In social sciences, the use of stringent methodological approaches is gaining increasing emphasis. Researchers have recognized the limitations of cross-sectional, nonmanipulative data in the study of causality. True experimental designs, in contrast, are preferred as they represent rigorous standards for achieving causal flows between variables. The Solomon four-group design, for example, is ideal for its positioning to account for, and factor out, confounded influences of predictors on outcomes. However, in daily life settings, it is often difficult to emulate true experimental conditions. Identified limitations include financial resources, logistic difficulties, time constraint, and small sample sizes in social science research settings. There are, of course, other experimental designs that are noteworthy for consideration. Time series and single-case designs, quasi in nature, are effective alternatives for educators and researchers to consider in their research foci. This article examines the different experimental designs that may be implemented in naturalistic classroom settings. In particular, one important inquiry of our theoretical discussion pertains closely to the conceptualization of two innovative designs that we have made, consequently as a result of our research development and examination of the literature: a 'sequential, multiple time series multi-group design and a multi time series, multi-group single-case design'. These experimental designs are innovative and enable comparisons for within and between differences under different experimental conditions.

The present research investigation explored the interrelations between three major theoretical orientations: personal self-efficacy (Bandura, 1986, 1997), components of motivational engagement (i.e., absorption, dedication, and vigor) (Schaufeli, Martinez, Pinto, Salanova and Bakker, 2002; Schaufeli, Salanova, González-Romá and Bakker, 2002), and effective functioning (Phan, 2015a, 2015b). This conceptualization, correlational in nature, reflects a non-deficit approach to the study of human behavior. For example, the concept of effective functioning is positive in terms of its characteristics and explanatory power, predicting academic learning and achievement-related outcomes. Based on previous empirical evidence, a number of structural paths are hypothesized for confirmation. 288 (137 females, 151 males) second-year university students participated in this study by answering a suite of questionnaires. Structural equation modeling (SEM) was used to test the a priori model. MPlus 7.2 statistical program produced some key findings, namely: (i) the importance of enactive learning experience as a source of information, (ii) the potent influence of self-efficacy and its mediating role, (iii) the differential influences of the three components of motivational engagement, and (iv) the positive influence of effective functioning. There are both educational and methodological implications arising from the results that are of important value. One theoretical contribution, in this case, is the validation of effective functioning as a central cognitive-motivational predictor of performance outcomes.

Hope is a psychological process that may yield positive educational and non-educational outcomes. Its characteristics, positive in nature, reflect a non-deficit positioning, enabling individuals to anticipate, plan, and persist in different courses of action. One inquiry that has credence for research development is the extent to which hope, as a collective entity, could facilitate and encourage the achievement of optimal best. We recently developed the 'optimal achievement bests theory' (Phan, Ngu, and Williams, 2016), which has been refined to include the 'continuum of achievement bests framework', whereby five progressive achievement bests are noted: 'historical achievement best', 'realistic achievement best', 'personal achievement best', 'optimal achievement best', and 'ultimate achievement best'. Optimal achievement best is a point of reference, which may serve to encourage individuals to strive for successful performance outcomes. Ultimate achievement best, differently, is more inspirational and outside the scope of capability for most individuals. Accomplishing ultimate achievement best, however, is a possibility that cannot be discounted, overall. We consider the possibility that hope, in effect, could positively relate to individual achievement bests (i.e., notably optimal outcomes) of enriched emotional well-beings, situated within the context of the period of adolescence. Emotional well-beings, encompassing a wide range of affective responses have been argued to feature centrally in human agency (Phan, 2015b; Phan and Ngu, 2015b), especially for adolescents who may experience both positives and negatives. Does hope, for example, facilitate the striving and achievement of enriched emotional well-beings in the face of difficulties and obstacles? To what extent does hope enable adolescents to experience positive affective responses (e.g., happiness) that may, in turn, counter detrimental personal functioning on a daily basis (e.g., feeling of pessimism)? Our conceptualization of achievement bests is significant, and may contribute substantive theoretical, methodological, and practical yields for consideration. This chapter then, makes attempts to explicate theoretically the impact of hope on adolescents' optimal achievement bests of their emotional well-beings. This theoretical positioning may provide grounding for advancement into the study of: (i) hope as a facilitator and central mediator of achievement best in relation to emotional well-being (e.g., optimal achievement best), and (ii) the achievement best theoretical framework as reflecting the nature and characteristics of positive psychology. Our in-depth analysis in particular, may explain the impact of emotional well-beings as a proactive vehicle for adolescents.

Progress in education has led to extensive studies, focusing on explanatory and predictive theoretical tenets that feature centrally in the teaching and learning processes. A synthesis of the empirical literature indicates that one major focus entails the importance of quality learning and enriched academic well-being experiences at school. Recently, we introduced a new concept for research development, titled optimized functioning, which is an expansion of the notionm of optimization. Quantitative validation of optimized functioning indicates a multifaceted structure, which consists of four major components: personal resolve, pathways and means, effective functioning, and school experience. We advance this avenue of inquiry by exploring the impact of optimized functioning, in its totality. Specifically, in the context of secondary school learning, we focus on the predictor-and-outcome pattern of optimized functioning with reference to the following motivational and psychosocial processes: enactive learning experience, task values, and the two major approaches to learning. Does academic success facilitate and heighten one's state of optimized functioning? Does optimized functioning lead to an adoption of a deep approach to learning? We used structural equation modeling (SEM) to analyze the correlational data collected ('N'=229 Year 10 students); MPlus 7.3 yielded some key findings, for example: (i) the positive impact of enactive impact on task values, a deep approach, and academic achievement, (ii) the positive impact of optimized functioning on a surface approach to learning and academic achievement, (iii) the negative impact of a surface approach to learning on academic achievement, and (iv) the positive indirect impact of enactive learning experience on academic achievement, mediated via task values and then optimized functioning.

The formation of self-efficacy, according to Bandura's (1997) social- cognitive theory, is an important area of inquiry. This theoretical tenet posits the importance of enactive learning experience, followed by lesser influences of vicarious experience, verbal persuasion, and emotional and physiological states. Quantitative research, predominantly, has produced clear and consistent evidence that supports this position. We argue that the elementary school years may indicate differently, whereby children's limited cognitive maturity and learning experiences could compel them to rely on other psychosocial informational sources. To date and to our knowledge, very few studies, if any, have explored the sustained influence of enactive learning experience across time. In this study, consequently, we tested a sequential predictive model that involved the differential influences of the 4 major informational sources on self-efficacy and then self-efficacy on academic achievement. Three time points of data (N = 328, Year 6) were collected across the calendar year, and Mplus 7.3 (Muthén & Muthén, 1998-2012) was used to assist us in our structural modeling testing. At Time 1, only enactive learning experience and vicarious experience positively influenced self-efficacy. At Time 2, after controlling for prior variance of Time 1 corresponding factors, only enactive learning experience remained significant. At Time 3, after controlling for autoregressive paths, enactive learning experience remained significant, and both verbal persuasion and emotional and physiological states positively influenced self-efficacy. The impact of self-efficacy on academic achievement was significant across the 3 occasions (βs = .20-.46).

The study of social cognitive theory has involved a number of inquiries, notably one of which concerns the formation and development of self-efficacy beliefs. Social cognitive theory indicates that we form our self-efficacy beliefs from four major sources of information: enactive performance accomplishments, vicarious experiences, verbal persuasion and emotional and physiological states. We advance this tenet by exploring across four occasions, and the four sources of information in the context of elementary school learning. Two cohorts of participants, at level 2 (N = 352 3rd–4th grade students) and level 3 (N = 264 5th–6th grade students), answered a Likert's-scale inventory that we developed and used in a previous study. We proposed and tested a number of a priori models using LISREL 8.80. Furthermore, factorial invariance analyses of the inventory were performed, a posteriori, to determine the stability/instability of the four sources of information.

School, like a second home, is a complex place that espouses different psychosocial experiences and influences. Aside from academic achievement, it is important for educators to recognize that there are other educational and noneducational successes, for example, the importance of social and psychological adjustment (e.g. proactive peer-peer relationship), the adoption of altruistic values and moralistic ideals, and individuals' willingness to accept cultural diversity and individual differences. It is in society's best interest that schools explore the pathways and means to assist students in their achievements of non-academic outcomes. Our work regarding the concept of optimal achievement best (Phan 2015; Phan, Ngu, and Williams In-press 2016) has produced some notable yields for consideration. Optimal achievement best is of significance for its emphasis on the striving of successful outcomes that reflects an individual's fullest capacity. Its characteristics, in a similar vein, indicate a positive, non-deficit positioning regarding human behaviors. This article, overall, focuses on an examination of optimal achievement best and how this theoretical orientation could account for and explain the non-academic attributes of successful schooling.

The study of effective learning and optimal schooling experiences is an important focus of inquiry in the field of Education. Why do some students show more inclination towards mastery, deep learning, and personal interests in schooling? Why do some students., in contrast, express discontentment, and work-avoidance behaviours (e.g., disengagement)? These questions have led to ongoing research development of theoretical models that could explain, account, and enhance educational outcomes and schooling experiences. We recently conceptualized a holistic framework of student well-being experiences that takes into consideration the combined influences of personal, motivational, affective, and social processes of schooling (Phan, In press-2015a; Phan & Ngu, In press-2015a). In this theoretical chapter, we discuss in detail eight distinctive components of student well-being experiences that we believe could foster and optimize positive educational and non-educational outcomes: optimized functioning, liking for school experience, emotional well-being, relating to others, personal well-being at school, appreciation and value, daily functioning, and academic striving.

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across linear equations revealed that multi-step equations are derivatives of two-step equations, which in turn, are derivatives of one-step equations. Hence, teaching and learning of linear equations can occur in a sequential manner so that learning new knowledge (e.g. two-step equations) is built on learners' prior knowledge (e.g. one-step equations), thus reducing working memory load. The number and nature of the operational line as well as the number of relational lines also affects the efficiency of instructional method for linear equations. Apart from the degree of element interactivity, the presence of complex element (e.g. fraction, negative pronumeral) also increases the complexity of linear equations and thus poses a challenge to the learners.

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.