The current study examines both student self-regulated learning (SRL) and teacher orchestration in a virtual learning environment (VLE), with respect to student achievement. The study used SRL indicators derived from the log data on how students used the VLE system, survey data on how teachers made use of the VLE for Algebra instruction, as well…

There have been recent pushes for more active learning in mathematics classrooms, especially at the undergraduate level. To incorporate more active learning, there is a need for tasks that explicitly support this type of instruction, attention to student reasoning and whose ideas are publicly acknowledged, and awareness of differences in students'…

This article reports on an analysis of the process in which "knowledge to be taught" was transposed into "knowledge actually taught," concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical…

Discovery learning has long been a part of mathematics teaching in the elementary and middle grades. Since the 1960s and 1970s, based on the work of Jean Piaget, Jerome Bruner, and others, helping students 'discover' or 'construct' their own understandings of mathematical concepts through well-designed activities facilitated by a competent teacher…

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…

This study is concerned with the reasoning that undergraduates apply when deciding whether a prompt is an example or non-example of the subspace concept. A qualitative analysis of written responses of 438 students revealed five unconventional tacit models that govern their reasoning. The models account for whether a prompt is a subset of a vector…

We present two empirical studies with 241 and 211 pre-service teachers that evaluate the explanatory power of word order matching and static comparison as models for the reversal error. We used tasks consisting of generating an algebraic equation representing a comparison given in a verbal statement. We introduce the types of magnitude involved in…

Even though algebraic ideas are addressed across a number of grades, algebra continues to serve as a gatekeeper to upper mathematics and degree attainment because of the high percentage of students that fail algebra classes and become halted in their educational progress. One reason for this is students not having the opportunity to build on their…

In this report, we present an analysis of two prospective secondary mathematics teachers' generalizing actions in quantitative contexts. Specifically, we draw from a teaching experiment to report how Lydia and Emma engaged in different generalizing processes for the same task. Based on these differences, we found Lydia's generalizing actions…

This research presents the analysis of image of the popular program packages: CAS (Computer Algebra Systems) Matlab, Mathcad, Mathematica, and the spreadsheet 'Microsoft Excel' among students of engineering specializations studying in Bauman Moscow State Technical University (BMSTU). The research has explored perception of program packages by all…

This study sought to answer if a relationship existed between required corequisite support and success in gateway College Algebra courses. Complete College America and Complete College Georgia initiatives over the last ten years have sought ways to increase access to higher education with high progression and completion rates. Efforts such as the…

The aim of this study is to question freshmen's conceptual knowledge on function. In this context, after the teaching of the function, students' skills of defining the concept of function, interpreting the definition and multirepresentation for the function were examined. In the study, qualitative research approach was adopted and was an example…

Prompted by the evidence of international tests of achievement that Swedish students have poor equation solving skills, this paper presents an interview study of upper secondary students' understanding of the topic. Students, from both vocational and academic tracks in two typical suburban upper secondary schools were invited to explain how a…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

The issue of early algebraic thinking is of great importance for the school life of young students. In this paper, the Father Woodland, a puzzle-like environment, is presented aiming to facilitate the use of algebraic thinking in early schooling. Seventy grade 3 students participated and their work was examined within Radford's (2011, 2014)…