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?


Summer 2015
Volume 7 N 4

List of Content

Ringbao Tu
Constructing Own-Featured Mathematics Instruction Theories

Xie Yang Chun
Case Study on Statistics Lessons by High School Mathematics Teachers

A. Pardala, R.A. Uteeva, N. K. Ashirbayev
Mathematical Education in Terms of Innovative Development

Brian Evans
Population and Exponential Growth Investigations

Pavel Satyanov
Using Calculators in Teaching Calculus

M. Alejandra Sorto, Zhonghong Jiang, Alexander White, Sharon Strickland
An Observation Protocol Measuring Secondary Teachers' Implementation of Dynamic Geometry Approach

Editorial: Concerns from Around the World

TWe start this late summer issue with the two PPP from China by Professor Tu from Nanjing Normal University, till recently, the head of the National Chinese Mathematics. Association and by the teacher of mathematics Xie Yang Chun from… The presentations are to a certain degree complementary; While Tu introduces us to the basis of Chinese didactic thinking through the theoretical diagram: classroom observation → case study→analytical framework→instruction design theories, Chun presents a concrete case study along that theoretical approach. It is the study of the teacher of statistics in Gansu (?) who finds that the high school curriculum published by the Ministry of Education doesn’t formulate core concepts of statistics and therefore decides to find it by herself through the study of research literature and classroom observations of two teachers. Chun formulates her own theory on the “data analysis” as the core concept of high school statistics. At the same time Tu proceeds to state the core concept of the scientific development view on education to be the essential question: What kind of people we are going to educate? Tu’s presentation is the fascinating answer to that question.

As if the continuation of the theme Pardala, Uteeva and Ashirbayev representing the didactic thought of Poland, Russia and Kazachstan presents a concerned view upon the innovative development of teaching and quality of high school student preparation, motivation to study mathematics and mathematics oriented disciplines. Their suggestions for improvement of the situation are interesting. In particular, in Poland they suggest the need for collaboration between teachers and academicians as well as strong supports for in-service teachers in terms of increasing the quality of their work. In other words they see the need for “substantive” teaching-research. “Substantive” is the term formulated by Stenhouse in the seventies as the research whose main objective is to benefit others rather than a research community itself. Here the substantive task of teaching-research is to improve student learning in the classroom. Their discussion of mathematics education in Russia and Kazachstan is equally interesting. What is however surprising is that, in general comparisons are still made with respect to the West European math ed, whereas the best PISA, for example, results are obtained by Asiatic countries rather than West European.

Evans contribution introduces us to the issue of exponential growth of population both from real world point of view as well through the Bacteria thought experiment of Bartlet.

Satyanov paper makes the pitch for the important role of calculators in the mathematics classrooms – a familiar issue. Whereas one can wonder whether indeed “it is impossible to stop technological progress”, the examples of the power of calculators are very impressive.

The contribution of Sorto et al continues the concern for the proper use of technology in the classroom this time from the point of the implementation fidelity of Dynamic Geometry (DG) technology. It is a very precise, one could say, an elegant work with the NSF-supported assessment instrument. To continue being contrary in this issue, or playing “the devils advocate” role one could say it’s important that just as the precise instrument measuring fidelity of the teaching approach has been needed so that one doesn’t have to be “relying solely on teachers’ self-report when capturing implementation fidelity” one probably should not also rely solely on the instrument itself. What is important in this work for teaching-research is that the instrument ultimately measures teacher interest, capability and possibility within the curriculum to work with Discovery (or inquiry) method of teaching. The Discovery method plays a very important role for TR/NYCity Model which was developed in the community colleges of the Bronx in that it allows to interact and to investigate authentic student mathematical thinking. Maybe the interest of teachers in the implementation fidelity would increase if together with the didactic use of DG, they would be exposed to the investigations of student geometrical thinking with its help.

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