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.

“Filling out the forms was a nightmare” : project evaluation and the reflective practitioner in community theatre in contemporary Northern Ireland

Since the Good Friday Agreement of 1998, large sums have been invested in community theatre projects in Northern Ireland, in the interests of conflict transformation and peace building. While this injection of funds has resulted in an unprecedented level of applied theatre activity, opportunities to maximise learning from this activity are being missed. It is generally assumed that project evaluation is undertaken at least partly to assess the degree of success of projects against important social objectives, with a view to learning what works, what does not, and what might work in the future. However, three ethnographic case studies of organisations delivering applied theatre projects in Northern Ireland indicate that current processes used to evaluate such projects are both flawed and inadequate for this purpose. Practitioners report that the administrative work involved in applying for and justifying funding is onerous, burdensome, and occurs at the expense of artistic activity. This is a very real concern when the time and effort devoted to ‘filling out the forms’ does not ultimately result in useful evaluative information. There are strong disincentives for organisations to report honestly on their experiences of difficulties, or undesirable impacts of projects, and this problem is not transcended by the use of external evaluators. Current evaluation processes provide little opportunity to capture unexpected benefits of projects, and small but significant successes which occur in the context of over-ambitious objectives. Little or no attempt is made to assess long-term impacts of projects on communities. Finally, official evaluation mechanisms fail to capture the reflective practice and dialogic analysis of practitioners, which would richly inform future projects. The authors argue that there is a need for clearer lines of communication, and more opportunities for mutual learning, among stakeholders involved in community development. In particular, greater involvement of the higher education sector in partnership with government and non-government agencies could yield significant benefits in terms of optimizing learning from applied theatre project evaluations.

Are low CO2 emitters in rural areas also socially excluded? An empirical investigation of travel diary data from rural Northern Ireland

The reduction of CO2 emissions and social exclusion are two key elements of UK transport strategy. Despite intensive research on each theme, little effort has so far been made linking the relationship between emissions and social exclusion. In addition, current knowledge on each theme is limited to urban areas; little research is available on these themes for rural areas. This research contributes to this gap in the literature by analysing 157 weekly activity-travel diary data collected from three case study areas with differential levels of area accessibility and area mobility options, located in rural Northern Ireland. Individual weekly CO2 emission levels from personal travel diaries (both hot exhaust emission and cold-start emission) were calculated using average speed models for different modes of transport. The socio-spatial patterns associated with CO2 emissions were identified using a general linear model whereas binary logistic regression analyses were conducted to identify mode choice behaviour and activity patterns. This research found groups that emitted a significantly lower level of CO2 included individuals living in an area with a higher level of accessibility and mobility, non-car, non-working, and low-income older people. However, evidence in this research also shows that although certain groups (e.g. those working, and residing in an area with a lower level of accessibility) emitted higher levels of CO2, their rate of participation in activities was however found to be significantly lower compared to their counterparts. Based on the study findings, this research highlights the need for both soft (e.g. teleworking) and physical (e.g. accessibility planning) policy measures in rural areas in order to meet government’s stated CO2 reduction targets while at the same time enhancing social inclusion.

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.