**List of Content**

**Winter 2020/2021**

**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*

**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