This paper initiates a teaching sequence that focuses on building up equivalent definitions to the standard ones for the limit concept in Real Analysis. It comprises two parts: The first provides a classroom assignment where students, guided by Analysis lecturers, are led to develop an alternative definition to the [epsilon] - [delta] one for…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Sports mega-events offer rich and varied opportunities for educating students on key concepts defining geographical ways of thinking. Concept-learning, central to students' development, can be enhanced by issue-based enquiries that enable them to personalise and apply concepts in meaningful and memorable ways. A diverse range of activities…

Research-based assessments (RBAs) measure how well a course achieves discipline-specific outcomes. Educators can use outcomes from RBAs to guide instructional choices and to request resources to implement and sustain instructional transformations. One challenge for using RBAs, however, is a lack of comparative data, particularly given the skew in…

When students think of evolution, they might imagine T. rex, or perhaps an abiotic scene of sizzling electrical storms and harsh reducing atmospheres, an Earth that looks like a lunar landscape. Natural selection automatically elicits responses that include "survival of the fittest," and "descent with modification," and with…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

This article discusses and elaborates on how concept mapping as a specific instructional strategy helps students to externalize and transform their understanding of qualitative research; and helps instructors to focus on their students' conceptual understanding of qualitative research. The discussion focuses on concept mapping as a learning…

As students learn physics, they are often required to reason about the behavior of macroscopic and microscopic phenomena, and to synthesize prior knowledge from several different areas of physics to construct understanding of new ideas. This can be a tremendously difficult cognitive task for novice students, especially when the unfamiliar…

Fractions are an imperative skill for students to master to achieve success in future mathematics concepts and classes. Yet many students, especially those experiencing math difficulties and/or characteristics of emotional and behavioral disorders, continue to exit elementary school without a concrete foundation of fractions skills required to…

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 premiere book in the STEM for Our Youngest Learners Series introduces the Infant Toddler Inquiry Learning Model, a new way to think about how young children (birth-age 3) explore, think, and learn STEM concepts. The book also demonstrates how the Inquiry Teaching Model can guide teachers in implementing STEM experiences for this age group.…

This bibliometric analysis investigates the impact of Project-Based Assessments (PBAs) on conceptual understanding in STEM education from 2019 to 2024. By examining a dataset of 996 publications, the study highlights significant fluctuations in research outputs and the evolving focus on educational methodologies, particularly noting an…

Math educators must engage students in deep learning and talk spanning shorter, medium, and longer time frames to offer both the structures and language so that secondary English learners can participate fully alongside their classmates. In this article, the authors present: (1) "structure and language" to facilitate full participation…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…