**MATHEMATICS TEACHING-RESEARCH JOURNAL ONLINE – ISSN # 2573-4377**

# Welcome

## Volume 12 N 4 Winter 2020/2021

**Editorial from Bronisław Czarnocha**

The Winter ’20 issue is devoted to different processes of assessment in our mathematics classrooms. This issue is especially important in the context of Covid-19 teaching and learning. The last two items on the other hand take us to the classical Greek and Renaissance mathematics.

MTRJ issue opens with the general discussion by Correa and Haslam addressing the possibility of holistic assessment based on mathematical proficiency. The authors propose 5 strands of mathematical proficiency: conceptual understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning,and Productive Disposition.. They propose Action Research as the methodological approach to the teaching experiment they plan to conduct. We expect the second part of this report after the teaching experiment has been conducted.

This general introduction is followed by two reports, one by Arnal-Palacian investigating student mathematical flexibility of student-teachers at a public university in Spain.as well as the second one by Ping Ye and Bautista Maye investigating the degree of Adult connectedness under the impact of WBAB program.

The flexibility assessment tasks is the calculation of area of polygons constructed on a grid and geoplane. The nature of student solutions provides information about the degree of student flexibility. One of the results indicates that student flexibility depends on the task. That relationship needs to be investigated deeper as flexibility is one the phenomenological characterization of creativity according to Torrance.

The second report in interested in the assessment of adult connectedness under the impact of the BWAB program that is a program whose aim is “to make cities better places by reaching young people and equipping them to be leaders capable in transformation of their communities. The results are very interesting. This is the second paper submitted by the authors (vol.10 N 1, Analyzing Student Data as a Measurement of Success for Boy With A Ball)

The fourth paper in the assessment collection come from our colleagues in Nepal, who focus their attention on the development of Digital Awareness in the context of rapid digitalization of education in Nepal, and more general in South East Asia. They present the results of the large scope survey, which however might have undergone the change due to Covid-19.

The last two items draw their inspiration from the elements of Renaissance mathematics as well as from Geometric Algebra of Euclid and Al Khwarizmi. The fascinating item by Retamoso, who points to an interesting irregularity in the classical drawing of Leonardo DaVinci presenting golden ratios in human body. Retamoso asks whether that irregularity can be corrected and provides a positive answer to the question.

Brenner and Czarnocha, on the other hand develop two new techniques in geometric manifestation of polynomial factorization with the help of Algebra tiles.

Bronisław Czarnocha

Chief Editor

**List of Content**

**Editorial from Bronisław Czarnocha**

**Mathematical Proficiency as the Basis for Assessment: A Literature Review and its Potentialities**

*Priscila D. Corrêa, Dayna Haslam*

**Mathematical Flexibility of Degree of Primary Education students in solving an area problem: Pick’s Theorem**

*Mónica Arnal-Palacián*

**Understanding the Hemingway measure of adult connectedness survey by utilizing data analysis**

*Ping Ye, Gildardo Bautista-Maya*

**Effect of Digital Awareness on Mathematics Achievements at School to University Levels in Nepal**

*Bishnu Khanal, Shashidhar Belbase, Dirgha Raj Joshi*

**“Perfecting” Leonardo da Vinci diagram**

*Ivan Retamoso*

**Spontaneous and reasoned approaches to the algebraic tiles’ factorization problem**

*Terence Brenner, Bronislaw Czarnocha*

#### Archives

## Special Issue Vol 12 N 2, PHILOSOPHY OF MATHEMATICS EDUCATION TSG 56

## Volume 12 N 3 Fall 2020

**Editorial from Bronisław Czarnocha**

Mathematics Teaching-Research in the time of Covid19:

Difficulties and Possibilities

COVID 19 is constantly on our minds to larger or smaller degree and investigations into student performance as well as learning mathematics during the pandemic are important to determine the best course of action. It is becoming clear that changes in pedagogy required from us by the pandemic will be substantial if we want to engage all possible available routes of e-learning. A bisociative frame is created between the past pedagogy and new circumstances, the structural frame, which is a prerequisite to creativity of Aha! Moment. Thus it is our own classroom creativity that is called here for engagement.

We start the issue with the work of Ariyanti and Santoso from Indonesia who inform about a simple yet statistically rigorous comparison of student work before and after Pandemic. Their results definitely demonstrate lowering of student achievement during the Covid19 distance learning.

We follow that analysis with the work of Baker and his colleagues in the Bronx who investigate the impact of COVID 19 restrictions upon the facilitation of creativity of Aha!Moment. Baker et al are using this occasion to lay the short background of the methodology of facilitation and assessment of the depth of creativity. They show that the characterization of Aha!Moment by three criteria of: search, connection and resulting novel process do a good job in the analysis of the depth of creativity within Aha!Moment.

They report that the main impact of the distance learning on the facilitation process is in the constraints upon interaction between students as well as upon student/teacher interaction created by the online approach. Since such an interaction is essential for the creativity facilitation process, one can expect lowering of the level of creativity in the mathematics classrooms.

The third article in the Covid series by Fuchs and Tsaganea provides multidimensional analysis of the COVID impact upon teaching in NYC as well as in the whole country. They discover quite a few advantages of online teaching in relation to the limitations of face-to-face teaching, which nonetheless has been seen as the best pedagogical method. However, they point out that the societal changes due to COVID will stay with us much longer and they urge educators and students to develop mastery of online teaching and learning.

We supplement these three COVID related papers by the interesting paper of Stokes and Sanfratello, which although written before the pandemic struck, nonetheless offers an interesting pedagogy of “learning through doing”, that eliminates math anxiety. As the long term effects of the pandemic upon learning are still unknown the experiential approach based on patterns and deliberate practice while grounded in the problem solving model of creativity/innovation offers the pathway of success for those students who have experienced higher levels of math anxiety in new online learning circumstances.

We complete this issue with two papers analyzing classroom effectiveness of two geometrical software, Geogebra and Geometer Sketchpad. At present, geometrical oriented mathematical software might be very useful in contemporary online mathematical classrooms. It can provide mediating visual pathway between the student and the teacher while increasing and deepening their interaction.

Raj Joshi and Singh from Nepal demonstrate high effectiveness of Geogebra for learning linear equation through the simple experimental group/control group investigation. They point out to the versality of Geogebra to teaching variety of mathematical domains from arithmetic to calculus; it could be especially useful for distance learning.

The paper of Hartono from Indonesia investigates effectiveness of Geometer Sketchpad (GSP) in guiding student understanding of two dimensional objects. The author describes three months long teaching experiment comparing student (7th grade) achievement between two cohorts, experimental with GSP software, and control with traditional learning. The positive result of the teaching experiment needs to be repeated during pandemic, however it’s clear that both geometrical software can positively impact mathematics learning and teaching during that critical time.

Bronisław Czarnocha

Chief Editor

**List of Content**

**Editorial from Bronisław Czarnocha**

**The Effects of Online Mathematics Learning in the Covid-19 Pandemic Period: A Case study of Senior High School Students at Madiun City, Indonesia**

*Gregoria Ariyanti, Fransiskus Gatot Iman Santoso*

**Covid-19 Pandemic and Its Impact on College Teaching: The Unexpected Benefits and their Consequences**

*Eric Fuchs, Doru Tsaganea*

**Solving the Math Anxiety Problem Before It Starts**

*Patricia D. Stokes and Andrew Sanfratello*

**Effect of Using Geogebra on Eight Grade Students’ Understanding in Learning Linear Equations**

*Dirgha Raj Joshi, Kailash Bahadur Singh*

**Effectiveness of Geometer’s Sketchpad Learning in Two-Dimensional Shapes**

*Sugi Hartono*