The purpose of this essay is not to answer the question posed in the title, but to specify the ''preconditions'' for the defense of two opposing stances: mathematical culturalism and mathematical anticulturalism. The names of these stances are not present in the source literature. Introducing them to the debate on the nature of the relationship between expert mathematical knowledge and its folk counterpart...

This short note is devoted to the role played by intuitive explanations in mathematical education. We provide a few examples of such explanations. They are related to: verbal commentaries, perception, physical models. We recall also some examples of internal explanations, inside mathematics itself.

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. Secondly, we provide theorems on the divisibility...

This paper draws on data from semi-structured interviews undertaken with year one teachers in England and Sweden. The broad aim was to explore how teachers construe their own and parents' roles in supporting year one children's learning of early number. The role of homework within those efforts, surfaced as a key theme. The two data sets were an\-a\-lysed independently by means of a~constant comparison...

The article concerns the research on students' perception of visual structures in van Hiele's sense (1986). The empirical % 1986 studies described in the paper make use of a combined methodology -- eye-tracking and a written study questionnaire. There was an analysis of the results of 14 pupils in the paper the 1st grade of a middle school and 19 pupils from a secondary school. The subjects were shown...

Stereotypes concerning women's mathematical abilities are widespread and can become an obstacle for some women to succeed in this domain, thus, they can be one of the possible reasons for the gap between men and women in mathematics. There is significant empirical evidence confirming that women in the situation of stereotype threat (i.e. when they are afraid of confirming that they are less gifted...

The main goal of the following article is to design an improved version of the negotiation game created by prof. Alan Fowler (Fowler, 1997). I have tried to achieve this by constructing four separate versions of the game which represent different approaches while preserving rules, chosen basic technical assumptions and the simplicity of the base game. Each version of the game is supposed to i.a. make...

The use of signs in the teaching of mathematics plays a crucial role in students' cognition. Trying to understand what signs both students and teachers use in the mathematics classes may help us understand their meaning making processes. From this point of view, this paper aims to reveal the use of semiotic resources both by students and a teacher while lecturing Cartesian plane in seventh grade level...

Individuals diagnosed with Autism Spectrum Disorder (ASD), the fastest growing disability group, exhibit varying degrees of intellectual ability. Students with ASD are increasingly held accountable to academic standards comparable to their peers. Applied Behavior Analysis (ABA) is widely considered best practice for supporting these students. Twenty-six single-case design (SCD) mathematics classroom...

Let f be a polynomial in two complex variables. We say that f is nearly irreducible if any two nonconstant polynomial factors of f have a common zero in C2. In the paper we give a criterion of nearly irreducibility for a given polynomial f in terms of its Newton diagram.

In this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered.

We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.

In this short note, we give some counter examples which show that [11, Proposition 3.5] is not true. As a consequence, the arguments in [11, Proposition 4.10] is not valid.

We consider the classic spring-mass model of running which is built upon an inverted elastic pendulum. In this paper we introduce new approximate solution of an interesting boundary value problem for the governing system of two nonlinear ordinary differential equations, which in a natural way we get in this model. We give theoretical support by deriving asymptotic behaviour of obtained approximations...

Variational methods for solving nonlinear equations (differential, integral, etc.) are perhaps the most common methods at the present time. However, the history of their origin and development, both in the USSR and in the whole world, has not been studied enough. The author attempts to fill this gap, limiting himself mainly to 1920's-1950's, starting with Hilbert’s works on justification of Dirichlet...

Chance has always accompanied man. He was afraid of the elusive forces behind him, but he was also fascinated. Relatively late from this fascination arose the understanding that in some circumstances chance can be measured and, consequently, with the help of mathematics to reveal the regularities behind it. It began with gambling games already known in ancient times, such as the dice game popular...

We apply multitype, continuous time, Markov branching models to study pathogenicity in E. coli, a bacterium belonging to the genus Escherichia. First, we examine briefly, the properties of multitype branching processes and we also survey some fundamental limit theorems regarding the behavior of such models under various conditions. These theorems are then applied to discrete, state dependent models,...

This paper contains some results for algebraic polynomials in the complex plane involving the polar derivative that are inspired by some classical results of Bernstein. Obtained results yield the polar derivative analogues of some inequalities giving estimates for the growth of derivative of lacunary polynomials.

We give the complete characterization of members of Kaplan classes of products of power functions with all zeros symmetrically distributed in \(\mathbb{T} := \{z \in\mathbb{C} : |z| = 1\}\) and weakly monotonic sequence of powers. In this way we extend Sheil-Small’s theorem. We apply the obtained result to study univalence of antiderivative of these products of power functions.

In this paper we present how identical columns affect the Cullis-Radić determinant of an \(m\times n\) matrix, where \(m\leq n\).