The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems--including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a…

Productive Failure is an instructional approach in which students engage in problem-solving attempts prior to instruction. The Productive Failure approach has been found to be more supportive for conceptual knowledge acquisition during subsequent instruction compared to a direct-instruction condition in which students receive instruction first…

A central practice in the discipline of organic chemistry is the ability to solve certain fundamental problems, including predicting reactivity, proposing mechanisms, and designing syntheses. These problems are encountered frequently by both students and practitioners, who need to utilize vast amounts of content knowledge in specific ways to…

Problem-solving skills are advantageous when resolving complicated and multidimensional challenges. Problem-solving skills can be developed through active learning models that engage students in the learning process. One active learning model is RICOSRE. The main focus of RICOSRE is problem-solving activities in (1) reading; (2) identifying the…

Research has extensively linked teacher collaborative work with opportunities for both explicit and implicit professional development. However, while teachers work together more often than before, little is known about how workplace collaborative contexts are structured in terms of who and how frames the problems of practice. Drawing on an…

The purpose of this study aimed to analyze the process of online collaborative problem solving (CPS) via brain-to-brain synchrony (BS) at the problem-understanding and problem-solving stages. Aiming to obtain additional insights than traditional approaches (survey and observation), BS refers to the synchronization of brain activity between two or…

Education professionals face myriad problems of practice, especially in the face of current trauma, injustice, and other stressors. To address those challenges, educators should work collaboratively to target the sources, not just the symptoms, of the problems. Asking why can begin to surface root causes, which may be related to systems,…

Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

Problem-solving strategies, such as visual imagining and self-questioning, may assist children with autism spectrum disorder (ASD) in recalling past events. In the current study, at the start of each session, a 7-year-old boy with ASD engaged in a novel activity with a behavior therapist who took pictures of the activity. Ninety minutes later, a…

Designing games from the ground up is a popular activity for helping students think in designerly ways. Despite their benefits, such game design activities may place higher-than-anticipated demands on cognitive and institutional resources. In an effort to alleviate these demands, this study explored how playing and fixing partially completed games…

The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

What are consequential world problems? As "grand societal challenges", one might define them as problems that affect a large number of people, perhaps even the entire planet, including problems such as climate change, distributive justice, world peace, world nutrition, clean air and clean water, access to education, and many more. The…

Little is known about the role of prompts to help learners solve ill-structured learning problems. Instructors do not devote adequate time to formulate pedagogically useful prompts, and the usefulness of different types of prompt is unclear. This mixed-methods study examined the role of argumentative prompts in the writing of essays based on…

We present a type of arithmetic called Proportional Arithmetic. The main properties and objects that emerge with this way of operating quantities are exposed. Finally, the antiderivative and the indefinite integral are defined in order to calculate the primitive of [equation omitted] in the Proportional context.

Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…