Zhu Ying

Constructivism was first popularised by Bruner (1960). The underlying theme in Bruner’s theoretical framework is that learning is an active process in which learners construct new ideas or concepts based upon their prior knowledge. This chapter describes how constructivism can be realised in instruction through a lesson design involving a carefully crafted task on the topic of Gradient of Function Curves at a point. The task affords opportunities to activate and differentiate students’ prior knowledge to generate, explore, critique and refine methods for problem solving. The lesson design allows teachers to first understand what students know about a new concept based on students’ representation and solution methods (RSMs) collected from the group work before the teacher teaches the canonical concept during lesson consolidation. The task, coupled with skillful facilitation and lesson consolidation built upon students’ RSMs, can help students develop a deep understanding of the targeted concept. Implications of such constructivist learning design on teachers’ classroom practice are also discussed.

Geographical origin of extra virgin olive oil is a factor that consumers may take into account when making purchasing decisions. Oils that are labelled to be from regions famous for olive cultivation may be assumed to be of higher quality. However, difficulties in the authentication of the geographical origin of olive oils arise due to the similarity in chemical compositions of the oils involved. Fourier-transform infrared (FTIR) spectroscopy has been found to be a viable technology for the classification of oil samples by geographical origin. However, classical methods involving dimension reduction before model fitting usually yield models that are more challenging to interpret. Sparse fused group lasso logistic regression (SFGL-LR) is used with FTIR spectroscopic data to discriminate between Greek and non-Greek organic extra-virgin olive oils. The prediction performance is also compared with that obtained by partial least squares linear discriminant analysis (PLS-LDA). While both methods give comparable good prediction performance, with more than 90% accuracy in classification, the SFGL-LR model demonstrates improvements in the interpretability of the model coefficients.