Although lesson study has been shown to improve the teaching and learning of mathematics, little research has focused on reasons for engaging in it from a teacher's perspective, particularly after sustained engagement with lesson study. This qualitative study reports on thirty-three teachers from the United States who were involved in twelve…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

This study examined the implication of the Algebra Connection Essay in a developmental algebra course. Undergraduate students (n=18) in four Intermediate Algebra courses were administered a pre-attitudinal survey prior to receiving information on the essay about their chosen or desired program of study. After submitting the essay, the students…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the…

The development of math reasoning and 3-d mental rotation skills are intertwined. However, it is currently not understood how these cognitive processes develop and interact longitudinally at the within-person level -- either within or across genders. In this study, 553 students (52% girls) were assessed from fifth to seventh grades on 3-d mental…

The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying algebraic equations and inequalities, and the extent to which teachers are aware of these mistakes and how they assess them. The study was conducted among 50 ninth grade students and 63 practicing teachers of mathematics. The data…

Poor completion outcomes in community colleges' developmental education programs have spurred reforms in developmental education policies and practices in order to increase students' chances of success. In the case of developmental math, the focus of this article, such changes include revisions to testing and placement policies, amendments to the…

Given the demands on Indiana schools to continually improve student performance results on End of Course Assessments, it is important to define the organizational structures, instructional methodologies and leadership strategies that result in student performance increases. This study compared student performance results on the Algebra I End of…

We developed generalizable affect detectors using 133,966 instances of 18 affective states collected from 69,174 students who interacted with an online math learning platform called Algebra Nation over the entire school year. To enable scalability and generalizability, we used generic interaction features (e.g., viewing a video, taking a quiz),…

The purpose of this study was to examine the effects of a vocabulary tutoring intervention with defining key vocabulary terms and algebraic problem-solving skills of students who struggle with mathematics. Literature shows that there is a need to further explore how students with mathematical learning difficulties learn mathematics vocabulary at…

Students experience great social and academic challenges during their first semester of college and for many, the completion of required mathematics courses is one of those challenges. This study investigated the relationship of first-time college freshmen's mathematics course enrollment, gender, and high school mathematics course experience to…

The purpose of this study is to investigate the effect of use of graphing calculators on student achievement in Common Core Algebra I. The following are the research questions of the proposed study. To what extent does use of graphing calculators in the math classroom affect student achievement? How might the use of graphing calculators in the…

Functions form a central part of the U.S. mathematics curriculum especially at the high school level. There is a considerable body of research showing that students at all levels, including preservice secondary mathematics teachers, have difficulties with the definition of function as a correspondence between two sets with a univalence condition.…