List of Contents

Fall and Winter 2015/2016

Editorial

Volume 8 Wisdom of Teaching Research: Creativity of Aha! Moments

What if it were you?
Bukurie Gjoci

Breakthrough Moments in Problem Solving
Brian Evans

Creativity ≠ Creativity
Hannes Stoppe

Phases of a ten-year old student’s solution process of an insight problem as revealed by eye-tracking methodology
Csaba Csicos, Janos Steklas

Teaching Research

Engaging elementary school students in mathematical reasoning using investigations: Example of a Bachet strategy game
Victor Freiman, Mark Applebaum

Mathematical Curriculum, Mathematical Competences and Critical Thinking
Dieter Scott

Analysing University Students’ Abilities in Making Assumptions in a Balistics Model: A Case Study
Sergiy Klymchuk, Zlatko Jovanosky

Teaching and Assessment of Statistics to Employees in the NZ State Sector
Murray Black

Reports from the field

Improving Gender Disparity in Scholarship Programs for Secondary-Level Mathematics Teachers
Rohitha Goonatilake, Katie D. Lewis, Runchang Lin, Celeste E. Kidd

Throwback Thursday
Kathleen Doyle

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Editorial

The present Vol. 8, N 1-2 double issue of MTRJ contains three components:

1. Wisdom of Teaching Research first collection of contributions discussing emergence of Aha!Moments in the classrooms among students and teachers. We will accept these contributions for each issue of the Volume 8, and at the end of the year, in the Winter 2016/2017 we will publish their full collection.
2. The Teaching-Research which has four contributions addressing different methods and approaches to the development of mathematical reasoning and its application in “real life”.
3. Reports from the Field with two interesting contributions:

A) The report of the NSF supported project from Texas A & M International University informing about increasing female participation in mathematics careers.

B) Throw Back Thursday is a new mtrj idea for accomplished mathematics educators to look back upon their thinking in graduate school and offering new comments from their professional experience

Editors of MTRJ are excited to have received four response to the call for the Hunt for Aha!Moments in mathematics classrooms announced recently. We start with the observations of the graduate student at the Teachers’ College, Bukurie Gjoci, who had experienced Aha!Moment as a teacher of remedial mathematics in a community college. She introduced a new approach to Word Problem Solving, which had turned the class on its head. To every problem situation she asked “What if it was you?” (in this situation). It is known that the personalization of a mathematical situation eases students into appreciation of the subject (Prabhu, 2016) and Bukurie Gjoci method is a next confirmation of that knowledge. The contribution by Brian Evans describes facilitation of Aha!Moments among student-teachers with the subsequent analysis of the components that led to such a moment of understand. This analysis, an example of which is Koestler’s based bisociative framework with its hidden analogies, is critical to enable teachers’ design of instruction which may lead to Aha!Moment. Hannes Stoppel, on the other hand, analyzes his students’ views on the role of creativity in problem solving. He demonstrates that students’ understanding of creativity depends on the type of problem they are engaged to solve.

The last paper in the series of Aha!Moments looks upon this phenomenon through the physiological angle by observing problem solver’s eye movements. The method can be quite good in precisely determining the timing of the Aha!Moment.

The Teaching-Research collection of reports focuses on the development of mathematical reasoning in different context and its impact upon reasoning in “real life”. Freiman and Applebaum report the high level of student engagement in mathematics in the context of strategy games. In particular they are interested in Bachet games, different versions of which are quite popular. They ask a standard Teaching-Research question:

A) What is effective methodology to introduce students to the strategy game?

B) What are the student methods of reasoning emerging during the implementation of A).

Dieter Shott, on the other hand investigates the transfer of reasoning from mathematics into every day’s life to “expose dubious arguments and interests”. His arguments lead to modelling of “real life” situations easing us into the theme of the next paper by Klymchuk and Javonoski, who are interested in the methods of student argumentations in the context of ballistic models.

The section culminates with Murray Black’s describing the knowledge assessment among the New Zealand State employees.

The Reports from the Field contain the report on the NSF-based project in Texas A&M. The interest of Goonatilake et al is in addressing the female participation in mathematics. They assert they have the approach but its successful implementation requires strong political will. The last short report of Doyle compares her contemporary experience with her own thinking as a graduate student of Teachers’ College. An important question which emerges from Doyle’s Throw Back is the role of Discovery method in teaching, especially in teaching remedial mathematics. We hope to come back to this question in the near future in MTRJ on line.