We examined Australian and Malaysian pre-service teachers' cognitive process in solving linear equations from a cognitive load perspective. Seventy six Australian and Malaysian pre-service teachers were randomly assigned to solve one-step, two-step and multi-step linear equations, and to undertake a concept test. For Australian pre-service teachers, both the one-step and two-step groups outperformed the multi-step group. In contrast, no difference between the one-step, two-step and multi-step groups was observed for Malaysian pre-service teachers. Moreover, all the three groups of Malaysian pre-service teachers outperformed the corresponding groups of Australian pre-service teachers. Regarding the concept test, both Australian and Malaysian pre-service teachers performed better on the inverse operation (e.g., -4 becomes +4) than the balance operation (e.g., +4 on both sides). The inverse operation incus half as many interactive elements as the balance operation, thus imposing lower cognitive load.

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.

This short-term longitudinal study involved the inclusion of personal self-efficacy and the 4 categories of reflective thinking practice within 1 conceptual framework. Using structural equation modeling, the author explored the temporally displaced effects of prior performance (Time 1) on self-efficacy (Time 2, Time 3) and the four categories of reflective thinking (Time 4). Similarly, the examination included the temporally displaced effect of self-efficacy on the four categories of reflective thinking and whether these 2 theoretical constructs would influence academic performance (Time 5). First-year university students (N = 269) were administered 2 inventories (Motivated Strategies and Learning Questionnaire, Reflective Thinking Questionnaire) that measured self-efficacy and the four categories of reflective thinking. The results showed that the hypothesized structural paths, in general, were supported - for example, the predictive effect of prior performance at Time 1 on self-efficacy at Time 2, and the predictive effects of self-efficacy at Time 2 and Time 3 on academic performance at Time 5. The decomposition of effects also suggests the possible mediating mechanisms of self-efficacy and reflective thinking.

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.

Existing research has yielded evidence to indicate that the expectancy-value theoretical model predicts students' learning in various achievement contexts. Achievement values and self-efficacy expectations, for example, have been found to exert positive effects on cognitive process and academic achievement outcomes. We tested a conceptual model that depicted the interrelations between the non-cognitive (task value, self-efficacy) and cognitive (deep-learning approach, reflective-thinking) processes of learning, and academic achievement outcomes in mathematics. University students (n = 289) were administered a number of Likert-scale inventories and LISREL 8.80 was used to test various a priori and a posteriori models. Structural equation modeling yielded some important findings: (1) the positive temporally displaced effects of prior academic achievement, self-efficacy expectations and task value on achievement in mathematics, (2) the positive relations between self-efficacy expectations and task values and cognitive process outcomes and (3) the possible mediating role of self-efficacy expectations and task value between prior academic achievement and deep learning, reflective-thinking practice and academic achievement. Overall, our research investigation has provided empirical groundings for further advancement into this area of students' learning.

Optimal best practice is a central feat of human agency. It emphasizes a state of flourishing and reflects, in this case, the paradigm of positive psychology. One research inquiry that is of interest relates to an explanatory account of how a person reaches a state of optimal best. Recent research development has considered an important psychological process, known as optimization, which may explain a person’s achievement of optimal best practice. Having said this, very little is known about the process of optimization. In this article, the authors report on a non-experimental study (N = 352 secondary school students), which focused on the testing of a theoretical model of optimization. Innovatively, derived from existing theorizations and empirical evidence, the authors provide a methodological rationalization of flourishing, which is defined as a “quantitative difference” between a person’s current level of best practice (denoted as L₁) and his/her optimal level of best practice (denoted as L₂). Structural equation modeling (SEM) indicated a few major findings, for example, (i) a positive association between a person’s optimal best practice and his/her academic performance in a subject matter, (ii) a person’s current level of best practice acts as a determinant of optimal best practice, and (iii) personal resolve, as a psychological optimizing agent, directly influences optimal best practice, and potentially mediating the effects of academic striving and a person’s current level of best practice on optimal best practice.

The subject of mathematics is a national priority for most countries in the world. By all account, mathematics is considered as being "pure theoretical" (Becher, 1987), compared to other subjects that are "soft theoretical" or "hard applied." As such, the learning of mathematics may pose extreme difficulties for some students. Indeed, as a pure theoretical subject, mathematics is not that enjoyable and for some students, its learning can be somewhat arduous and challenging. One such example is the topical theme of Trigonometry, which is relatively complex for comprehension and understanding. This Trigonometry problem that involves algebraic transformation skills is confounded, in particular, by the location of the pronumeral (e.g., x)—whether it is a numerator sin30° = x/5 or a denominator sin30° = 5/x. More specifically, we contend that some students may have difficulties when solving sin30° = x/5, say, despite having learned how to solve a similar problem, such as x/4 = 3. For more challenging Trigonometry problems, such as sin50° = 12/x where the pronumeral is a denominator, students have been taught to “swap” the x with sin30° and then from this, solve for x. Previous research has attempted to address this issue but was unsuccessful. Learning by analogy relies on drawing a parallel between a learned problem and a new problem, whereby both share a similar solution procedure. We juxtapose a linear equation (e.g., x/4 = 3) and a Trigonometry problem (e.g., sin30° = x/5) to facilitate analogical learning. Learning by comparison, in contrast, identifies similarities and differences between two problems, thereby contributing to students’ understanding of the solution procedures for both problems. We juxtapose the two types of Trigonometry problems that differ in the location of the pronumeral (e.g., sin30° = x/5 vs. cos50° = 20/x) to encourage active comparison. Therefore, drawing on the complementary strength of learning by analogy and learning by comparison theories, we expect to counter the inherent difficulty of learning Trigonometry problems that involve algebraic transformation skills. This conceptual analysis article, overall, makes attempts to elucidate and seek clarity into the two comparative pedagogical approaches for effective learning of Trigonometry.

Aims: Situating within the 2 x 2 model of achievement goals, we explored the antecedents (emotional and physiological states, academic buoyancy, task values) and consequences (academic engagement, intrinsic motivation) of both mastery-approach and mastery-avoidance goals. Our hypothesized a priori model for testing entails direct and indirect effects, emphasizing in particular the central mechanism of both mastery goal types. Methodology: Secondary school students (N = 288) participated in the present study, and data were collected across four occasions. Results: Structural equation modeling yielded some notable findings, such as the negative effects of emotional and physiological states on mastery-approach and mastery-avoidance goals and the negative effect of mastery-avoidance goals on academic engagement. Task values and emotional and physiological states also influenced intrinsic motivation. Evidence from our investigation, overall, provided additional clarity into the characteristics of the two mastery goal types.

Situating within the 2 x 2 model of achievement goals, this short-term study examined the central roles of tasks values, mastery-approach and mastery-avoidance goals, and academic engagement and disengagement in students' future achievement outcome in mathematics. Enactive learning experience was also considered as antecedent of the mentioned variables. A sample of 262 (139 boys and 123 girls) 12th grade students participated in the study. Structural equation modelling analyses yielded some notable findings, such as temporally displaced effects of both mastery-approach and mastery-avoidance goal orientations on academic engagement and disengagement, respectively. The two types of mastery goals also influenced achievement in mathematics, whereas task values inversely related to academic disengagement. In general, from a decomposition of direct and indirect effects, it can be suggested that mastery goals exist in a central system that includes both antecedents and consequences.