Welcome

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.

ANNOUNCES

Hunt for Aha!Moments in Mathematics Classrooms

 

 

For
The Volume 8

Mathematics Teaching-Research Journal: Wisdom of Teaching-Research: Creativity.

RULES OF THE HUNT

As the evidence of the successful hunt we will accept the description of the Aha!Moment that took place among students in the mathematics classroom of the author or the Aha!Moment author experienced while designing and participating in the Hunt or reported by students from outside. Accounts of integrated teacher/student double Aha!Moments will be of distinguished value.

The completed evidence/ the paper to be published in the Vol 8 Wisdom of Teaching-Research: Creativity will include:

  1. Description of the mathematics situation or environment when Aha!Moment took place
  2. Some assessment, craft-based or theoretical, of the depth of learning, which took place as a result of the Aha!Moment.
  3. Reflection upon the bisociative framework within which Aha!Moment took place together with the possible hidden analogy “unearthed” with its help.
  4. Post-Aha!Moment interview with the student will be raise the value of the submission.

Questions, help and submission
To Bronislaw Czarnocha
Editor: Mathematics Teaching-Research Journal
            on line.
bczarnocha@hostos.cuny.edu or bronisuavec2@gmail.com

With this new, although delayed Vol. 8 of MTRJ (Mathematics Teaching-Research Journal on line) we start our eighth year of existence. 8 is the number of wisdom because it’s the symbol of infinity  ∞ turned 90 degrees either direction.
A natural conclusion suggests itself: let’s devote this volume to the Wisdom of Teaching-Research, of Mathematics Teaching-Research. That brings the essential question, where is the wisdom of MTR hidden? In which of its aspects? What is it in our work that brings its wisdom to fore? That is what we want to explore in this Eighth Volume.

For us in the South Bronx the wisdom of MTR is in its theoretically grounded enhancement of creativity of Aha!Moment. Therefore one of issue of Eighth volume will devoted to the creativity of Teaching-Research, possibly expressed through Aha!Moments caught during our work which in the light of Koestler theory of the Act of Creation, should and are appearing while doing teaching-research. They appear amongst the students and amongst the teachers, instructors. The pathway of development of our TR Team of the Bronx has been full of unexpected Aha!Moments. And with good reasons for it.

Balanced Teaching-Research takes place when the craft knowledge of the teacher and research knowledge of the researcher contribute, conceptually, in equal measure to the activity of Teaching-Research. Once this condition is reached, it turns out, with the help of the Koestler  bisociation theory of the Act of Creation (1964), that balanced teaching-research is the creative bisociative framework pregnant with as yet “hidden analogies”.

Koestler definition of bisociative creativity as “a spontaneous flash of insight, which…connects the previously unconnected frames of reference and makes us experience reality at several planes at once ” –an Aha!Moment, formulates  the condition, which we call a “bisociative framework” specially suitable for the facilitation of Aha!Moments: the presence of  previously unconnected frames of reference. Moreover, as Koestler (1964) describes the main mechanism of creativity in terms of  “unearthing hidden analogies” (p. 179) between two or more previously unrelated frames of reference,
we define the bisociative framework as composed of unconnected frames of reference with enhanced possibility of unearthing hidden analogies.

Teaching and Research, essentially and unfortunately unconnected professions, methodologies, goals, yet at the same, Teaching-Research, their bisociative framework time is pregnant with hidden analogies, which can facilitate the creativity of both.

That means that balanced Teaching-Research or TR/NYCity model is the creative bisociative framework ready for Aha!Moments, it is the creative approach to both Teaching and Research.

It means a lot. Teaching-Research gains through bisociation its own intrinsic identity as the bisociative framework composed of previously unconnected frames of reference with enhanced possibility of unearthing hidden analogies. Looking from this perspective, one immediately establishes contact with Stenhouse work who introduced the concept of  “an act [which is] at once an educational act and a research act” – an expression of the bisociativity of teaching-research (Rudduck and Hopkins, 1985).  That single concept allowed to classify the Discovery Method of teaching, the Teaching-Research Interviews and Concept maps methodology as characteristic instruments for Teaching-Research. The same pathway of associations leads to Margaret Eisenhart (1991) formulations of frameworks for inquiry: theoretical, practical, and conceptual. “ A conceptual framework is an argument that the concepts chosen for investigation, and any anticipated relationships among them, will be appropriate and useful given the research problem under investigation. Like theoretical frameworks, conceptual frameworks are based on previous research, but conceptual frameworks are built from an array of current and possibly far ranging sources. The framework used may be based on different theories and various aspects of practitioner knowledge.”(Lester, 2010).Therefore Teaching-Research is a conceptual framework of inquiry, which acquires this way insignias of academic discipline as much as it has acquired the bearings of the craft knowledge discipline. We see here the strength of bisociation as its integrating foundational principle.

So we, Mathematics Teacher-Researchers have quite a lot, a creative methodology, which induces creativity in the classroom. Let’s do it then!

Hunt for Aha!Moments in Mathematics Classrooms

Mathematics Teaching – Research Journal (www.hostos.cuny.edu/mtrj)

  1. Invites submissions describing, analysing moments of creativity in mathematics in general, in mathematics classroom, in particular,  to  its 8th year anniversary volume titled
    Vol 8 Wisdom of Teaching-Research : Creativity.
  1. Announces Hunt for Aha!Moments in Mathematics Classrooms

RULES OF THE HUNT

As the evidence of the successful hunt we will accept the description of the Aha!Moment that took place among students in the mathematics classroom of the author or the Aha!Moment author experienced while designing and participating in the Hunt or reported by students from outside. Accounts of integrated teacher/student double Aha!Moments will be of distinguished value.

The completed evidence/ the paper to be published in the Vol 8 Wisdom of Teaching-Research: Creativity will include:

  1. Description of the mathematics situation or environment when Aha!Moment took place
  2. Some assessment, craft-based or theoretical, of the depth of learning, which took place as a result of the Aha!Moment.
  3. Reflection upon the bisociative framework within which Aha!Moment took place together with the possible hidden analogy “unearthed” with its help.
  4. Post-Aha!Moment interview with the student will be raise the value of the submission.

Questions, help and submission
To Bronislaw Czarnocha
Editor: Mathematics Teaching-Research Journal
            on line.
bczarnocha@hostos.cuny.edu or bronisuavec2@gmail.com

MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE

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.

Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.



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