Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…

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.

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

Graph Signal Processing (GSP) plays a crucial role in addressing the growing need for information processing across networks, especially in tasks like supervised classification. However, the success of GSP in such tasks hinges on accurately identifying the underlying relational structures, which are often not readily available and must be inferred…

Critical thinking refers to a mode of thinking--about any subject, content, or problem--in which the thinker improves the quality of his or her thinking by skillfully analyzing, assessing, and reconstructing knowledge. This study evaluates the critical thinking skills of private and public high school students in Kuwait and examines the practices…

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

A Prolog program consists of a set of facts and rules rather than imperative statements, commonly used in most other programming languages. Therefore, the Prolog language is used to encode logic, from which the inference engine deduces logical conclusions. In this article, we argue that the use of the Prolog language can be useful to help students…

To reach rational conclusions, we often draw inferences about the evidence that supports one solution over another. This evidence can be "direct" and indicate why one option is correct, or "indirect" and indicate why the alternative option is incorrect. Understanding how young children interpret and use different types of…

Given the relevance of graphs of functions, we consider their inclusion in primary education from the functional approach to early algebra. The purpose of this article is to shed some light on the students' production and reading of graphs when they solved generalization problems from a functional thinking approach. We aim to explore how 3rd and…

The objective of this study was to measure the contribution of the left frontopolar cortex (FPC) to analogical reasoning. Our measure of analogical reasoning derives from performance on the radiation problem, a creative problem-solving task first used in Gestalt psychology (Duncker, 1945). Success on this task is as low as 10 % without the…

Intuition is one of the main factors that drive our everyday decision-making which happens quickly and unconsciously. Individuals often rely on the use of intuition to solve either simple or complex problems. The purpose of this research study is to further break down an individual's thinking processes by understanding how different groups of…

Holistic data science education places data science in the context of real world applications, emphasizing the purpose for which data were collected, the pedigree of the data, the meaning inherent in the data, the deploying of sustainable solutions, and the communication of key findings for addressing the original problem. As such it spends less…

This commentary provides an overview of abduction, also known as Inference to the Best Explanation, and argues that the term and relevant problem-solving methods should be adopted by chemistry educators. Abductive reasoning, especially within the context of science and medicine, continues to be an active area of exploration for philosophers and…

Research confirms that critical thinking plays a fundamental role in decision making and problem solving, skills that are essential to function as successful adults in a complex world. Consequently, it has been a focus of educational research for decades. Faculty meetings and teacher training sessions repeatedly run sessions on ways that teachers…

Conventional advice discourages controlling for postoutcome variables in regression analysis. By contrast, we show that controlling for commonly available postoutcome (i.e., future) values of the treatment variable can help detect, reduce, and even remove omitted variable bias (unobserved confounding). The premise is that the same unobserved…