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…

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…

This study examined the effects of shared representational guidance (collaborative textural representative tool vs. collaborative graphical representative tool; TR vs. GR) and prior knowledge (low vs. high; LPK vs. HPK) on different levels of individuals' understanding of specific-domain knowledge after collaborative problem solving (CPS). A total…

Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep…

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…

Kinetic energy is usually the entry point for the study of energy in physics and is often perceived as unproblematic. We present evidence, however, that some learners who seem to have accepted the concept, from elementary school students to college physics majors and in-service teachers, nevertheless do not consistently attribute kinetic energy to…

The Force Concept Inventory (FCI) is a popular multiple-choice instrument used to measure a student's conceptual understanding of Newtonian mechanics. Recently, a network analytic technique called module analysis has been used to identify responses to the FCI and other conceptual instruments that are preferentially selected together by students;…

This lesson focuses specifically on teaching concepts of speed and its impact on energy, as well as providing a basic introduction to potential and kinetic energy to fourth-grade students. "Next Generation Science Standards" ("NGSS") 4-PS3-1 states that students should be able "to use evidence to construct an explanation…

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 COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

In this article, the author describes strategies to support students in conjecturing in ways that promote their agency. Conjecturing involves justifying (i.e., a practice that promotes epistemic agency and engages students in mathematical reasoning to defend their claims; Bieda & Staples, 2020) by which a conjecture becomes proven, modified,…

Queer theory taught at historically Black colleges and universities often meets with resistance from students. This article proposes a means by which to overcome this resistance. Deferring resistance involves encouraging students to approach queer theory texts in the same vein as they have approached texts earlier in the course. By building upon…

This study examined the extent to which college algebra instructors employ pedagogical practices previously found to assist students master difficult STEM content material and address their own previous math deficits. Faculty classroom behaviors were assessed with a modified version of the Generalized Observation and Reflection Platform (GORP).…

Introductory science courses can be a struggle for instructors and students not only because of the challenging nature of the material, but also due to differences in the background knowledge of students. Provision of pre-lecture resources reviewing or introducing key concepts is recommended to support diverse students. In this paper, we describe…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…