Inquiry activities in a classroom: extra-logical processes of illumination vs logical process of deductive and inductive reasoning. A case study

The paper presents results of the research, which was focused on studying students’ inquiry work from a psychological point of view. Inquiry activities of students in a classroom were analysed through the evaluation of the character of these activities within learning process with respect to mathematician’s research practice. A process of learning mathematical discovery was considered in detail as a part of inquiry activities of students in a classroom

Problem set 3

The article presents several mathematical problems concerning Euclidean geometry

Problem set 10

This article introduces a regular problem section in the Australian Senior Mathematics Journal. It notes that the section aims to give readers an opportunity to exchange interesting mathematical problems and solutions. It adds that the set in each issue will consist of up to five problems

About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry

The paper describes processes that might lead secondary school students to produce conjectures in a plane geometry. It highlights relationship between conjecturing and proving. The author attempts to construct a teaching-learning environment proposing activities of observation and exploration of key concepts in geometry favouring the production of conjectures and providing motivation for the successive phase of validation, through refutations and proofs. Supporting didactic materials are built up in a way to introduce production of conjectures as a meaningful activity to students

Using the history of mathematics for mentoring gifted students: Notes for teachers

The paper presents a theoretical framework, methodology and practical implications for the work with gifted students using history of mathematics. A teaching-learning model, where history of mathematics is integrated in problem-solving activities, is described. Didactical material based on the concepts of triangle geometry is given in the scope of this model. A beautiful and intriguing piece of geometry – the Lemoine point is the focus of consideration. Its properties are investigated through appropriately designed activities for students. Different examples show the importance of history of mathematics for the development of students’ mathematical thinking

Network of Hydrogen Bonds as a Medium for DNA Interaction in Solvents

We suggest that the DNA molecules could form the cholesteric phase owing to an interaction mediated by the network of the hydrogen bonds (H-network) in the solvent. The model admits of the dependence of the optical activity of the solution on the concentration of the PEG, and the change in the sense of the cholesteric twist due to the intercalation by the daunomicyn. Using the experimental data for the cholesteric phase of the DNA dispersion, we obtain a rough estimate for the energy given by our model, and show that it should be taken into account as well as the energy due to the steric repulsion, van der Waals, and electrostatic forces, generally used for studying the DNA molecules. The elastic constant of the H-network generating the interaction between the DNA molecules is determined by the energy due to the proton's vibration in the hydrogen bonds.Comment: 12 pages, Latex, 2 figure