List of Contents

Spring 2015

Editorial

The limits of a rational mind in an irrational world – the language of mathematics as a potentially destructive discourse in sustainable ecology
Steven Arnold

Logic and Inequalities: A Remedial Course Bridging Secondary School and Undergraduate Mathematics
Alexandre Borovik

Solving Application Problems Using Mathematical Modelling Diagrams
Sergiy Klymchuk

Using Common Sense in a Mathematical Modelling Task
Sergiy Klymchuk, Tatyana Zvierkova

Creativity and Bisociation
Bronislaw Czarnocha, William Baker

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Editorial: Building Bridges

This, 23rd issue of MTRJ presents a bridge of Mathematics Education starting in New Zealand, via Odessa in Ukraine through Great Britain and anchoring final in NYC in US. The bridge starts very gently with wisdom of Steve Arnolds’ recognition of a deep contemporary contradiction between our mathematical conceptions and the human world. He asks for the a fundamental change in the nature of our thinking mathematics so that it is at one with contemporary reality of our human world. This quest for unity is reflected also in the very concept of Teaching-Research facilitated by MTRJ whose ultimate goal so succinctly expressed by Steenhouse as the creation of the classroom methodology through “acts which are at once educational act and a research act”. The question is how to do it. For us, the hint along that heroic pathway is given by the following realization that “ humanity hasn’t noticed that we have left behind To Be OR not To Be of Hamlet and have arrived at To Be AND not To Be of the Schroedinger Cat.”

Alexandre Borovik’s paper pursues similar pathway in search of unity between remedial and advanced mathematics with methods that bring envy to the remedial mathematics instructors who have to conform to mind –dumbing curricula imposed by the central headquarters of the university.

The papers by Klymchuk and Zverova take us into the “bread and butter” zone of our profession that is into the process and the role of mathematical modelling, and interestingly, they also are concerned about connection of mathematics to, this time, real world. What is the effective methodology of that walk back and forth between the mathematics and “real world”? That we might be able to learn from the last paper which anchors the bridge spanning half of the world in the creativity of the Aha moment, which as it turns out from Koestler’s theory of bisociation in the Art of Creation (1964) is that bridge we are looking for, so it seems. “Bisociation is the spontaneous leap of insight which connects two planes of thinking which by themselves are unconnected”. So it seems that the bridge we’ve been looking for is in our creativity.