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…

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…

An understanding of structure-function relationships in proteins is essential for modern biochemical studies. The integration of common freely accessible bioinformatics tools available online with the knowledge of protein-engineering tools provide a fundamental understanding of the application of protein structure-function for biochemical…

This Family and Practitioner Brief discusses how deaf children who have not had access to a complete language from birth often encounter unique challenges in developing academic language skills, particularly in the realm of inference-making.

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…

We use the framework of cognitive resources to investigate how students construct understanding of a complex physics topic, namely, a photovoltaic cell. By observing students as they learn about how a solar cell functions, we identified over 60 distinct resources that learners may activate while thinking about photovoltaic cells. We classify these…

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…

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…

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…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Analogy is a powerful tool for fostering conceptual understanding and transfer in STEM and other fields. Well-constructed analogical comparisons focus attention on the causal-relational structure of STEM concepts, and provide a powerful capability to draw inferences based on a well-understood source domain that can be applied to a novel target…

Visualizations are useful tools for helping students to understand chemistry concepts at the particulate level. A classroom activity was developed based on learning theory and evidence-based practices, combining protein visualization with thermodynamic parameters from differential scanning fluorimetry (DSF) data analysis. Coding of student…

The abstract nature of quantum mechanics makes it difficult to visualize. This is one of the reasons it is taught in the language of mathematics. Without an opportunity to directly observe or interact with quantum phenomena, students struggle to develop conceptual understandings of its theories and formulas. In this paper we present the process of…