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).

Fellowship plan and conceptual framework

This document is written to provide: (1) a brief plan of the intended directions of the ALTC program ‘A Pedagogy of Supervision in the Technology disciplines’; and (2) an overview of existing research outcomes which are likely to be of interest to the technology disciplines, including some cross disciplinary research and some focussed specifically on some part of the technology field.

A review of the conversations and their content

This is the 2nd of a series of discussion papers (Table 1) around the pedagogy of supervision in the technology disciplines. The papers form part of an Australian Learning and Teaching Council Fellowship program conducted by ALTC Associate Fellow, Professor Christine Bruce, Queensland University of Technology.

Cases from the technology disciplines

This document is a collection of ‘cases’ adapted from interviews with supervisors of higher degree research students from the technology disciplines. The supervisors come from a wide range of sub disciplines and represent many levels of experience. We follow in this document Hammond and Ryland’s (2009)2 suggested ranking of supervision experience:  No completions – No experience or new supervisors, with no doctoral completions as principal supervisor  Experienced – 1 to 5 doctoral completions as principal supervisor  Very experienced – over 6 doctoral completions as principal supervisor The cases focus attention on thinking about supervision as a teaching and learning practice; a dimension of higher degree research supervision that is increasingly being recognized as important. They are offered as prompts for individuals and groups of supervisors in thinking about their supervision as a teaching and learning practice.

Student resources for the use of supervisors

The materials presented here are intended to: a) accompany the document Supervisor Resource and b) provide technology supervisors with materials that may be readily shared with students. These resources are not designed to be distributed to students without contextualization, they are intended for use in workshops or in discussions between supervisors and students. As authors, we anticipate that supervisors or workshop facilitators are most likely to extract individual resources of interest for particular occasions. The materials have been developed from conversations with supervisors from the technology disciplines.

Resource for supervisors and cases

The framework presented in the resource is intended to provide technology supervisors with a range of options available to them with respect to supervisory pedagogy. It has been developed to highlight different aspects of thinking about supervision as a teaching and learning practice; as well as approaches, strategies and roles associated with supervision. It will enable technology supervisors to become aware of the diverse options available to them and provide systematic ways of thinking about supervisory practices. Use of this framework will encourage supervisors to make choices based on broader, rather than more limited, repertoires. It will also encourage thinking about supervision as a teaching and learning practice.

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.

Effective models of employment-based training

Australia needs highly skilled workers to sustain a healthy economy. Current employment-based training models have limitations in meeting the demands for highly skilled labour supply. The research explored current and emerging models of employment-based training to propose more effective models at higher VET qualifications that can maintain a balance between institution and work-based learning.

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.

Engaging students in programming

Poor student engagement and high failure rates in first year units were addressed at the Queensland University of Technology (QUT) with a course restructure involving a fresh approach to introducing programming. Students’ first taste of programming in the new course focused less on the language and syntax, and more on problem solving and design, and the role of programming in relation to other technologies they are likely to encounter in their studies. In effect, several technologies that have historically been compartmentalised and taught in isolation have been brought together as a breadth-first introduction to IT. Incorporating databases and Web development technologies into what used to be a purely programming unit gave students a very short introduction to each technology, with programming acting as the glue between each of them. As a result, students not only had a clearer understanding of the application of programming in the real world, but were able to determine their preference or otherwise for each of the technologies introduced, which will help them when the time comes for choosing a course major. Students engaged well in an intensely collaborative learning environment for this unit which was designed to both support the needs of students and meet industry expectations. Attrition from the unit was low, with computer laboratory practical attendance rates for the first time remaining high throughout semester, and the failure rate falling to a single figure percentage.

Peace education

There are various understandings of peace education. What might be called maximalist peace education refers to educating students towards personal fulfilment and the creation of a just and co-operative society. What might be called minimalist peace education refers to educating students to avoid war, militarism and arms races. Peace education is only now being formally accepted as an integral part of educational endeavour, and an important part of this acceptance is recognition in international pronouncements and instruments, emphasizing the importance of a culture of peace and the right to peace. In terms of methodology, peace education includes curriculum, structures and process, and personal leadership. This last element is clearly the most challenging of all.

Third space in cyberspace : Indigenous youth, new technologies and literacies

This chapter analyses the affordances and constraints of an online literacy program designed for Indigenous Australian youth through a partnership between the Indigenous community, university staff and local schools. The after-school program sought to build on the cultural resources and experiences of the young people through a dialogic process of planning, negotiating, implementing, reflecting, and renegotiating the program with participants and a range of stakeholders. In the majority of cases, students presented themselves as part of pervasive global popular cultures, often hot-linking their webpages to pop icons and local sports stars. Elders regarded their competency as a potential cultural tool and community resource.