2012, Ngu, Bing, Yeung, Alexander

Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated multiple components (symbolic equations, symbols, categorization, hint) in the source, or target, or both, to address the four analogical tasks. Different combinations of the components were tested in a series of four experiments. Symbolic equations (main component) fostered a mental construction of the problem in its solution mode. Categorization enabled an identification of the problem category. A hint in the target directed the learners to the source problem. The interaction between these components facilitated the mapping of the symbolic equations in the source onto the target, resulting in the superiority of the MC approach in fostering analogical transfer. Neither the main component alone nor the main component plus one sub-component was sufficient for analogical transfer. Hence for analogical transfer to occur, at least the main component (symbolic equations) and two sub-components (categorization and hint) are required. However, symbols may not have additional effects for transfer to occur.

2015, Kadir, Munirah, Ngu, Bing, Yeung, Alexander

Learning mathematics and science entails learning the relations among multiple interacting elements, especially when solving problems. Assimilating multiple interacting elements simultaneously in the limited working memory capacity would incur cognitive load. Unless the instructions provide a mechanism to manage the high cognitive load involved, learning effectiveness may be compromised. Researchers have investigated instructional efficiency across diverse domains from the perspective of cognitive load theory. Progress in educational theory has enabled a better understanding of three types of cognitive load that students experience during the learning process: intrinsic, extraneous, and germane cognitive load. Processing the intrinsic nature of a task constitutes intrinsic cognitive load (e.g., complexity of elements). Sub-optimal instruction requiring unnecessary processing of elements constitutes extraneous cognitive load. Investing mental effort in multiple practices constitutes germane cognitive load. Recent advance in cognitive load theory highlights element interactivity (i.e., the interaction among elements to be processed) as a common thread among different types of cognitive load. However, despite progress in cognitive load research, little is known about the effects of element interactivity in secondary school mathematics and science education. Using element interactivity as a point of reference, this article reviews the design features of different approaches to teaching linear equations in mathematics and the topic of density in science. Evidence seems to point to the practical benefit of using instructional approaches that address the issue of multiple elements interacting with each other to facilitate learning. As such, the conceptualization of cognitive load in terms of element interactivity will bring further progress in the research on cognitive load in mathematics and science learning.

2017, Phan, Huy, Ngu, Bing, Yeung, Alexander

We recently developed the Framework of Achievement Bests to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as optimal achievement best, which stipulates the idea that individuals may, in general, strive to achieve personal outcomes, reflecting their maximum capabilities. Realistic achievement best, in contrast, indicates personal functioning that may show moderate capability without any aspiration, motivation, and/or effort expenditure. Furthermore, our conceptualization indicates the process of optimization, which involves the optimization of achievement of optimal best from realistic best. In this article, we explore the Framework of Achievement Bests by situating it within the context of student motivation. In our discussion of this theoretical orientation, we explore in detail the impact of instructional designs for effective mathematics learning as an optimizer of optimal achievement best. Our focus of examination of instructional designs is based, to a large extent, on cognitive load paradigm, theorized by Sweller and his colleagues. We contend that, in this case, cognitive load imposition plays a central role in the structure of instructional designs for effective learning, which could in turn influence individuals' achievements of optimal best. This article, conceptual in nature, explores varying efficiencies of different instructional approaches, taking into consideration the potency of cognitive load imposition. Focusing on mathematical problem solving, we discuss the potentials for instructional approaches to influence individuals' striving of optimal best from realistic best.

2014, Ngu, Bing, Yeung, Alexander, Tobias, Stephen

Eighth grade students in Australia (N = 60) participated in an experiment on learning how to solve percentage change problems in a regular classroom in three conditions: unitary, pictorial, and equation approaches. The procedure involved a pre-test, an acquisition phase, and a post-test. The main goal was to test the relative merits of the three approaches from a cognitive load perspective. Experimental results indicated superior performance of the equation approach over the unitary or pictorial approach especially for the complex tasks. The unitary approach required students not only to process the interaction between numerous elements within and across solution steps, but also to search for critical information, thus imposing high cognitive load. The pictorial approach did not provide a consistent approach to tackling various percentage change problems. Coupled with the need to coordinate multiple elements within and across solution steps, and the need to search for relevant information in the diagram, this approach imposed high cognitive load. By treating the prior knowledge of percentage quantity as a single unit, the equation approach required students to process two elements only. Empirical evidence and theoretical support favor the equation approach as an instructional method for learning how to solve percentage change problems for eighth graders.