Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

Promoting Statistical Literacy Through Data Modelling in the Early School Years

This chapter addresses data modelling as a means of promoting statistical literacy in the early grades. Consideration is first given to the importance of increasing young children’s exposure to statistical reasoning experiences and how data modelling can be a rich means of doing so. Selected components of data modelling are then reviewed, followed by a report on some findings from the third-year of a three-year longitudinal study across grades one through three.

Time, space, and text in the elementary school digital writing classroom

Theorists of multiliteracies, social semiotics, and the New Literacy Studies have drawn attention to the potential changing nature of writing and literacy in the context of networked communications. This article reports findings from a design-based research project in Year 4 classrooms (students aged 8.5-10 years) in a low socioeconomic status school. A new writing program taught students how to design multimodal and digital texts across a range of genres and text types, such as web pages, online comics, video documentaries, and blogs. The authors use Bernstein’s theory of the pedagogic device to theorize the pedagogic struggles and resolutions in remaking English through the specialization of time, space, and text. The changes created an ideological struggle as new writing practices were adapted from broader societal fields to meet the instructional and regulative discourses of a conventional writing curriculum.

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.

Mapping the language of science and science teaching practices : a case study of early childhood school science

Concerns raised in educational reports about school science in terms of students. outcomes and attitudes, as well as science teaching practices prompted investigation into science learning and teaching practices at the foundational level of school science. Without science content and process knowledge, understanding issues of modern society and active participation in decision-making is difficult. This study contended that a focus on the development of the language of science could enable learners to engage more effectively in learning science and enhance their interest and attitudes towards science. Furthermore, it argued that explicit teaching practices where science language is modelled and scaffolded would facilitate the learning of science by young children at the beginning of their formal schooling. This study aimed to investigate science language development at the foundational level of school science learning in the preparatory-school with students aged five and six years. It focussed on the language of science and science teaching practices in early childhood. In particular, the study focussed on the capacity for young students to engage with and understand science language. Previous research suggests that students have difficulty with the language of science most likely because of the complexities and ambiguities of science language. Furthermore, literature indicates that tensions transpire between traditional science teaching practices and accepted early childhood teaching practices. This contention prompted investigation into means and models of pedagogy for learning foundational science language, knowledge and processes in early childhood. This study was positioned within qualitative assumptions of research and reported via descriptive case study. It was located in a preparatory-school classroom with the class teacher, teacher-aide, and nineteen students aged four and five years who participated with the researcher in the study. Basil Bernstein.s pedagogical theory coupled with Halliday.s Systemic Functional Linguistics (SFL) framed an examination of science pedagogical practices for early childhood science learning. Students. science learning outcomes were gauged by focussing a Hallydayan lens on their oral and reflective language during 12 science-focussed episodes of teaching. Data were collected throughout the 12 episodes. Data included video and audio-taped science activities, student artefacts, journal and anecdotal records, semi-structured interviews and photographs. Data were analysed according to Bernstein.s visible and invisible pedagogies and performance and competence models. Additionally, Halliday.s SFL provided the resource to examine teacher and student language to determine teacher/student interpersonal relationships as well as specialised science and everyday language used in teacher and student science talk. Their analysis established the socio-linguistic characteristics that promoted science competencies in young children. An analysis of the data identified those teaching practices that facilitate young children.s acquisition of science meanings. Positive indications for modelling science language and science text types to young children have emerged. Teaching within the studied setting diverged from perceived notions of common early childhood practices and the benefits of dynamic shifting pedagogies were validated. Significantly, young students demonstrated use of particular specialised components of school-science language in terms of science language features and vocabulary. As well, their use of language demonstrated the students. knowledge of science concepts, processes and text types. The young students made sense of science phenomena through their incorporation of a variety of science language and text-types in explanations during both teacher-directed and independent situations. The study informs early childhood science practices as well as practices for foundational school science teaching and learning. It has exposed implications for science education policy, curriculum and practices. It supports other findings in relation to the capabilities of young students. The study contributes to Systemic Functional Linguistic theory through the development of a specific resource to determine the technicality of teacher language used in teaching young students. Furthermore, the study contributes to methodology practices relating to Bernsteinian theoretical perspectives and has demonstrated new ways of depicting and reporting teaching practices. It provides an analytical tool which couples Bernsteinian and Hallidayan theoretical perspectives. Ultimately, it defines directions for further research in terms of foundation science language learning, ongoing learning of the language of science and learning science, science teaching and learning practices, specifically in foundational school science, and relationships between home and school science language experiences.

Early and middle years of schooling

What to look for in the chapter • how inclusion for the early and middle years offers a set of unique challenges; • how school communities can promote inclusion for children and young adolescents; • strategies that teachers can use to build and maintain community in early and middle years’ settings; • factors that influence the success of teachers working with children and young adolescents in inclusive schools; • practical measures that teachers can take, in light of these factors, to promote the success of inclusion; and • the different responses that children in the early and middle years have to inclusion, how teachers can identify those responses, and what they can do to ensure that they are positive.

Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

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.

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.

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.