The aim of the research was to explore the levels of cognitive loading induced by certain tenets of constructivist pedagogy namely self-directed learning complex questions and zone of proximal development. The study also sought to investigate the associations between these constructs and with cognitive loading and complex questions. Data for the…

This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…

Design education exists to prepare students for design practice. Yet the goal state, design expertise, remains poorly defined. This paper presents a critical cross disciplinary literature synthesizing literature across design, engineering, expertise, creativity, and new evidence from a cognitive task analysis of expert designers to explore…

This article revisits the cognitive load theory to explore the use of worked examples to teach a selected topic in a higher level undergraduate physics course for distance learners at the School of Distance Education, Universiti Sains Malaysia. With a break of several years from receiving formal education and having only minimum science…

According to cognitive load theory, using worked examples is an effective and efficient instructional strategy for initial cognitive skill acquisition for novice learners, as it reduces cognitive load and frees up cognitive resources to build task competence. Contrary to this, productive failure (as well as invention learning, desirable…

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs.…

The trends of teaching mathematical thinking and the existence of two thinking skills (critical dan creative thinking) the required by 21st century skills have created needs for teachers to know their students' thinking processes. This study is intended to portray how mathematics teachers expect their students showing their thinking processes in…

The ability to learn in a self-regulated way is important for adolescents' academic achievements. Monitoring one's own learning is a prerequisite skill for successful self-regulated learning. However, accurate monitoring has been found to be difficult for adolescents, especially for learning problem-solving tasks such as can be found in math and…

In order to maintain the United States' global competitiveness and create new and innovative solutions to solve global challenges, more and diverse numbers of STEM graduates need to be attracted and retained in technical disciplines (Committee on Prospering in the Global Economy of the 21st Century: An Agenda for American Science and Technology,…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

Based on L. S. Vygotsky's sociocultural theory, previous scaffolding studies have examined some factors associated with adjustment of parental support during collaborative problem solving. However, a factor that remains unexplored in the literature is the potential relationship between parental empathy and parental support in collaborative problem…

Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…