Metacognitive knowledge of effort, personality factors, and mood state: their relationships with effort-related metacognitive experiences

The present study aimed at identifying the effects of mood treatment, personality factors, and metacognitive knowledge of effort–i.e., conceptualization of effort and perceptions of effort regulation–on metacognitive experiences of students, particularly on their reported feeling of difficulty and estimate of effort. The sample comprised 474 students of 5th and 7th grade of both genders. The participants were tested in two phases. In the first phase, they were asked to respond to questionnaires measuring (a) metacognitive knowledge of effort, (b) maths self-concept, (c) goal orientations, and (d) a test of maths ability. In the second phase, participants were subjected to mood treatment–neutral, positive, and negative– and were asked to solve a mathematical problem. They also rated their prospective metacognitive experiences before solving the problem and the retrospective ones after solving it. Mood treatment interacted with gender in the case of performance but it had no effect on metacognitive experiences. A series of regression analyses showed that positive mood, personality factors, and feeling of difficulty predicted the prospective estimate of effort. Only feeling of difficulty and performance predicted the retrospective estimate of effort. No effect of metacognitive knowledge of effort on estimate of effort was found.     

On the front-line: Teachers as active observers of pupils’ mental health

There is a growing expectation that schoolteachers should not only act as educators by delivering the national curriculum, but also be more involved as tier one mental health professionals. In this role they are expected to assume some responsibility in the early identification of children's mental health problems and to refer these children for appropriate support as required [NHS Health Advisory Service. (1995). Together we stand: The commissioning, role and management of child and adolescent mental health services. London, UK: HMSO]. In this paper, we examine teachers’ experiences in light of these expectations and in the context of greater inclusion. We undertook in-depth interviews, to explore teachers’ views on competency and training in mental health management. Our findings indicate a widespread perception that teachers feel inadequately prepared to manage pupils with mental health needs. The findings are discussed with reference to the changing role of the teacher, current education policy and teacher training.     

Revitalizing Algebra: the effect of the use of a cognitive tutor in a remedial course

This study investigated the effect of instruction with a cognitive tutoring software system in a remedial algebra course. The performance on algebra tasks of students who attended the experimental (cognitive tutor) and a control class was compared. The results indicated that the two groups of students were equally proficient with respect to algebraic manipulation skills. However, students who attended the experimental algebra section performed significantly better in problem solving than students in the control section. This finding suggested that the use of the cognitive tutor (a) improved students' problem‐solving abilities; (b) fostered student development of richer concepts of variable and function; and (c) improved students' procedural abilities in approaching and carrying through mathematical analyses of relatively complex situations.     

Learning about ‘learning identities’ in the school arithmetic practice: The experience of two young minority Gypsy girls in the Greek context of education

The present study explores the experience of two young Gypsy girls in solving school arithmetic tasks in interaction with an adult who supports their participation. Along with learning the use of arithmetic tools, a basic element concerning the experience of the two girls as they try to gain entry into the school practice is learning about developing relevant ‘learning identities’. Analysis of the girls’ interaction with an adult identifies that the type of ‘learning identities’ required involve at least two dimensions: (a) learning to value the use of formal arithmetic tools, and (b) learning about relevant ways of behaving in the school mathematics practice.     

The Nature of Argumentation in School Mathematics and Physics Texts: The Case of Periodicity

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was applied on 71 thematic units taken from 4 mathematics and 4 physics textbooks, and a coding system of categories and subcategories of MsoR was produced. Our analysis discerned 4 main categories of MsoR: empirical, logical-empirical, nomological, and mathematical; we argue that each mode of reasoning (MoR) plays a different role in conceptualizing aspects of periodicity. Analysis of the sequence of MsoR in two thematic units raised pragmatic considerations on the text understanding in relation to the scientific argumentation discourse and highlights ontological differences in the two subjects when ascending from observations to generalizations. Educational implications of the findings are discussed.     

Teachers’ conceptions of representation in middle school mathematics

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications for mathematics teacher education, prospective and practicing, are discussed.