If an empty coffee cup is spun on a horizontal surface about a vertical axis in an anti-clockwise direction, then the whole cup rotates slowly backwards, in a clockwise direction, about a vertical axis located outside the cup. Clues to this curious behaviour are presented by comparing it with other spinning objects.

How many vertical jumps does it take to jump off of a rotating merry-go-round (MGR)? The answer is hidden in the expression: "r[subscript n]" = "r[subscript 0]" (1 + ["beta superscript 2") ["superscript n/2"]. When you make a vertical jump on a train moving on a straight line at constant speed (inertial…

Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students' conceptual understanding of these important ideas. We describe how students' work with digital activities, "techtivities," linking two different looking graphs that represent relationships…

Genetic variation is historically challenging for undergraduate students to master, potentially due to its grounding in both evolution and genetics. Traditionally, student expertise in genetic variation has been evaluated using Key Concepts. However, Cognitive Construals may add to a more nuanced picture of students' developing expertise. Here, we…

Introduction: Psycholinguistics presents a challenge to teaching and learning because of the many abstract models in the field. Language-related games provide a vehicle for students to ground and demonstrate their understanding of these models. Statement of the problem: Models in psycholinguistics are challenging to teach and learn because they…

Evaluating evidence and restructuring beliefs based on anomalous evidence are fundamental aspects of scientific reasoning. These skills can be challenging for both children and adults, especially in domains where they possess inaccurate prior beliefs that can interfere with the acquisition of correct scientific information (e.g., heavier objects…

Design-based learning (DBL), a pedagogical approach to integrating science, technology, engineering, and mathematics (STEM) education, has been internationally promoted in K-12 curricula. Despite DBL's variations, research has indicated it can facilitate students' content learning. However, it is less clear whether DBL can foster students' STEM…

In many cultural contexts, judging another as conscious or not has profound practical, legal, and philosophical consequences. However, little research focuses on how our ability to make such judgements arises. Thirty years ago a classic set of studies by Flavell et al. demonstrated that children do not develop a complex understanding of conscious…

In order to create and foster learning spaces that build upon children's knowledge and experiences, we must respect and value their ways of knowing and being, including their play. Accordingly, this study highlights the ways that young children (re)imagined spaces, materials, and identities through their digital play in an analog (containing no…

Data reported from memory can be unreliable. A simple activity lets students experience this firsthand.

Here we build from the central strength of the existing definition of dyslexia--its emphasis on neurobiological origins--and proffer a set of seven core principles for a new, more comprehensive conceptualization of dyslexia. These principles derive from two major research directions: (1) the still evolving history of attempts to explain dyslexia,…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

In this report, we analyze students' learning of compound probability by describing connections they generated while engaged with tasks involving two independent events. Several of their connections were compatible with the development of expertise, such as recognizing the need to determine sample spaces across a variety of situations and noting…

We attend to the composition of even and odd functions, as featured in imagined dialogues between a teacher and students, composed by sixteen teachers in a professional development program. Data were analyzed as aimed at addressing students' intellectual needs, with particular attention to the need for causality and the need for certainty. The…

This study aims to explore the middle schoolers' common naive conceptions of AI and the evolution of these conceptions during an AI summer camp. Data were collected from 14 middle school students (12 boys and 2 girls) from video observations and learning artifacts. The findings revealed 6 naive conceptions about AI concepts: (1) AI was the same as…