To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

The purpose of this study was to examine the impact and interactions of student-centered instructional techniques on College Algebra student engagement, mathematics attitudes, and achievement. At my place of practice, instructional shifts towards student-centered and social-efficiency models of instruction are taking place, supported by…

This preliminary study examined whether distinct student profiles (N = 760) emerged based on their behavioral patterns in an online algebraic learning game. We applied k-means clustering analysis to clickstream data collected in the game and then examined how students' behavioral patterns varied across the clusters using data visualization. The…

In online virtual-based learning, combining more adaptive personal student characteristics with risk factors, the purpose of this study was to examine the relationship between student at-risk factors and mathematics achievement. Further, the study examined how personal student characteristics, which are sometimes amenable to change and…

To address the disconnect and bridge the gap between mathematics and science education, we developed interdisciplinary lessons and real-world applications by integrating Algebra 1 and Biology in a collaborative cohort model. We aim to improve student engagement, knowledge transfer, and performance on assessments in both disciplines. The…

In issue 31(2) of the "Australian Senior Mathematics Journal", Kok (2017) describes a useful four-step process for investigating number patterns and identifying the underlying function. The process is demonstrated for both linear and quadratic functions. With respect to the quadratic example, I provide an additional idea relevant to step…

Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…

Issues within college algebra are well-documented. Over the past two decades, reform has brought about significant modifications in the course, yet to date there has been no synthesis of the efficacy of these efforts. This paper situates college algebra within a historical context, and synthesizes research on reform. I argue that, notwithstanding…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

Purpose: WebQuests are employed for many different instructional aims by offering students to take an active role and encouraging their critical thinking skills to construct their own meaning about an inquiry. The purpose of the study was to explore pre-service mathematics teachers' decisions about the organization of information sources in which…

Examples are an essential part of mathematics teaching and learning, used on a daily basis to teach and practice content. Yet, selecting good examples for teaching is complex and challenging. This article presents ideas to consider when selecting examples, drawn from a research study with algebra 2 teachers.

The purpose of this study was to examine the effects of algebraic equation solving intervention for sixth graders with mathematics learning difficulties (MD). A total of 48 students with MD were randomly assigned to either the algebraic equation solving intervention, "Mystery Math" (n = 24) or control condition (n = 24). The…

We present results of a grounded analysis of individual interviews in which students play Vector Unknown -- a digital game designed to introduce visualizing vectors, scaling vectors, vector addition, and vector equations, attending to the geometric and algebraic representations of vectors. The game was designed to be used at the beginning of a…

Randomized evaluations of educational technology produce log data as a bi-product: highly granular data on student and teacher usage. These datasets could shed light on causal mechanisms, effect heterogeneity, or optimal use. However, there are methodological challenges: implementation is not randomized and is only defined for the treatment group,…

This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…