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Mathematics Teaching-Research Journal (MTRJ) on line:
www.hostos.cuny.edu/MTRJ

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?

MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE

December 2012
Volume 5 N 4

Editorial

The Bronx mathematics Teaching-Research Team operating in BCC and Hostos CC have conjectured on the basis of several teaching experiments that student success in our communities depends on three components: affective, cognitive and self-regulated learning. The central manifestation of the affective component of students is the degree of their motivation to learn mathematics. The search for the optimal mixture with high effectiveness in producing the student success is in progress.

MTRJ on line V5 N4 presents four papers that touch upon the question of facilitating student mathematical curiosity, desire to understand mathematical problem, challenge and adventure.

Our steady contributor Sergiy Klymchuk from New Zealand completes his discussion of the role of counterexamples in teaching mathematics, which challenge and deepen student understanding of mathematics by presenting them with a "real world" problems of mathematical contradiction. Hirsch and Pfeil re-institute the Socratic method in service of the discovery method of teaching in the intermediate remedial algebra hoping to stimulate student interest by posing problems that lead to the discovery. Brenner wants to reach a similar effect by creating fictionalized word problems in the context of short detective stories, while Czarnocha introduces us to a possible new field of study, Mathematics of Fairy Tales. His conjecture is that the structure of dialogs facilitating the discovery moment in mathematics classrooms is similar to the structure of heroic quests of certain type of fairy tales.

MTRJ, V5N4 brings also news from teaching mathematics in Uganda, Africa and in Tamil Nadu, India. While report from Uganda by Brian Evans and Janet Mulvey professional development activities for the teachers of government schools, Vrunda Prabhu and Bronislaw Czarnocha with the help of Mark Dunetz present the visual report from community based schools created by Dalits of Tamil Nadu in India. It's worthwhile to compare the two and reflect upon the situation.

List of Content

Teaching-Research
Sergiy Klymchuk Using Counterexamples in Teaching and Learning Calculus: students attitudes and performance.


Teaching Practice
Jena Hirsch and Jessica PfeilOn Teaching Logarithms using the Socratic Pedagogy.

Terence Brenner
Seven Mysteries for Your Algebra Class.


Teaching-Research Investigations
Bronislaw CzarnochaThe Triad of Piaget and Garcia, Fairy Tales and Learning Trajectories.


Mathematics Education
Brian Evans and Janet MulveyTeaching Elementary and Secondary Teachers in Uganda: Mathematical Problem Solving, Mathematics for Understanding and Reducing Mathematics Anxiety.

Vrunda Prabhu and Bronislaw Czarnocha
Beyond Numbers - Community Education in Tamil Nadu, India.



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