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 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.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

Torres Strait Island parents' involvement in their children's mathematics learning : a discussion paper

This paper is a beginning point for discussing what the literature states about parents’ involvement in their children’s mathematics education. Where possible it will focus on Torres Strait Islander Peoples. Little is known about how Torres Strait Islander parents approach their children’s learning of mathematics and how important early mathematics is to mothers. What is known is that is they are keen for their children to receive an education that provides them with opportunities for their present and future lives. However, gaining access to education is challenging given that the language of instruction in schools is written to English conventions, decontextualised and disconnected from the students’ culture, community and home language. This paper discusses some of the issues raised in the literature about what parents are confronted with when making decisions about their children’s education.

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.

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.

When 'listeners can't talk' : comparing active listening in opening sequences of telephone and online counselling

While there is growing use of online counselling, little is known about its interactional organisation and how it compares to telephone counselling. This is despite past research suggesting that both counsellors and clients report the impact of the different modalities on the presentation and management of the counselling interaction. This paper compares the interactional affordances of telephone and online web counselling in opening sequences on Kids Help Line, a 24-hour Australian counselling service for children and young people up to the age of 25. We examine two ways that counsellors show active listening through response tokens and formulations. The analysis describes how counsellors’ use of minimal response tokens facilitate the clients’ problem presentation and are used in the management of turn taking and sequence organisation. For example, counsellors use the response token Mm hm to show that they understand that the client’s unit of talk to is not yet complete, and to affirm or invite the client to continue speaking. Formulations in phone and web counselling are another way that counsellors display active listening to re-present stretches of the clients’ preceding talk. In phone and web counselling, however, the respective modalities can complicate matters of turn transition and sequence organisation. By examining actual phone and online counselling sessions, this paper offers empirical demonstrations of the interactional affordances of phone and online counselling, and shows how the institutional practice of active listening is accomplished across different counselling modalities

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).

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.