Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these…

Collaborative problem-solving (CPS) learning is increasingly valued for its role in promoting higher-order thinking of learners. Despite the widespread application of role scripts in CPS, little is known about the mechanisms by which roles influence learners' cognition and the impact of goal orientation on roles. In this study, we designed role…

The discipline of film studies often engages in analyses of the functions of filmmakers' decisions in terms of their effects on viewers. Behavior analysis uses a similar, functional-analytic approach toward understanding the relationship between individuals' behavior and the environmental effects that maintain their behavior. Given converging…

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

This article aims to implement an engineering design-based STEM activity for young children and evaluate the implementation process of the activity, along with providing some revision ideas. The activity was held as a 90-minute weekend workshop with the participation of six children aged four to seven. Data were collected through digital…

Nature-inspired designs/organic designs exhibit a very close resemblance with nature especially in terms of form and structure. Form giving for organic design is a special class of design problem that involves the use of inspiration and analogies from nature for creative problem-solving. There is insufficient research in understanding this…

Recent work suggests that common knowledge is an important cognitive mechanism for coordinating prosocial behavior, in part because it reduces uncertainty about others' cooperative behavior. However, it remains unclear whether children also rely on common knowledge to solve coordination problems. Here we examined whether 6- to 9-year-old children…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised…

In learning to program and understanding how a programming language controls a computer, learners develop both insights and misconceptions whilst their mental models are gradually refined. It is important that the learner is able to distinguish the different elements and roles of a computer (compiler, interpreter, memory, etc.), which novice…

This study is focusing on synthesizing the theoretical and designing framework of constructivist gamification environment models to enhance ill-structured problem solving in learning science. The research model used is based on model development (phase 1) proposed by Richey & Klein. This research consists of two phases as follow: (1) to…

In this article, the author presents a teaching prompt--Write-it-Out--to instruct readers who seemingly guess at words with no or limited use of grapheme-phonemic correspondences to recontextualize word-solving into writing. Through the nature of this prompt, slowing down the pace of solving words on the run with writing also reciprocally builds…

A very common Applied Optimization Problem in Calculus deals with minimizing a distance given certain constraints, using Calculus, the general method for solving these problems is to find a function formula for the distance that we need to minimize, take the derivative of the distance function, set it equal to zero, and solve for the input value,…

We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.

Problem posing research in mathematics education has increased in the last decade. As a result, the intent of the present study is to examine and summarize the research that has been conducted. Specifically, we examined articles published from 2011-2020 that studied the impact of problem-posing instruction on students' problem-solving abilities.…