We shall concentrate on an integrated college course in algebra and trigonometry. In order to allay anxieties, the first few minutes of every session are devoted to a review of topics already covered. Contrary to the way mathematics was taught in the past, no time is allotted for writing calculations on the blackboard while the students arduously take notes. A board however should be used to draw interconnections between mathematical disciplines. Following the presentation of a new principle automatically transmitted to smartphones or laptop computers brought to the classroom, the remaining time is spent on an open exchange of student reactions, teacher criticisms, and further clarifications. Teacher-student interaction — one speaks and others listen —can lead to improvements in comprehension. Even at the elementary level, the learner must possess some ability for choosing a strategy before working on details. To prove the square root of two is irrational, a feasible approach involves proof by contradiction, definitions of rational and even numbers, and a mathematical valid substitution of variable, all of which when applied implies an apparent contradiction. Only with repeated readings of theory and extensive practice of reviewing solutions of similar problems at home can this skill be acquired. No time is allotted for writing calculations on the blackboard while the students take notes. Following presentation of a new principle of algebra or trigonometry, transmitted to smartphones or laptop computers brought to the classroom, time is spent on an open exchange of student reactions, teacher criticisms, and further clarifications.

Mathematics, Learning, Discussion

Paper Presentation in a Themed Session

- Prof. Samuel Moskowitz
- Research Professor and Emeritus Professor of Applied Mathematics, Applied Mathematics, The Hebrew University of Jerusalem
- Prof. Moskowitz is currently Research Professor and Emeritus Professor of Applied Mathematics at The Hebrew University of Jerusalem, Jerusalem, Israel. His professional interest is Mathematical Modeling in Healthcare. Recent publications include: Recent Advances in Optical Coherence Tomography (South Korea), Wireless Route Planner for a Programmable Wheelchair, Retinal Curvature in Age-Related Macular Degeneration, Controlled Inquiry Rates of Clinical Interviews in Telehomecare (South Korea), and Guidelines of Telehomecare for the Underserved, and The Hausdorff Measure of Progress Made by the Homeless and Mentally Ill. Prof. Moskowitz was Head of the Israeli delegation to ISO/TC 215, which prepares standards in Health Informatics, and contributed to Working Group Standards Association 1073, in the field of Medical Devices. He collaborated with Hadassah Medical School healthcare providers. Joint collaboration with cardiologists, ophthalmologists, and cardio-thoracic surgeons led to several technological developments. These included an air-cushioned eye bandage (patent 3952735), a look-up table of refractive errors used in ophthalmic surgery, measures of astigmatism in an improved keratometer, a rule-of-thumb for matching arterial grafts, dimensional criteria for shunt implantation in the treatment of hydrocephalus, finite element software for the simulation of heart performance in artery stenosis, and requirements for central heart valve prosthesis.