Complex modelling in the primary/middle school years

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual (Katehi, Pearson, & Feder, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to significant changes in the forms of mathematical and scientific thinking that are required beyond the classroom. Modelling, in its various forms, can develop and broaden children’s mathematical and scientific thinking beyond the standard curriculum. This paper first considers future competencies in the mathematical sciences within an increasingly complex world. Next, consideration is given to interdisciplinary problem solving and models and modelling. Examples of complex, interdisciplinary modelling activities across grades are presented, with data modelling in 1st grade, model-eliciting in 4th grade, and engineering-based modelling in 7th-9th grades.

Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.

Engaging parents in STEM: Coteaching and cogenerative dialoguing in a Queensland high school

Diminished student interest in science, technology, engineering and mathematics (STEM) is recognised by educators, researchers and public policy makers as a concerning global trend. Inviting stakeholders like scientists and industry specialists to discuss their work is one means schools use to facilitate student engagement in the sciences. However, these visits generally comprise one-off sessions with minimal relevance to students’ particular and ongoing learning needs. This case study investigated coteaching and cogenerative dialoguing with parents in teaching a Year-8 multidisciplinary unit with science and technology foci. Two parents cotaught alongside the resident teacher and researcher over eight months. This paper concentrates on one parent, a medical scientist by profession. Data sources included video and audio recordings of cogenerative dialogues and classroom interactions, student work samples and journal entries. Data were interrogated using the sociological constructs of fields and capitals and the dialectic of structure|agency. The findings reveal how (a) the parent’s science and technology knowledge was tailored to the students’ needs initially and continually and (b) student-generated data indicated enhanced engagement in science and technology. The research speaks to schools and governments about enhancing STEM education by furthering collaborative relationships with relevant stakeholders.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Practices of interactive courseware at Malaysia primary smart school : usage standing and causes attributing

Malaysian teachers are now using interactive courseware in their teaching practices as part of teaching activity in classroom, to teach some subjects such as languages, mathematics, and science. Towards this, there is some debate going on the effectiveness of interactive courseware used in classroom. This paper reports data from interviews conducted with school principals and teachers from six selected primary Smart Schools across Malaysia.The interview conducted is looked on their current school practices and challenges in the implementation of interactive courseware in the classroom. The interview covers several aspects of their school facilities, the causes attributed and their concerns. However, the findings revealed that these six schools generally need more supports in the physical and technical form, in order to utilize the interactive courseware. Initially, the current support from the Malaysian Ministry of Education in physical form has proved that not very helpful. Thus, the respondents suggested that supports should be both: physical and technical. Therefore, this preliminary findings could be used as a pointer to the Malaysian government and other stakeholders to the improvement of interface design for future interactive courseware.

Mathematics funds of knowledge : sotmaute and sermaute fish in a Torres Strait Islander community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

Engineering education in the middle school : exploring foundational structures

The recently released Mathematics, Engineering & Science in the National Interest report (May, 2012) highlights the universal perspective that an education in these disciplines is essential to a nation’s future prosperity. Although studies in STEM (Science, Technology, Engineering, Mathematics) are being implemented across many schools, progress to date has been slow especially with respect to incorporating engineering experiences in the middle and primary grades. Our concerns for the limited attention given to engineering in STEM and the low uptake of university engineering courses in universities, prompted us to conduct a longitudinal project on engineering education across grade levels 7-9.

Catapulting into STEM education : female students’ interactions within a middle school engineering project

Despite efforts to motivate students to engage in Science, technology, engineering and mathematics (STEM) education, women are still underrepresented in these areas in the workforce and higher education. Targeting females at high school or earlier may be a key towards engaging them in STEM. In this paper we report on the research question: How do middle school females interact for learning about engineering education? This ethnographic study, part of a three-year longitudinal research project, investigated Year 8 female students’ learning about engineering concepts associated with designing, constructing, testing, and evaluating a catapult. Through a series of lead-up lessons and the four lesson catapult challenge (total of 18 x 45-minute lessons over 9 weeks), data from two girls within a focus group showed that the students needed to: (1) receive clarification on engineering terms to facilitate more fluent discourse, (2) question and debate conceptual understandings without peers being judgemental, and (3) have multiple opportunities for engaging with materials towards designing, constructing and explaining key concepts learnt. Implications for teachers undertaking STEM education are evident, including outlining expectations for clarifying STEM terms, outlining to students about interacting non-judgementally, and providing multiple opportunities for interacting within engineering education.

Contextualizing a university-school STEM education collaboration : distributed and self-activated leadership for project outcomes

Implementing educational reform requires partnerships, and university-school collaborations in the form of investigative and experimental projects can aim to determine the practicalities of reform. However, there are funded projects that do not achieve intended outcomes. In the context of a new reform initiative in education, namely, science, technology, engineering and mathematics (STEM) education, this article explores the management of a government-funded project. In a university school partnership for STEM education, how can leadership be distributed for achieving project outcomes? Participants included university personnel from different STEM areas, school teachers and school executives. Data collected included observations, interviews, resource materials, and video and photographic images. Findings indicated that leadership roles were distributed and selfactivated by project partners according to their areas of expertise and proximal activeness to the project phases, that is: (1) establishing partnerships; (2) planning and collaboration; (3) project implementation; and (4) project evaluation and further initiatives. Leadership can be intentional and unintentional within project phases, and understanding how leadership can be distributed and selfactivated more purposefully may aid in generating more expedient project outcomes.