Background/purpose: This research aims to classify and show the characteristics of the types of abstract thinking students use when solving mathematical problems. Materials/methods: This descriptive qualitative research was conducted in a structured manner on students of the University of Muhammadiyah Surakarta, Faculty of Teacher Training and…

Counterfactual reasoning is the ability to reason about how the world might have been if past events or states had been different. It is helpful for making sense of past experiences to create future blueprints. Languages like English apply subjunctive forms to directly mark counterfactual premises. In contrast, Chinese does not apply subjunctive…

Design thinking fundamentally relies on abductive reasoning. Diverse thinking types such as divergent thinking, systems thinking, and empathetic thinking have been adopted in design thinking education. Yet, it is very rare to address abductive reasoning to be integrated in a design thinking course because of deductive validity and inductive…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

Immanuel Kant famously wants us to think for ourselves. However, thinking collaboratively is often preferable to solitary thinking, especially in educational contexts. In this paper, I argue that Kant does not advocate a problematic form of epistemic or pedagogical individualism. For my argument, I focus on the area that, one might suspect, lends…

How do we deal with unlikely witness testimonies? Whether in legal or everyday reasoning, corroborative evidence is generally considered a strong marker of support for the reported hypothesis. However, questions remain regarding how the prior probability, or base rate, of that hypothesis interacts with corroboration. Using a Bayesian network…

The current research investigates how prior preferences affect causal learning. Participants were tasked with repeatedly choosing policies (e.g., increase vs. decrease border security funding) in order to maximize the economic output of an imaginary country and inferred the influence of the policies on the economy. The task was challenging and…

Among many perspectives in discussions of design, this study re-asserts the relation between "intuition" and "reasoning." The aim is to comprehend the role of intuition and reasoning in the design process. In order to do this, retrospective self-reports of the first year, rule-based architectural design studio students were…

Previous research has shown that people who endorse conspiracy theories are more prone to the conjunction fallacy: the tendency to perceive conjunct events as more probable than constituent events. The present study examined the relationship between specific beliefs (belief in conspiracy theories, religiosity) and the susceptibility to conjunction…

A good paradox has the viewer confused, but the best paradoxes lead the viewer to try to understand what is happening. One of the author's favorites is the hydrostatic paradox, in which a short and slender column of water supports a relatively enormous weight. He describes the paradox using an illustration of a student who weighs 60 points stands…

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

Contribution: This study contributes to understand the current state of electronics education in Brazil, comparing it with market demand for professionals in the context of Industry 4.0 (I4.0). This study can be used to improve and update education programs and disciplines, as well as to assess whether the graduate's profile is aligned with the…

This article argues that hope is not an adequate affective response to dread. Indeed, hope and dread are more closely aligned than either critical or postcritical forms of educational philosophy would like to admit. The article proposes a shift from hope to joy as an under appreciated educational affect. To make this claim, the author pivots to…

Previous studies on Bayesian situations, in which probabilistic information is used to update the probability of a hypothesis, have often focused on the calculation of a posterior probability. We argue that for an in-depth understanding of Bayesian situations, it is (apart from mere calculation) also necessary to be able to evaluate the effect of…

This article offers the construct "unitizing predicates" to name mental actions important for students' reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and…