Barbara Barańska

• Professor (Associate) at University of the National Education Commission, Krakow

Postgraduate studies are one of the forms of undertaking lifelong learning. This paper presents findings from the authors’ study on teachers who received credentials from postgraduate qualifying studies to teach mathematics. Among other observations, the findings indicate that there is irrational variation in the programs and outcomes obtained duri...

In this chapter, we present a Polish perspective on the phenomenon of out-of-field teaching. The group that we refer to are teachers with expertise in teaching different school subjects who have decided to start teaching mathematics as a second subject. In Poland, these teachers typically are required to complete pedagogical qualifying non-degree p...

In order to be successful with a certain concept at school, it is often sufficient to master some types of tasks, without having to be aware of the different perspectives that a concept can be viewed from. It is, however, definitely not enough when the goal is to understand mathematics and become flexible and creative in solving mathematical tasks....

According to previous findings, math anxiety already occurs at early school age and is negatively correlated with math achievement. So far, however, little is known about the nature of math anxiety in young children. To fill this gap, we present the results of a longitudinal study on the math anxiety of children that were followed in the first year...

In this paper we explore different ways of solving quadratic equations. Our main goal is to review traditional textbooks methods and offer an alternative, often side-stepped method based on the area model. We conclude that whereas traditional methods offer effective algorithms that quickly lead to the desired results, alternative methods may enhanc...

This manuscript elaborates on the construct of mathematical resilience and the importance of engaging children in mathematically rich conversations from the earliest age. We begin with a review of the existing literature addressing these issues. Since little has been written thus far on how exactly the early childhood facilitators, such as parents...

This article draws on the work of Wittmann and his followers who conceived and developed the notion of substantial learning environment (SLE). The paper contains a proposal of a teaching unit based on the definition of Factorial Number System (FNS). First, we illustrate the process of conversion from FNS to the Decimal Number System (DNS) and back....

According to humanistic psychology, human beings have the potential to shape and change their lives. People are self-determining creatures capable of making decisions about what their existence will be like and who they will become. We interpret this specifically human feature as an empowerment to design one’s life and also to influence constructiv...

Students’ fear about and reluctance toward mathematics have been a great concern to mathematics educators for many decades. The problem is such well known that one may hardly believe there is anything left to say. Sometimes, however, to see some new aspects of the object that seems to be well known, it is good to consider it from another angle. Thu...

Podczas gdy współczesny dyskurs naukowy oraz debaty edukacyjne są przesycone nie zawsze efektywnymi pytaniami o treści i metody nauczania matematyki, fundamentalne z punktu widzenia jednostki pytania o cel, sens i wartość nauczania i uczenia się matematyki zdają się pozostawać w cieniu. W artykule podjęto temat humanistycznych aspektów matematyki....

One of the main problems of modern teaching and learning of mathematics is the inefficiency of this process, manifesting itself in low educational and examination results achieved by students. We can put the issue into the wider problem of the underachievement syndrome. There are grounds to believe that there are many undiscovered talents among the...