Yeo, Amelia

Teachers’ efforts to guide students’ attention are potentially important for students’ learning. In this chapter, we consider two types of external supports that teachers frequently use to guide students’ attention: diagrams and gestures. We argue that teachers use diagrams and gestures to schematize specific features of mathematical problems or tasks, such as important elements and structural relations. In turn, teachers’ schematizing increases the likelihood that students encode those features. If the schematized features are relevant to the problem or task at hand, students’ appropriate encoding of those features will support their performance and learning. We present a selective review of research (including our own) on the roles of diagrams and teacher gestures in helping students encode key features and discern structure in instructional material.

Student well-being is inexorably bound to modern educational systems and schools have an inherent responsibility to examine student well-being. It is vital that schools have at their disposal a valid and reliable measurement tool to assess student well-being. A popular conceptual framework of well-being is the PERMA model (positive emotions, engagement, relationships, meaning, and a sense of accomplishment). The PERMA-Profiler is a scale that focuses exclusively on measuring these factors. However, results from previous validation studies have been mixed with issues arising from items on engagement and its model structure. Thus, the aims of the present study were to (1) modify the PERMA-Profiler to assess student well-being in secondary schools, and (2) evaluate the psychometric properties of the modified PERMA-Profiler. Study one included focus group discussions with 5 teachers and 20 students, followed by a preliminary trial to 387 secondary one (year 7 equivalent) students (194 boys, 193 girls). Several items were modified after analysing the results from study one. Study 2 aimed to validate the amended questionnaire by extending its administration to 3788 secondary one students (2202 boys, 1586 girls) over 17 schools. Results indicated that the questionnaire exhibited good psychometric properties, namely (a) it had excellent reliability indices of coefficient omega, (b) convergent validity was established with school satisfaction and test anxiety and (c) it demonstrated excellent fit with a five-factor model. Furthermore, there was measurement invariance between gender. The modified PERMA-Profiler shows promise as a valid and reliable measurement of student well-being in secondary schools.

A recurrent dimension occurring in wellbeing models pertains to positive relationships of individuals. Yet there is little information elucidating the link between positive relationships and subjective wellbeing in different cultures. Thus, the aims of this paper were (1) to examine whether there is an association between positive relationships and adolescent wellbeing across several culturally distinct countries and (2) explore whether the association between positive relationships and adolescent wellbeing differed for these countries along the cultural dimensions of individualism/collectivism and indulgence/restraint. Well-being measures were obtained from the large-scale assessment PISA 2018 and cultural dimensions indices were obtained. The results provide compelling evidence that positive relationships are positively associated with both affective and eudemonic wellbeing. Furthermore, there may be a greater association between positive relationships and positive affect in collectivist-indulgent countries than in collectivistic restraint countries. The study furthers our understanding of adolescent wellbeing across different cultural dimensions.

Mathematics instruction often involves multiple representations of concepts. Understanding connections among representations is a hallmark of conceptual understanding. In this research, we examine how teachers connect representations in elementary mathematics lessons about equality. We focused on three first-grade mathematics lessons from China, because students in China generally demonstrate a relational conception of the equal sign (i.e., interpreting it as indicating “sameness” or the idea that two expressions have the same quantity). We sought to understand how teachers in China support students’ acquisition of this conceptual understanding. Teachers used a wide variety of different representations in lessons about equality, including counters, picture equations, number words, and symbolic equations. Teachers expressed links between representations repeatedly and in multiple ways, and they frequently engaged their students in co-constructing links. Teachers expressed most links multi-modally, frequently using gestures, actions, and drawing to indicate the linked representations and to highlight correspondences between them. The sequence of linking episodes within each lesson tended to follow principles of “concreteness fading”, starting with more concrete representations and progressing to more abstract ones. The findings suggest new directions for the analysis of mathematics instruction, both within and across cultures.