**Achievement Bests Framework, Cognitive Load Theory, and Equation Solving and Equation Solving**

**Achievement Bests Framework, Cognitive Load Theory,** 

DOI: 10.5772/intechopen.70568

Bing H. Ngu and Huy P. Phan Additional information is available at the end of the chapter

Bing H. Ngu and Huy P. Phan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70568

#### **Abstract**

The Framework of Achievement Bests provides an explanatory account into the process of optimization, which details how a person reaches from one level of best practice to that of a more optimal level. This framework, we contend, is significant in its explanatory account of personal growth, an internal state of flourishing, and the achievement of exceptionality. This chapter conceptualizes the applicability of the Framework of Achievement Bests to the context of instructional designs. We highlight the tenet of element interactivity, which is integral to the design of a particular mathematics instruction and its potential effectiveness. Element interactivity entails the interaction between elements within a learning material. Owing to the limited working memory capacity, an instruction that incurs high level of element interactivity would impose high cognitive load leading to reduced learning. Our conceptualization postulates the possible alignment between suboptimal and optimal instructional designs with realistic and optimal levels of best practice, respectively. This postulation (e.g., suboptimal instructional design → realistic level of best practice), which recognizes the importance of cognitive load imposition, is significant from a practical point of view. By focusing on instructional designs, it is possible to assist individuals to achieve optimal best practice in learning.

**Keywords:** achievement best frameworks, cognitive load theory, appropriate instructional design, element interactivity, equation solving

### **1. Introduction**

Effective learning in school contexts is an important notion to consider. By all account, effective learning entails personal experience of deep, mastery learning, improvement in cognitive skills (e.g., problem solving), and the stimulation of interest and intellectual curiosity. The product of effective learning, in this sense, may include an improvement in academic

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

performance at the end of the school term. Ineffective learning, by contrast, may result in loss of interest, engagement in maladaptive outcomes, and superficial learning. This recognition places emphasis on a need for educators and researchers, alike, to focus on motivational initiatives, pedagogical strategies, and educational programs that could foster *engagement of* and *preference for* effective learning.

detailing an underlying internal mechanism that could explain how an individual reaches a state of optimal functioning. This framework is significant as it contributes to existing work

Achievement Bests Framework, Cognitive Load Theory, and Equation Solving

http://dx.doi.org/10.5772/intechopen.70568

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The Framework of Achievement Bests, developed by Phan and colleagues [3, 4, 10], explores the personal experience of optimal functioning. Optimal functioning, according to the authors, is defined as an internal state of experience and accomplishment that reflects maximization in capability (e.g., a Year 8 student's indication to learn and understand linear equations that involve multiple solution steps (e.g., 4/*x* = 11, solve for *x*). "What is the best that I can accomplish?", in this instance, is a question that indicates an individual's self-awareness of his/her

The Framework of Achievement Bests draws comparison with Fraillon's [27] theorization of *optimization*, which is a psychological process that focuses on an individual's optimal best from some point of self-reference. Phan and colleagues' [3, 4, 10] conceptualization of achievement bests depicts two major levels of best practice: (i) *realistic level of best practice* (i.e., denoted as RL), which entails what an individual is realistically capable of accomplishing, at present (e.g., what can I actually do, at present, in Algebra?; how much do I know…..?), and (ii) *optimal level of best practice* (i.e., denoted as OL), which is defined as an individual's accurate indication of projected accomplishment that is exceptional, in nature (i.e., as of today, what is the best that I can do for this topical theme, realistically?). Reaching an optimal level of best practice from a realistic level of best practice reflects, in this case, a state of flourishing or optimal experience. **Figure 1** illustrates the Framework of Achievement Bests, in its totality [4, 11].

A state of personal flourishing

Current Level of Best Practice Exceptional Level of

Volume of

> Proxy-EL Exceptional Level of Best Subscale Accomplishment in a domain

Best Practice

optimization

Process of Optimization

Psychological Mechanism Psychosocial Mechanism

Educational Mechanism

Intensity of optimizatoion

[7–9], and advances the inquiry into the tenets of optimal best.

**2.1. The Framework of Achievement Bests**

Current Level of Best Subscale Previous Track Record

Proxy-CL

**Figure 1.** The Framework of Achievement Bests. Source: Adapted from Ref. [1].

potential best practice.

Historical Level of Best Practice

Our postulated positioning, based on previous research undertakings in the area of mathematics [1, 2], is that *appropriate instructional designs* may serve to facilitate and promote effective learning. Instructional designs, an important element of pedagogical practices in the teaching and learning processes, are central to the achievement of effective learning. We contend that, in this case, a particular instructional design is efficient when it imposes minimal *cognitive load on an individual's processing of information*. Instructional designs that impose high levels of cognitive load, by contrast, are ineffective and inefficient for implementation and practice. This line of research development, in general, has notable implications for us to consider, especially in relation to Teacher Education Pre-service preparation and training.

This chapter then, in accordance with the scope of the edited book, explores the importance of comparative instructional designs in the context of mathematics learning. Drawing from our previous work, we focus on the development of a conceptualization that emphasizes on the choosing of an appropriate instructional design for implementation. This conceptualization, in particular, focuses on the *achievement of optimal best in mathematics* [3, 4], taking into consideration *the negative impact of cognitive load imposition* [5, 6]. Furthermore, arising from this discussion, we consider methodological and theoretical issues for continuing research development into the area of instructional designs.
