of thinking about the relationships it describes. It is not surprising that students can see formulas as a way to…

This paper reports a study developed with twenty-six students from a 7th-grade class and was carried in the context of teaching experience in the school year of 2016/2017, using an applet, Equation Buster, on the learning of solving single-variable linear equations. The research objectives are to assess how this applet can help students to see the…