Exploring variation in measurement as a foundation for statistical thinking in the elementary school

This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3).

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.

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.

Self-talk in upper primary school children : its relationship with irrational beliefs, self-esteem and depression

Self-talk, irrational beliefs, self-esteem and depression were measured in a sample of 105 elementary school children in Grades 4 to 7. Sex and grade differences in positive self-talk were found. The pattern of correlation coefficients for positive self-talk supported the substantive position that positive self-talk is positively related to self-esteem and negatively related to irrational beliefs and depression in a non-clinical sample of children. However, the same support was not forthcoming for the reverse relationships for negative self-talk. Therapeutic implications are outlined as are suggestions for future research in the area of children's self-talk.

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 Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Leadership construction : an exploratory case study of two exemplary female principals in urban primary schools in mainland China

Worldwide, education systems have undergone unprecedented change due to a variety of economic, social, and political forces (Limerick, Cunnington & Crowther, 2002). The People’s Republic of China (PRC) is no exception. Continuous educational reform at primary and secondary levels in Mainland China has created new challenges and accountabilities for school principals. The important role of principals in primary and secondary schools has been acknowledged in both policy documents and the broader literature (Central Committee of the Chinese Communist Party, 1985; F. Chen, 2005; Chu, 2003; W. Huang, 2005; T. Wang, 2003). Yet, most of the literature on primary and secondary school principals in Mainland China is prescriptive in nature, identifying from the perspectives of researchers and academics what principals should do and how they should enact leadership. Lacking in this research is an awareness of the daily practices and lived experiences of principals. Furthermore, within the small body of writing on primary and secondary school principals in Mainland China, gender is seldom given any attention. To date, only a small number of empirical studies have focused on female principals as a specific category of research (Zen, 2004; Zhong, 2004). This study aimed to explore the professional lives of two female exemplary school principals in urban primary schools in Mainland China. A qualitative exploratory case study was used. Semi-structured interviews with each individual female principal, with six teachers in each of the school sites and with the superintendent of each principal were conducted. Field observations and document analysis were also undertaken to obtain multiple insights about their leadership practices. The conceptual framework was based largely on the theory of Gronn (1999) and incorporated five core leadership practices (vision building, ethical considerations, teaching and learning, power utilisation, and dealing with risks and challenges) taken from the wider literature. The key findings of this study were twofold. Firstly, while the five leadership practices were evident in the leadership of the two principals, this study identified some subtle differences in the way they approached each of them. Secondly, contextual factors such as Chinese traditional culture, the contemporary societal context, and the school organisational context, in addition to the biographical experiences of each principal were significant factors in shaping the way in which they exercised their leadership practices in the schools.

A principal at work : a story of leadership for building sustainable capacity of a school

This study explores through a lifestream narrative how the life experiences of a female primary school principal are organised as practical knowledge, and are used to inform action that is directed towards creating a sustainable school culture. An alternative model of school leadership is presented which describes the thinking and activity of a leader as a process. The process demonstrates how a leader's practical knowledge is dynamic, broadly based in experiential life, and open to change. As such, it is described as a model of sustainable leadership-in-process. The research questions at the heart of this study are: How does a leader construct and organize knowledge in the enactment of the principal ship to deal with the dilemmas and opportunities that arise everyday in school life? And: What does this particular way of organising knowledge look like in the effort to build a sustainable school community? The sustainable leadership-in-process thesis encapsulates new ways of leading primary schools through the principalship. These new ways are described as developing and maintaining the following dimensions of leadership: quality relationships, a collective (shared vision), collaboration and partnerships, and high achieving learning environments. Such dimensions are enacted by the principal through the activities of conversations, performance development, research and data-driven action, promoting innovation, and anticipating and predicting the future. Sustainable leadership-in-process is shared, dynamic, visible and transparent and is conducted through the processes of positioning, defining, organising, experimenting and evaluating in a continuous and iterative way. A rich understanding of the specificity of the life of a female primary school principal was achieved using story telling, story listening and story creation in a collaborative relationship between the researcher and the researched participant. as a means of educational theorising. Analysis and interpretation were undertaken as a recursive process in which the immediate interpretations were shared with the researched participant. The view of theorising adopted in this research is that of theory as hermeneutic; that is, theory is generated out of the stories of experiential life, rather than discovered in the stories.

Practices of interactive courseware at Malaysia primary smart school : usage standing and causes attributing

Malaysian teachers are now using interactive courseware in their teaching practices as part of teaching activity in classroom, to teach some subjects such as languages, mathematics, and science. Towards this, there is some debate going on the effectiveness of interactive courseware used in classroom. This paper reports data from interviews conducted with school principals and teachers from six selected primary Smart Schools across Malaysia.The interview conducted is looked on their current school practices and challenges in the implementation of interactive courseware in the classroom. The interview covers several aspects of their school facilities, the causes attributed and their concerns. However, the findings revealed that these six schools generally need more supports in the physical and technical form, in order to utilize the interactive courseware. Initially, the current support from the Malaysian Ministry of Education in physical form has proved that not very helpful. Thus, the respondents suggested that supports should be both: physical and technical. Therefore, this preliminary findings could be used as a pointer to the Malaysian government and other stakeholders to the improvement of interface design for future interactive courseware.

Evaluation of implementation of a healthy food and drink supply strategy throughout the whole school environment in Queensland state schools, Australia

BACKGROUND/OBJECTIVES: This paper reports on the evaluation of the Smart Choices healthy food and drink supply strategy for Queensland schools (Smart Choices) implementation across the whole school environment in state government primary and secondary schools in Queensland, Australia. SUBJECTS/METHODS: Three concurrent surveys using different methods for each group of stakeholders that targeted all 1275 school Principals, all 1258 Parent and Citizens’ Associations (P&Cs) and a random sample of 526 tuckshop convenors throughout Queensland. Nine hundred and seventy-three Principals, 598 P&Cs and 513 tuckshop convenors participated with response rates of 78%, 48% and 98%, respectively. RESULTS: Nearly all Principals (97%), P&Cs (99%) and tuckshop convenors (97%) reported that their school tuckshop had implemented Smart Choices. The majority of Principals and P&Cs reported implementation, respectively, in: school breakfast programs (98 and 92%); vending machine stock (94 and 83%); vending machine advertising (85 and 84%); school events (87 and 88%); school sporting events (81 and 80%); sponsorship and advertising (93 and 84%); fundraising events (80 and 84%); and sporting clubs (73 and 75%). Implementation in curriculum activities, classroom rewards and class parties was reported, respectively, by 97%, 86% and 75% of Principals. Respondents also reported very high levels of understanding of Smart Choices and engagement of the school community. CONCLUSIONS: The results demonstrated that food supply interventions to promote nutrition across all domains of the school environment can be implemented successfully.

Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.