Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Gender and grade differences in upper elementary school children’s descriptive and evaluative self-statements and self-esteem

Gender and developmental differences in self-description, self-evaluation and self-esteem were investigated using 957 elementary school children in grades 3 to 7. Gender differences were found for six of the seven descriptive statements and for five of the seven evaluative statements. The major gender stereotypical findings from previous studies were replicated. Boys reported higher scores than girls on descriptive and evaluative statements about their physical abilities and mathematics, while girls reported higher scores on descriptive and evaluative statements about reading. Declines over time were noted for all self-evaluations except having good relations with peers and for global self-esteem, providing some support for the notion that the decline in self-concepts and self-esteem may be attributed to the children's perceptions of themselves becoming more accurate and less egocentric in line with their cognitive capacity to integrate external feedback realistically.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

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.

All-terrain vehicle crashes and associated injuries in North Queensland : findings from the Rural and Remote Road Safety Study

Objective: To define characteristics of all-terrain vehicle (ATV) crashes occurring in north Queensland from March 2004 till June 2007 with the exploration of associated risk factors. Design: Descriptive analysis of ATV crash data collected by the Rural and Remote Road Safety Study. Setting: Rural and remote north Queensland. Participants: Forty-two ATV drivers and passengers aged 16 years or over hospitalised at Atherton, Cairns, Mount Isa or Townsville for at least 24 hours as a result of a vehicle crash. Main outcome measures: Demographics of participants, reason for travel, nature of crash, injuries sustained and risk factors associated with ATV crash. Results: The majority of casualties were men aged 16–64. Forty-one per cent of accidents occurred while performing agricultural tasks. Furthermore, 39% of casualties had less than one year’s experience riding ATVs. Over half the casualties were not wearing a helmet at the time of the crash. Common injuries were head and neck and upper limb injuries. Rollovers tended to occur while performing agricultural tasks and most commonly resulted in multiple injuries. Conclusions: Considerable trauma results from ATV crashes in rural and remote north Queensland. These crashes are not included in most general vehicle crash data sets, as they are usually limited to events occurring on public roads. Minimal legislation and regulation currently applies to ATV use in agricultural, recreational and commercial settings. Legislation on safer design of ATVs and mandatory courses for riders is an essential part of addressing the burden of ATV crashes on rural and remote communities.

Torres Strait Islander 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.

Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

Getting skilled for education, training and employment : Indigenous Cultural Knowledges and mainstream knowledges of mathematics

This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.

Humanistic science education : moves from within and challenges from without

For a number of years now it has been evident that the major issue facing science educators in the more developed countries of the world is the quantitative decline in enrolments in the senior secondary sciences, particularly the physical sciences, and in the number of higher achieving students applying for places in universities to undertake further studies in science. The deep malaise in school science to which these quantitative measures point has been elucidated by more qualitative studies of the students’ experience of studying science in secondary school in several of these countries (Sweden, Lindahl (2003); England, Simon and Osborne (2002); and Australia, Lyons (2005)). Remarkably concordant descriptions of these experiences can be summarized as: School science is: • transmission of knowledge from the teacher or the textbook to the students. • about content that is irrelevant and boring to our lives. • difficult to learn in comparison with other subjects Incidentally, the Australian study only involved consistently high achieving students; but even so, most of them found science more difficult than other more interesting subjects, and concluded that further science studies should be avoided unless they were needed for some career purpose. Other more representative confirmations of negative evaluations of the science curricula across Australia (and in particular states) are now available in Australia, from the large scale reviews of Goodrum, Hackling and Rennie (2001) and from the TIMSS (2002). The former reported that well under half of secondary students find the science at school relevant to my future, useful ion everyday life, deals with things I am concerned with and helps me make decisions about my health.. TIMSS found that 62 and 65 % of females and males in Year 4 agree with I like learning science, but by Year 8 only 26 and 33 % still agree. Students in Japan have been doubly notably because of (a) their high performance in international measures of science achievement like TIMSS and PISA and (b) their very low response to items in these studies which relate to interest in science. Ogura (2003) reported an intra-national study of students across Years 6-9 (upper primary through Junior High); interest in a range of their subjects (including science) that make up that country’s national curriculum. There was a steady decline in interest in all these subjects which might have indicated an adolescent reaction against schooling generally. However, this study went on to ask the students a further question that is very meaningful in the Japanese context, If you discount the importance of this subject for university entrance, is it worth studying? Science and mathematics remained in decline while all the other subjects were seen more positively. It is thus ironic, at a time when some innovations in curriculum and other research-based findings are suggesting ways that these failures of school science might be corrected, to find school science under a new demands that come from quite outside science education, and which certainly do not have the correction of this malaise as a priority. The positive curricular and research findings can be characterized as moves from within science education, whereas the new demands are moves that come from without science education. In this paper I set out these two rather contrary challenges to the teaching of science as it is currently practised, and go on to suggest a way forward that could fruitfully combine the two.

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.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

A Malaysian tale : pre-service teacher education and ICT integration for a better world

The use of Information and Communication Technologies (ICT) in education is often a topic of much discussion within all sectors of education with educators and educational researchers continually looking for innovative ways of using these technologies to support and enhance student outcomes in education. Consequently, Malaysia is no exception to this and as the Ministry of Education (MOE), Malaysia strives to meet its government’s Vision 2020, educational reform across all educational sectors has become imperative. ICT will play an integral role in the educational reform process and teacher education programs are no exception to this. ICT and capacity building will play an important role in the re-conceptualisation of teacher education programs. This paper reports on how a collaborative capacity building project between two Malaysian teacher education Institutes and an Australian University has given lecturers and pre-service teachers an opportunity to redefine their use of ICT in their prospective teaching areas of science, mathematics and design and technology. It also highlights the positive capacity building programs that occurred between both Australian university lecturers and Malaysian Institute lecturers and how this contributed to the effective integration and use of ICT.

One size doesn't fit all. Exploring marketing strategies for influencing three dimensions of brand loyalty

Brand loyalty is a concept that has garnered considerable interest over recent years from both marketing practitioners and academics alike. While marketers are primarily interested in ways they can generate and increase brand loyalty from their customers, academics strive to conducts research which investigates the antecedents and consequences of customer loyalty (See DeWitt, Nguyen and Marshall 2008; Russell-Bennett, McColl-Kennedy and Coote 2007).

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.