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…

While mathematics and reading instruction share an emphasis on vocabulary, strategies may seem in conflict. Use the strategies presented here for connecting new learning to previous knowledge and experiences and providing meaningful paths for students' vocabulary development in the mathematics classroom.

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

This paper describes a course designed to introduce students to mathematical thinking and a variety of lower level mathematics topics using baseball while satisfying the goals of quantitative reasoning. We give suggestions for sources, topics, techniques, and examples so any mathematics teacher can design such a course to fit their needs. The…

This paper focuses on the importance of identifying students' Prior Knowledge (PK) for the teaching and learning of mathematics. Specifically, we present a framework that exemplifies the core elements teachers need to consider in relation to the purpose, design and implementation of learning experiences that enable PK to be activated and assessed.…

Introductory calculus is mandatory for postsecondary science, technology, engineering, and mathematics (STEM) majors (Bressoud, 2015); however, many students do not persist through introductory calculus to further STEM study (Rasmussen et al., 2019). One reason for this may be that students struggle with the prior mathematical knowledge required…

Poor mathematics preparation severely restricts students' future educational and occupational choices. This paper explores the extent to which differences were observed in the pedagogical practices of those teaching college introductory college math at a community college and at a four-year college. Although college math instructors generally may…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math…

Digital curricula can constrain teachers with ready-made instructional materials. The authors used Mathematics Teaching Practices (MTPs) to modify a digital curriculum to engage students in more thoughtful and meaningful lessons. In this article, the authors visit one of their third-grade classrooms, in which they used the prescriptive digital…

This article describes students learning to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values. The students used the Egyptian hieroglyphic numeral system in conjunction with this activity to connect learning in other subjects. Students used prior knowledge of place value to…

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…

Previous studies have proposed that students' mathematical understanding develops dynamically through the process known as folding back, in which learners revisit earlier forms of understanding and use them to build even deeper levels of mathematical understanding. Digital learning environments, where students can manipulate representations, are…

The aim of this study is to provide data to better understand the processes of early mathematical modelling. According to this, an early mathematical modelling activity carried out by 21 Spanish schoolchildren aged 5-6 years is analysed, using the validated tool "Rubric for the Evaluation of Mathematical Modelling Processes" (REMMP). The…