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.

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.

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 education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

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.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Teachers' and education students' perceptions of and reactions to children with and without the diagnostic label 'ADHD'

Thirty-four elementary school teachers and 32 education students from Canada rated their reactions towards vignettes describing children who met attention-deficit/hyperactivity disorder (ADHD) symptom criteria that included or did not include the label “ADHD.” “ADHD”-labeled vignettes elicited greater perceptions of the child's impairment as well as more negative emotions and less confidence in the participants, although it also increased participants' willingness to implement treatment interventions. Ratings were similar to vignettes of boys versus girls; however, important differences in ratings between teachers and education students emerged and are discussed. Finally, we investigated the degree to which teachers' professional backgrounds influenced bias based on the label “ADHD.” Training specific to ADHD consistently predicted label bias, whereas teachers' experience working with children with ADHD did not.

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.

Engineering-based modelling experiences in the elementary classroom

Introducing engineering-based model-eliciting experiences in the elementary curriculum 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 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 indicate that engineering model-eliciting activities can be introduced effectively into the elementary curriculum, providing rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Perspectives of teaching in Papua New Guinea : a case study of elementary teacher trainers and their mentors

Global and national agenda for quality education led to reform in Papua New Guinea (PNG) based on the provision of quality basic education. “Education for All” (EFA) is a worldwide emphasis on the review and restructure of existing curriculum and teacher training programs to provide quality education and quality life. The provision of quality education is seen as an investment in developing countries including PNG. Quality education is facilitated through structural and curriculum reform, and teacher education programs. One such influence on quality education in teacher education relates to perspectives of teaching. Existing research shows teachers’ beliefs and perceptions of teaching influence their practice (Kember & Kwan, 2000; Prosser & Trigwell, 2004). However, there is no research focusing on perspectives of teaching for elementary education in PNG. This single exploratory case study (Yin, 2009) investigated the perspectives of teaching of eighteen elementary teacher trainers and their five mentors in the context of an Australian university Bachelor of Early Childhood (in teacher education) degree programme. The study drew on an interpretivist paradigm to analyse journals, semi-structured interviews and course planning documents using a thematic approach to data analysis (Braun & Clark, 2006). The findings revealed that participants held perspectives of teaching related to teaching children and teaching adults. The perspective of teaching children described by the trainers and mentors was learning-centred (the focus is on what the teacher does); while the perspective of teaching adults was both learning-centred and learner-centred (the focus is on what the learner does). The learning-centred perspective is at odds with the learner-centred perspective espoused in the PNG reform. The perspectives of teaching adults reflected a culturally nuanced view; providing insights about how teaching and learning are understood in different sociocultural contexts. Based on these findings, the study proposes a perspective of teaching for elementary education in PNG known as culturally connected teaching. This perspective enables the co-existence of both the learning-centred and learner-centred perspectives of teaching in the PNG cultural context. This perspective has implications for teacher training and the communities involved in elementary education.

Understanding learning and teaching : elementary teacher trainers in Papua New Guinea engaged in cultural authorship in the context of national educational reform

Over the last decade, Papua New Guinea (PNG) has pursued educational reform in elementary teacher education. Because elementary teachers and teacher education are central to the reform agenda, there is a need to gain empirical evidence about how PNG teacher trainers’ understandings about learning and teaching impact on their practice. The study uses cultural-authorship as a theoretical framework to investigate the nature of changes in understanding about learning and teaching for 18 teacher trainers as they progressed through a two-year Bachelor of Early Childhood upgrade course. It addresses the research question: What do elementary teacher trainers in PNG understanding about learning and teaching and how has this changed during their course? The focus on such understandings provides valuable insights into their professional identities at a critical time in PNG’s education reform agenda. Analysis of journal entries at the beginning and end of the course showed that, over time, teacher trainers described increasingly more complex ways of understanding learning and teaching. These views shifted from a focus on learning and teaching as transmission of ideas to one in which the critical role played by communities and families in educational processes and the teacher as a change agent became focal. This watershed finding demonstrates notable shifts in teacher trainers’ professional identities from trainers to community leaders in elementary education.

Learning to lead : a social justice perspective on understanding elementary teacher leadership in Papua New Guinea

Leadership in elementary education is currently recognized as a political imperative in Papua New Guinea (PNG), as the nation develops strategies towards equitable access to schooling. One recent initiative aimed at building educational leadership was an intensive Australian Leadership Award Fellowship (ALAF) program funded by AusAID, involving a group of 10 teacher trainers from PNG. As part their involvement participants completed self-authored journal entries at the beginning and end of the leadership program. Participants were also involved in focus groups after completion of the initiative. Referring to the experiences of these teacher trainers, this paper draws on Nancy Fraser’s (2005, 2008) social justice framework to examine participants’ views of what constituted effective leadership in elementary education in PNG and how these views may have changed throughout the ALAF program. Key findings of this study included participants’ emphasis on relationships and valuing people in elementary education leadership contexts, participants’ concern about economic/financial barriers to effective leadership in the PNG context and participants’ perception of research as a way to support leadership roles.