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…

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…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

Students' previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding…

A cohort of pre-service mathematics students was exposed to a teaching strategy based on retrieval practice and test-potentiated learning. The aim of the study was to determine how high and low prior topic knowledge study participants compare in terms of their procedural fluency and conceptual understanding after exposure to the teaching strategy.…

This study presents the lived experiences of eight African American male recent high school graduates in their mathematics classes. These young men are currently attending various colleges across the United States in pursuit of obtaining a college degree. A few of the young African American men who were interviewed faced challenges during their…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

The goal of the paper is to understand to what degree the student success depends on teaching practices and materials, and to what degree it is due to differences in background, including prior knowledge, skills, preparation, abilities, etc. We analyzed the existing research on outcomes of the SAT and ACT in the United States and the Unified…

This study was conducted at a college in Ontario with a sample of students from the Game Development program for 5 intake years: 2014-2018, with the purpose of determining the validity of the Mathematics Diagnostic Test used to place 1st semester college students directly into an advanced math course (Math 10), or to leave them in the introductory…

Rubric has been associated with the term assessment used for grading and/or scoring. However, it might observe less, but it is also designed as students 'learning tool. This study was conducted to provide empirical facts on its effectiveness as a learning tool in teaching Applications of Derivatives in Basic Calculus. It used the…

One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

We present an embodied theory of transfer as applied to mathematical ideas. Project-based learning (PBL) offers important sites for investigating transfer because students and teachers must track mathematical invariant relations that are embedded in complex settings where knowledge and information is distributed and extended across various…

We examined whether students were accurate in predicting their test performance in both low-stakes and high-stakes testing contexts. The sample comprised U.S. high school students enrolled in an advanced placement (AP) statistics course during the 2017-2018 academic year (N = 209; M[subscript age] = 16.6 years). We found that even two months…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…