Complex Modelling in the Primary and Middle School Years : An Interdisciplinary Approach

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. With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to signifi cant changes in the forms of mathematical and scientifi c thinking required beyond the classroom. Modelling, in its various forms, can develop and broaden students’ mathematical and scientific thinking beyond the standard curriculum. This chapter first considers future competencies in the mathematical sciences within an increasingly complex world. Consideration is then given to interdisciplinary problem solving and models and modelling, as one means of addressing these competencies. Illustrative case studies involving complex, interdisciplinary modelling activities in Years 1 and 7 are presented.

A biological staging model for operable non-small cell lung cancer

Background Currently the best prognostic index for operable non-small cell lung cancer (NSCLC) is the TNM staging system. Molecular biology holds the promise of predicting outcome for the individual patient and identifying novel therapeutic targets. Angiogenesis, matrix metalloproteinases (MMP)-2 and -9, and the erb/HER type I tyrosine kinase receptors are all implicated in the pathogenesis of NSCLC. Methods A retrospective analysis of 167 patients with resected stage I-IIIa NSCLC and >60 days postoperative survival with a minimum follow up of 2 years was undertaken. Immunohistochemical analysis was performed on paraffin embedded sections for the microvessel marker CD34, MMP-2 and MMP-9, EGFR, and c-erbB-2 to evaluate the relationships between and impact on survival of these molecular markers. Results Tumour cell MMP-9 (HR 1.91 (1.23-2.97)), a high microvessel count (HR 1.97 (1.28-3.03)), and stage (stage II HR 1.44 (0.87-2.40), stage IIIa HR 2.21 (1.31-3.74)) were independent prognostic factors. Patients with a high microvessel count and tumour cell MMP-9 expression had a worse outcome than cases with only one (HR 1.68 (1.04-2.73)) or neither (HR 4.43 (2.29-8.57)) of these markers. EGFR expression correlated with tumour cell MMP-9 expression (p<0.001). Immunoreactivity for both of these factors within the same tumour was associated with a poor prognosis (HR 2.22 (1.45-3.41)). Conclusion Angiogenesis, EGFR, and MMP-9 expression provide prognostic information independent of TNM stage, allowing a more accurate outcome prediction for the individual patient. The development of novel anti-angiogenic agents, EGFR targeted therapies, and MMP inhibitors suggests that target specific adjuvant treatments may become a therapeutic option in patients with resected NSCLC.