The goal of this article is to propose a framework for understanding the nature of "how people construct problems" by interacting with situations and subsequently to offer implications for instructional design and future research. We propose that people must interactively frame the components of a situation in order to establish the…

Modern online education has the capacity to provide intelligent educational services by automatically analyzing substantial amounts of student behavioral data. Knowledge tracing (KT) is one of the fundamental tasks for student behavioral data analysis, aiming to monitor students' evolving knowledge state during their problem-solving process. In…

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…

Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

In the 21st-century context, problem solving, creativity, critical thinking, collaboration, and communication are the most valued skills in the workplace. Thus, those in positions often labeled as "leadership" need to make a valuable shift: to "guiding," "inspiring," and "facilitating" rather than directing.…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

Constructing a consensus problem space from extensive qualitative data for an ill-structured real-life problem and expressing the result to a broader audience is challenging. To effectively communicate a complex problem space, visualization of that problem space must elucidate inter-causal relationships among the problem variables. In this…

This paper identifies the need for a pedagogical re-orientation in UK higher education to prepare graduates to overcome wicked problems. In addition to key knowledge sets, graduates need attributes of critical self-reflection, risk-awareness and management, collaboration, creativity, agility, reflexivity - enabling the ability to manage the…

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately…

Even though agent-based modelling is seen as committing to a mechanistic, generative type of causation, the methodology allows for representing many other types of causal explanations. Agent-based models are capable of "integrating" diverse causal relationships into coherent causal mechanisms. They mirror the crucial, multi-level…

When students are solving problems they often turn to examples when they need assistance. Examples are helpful because they illustrate how a problem can be solved. However, when examples are very similar to the problems, students default to copying the example solutions, which hinders learning. To address this, prior work has investigated the…

Purpose: The purpose of this paper is the presentation of a learning model for a manager and employee working collaboratively to make advances in knowledge, skills, work performance and in the quality of their relationship. The model is called reciprocal action learning. Design/methodology/approach: The approach was to examine concepts and…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…