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…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

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…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

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 research delves into the attitudes, perceptions, and motivations of student-athletes enrolled in Intermediate Algebra courses. It focuses on the distinct challenges they encounter in juggling academic and athletic responsibilities at a southeastern university in the United States. Employing a mixed-methods approach, the study gathered…

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…

This study explores learning vector addition and demonstrating the understanding of vector addition. Vector addition is a key skill in mathematics and science education, but there is a limited amount of research that focuses on this topic. My study investigates how an instructional design framework "concreteness fading" can be used for…

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…