Many students struggle with the transition from arithmetic to algebra. Despite meta-analytic work on algebra instruction and calls for meta-syntheses of mathematics education topics, little has been done to synthesize the corpus of qualitative mathematics education research in algebra. The purpose of this meta-synthesis is to summarize the…

Completion of a quality Algebra course by 8th grade is a prerequisite for successful entry into STEM majors; thus best practices in this critical course must be as equitable as possible to support STEM recruitment and retention. However, if the research base for Algebra is under-examines some populations of students, structural inequity may be…

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

When students solve an algebra problem, students try to deduce the facts in the problem. This step is imperative, students can draw conclusions from the facts and devise a plan to solve the problem. Drawing conclusions from facts is called reasoning. Some kinds of reasoning are deductive, inductive, and abductive. This article explores the…

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

The Rural Math Innovation Network (RMIN) is a 4-year project that launched in January 2017 after receiving a $2.9 million Investing in Innovation (i3) development grant from the U.S. Department of Education (ED) and matching funds from the private sector. Virginia Ed Strategies and rural local education agencies (LEAs) in Virginia are implementing…

We investigated the impact of assistance on learning and affect during problem-solving activities with a computer tutor we built using the Cognitive Tutor Authoring Tools framework. The tutor delivered its primary form of assistance in the form of worked-out examples. We manipulated the level of assistance the examples in the tutor provided, by…

Grade inflation is pervasive in American high schools. Is rampant grade inflation cause for concern? How teachers' grading standards affect student success is an empirical question--one that the author addresses in this article in a new study of roughly 350,000 North Carolina students taking Algebra I between 2006 and 2016. The author first…

One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, can help us to meet this goal. In this case, it is presented the use of two techniques, which are a digital escape room, using…

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…

The learning of algebra represents a difficulty within the mathematics learning process. Precisely because of their epistemological and ontological nature, semiotics provides a good key to understanding the main difficulties that hinder the learning of algebraic objects. The answers to a large scale assessments task that requires a treatment in…

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

Dual-credit courses expose high school students to college-level content and provide the opportunity to earn college credits, in part to smooth the transition to college. With the Tennessee Department of Education, we conduct the first randomized controlled trial of the effects of dual-credit math coursework on a range of high school and college…

We describe how we supported middle-school students developing meanings for quadratic growth by bringing together three theoretical framings and designing a task sequence grounded in that framework. Specifically, this framework was assembled from the research on students' quantitative and covariational reasoning, Realistic Mathematics Education,…