In this article, we present the results of a research study that explores secondary students' capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school…

The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theory has been used to analyze teaching and students' learning in classrooms. In mathematics education, variation theory has also been used to explore…

In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P[subscript k](n) and Q[subscript k](n), such that P[subscript k](n) = Q[subscript k](n) = f[subscript k](n) for n = 1, 2,… , k, where f[subscript k](1), f[subscript k](2),… , f[subscript k](k) are k arbitrarily chosen…

Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.

In the present paper, we develop a teaching methodology for economic theory. The main contribution of this paper relies on combining the interactive characteristics of spreadsheet programs such as Excel and Unicode plain-text linear format for mathematical expressions. The advantage of Unicode standard rests on its ease for writing and reading…

A common formula presented in many managerial- and cost-accounting textbooks makes possible the determination of the quantity of units which must be produced and sold to generate a desired dollar-amount of operating income. This article addresses the question "What formula can be used to determine the quantity of units needed to yield a…

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),…