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 or

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 (

  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.
  2. Announces Hunt for Aha!Moments in Mathematics Classrooms

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