Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

Measuring the quality of teaching in elementary school classrooms

This paper reviews the means by which teacher quality has been measured. It considers data sources such as students, peers, experts, and examines the psychometrics and scaleproperties of teacher quality assessment instruments with respect to reliability and validity. A list of items for possible inclusion in an elementary student focussed instrument is considered, together with the potential use of such an instrument in measuring teacher quality.

Elementary school students’ learner self-concept, academic self-concepts and approaches to learning

The present study investigated the relationships between academic selfconcepts, learner self-concept, and approaches to learning in elementary school students. A sample of 580 Australian Grade 6 and 7 school students with a mean age of 10.7 years participated in the study. Weak negative correlations between learner self-concepts and surface approaches to learning were identiŽ ed. In contrast, deep approaches for both boys and girls showed the highest positive correlations with school self-concept and learning self-concept. Only slight variations in these Ž gures were found between boys and girls.

Elementary students, creativity, and technology

This article reports on the impact on student personal creativity of a longitudinal study that had as its major goal the creation of a unique intervention program for elementary students. The intervention was based on the National Profile and Statement (Curriculum Corporation, 1994a, 1994b) for the curriculum area of technology. The intervention program comprised thematically based units of work that integrated all eight Australian Key Learning Areas (KLA). A pretest/posttest control group design investigation (Campbell & Stanley, 1963) was undertaken with 580 students from 7 schools and 24 class groups that were randomly divided into 3 treatment groups. One group (10 classes) formed the control group. Another 7 classes received the year-long intervention program, while the remaining 7 classes received the intervention, but with the added seamless integration of their available classroom computer technologies. The effect of the intervention on the personal creativity characteristics of the students involved in the study was assessed using the Creativity Checklist, an instrument that was developed during the study. The results suggest that the purposeful integration of computer technology with the intervention program positively affects the personal creativity characteristics of students.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Gender and grade differences in upper elementary school children’s descriptive and evaluative self-statements and self-esteem

Gender and developmental differences in self-description, self-evaluation and self-esteem were investigated using 957 elementary school children in grades 3 to 7. Gender differences were found for six of the seven descriptive statements and for five of the seven evaluative statements. The major gender stereotypical findings from previous studies were replicated. Boys reported higher scores than girls on descriptive and evaluative statements about their physical abilities and mathematics, while girls reported higher scores on descriptive and evaluative statements about reading. Declines over time were noted for all self-evaluations except having good relations with peers and for global self-esteem, providing some support for the notion that the decline in self-concepts and self-esteem may be attributed to the children's perceptions of themselves becoming more accurate and less egocentric in line with their cognitive capacity to integrate external feedback realistically.

Self-concept and self-esteem in elementary school children

Confusion exists with regard to the empirical and substantive link between self-concept and self-esteem in elementary school children and their relationship to self-description, self-evaluation, and global beliefs and feelings about oneself as a person. This study reports the results of investigating the relationships between these self-constructs using 957 elementary school children in Grades 3 to 7. The evidence suggests that self-concept is comprised of both descriptive and evaluative beliefs that children hold about certain characteristics, whereas self-esteem can be viewed as the global feelings and beliefs that children have about themselves as people.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Integrating engineering model eliciting activities in elementary school curricula

This paper argues for a future-oriented, inclusion of Engineering Model Eliciting Activities (EngMEAs) in elementary mathematics curricula. In EngMEAs students work with meaningful engineering problems that capitalise on and extend their existing mathematics and science learning, to develop, revise and document powerful models, while working in groups. The models developed by six groups of 12-year students in solving the Natural Gas activity are presented. Results showed that student models adequately solved the problem, although student models did not take into account all the data provided. Student solutions varied to the extent students employed the engineering context in their models and to their understanding of the mathematical concepts involved in the problem. Finally, recommendations for implementing EngMEAs and for further research are discussed.