This article aims to illustrate how the collective resolution of routine mathematical tasks can give rise to uncertainties, fostering and supporting a rich and authentic mathematical activity. While solving routine tasks may not typically be classified as problem-solving, the research presented in this paper shows that, at the collective level,…

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

Purpose: The purpose of this paper is to understand the role of perplexity in young players' experiences within an educational videogame and how reflective thinking can help them to get out of perplexing scenarios. Design/methodology/approach: We used a constructivist grounded theory approach and the lenses of Dewey's conceptualization of…

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: Dealing with uncertainties is inherent in the engineering design process and often poses challenges for young learners. This necessitates providing learners with adequate support to navigate their uncertainties effectively. However, achieving this requires a deeper understanding of the factors influencing learners' uncertainty…

Monte Carlo (MC) simulation is widely used in many different disciplines in order to analyze problems that involve uncertainty. Simulation decomposition has recently provided a simple, but powerful, advancement to the standard Monte Carlo approach. Its value for better informing decision making has been previously shown in the investment-analysis…

Science education researchers have highlighted how uncertainty can foster meaningful scientific sense-making, supporting students to re-evaluate their understandings of scientific phenomena and pursue deeper causal accounts. However, facilitating whole-class conversations motivated by uncertainty is complex and challenging, calling for further…

Constructing an intuitive theory from data confronts learners with a "chicken-and-egg" problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing…

Real-world design settings can be complex, ill-structured, open and typically uncertain and/or ambiguous about their goals and solution paths. This study contributes to understanding how to work with these types of problems in a course project setting. The main objective of the study is to identify, propose and validate a set of practical…

Background: As engineers solve problems that are ill-structured and require collaboration, a common goal of engineering programs is to develop students' competencies for solving such problems in teams, often using cornerstone design experiences. Purpose: With the goal of designing effective learning environments, this study identifies…

We live in a world and a time full of challenges. Social inequality, discrimination, global political instability, wars, genocides, terrorism, nuclear and biological weapons, climate change, waste disposal, and species extinction, among others, are constant threats. These pressing issues require attention and solution. Wisdom rises as the…

To effectively employ inquiry-based learning to enhance students' inquiry practices and encourage them to think and act like scientists, science teachers must have a deeper understanding of the factors that influence scientific research and attitudes about scientist practice. This research contains the experience of two postdoctoral researchers in…

Maker-centered learning is a creative hands-on educational strategy that uses a variety of tools and materials to support the iterative design of physical or digital artifacts. It involves the "messy" process of trial and error; therefore, authentic integration of maker-centered learning requires teachers to embrace ambiguity. This…

The statistical concept of sampling is often given little direct attention, typically reduced to the mantra "take a random sample". This low resource and adaptable activity demonstrates sampling and explores issues that arise due to biased sampling.

Empirical studies of creativity emphasize the importance of ambiguity advantage in idea generation and creative problem-solving. This study examined whether ambiguous figures could directly induce a mind-set that would transfer to the creative problem-solving. In Experiment 1, we examined whether presentation of ambiguous figures would influence…