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TR32 vol 12 N 1 of the Mathematics Teaching-Research Journal

Editorial from Bronisław Czarnocha

This Spring 2020 issue of MTRJ is delayed, of course, due to the COVID-19 pandemic. While in many respect it has been a difficult period for all of us yet at the same time, the lockdown coupled with distant teaching, offered an unusual time for reflection upon our own teaching, and especially reflections upon facilitating creativity in our classrooms as well as in our own life. We start the issue with a short note of Małgorzata Marciniak reflecting exactly upon teaching in lockdown conditions. She has used Csikszentmihaly (2015) notion of creative flow to guide her classroom teaching as well as the organization of her own life during the lockdown with interesting and motivating results. We are interested in publishing reflections upon Covid-19 teaching in the follow up issues of MTRJ.

The next presentation by Bukurje Gjoci has also been impacted by the Covid-19 lockdown. It is the first part of the work focused on the design and implementation of the Freshman calculus course around two basic themes:

1. Teaching Mathematics Thematically, which emphasizes the use of mathematics applications around a central theme, narrowing the gap between school and out-of-school mathematics.

2. Top-down Instructions focuses on providing students a large view of the subject, immersing them into the big picture of it. The explaining of the components that make up the subject will be the implicit part of teaching instructions.

Gjoci provides us with the design of calculus syllabus on the basis of these two approaches, however the report on implementation and collection of data has to wait till the next semester, which, most probably will also be taught through distant learning.

With the next presentation by Goonatilake and Casas from the Texas A&M International University we take the break away from didactics of mathematics and delve into mathematics of fractals and Julia sets nicely presented by the authors. They provide a series of examples of fractals as well as programming codes for plotting Julia sets, and other fractals. The central concepts of the article are those of self-similarity and fractals dimension, which has quite a few open research problems. The concept of self-similarity seems to be one of the concepts on which didactic attention could be focused. This course provides insight for those of us who want to advance a college course beyond typical discrete mathematics and geometry courses.

Coming back to the issues of didactics and its assessment we present a succinct analysis of the First in Math (FIM) program intervention in the Elementary School with decisive majority of “underrepresented and underserved” student population. The presentation describes investigation into the students’ thinking processes as they were engaged in the FIM online program and the effect of this interaction on their mathematics achievement scores as measured by the PSSAs. The data overwhelmingly reflect positive outcomes when the FIM online program is implemented during the regular scheduled block of time. This issue of MTRJ culminates with extremely interesting description of students of universities and secondary schools by Pavlova and Shabanova, who have made a holistic interactive exposition “Experimental Mathematics” for a museum of entertaining sciences in Archangelsk, Russia. The students wanted to present mathematics in a new, unusual perspective of “experimental science”, to tell about the role of experiments in mathematical discoveries, and about seeing themselves like real researchers and experimental mathematicians. The approach facilitates the development of museum pedagogy as an independent branch of science and further understanding the role of museums, their mission, and forms of museum communication.

Bronisław Czarnocha
Chief Editor of MTRJ

Contents

Creativity during the time of pandemics (page 3)
Małgorzata Marciniak

Learning to use Mathematics vs Mastering Basics (page 9)
Bukurie Gjoci

Fractals, Self-Similarity, and Beyond (page 17)
Rohitha Goonatilake, Ray A. Casas

Computational Thinking Using the First in Math® Online Program (page 45)
Lynn Columba

Students make interactive exhibition “Experimental Mathematics” for the Museum of Entertaining Sciences (page 58)
Maria Pavlova, Maria Shabanova

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