Although algebraic reasoning has been considered as an important factor influencing students' mathematical performance, many students struggle to build concrete algebraic reasoning. Metacognitive training has been regarded as one effective method to develop students' algebraic reasoning; however, there are no published meta-analyses that include…

The paper focuses on four upper secondary students' collaborative small-group mathematical reasoning (MR) with respect to a sinusoidal function. The students were collaboratively engaged in a process of MR regarding the relationships between mathematical theoretical descriptions of parameters in the algebraic expression of the sinusoidal function…

The purpose of this mixed-methods case study is to analyze the engagement levels of low-achieving high school seniors enrolled in a basic algebra course called Pre-College Algebra. The term low-achieving pertains to the class member participants enrolled in a course that is perceived and even described as the less rigorous of the choices of all…

Thirty-seven preservice teachers engaged in a self-regulated learning experience proposed to increase their algebra content knowledge and to examine their use of data to make instructional decisions. Using weekly algebra curriculum-based measures, preservice special education teachers set learning goals and objectives, individually selected and…

There is increasing evidence for the impact of spatial training on mathematics performance in early years of education, however little research has focused on secondary school environments, which are traditionally more discipline driven. In the present study, a large-scale classroom-based intervention saw the introduction of twelve hours of…

This paper explores misconceptions and errors (M/Es) of eighth-grade students in Nepal with a quasi-experimental design with nonequivalent control and experimental groups. The treatment was implemented with teaching episodes based on different remedial strategies of addressing students' M/Es. Students of control groups were taught under…

In this study, conceptual and algebra-based physics students were engaged in scientific inquiry using Physics Education Technology (PhET) interactive simulations via semester-long group projects. The instructor and students used the Scientific Abilities Assessment Rubrics (SAAR) to evaluate project presentations and papers (formative assessment).…

Students with a mathematics learning disability face many challenges learning algebraic curricula. To support this population, targeted supplementary instruction beyond what is provided by a classroom teacher may benefit their learning outcomes. In this context, video modeling designed in accordance with an established instructional design…

This paper analyzes the content and tasks involving quadratic equations in eight mathematics textbooks published during the period 2000-2012 at the uppersecondary level in Sweden. The study applies the theoretical "hypothetical learning trajectory" (HLT) framework combining "conceptual" and "procedural" knowledge. The…

Quantitative Reasoning for Professionals is a two-semester general education sequence that teaches basic and intermediate algebra through the lens of quantitative reasoning. In this course sequence, we emphasize communication and inference-making while teaching practical algebra skills for students in programs such as business, nursing, and social…

We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom's taxonomy and then used to code exam problems. We have analyzed historical and recent exam problems in both algebra-based and calculus-based exams. In…

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either…

The percentage of college students receiving unproductive grades in introductory mathematics courses is a concern for post-secondary institutions across the country. Many factors can be targeted as potential explanations for this lack of success, yet none of these issues are more noteworthy than the fact that many students enter college…

Generalization is a critical component of mathematics learning, but it can be challenging to foster generalization in classroom settings. Teachers need access to better tools and resources to teach for generalization, including an understanding of what tasks and pedagogical moves are most effective. This study identifies the types of instruction,…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…