Khng Kiat Hui

Test anxiety is a non-trivial issue in schools, especially in settings with high stakes examinations like Singapore. It is estimated that 10–40% of students, as young as age 7, suffer from test anxiety (von der Embse, Barterian, & Segool, 2013). Test anxiety can adversely impact psychological well-being and performance; schools are recognizing the need to equip students with skills to ameliorate the adverse effects of test anxiety. One technique that has been found to help children with test anxiety is deep breathing. In the PI’s previous ERFP study, it was found that teaching children to take deep breaths before a timed math test reduced their feelings of anxiety and enhanced their test performance (Khng, 2017). However, although it was hypothesized that deep breathing might enhance performance by increasing attentional focus, the authors found no significant effects of the deep breathing intervention on reducing behavioural measures of interference on a Flanker task (Eriksen & Eriksen, 1974), commonly used to index inhibitory control of attention to distractors.
Interventions, such as attention training, have at times been found to enhance brain functioning at the neurophysiological level without necessarily manifesting as improvements in direct behavioural performance. For instance, an attention training study with preschool children found EEG indicators of a more efficient executive attention network following training, despite the lack of significant behavioural effects during an attention task (Rueda, Checa, & Cómbita, 2012). Thus, the deep breathing intervention might have enhanced attentional focus at a neurofunctional level, at the level of brain functioning—even if no evidence was found at the behavioural level—and translate into better performance on the math test.
Electrophysiological and neuroimaging data are important sources of information for validating the efficacy/effects of interventions. Many interventions for children are carried out in the schools especially if they are educationally relevant. However, collecting data such as electroencephalography (EEG) from children during school-based tasks or interventions is difficult due to the costs and physical constraints of conventional equipment. High-resolution, medical/research-grade EEG systems tend to be very expensive, cumbersome and take a long time to set up, and can be uncomfortable for the child. This can deter children from participating in EEG studies, and limit the possibilities of collecting data for large-scale, school-based interventions. The recent development of low cost, lightweight, wireless, mobile EEG headsets that are quick and easy to set up and reasonably comfortable for children to wear, brings new possibilities to collect ecologically-valid EEG data in situ, during large-scale, school-based interventions.

This dissertation considered the interface between cognitive psychology and education by examining the contribution of inhibitory abilities to algebra word problem solving. The ability to inhibit interference from prior learning or experience has been proposed to be an important variable in learning and performance. In mathematics education, it has been observed that many students’ progression to letter-symbolic algebra is hampered by a persistent reliance on previously learnt arithmetic methods or reasoning. Over four studies, I examined the hypothesis that performance in algebra word problem solving is related to the ability to inhibit interference from prior arithmetic knowledge. The first study examined the contribution of inhibition to algebra word problem solving performance in relation to contributions from algebraic knowledge, intelligence, and working memory span. Two forms of inhibitory function were found to predict algebra problem solving performance in beginning algebra (Secondary 2) students. Inhibition-of-prepotent/reified-processes predicted problem-solving accuracy through the inhibition of intrusions from arithmetic methods of problem solving. Inhibition-of-recently-learntassociations predicted accuracy through intellectual ability. The second and third studies followed up on findings from the first study, focusing on the finding that the Stroop and stop-signal tasks may be reflecting different kinds of inhibition—inhibition-ofprepotent/reified-processes and inhibition-of-recently-learnt-associations, respectively. The relationship amongst Stroop and stop-signal measures of inhibition, accuracy, speed, and response variability, were examined in adolescent and adult samples, respectively. Stroop and stop-signal measures of inhibition (Stroop interference reaction time and stopsignal reaction time) were found to be not reliably correlated and developed at different rates. Stroop and stop-signal inhibition were also differently associated with accuracy, speed, and response variability—indicating possible different relationships with task performance and strategies involving speed and attention. The final study investigated if the relationships found between Stroop and stop-signal inhibition—between each other as well as with interference from prior knowledge—will also be observed at the neural level. Using functional magnetic resonance imaging, adults exhibiting high and low susceptibility to interference from prepotent belief-bias were compared on their neural activity during Stroop and stop-signal inhibition. Stroop and stop-signal inhibition were found to implicate a common parietal region. However, differences exceeded commonalities. The engagement of inhibitory mechanisms was modulated by both task and susceptibility group differences. Consistent with findings from the preceding studies, results suggest that the form of inhibition involved in the Stroop task is more closely related to prepotent interference from prior knowledge. Current findings suggest that inhibitory abilities contribute to performance in algebra word problem solving in at least two ways. The ability to inhibit recently learnt associations is a more general ability contributing via intelligence. The ability to inhibit prepotent/reified processes relates to prior knowledge and contributes via preventing intrusions. The inhibition-ofprepotent/reified-processes is particularly important in the transition from old to new knowledge. Educators can help in this transition by teaching in a way that facilitates the formation of superordinate knowledge structures and minimizes interference from previously learnt dominant strategies. New knowledge should be built on children’s old knowledge, with an emphasis on establishing linkages between them.

Mindfulness and democratic attitudes in teachers seem to overlap in promoting teacher-student relationships and student learning in classrooms. To examine if there are positive associations between teachers' mindfulness and democratic attitudes, the current study examined relationships between dispositional mindfulness and teacher attitudes (democratic and autocratic) among 50 pre-service teachers in Singapore. Correlation analyses revealed a positive relationship between teachers ' democratic attitudes and their dispositional mindfulness and significant associations between specific components of mindfulness (Observing, Describing and Non-reactivity) and teachers' democratic and autocratic attitudes. A marginally significant difference was shown in democratic attitudes according to the experience of International Practicum (IP), where teachers with IP experience have lower democratic attitudes. This is contrary to what existing literature predicts. Overall , this study's findings can potentially provide directions for future programmes in Singapore to promote mindfulness and democratic attitudes in prospective teachers .

Across cultures and curricula, it is commonly observed that many beginning learners of formal algebra revert to familiar methods rooted in arithmetic reasoning to solve algebra problems. Though a prevalent cause for frustration in teachers trying to get students to practice and master letter-symbolic algebra, some have argued that such displays of “flexibility” in strategy choice should not be discouraged. Some even found children to be more successful in solving algebra problems when they use arithmetic methods (e.g., Nathan and Koedinger, 2000a). Are arithmetic methods more effective than algebraic methods in solving algebra word problems? Are students truly being “flexible” when they use arithmetic methods in situations calling for algebraic methods? Is it a case of flexibility or inflexibility when students persist in using arithmetic methods when they are no longer appropriate or effective? Are students’ strategy choices and their resulting success in solving algebra word problems contingent upon their cognitive capabilities and their understanding of algebra? We examined these questions by giving 157 Secondary 2 students a set of algebra word problems under specific instructions to use letter-symbolic algebra, as well as tests of their algebraic knowledge, intellectual ability, working memory, and inhibitory ability. Results revealed that(i) despite the specific instructions, a substantial number of students persisted in using arithmetic methods, suggesting a reluctance or inability to use letter-symbolic algebra; (ii)students were not more successful in solving algebra word problems when they used arithmetic methods; (iii) algebraic knowledge, intellectual ability, working memory, and inhibitory abilities contribute in both unique and overlapping ways to both strategy choice and success in solving algebra word problems.

In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems. However, little is known about students’ understanding of these graphical representations. We investigated whether students use and think of the bar diagrams in a concrete or a more abstract fashion. We also examined whether usage and understanding varied with grade. Secondary 2 (N = 68, Mage = 13.9 years) and Primary 5 students (N = 110, Mage = 11.1 years) were administered a production task in which they drew bar diagrams of algebraic word problems with operands of varying magnitude. In the validation task, they were presented with different bar diagrams for the same word problems and were asked to ascertain, and give explanations regarding the accuracy of the diagrams. The Küchemann algebra test was administered to the Secondary 2 students. Students from both grades drew longer bars to represent larger numbers. In contrast, findings from the validation task showed a more abstract appreciation for how the bar diagrams can be used. Primary 5 students who showed more abstract appreciations in the validation task were less likely to use the bar diagrams in a concrete fashion in the production task. Performance on the Küchemann algebra test was unrelated to performance on the production task or the validation task. The findings are discussed in terms of a production deficit, with students exhibiting a more sophisticated understanding of bar diagrams than is demonstrated by their usage.

This paper provides an overview of key research conducted locally and internationally in the field of applied cognitive development, particularly working memory and executive functioning from early childhood to mid-adolescence. The focus is on understanding the reasons for low achievement in children, with a particular emphasis on the interaction of domain-specific knowledge, attentional, social-emotional, and motivational predictors of academic achievement. We also focus on research examining the efficacy of interventions to enhance cognitive, social-emotional, and academic skills. We highlight the directions in which we believe future work should proceed given current developments in the field, our own interests and core capacity, and the need to address important educational questions in Singapore. These include the need to develop more sensitive tests of specific cognitive abilities, continued efforts to develop interventions to support the development of both domain-general skills and domain-specific numeracy and mathematics skills, an understanding of individual differences in response to pedagogy and training, and the examination of social-emotional factors (e.g., anxiety) on cognition and learning. Continued collaborative efforts will allow us to address these questions with behavioural, physiological, and neurological data and will provide a deeper understanding of the child’s outcomes in response to the pedagogical environment.