Integrating engineering education within the elementary and 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 discussion paper argues for the integration 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.

Why ask new questions?

It can probably be said those people who work in the world of the natural sciences— chemistry, biology, mathematics, and so on—regard themselves as inhabiting a fairly straight-forward epistemological world. They have a body of knowledge to draw upon from within any given area, much like a set of bricks in a wall, and when they conduct their experiments, they add another brick to that wall … and the wall gets taller, and they know more than they did before. Such scientists would contend that the questions they ask as part of their research flow naturally from the very nature of the world itself. But even then, they could also argue that the specifics of the question ultimately don‟t really matter that much, because if enough people work on any given brick, the truth will eventually emerge anyway.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Teaching and learning science and mathematics through technology practice

In this chapter we review studies of the engagement of students in design projects that emphasise integration of technology practice and the enabling sciences, which include physics and mathematics. We give special attention to affective and conceptual outcomes from innovative interventions of design projects. This is important work because of growing international concern that demand for professionals with technological expertise is increasing rapidly, while the supply of students willing to undertake the rigors of study in the enabling sciences is proportionally reducing (e.g., Barringtion, 2006; Hannover & Kessels, 2004; Yurtseven, 2002). The net effect is that the shortage in qualified workers is having a detrimental effect upon economic and social potential in Westernised countries (e.g., Department of Education, Science and Training [DEST], 2003; National Numeracy Review Panel and National Numeracy Review Secretarial, 2007; Yurtseven, 2002). Interestingly, this trend is reversed in developing economies including China and India (Anderson & Gilbride, 2003).

Context-based chemistry : creating opportunities for fluid transitions between concepts and context

Nationally and internationally, context-based programs have been implemented in an attempt to engage students in chemistry through connecting the canonical science with the real-world. In Queensland, a context-based approach to chemistry was trialled in selected schools from 2002 but there is little research that investigates how students learn in a context-based setting. This paper presents one significant finding from an ethnographic study that explored the learning that occurred in an 11th grade context-based chemistry classroom in Queensland. The study found that by providing students with the opportunity to write, fluid transitions (or to-ing and fro-ing) between concepts and context were an outcome of context-based learning.

Implications of precursor chemistry on the alkaline hydrothermal synthesis of titania/titanate nanostructures

A systematic study of four parameters within the alkaline hydrothermal treatment of three commercial titania powders—anatase, rutile, and Degussa P25—was made. These powders were treated with 5, 7.5, 9, and 10 M NaOH between 100 and 220 °C for 20 h. The effects of alkaline concentration, hydrothermal temperature, and precursor phase and crystallite size on the resultant nanostructure formation have been studied through X-ray diffraction, Raman spectroscopy, transmission electron microscopy, and nitrogen adsorption. Through the correlation of these data, morphological phase diagrams were constructed for each commercial powder. Interpretation of the resultant morphological phase diagrams indicates that alkaline concentration and hydrothermal temperature affect nanostructure formation independently, where nanoribbon formation is significantly influenced by temperature for initial formation. The phase and crystallite size of the precursor also significantly influenced nanostructure formation, with rutile displaying a slower rate of precursor consumption compared with anatase. Small crystallite titania precursors formed nanostructures at reduced hydrothermal temperatures.

Leading learning within a PLC : implementing new mathematics content

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Teaching and learning in a context-based chemistry classroom

Many current chemistry programs privilege de-contextualised conceptual learning, often limited by a narrow selection of pedagogies that too often ignore the realities of studentse own lives and interests (e.g., Tytler, 2007). One new approach that offers hope for improving studentse engagement in learning chemistry and perceived relevance of chemistry is the context-based approach. This study investigated how teaching and learning occurred in one year 11 context-based chemistry classroom. Through an interpretive methodology using a case study design, the teaching and learning that occurred during one term (ten weeks) of a unit on Water Quality are described. The researcher was a participant observer in the study who co-designed the unit of work with the teacher. The research questions explored the structure and implementation of the context-based approach, the circumstances by which students connected concepts and context in the context-based classroom and the outcome of the approach for the students and the teacher. A dialectical sociocultural theoretical framework using the dialectics of structure | agency and agency | passivity was used as a lens to explore the interactions between learners in different fields, such as the field of the classroom and the field of the local community. The findings of this study highlight the difficulties teachers face when implementing a new pedagogical approach. Time constraints and opportunities for students to demonstrate a level of conceptual understanding that satisfied the teacher, hindered a full implementation of the approach. The study found that for high (above average) and sound (average) achieving students, connections between sanctioned science content of school curriculum and the studentse out-of-school worlds were realised when students actively engaged in fields that contextualised inquiry and gave them purpose for learning. Fluid transitions or the toing and froing between concepts and contexts occurred when structures in the classroom afforded students the agency to connect concepts and contexts. The implications for teaching by a context-based approach suggest that keeping the context central, by teaching content on a "need-to-know" basis, contextualises the chemistry for students. Also, if teachers provide opportunities for student-student interactions and written work student learning can improve.

Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.