Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Problem solving in a middle school robotics design classroom

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, Labview programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social construction of meaning. There was a focus on the effect of teachers’ goals and the rules they enacted upon student use of the flow chart planning tool, and the tools of the programming language Labview and Lego construction. It was found that the articulation of a teacher’s goals via rules and divisions of labour helped to form distinct communities of learning and influenced the development of different problem solving strategies. The use of the planning tool flow charting was associated with continuity of approach, integration of problem solutions including appreciation of the nexus between construction and programming, and greater educational transformation. Students who flow charted defined problems in a more holistic way and demonstrated more methodical, insightful and integrated approaches to their use of tools. The findings have implications for teaching in design dominated learning environments.

Histology challenge : an interactive program for 1st year students

Our students come from diverse backgrounds. They need flexibility in their learning, and opportunities to review aspects of curriculum they are less confident with. An online teaching and learning programme called the Histology Challenge has been developed to supplement learning experiences offered in several first year anatomy and anatomy & physiology units at QUT. The programme is designed to be integrated with the existing Blackboard sites. The Histology Challenge emphasises the foundation concept that a complex system, such as the human body, can be better understood by examining its simpler components. The tutorial allows students to examine the cells and tissues which ultimately determine structural and functional properties of body organs. The program is interactive, asking students to make decisions and choices, demonstrating an integrated understanding of systemic and cellular aspects. It provides users with the ability to progress at their own pace and to test their understanding and knowledge. For the developer the learning activity can be easily controlled and modified via the use of text files. There are several key elements of this programme, designed to promote specific aspects of student learning. Minimum text is used, instead there is a strong emphasis on instructive artwork and original, high quality histology images presented within a framework that reinforces learning and promotes problem solving skills.

Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

Interdisciplinarity vs disciplinarity : developing knowledge for problem solving in middle years of schooling

Interdisciplinary studies are fundamental to the signature practices for the middle years of schooling. Middle years researchers claim that interdisciplinarity in teaching appropriately meets the needs of early adolescents by tying concepts together, providing frameworks for the relevance of knowledge, and demonstrating the linking of disparate information for solution of novel problems. Cognitive research is not wholeheartedly supportive of this position. Learning theorists assert that application of knowledge in novel situations for the solution of problems is actually dependent on deep discipline based understandings. The present research contrasts the capabilities of early adolescent students from discipline based and interdisciplinary based curriculum schooling contexts to successfully solve multifaceted real world problems. This will inform the development of effective management of middle years of schooling curriculum.

Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.

Lego robotics : an authentic problem solving tool?

With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the students were able to effectively relate their problem solving strategies to real-world contexts. The qualitative study involved 23 Grade 6 students participating in robotics activities. The study included data collected from researcher observations of student problem solving discussions, collected software programs, and data from a student completed questionnaire. Results from the study indicated that the robotic activities assisted students to reflect on the problem-solving decisions they made. The study also highlighted that the students were able to relate their problem solving strategies to real-world contexts. The study demonstrated that while LEGO robotics can be considered useful problem solving tools in the classroom, careful teacher scaffolding needs to be implemented in regards to correlating LEGO with authentic problem solving. Further research in regards to how teachers can best embed real-world contexts into effective robotics lessons is recommended.

Towards a transdisciplinary approach to integrating dance in a middle school curriculum

Within Queensland middle schools the implementation of an integrated curriculum has been challenging for many practitioners. In working to enhance dance learning in a Queensland middle school this research has focused on how dance can be integrated using a transdisciplinary approach. The research has investigated and reflected on the teaching and learning strategies used to integrate dance and has identified the key issues and challenges associated with the complex nature of an integrated curriculum in this context. Action research was used to review, plan for and implement integrated curriculum approaches and give insight into the external and internal challenges within the practice. This research has identified challenges associated with sustaining the integrity of dance as a subject area when integration requires designing curricula that go across key learning area boundaries. It has also revealed working within an integrated curriculum requires using common planning principles that focus on the students’ problem solving skills, making connections with the concepts, topics or ideas from the unit of work. The discussion of ways of working highlights a set of values, strategies or attributes a dance teacher can use while working within this middle school context. These include making collaborative partnerships and showing a willingness to work outside your area of expertise. For the school community, it outlines issues for attention and recommendations to assist in implementing dance while using a transdisciplinary approach. These recommended steps include embedding opportunities for teachers to partake in common planning, and time for professional development around transdisciplinary learning and Arts education.