Backward transfer is defined as the influence that new learning has on individuals' prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students' prior ways of reasoning about linear functions. Two algebra classes and their teachers…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students' errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many…

The study examines pre-service mathematics teachers' perceptions of the integration of technology into algebra education. With the growing emphasis on technology in education, it is crucial to understand how pre-education teachers see technology and engage in it when teaching mathematics. The research aims to gain a view of their beliefs,…

AB 1705 requires colleges to validate their math placement policies and associated enrollment practices to ensure that students begin in coursework that gives them the best chance of completing the initial transfer-level math requirements for their academic goal. If students are required to enroll in prerequisite coursework prior to the…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

Well-designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th-grade students' (N =…

This exploratory study examined whether instruction aligned with the Institute of Education Sciences recommendations (i.e., use of worked examples, representations, deep questions) predicts student learning of early algebra, particularly inverse relations, in elementary classrooms. Instructional quality was determined through an…

The current study investigated how prior knowledge moderated the effects of three educational technologies ("From Here to There," "DragonBox 12+," and problem sets in "ASSISTments") on seventh-grade students' later algebraic knowledge. Pretest scores only moderated effects of "From Here to There," with…

According to the Standards for Educational and Psychological Testing (2014), one aspect of test fairness concerns examinees having comparable opportunities to learn prior to taking tests. Meanwhile, many researchers are developing platforms enhanced by artificial intelligence (AI) that can personalize curriculum to individual student needs. This…

According to the "Standards for Educational and Psychological Testing" (2014), one aspect of test fairness concerns examinees having comparable opportunities to learn prior to taking tests. Meanwhile, many researchers are developing platforms enhanced by artificial intelligence (AI) that can personalize curriculum to individual student…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

Educators increasingly recognize the importance of students' learning orientations, but relatively little is known about how these mindsets vary across and potentially shape educational settings. We use nationally representative data to document contextual variation in mathematics orientations in U.S. high schools. We find systematic variation in…

Comparison is an important mechanism for learning in general, and comparing two worked examples has garnered support over the last 15 years as an effective tool for learning algebra in mainstream classrooms. This study was aimed at improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to…

At a research university near the east coast, a college algebra class has been restructured into two large lectures a week, an active recitation size laboratory once a week, and an extra day devoted to active group work called Supplemental Practice (SP). SP was added as an extra day of class where the SP leader has students work in groups on a…