In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

Background: In learning astronomy, students need to shift between 3D and 2D representations involving complex interactions between the body and material environment. Little attention has been paid to the iconic nature of this astronomical diagramming. Purpose: This research explored the value for students of diagramming to reveal the structural…

Science, Technology, Engineering, and Math (STEM) education is essential to the economic growth, health, and progress of the modern world. One cognitive ability that underpins thinking and learning in STEM, as well as other disciplines, is relational ability. This ability to spot common relations shared by different objects, events, ideas, or…

Causal reasoning is a fundamental cognitive ability that enables individuals to learn about the complex interactions in the world around them. However, the mechanisms that underpin causal reasoning are not well understood. For example, it remains unresolved whether children's causal inferences are best explained by Bayesian inference or…

As a wide variety of intelligent technologies become part of everyday life, researchers have explored how people conceptualize agents that in some ways act and think like living things but are clearly machines. Much of this work draws upon the idea that people readily default to generalizing human-like properties to such agents, and only pare back…

The ability to consider multiple possibilities forms the basis for a wide variety of human-unique cognitive capacities. When does this skill develop? Previous studies have narrowly focused on children's ability to prepare for incompatible future outcomes. Here, we investigate this capacity in a causal learning context. Adults (N = 109) and 18- to…

Cognitive flexibility (CF) is the ability to shift between concepts or rules. Difficulty with CF is associated with autism (i.e., ASD) as it contributes to repetitive behaviours. However, little is known about CF skills of autistic adolescents with low intelligence. This study uses the Wisconsin Card Sorting Task (WCST) to assess the CF of 36…

Background: The use of analogies as reasoning tools that play a key role in human cognition at all ages has been of interest to educators, scientists, and philosophers ever since Aristotle. Indeed, research has consistently found that analogies provided by teachers can, and do, play an important role in facilitating student understanding of…

Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical uncertainty in upper-division courses. This study is part of a larger project evaluating student thinking about…

This paper reports on a case study of undergraduate biology students' drawing-based modeling and how this process plays out in naturalistic dialogues. Recent research has revealed the importance of drawings, talk, and gestures in students' model-based reasoning. This study provides further insight into the complementary role of these multimodal…

Although elected representatives play an imperative role for the functioning of a formal democracy, educational research has so far not given much attention to the education and training offered to this group of people. A democratic dilemma may arise in the design and organisation of this education that relate to local governance and policy…

Reading is a fascinating cognitive process through which individuals perceive arbitrary symbols on a page and turn them into vivid mental representations of text. Most available evidence supports an embodied explanation for how readers are capable of such representations--they recruit supralinguistic brain regions in order to mentally simulate the…

For decades, researchers have struggled with measurement problems related to the "construct validity" of divergent and convergent thinking in creativity assessments. In response, some have called for battery-based approaches. Recently, digital games have emerged as a potential alternative, offering increased "scalability" and…

Mental model (Johnson-Laird, 2001) and probabilistic theories (Oaksford & Chater, 2009) claim to provide distinct explanations of human reasoning. However, the dual strategy model of reasoning suggests that this distinction corresponds to different reasoning strategies, termed "counterexample" and "statistical,"…

Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…