Mathematics Teaching-Research Journal (MTRJ) on line:

The editorial team of the Mathematics Teaching Research Journal on line informs with great sadness about passing away of one of its founding editors, VRUNDA PRABHU 1961- 2013. Her creative spirit will always be with us.

Message to Mathematics Teacher-Researchers of the World;

Colleagues Teacher-Researchers of Mathematics;

Our profession, Mathematics Teaching-Research is standing in front of an unusual responsibility/opportunity to impact mathematics teaching and learning in US and possibly, in the World through the introduction of the Common Core State Standards(CCSM) in Mathematics in 2014 in the nation. Common Core Standards in Mathematics represent an unusual integration of research, curriculum development and teaching practice. The aim of this integration is to provide tools with the help of which mathematics teachers could successfully address successes, challenges and needs of every student in the class while fulfill the dream of “Mathematics for all”.

Whenever there is an integration of research and teaching, the framework of teaching-research is generally most straightforward. Indeed, the success of CCSS in Mathematics is conditioned on understanding of two mutually connected constructs, that of a Learning Trajectory (research construct) and that of Adaptive Instruction (teaching construct) together with the relationship between the two. The relationship between the two turns out to be standard Teaching-Research NYCity model’s relationship that on one hand involves the application of research to classroom teaching, and on the other hand, it is motivated by the research needed for successful development of the teaching “Mathematics for All.”

Analysis of the requirements of the adaptive instruction for the success of CCSS approach show its closeness with the standard teaching-research classroom activity: “For that [success] to happen, teachers are going to have to find ways to attend more closely and regularly to each of their students during instruction to determine where they are in their progress toward meeting the standards, and the kinds of problems they might be having along the way. Then teachers must use that information to decide what to do to help each student continue to progress, to provide students with feedback, and help them overcome their particular problems to get back on a path toward success. This is what is known as adaptive instruction and it is what practice must look like in a standards-based system.” Consortium of Public Research in Education, CPRE (Daro et al. 2011).

Every of these steps of adaptive instruction is in the “tool box” of a teacher-researcher whose aim is to improve student learning (…). Moreover, the same report continues:

“Teachers must receive extensive training in mathematics education research on the mathematics concepts that they teach so that they can better understand the evidence in student work (from OGAP-like probes or their mathematics program) and its implications for instruction. They need training and ongoing support to help capitalize on their mathematics program’s materials, or supplement them as evidence suggests and help make research based instructional decisions.”

The words above outline the scope of the transformation of teachers‘ pedagogy from the standard one to one based on research and evidence. In other words, what is required for the success of CCSS in Mathematics is the transformation of teachers into teacher-researchers on the national scale.

And that is, colleagues, our opportunity to transform teaching on a large scale.
Are we prepared to do it, to assume this responsibility?


Spring 2015
Volume 7 N 3

List of Content

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

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

Sergiy Klymchuk
Solving Application Problems Using Mathematical Modelling Diagrams

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

William Baker and Bronislaw Czarnocha
Creativity and Bisociation

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.

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