Over the past few years, a great deal of research has been conducted concerning the mathematical skills of children after the first stage of education. In my report, I present a selection of results from this research in order to illustrate the most typical didactical effects of the style in which mathematical education is performed in our schools. Comparing some detailed results from research in a number of chosen fields, I also try to assess whether or not, and how, the level of schoolchildren’s skills has changed in the recent years.
The development of megasporocytes and the functional megaspore formation in Deschampsia antarctica were analyzed with the use of microscopic methods. A single archesporial cell was formed directly under the epidermis in the micropylar region of the ovule without producing a parietal cell. In successive stages of development, the meiocyte was transformed into a megaspore tetrad after meiosis. Most megaspores were arranged in a linear fashion, but some tetrads were T-shaped. Only one of the 60 analyzed ovules contained a cell in the direct proximity of the megasporocyte, which could be an aposporous initial. Most of the evaluated D. antarctica ovules featured monosporic embryo sacs of the Polygonum type. Approximately 30% of ovules contained numerous megaspores that were enlarged. The megaspores were located at chalazal and micropylar poles, and some ovules featured two megaspores - terminal and medial - in the chalazal region, or even three megaspores at the chalazal pole. In those cases, the micropylar megaspore was significantly smaller than the remaining megaspores, and it did not have the characteristic features of functional megaspores. Meiocytes and megaspores of D. antarctica contained polysaccharides that were detectable by PAS-reaction and aniline blue staining. Starch granules and cell walls of megasporocytes, megaspores and nucellar cells were PAS-positive. Fluorescent callose deposits were identified in the micropylar end of the megasporocytes. During meiosis and after its completion, thick callose deposits were also visible in the periclinal walls and in a small amount in the anticlinal walls of megaspores forming linear and T-shaped tetrads. Callose deposits fluorescence was not observed in the walls of the nucellar cells.
The form, waviness and roughness components of a measured profile are separated by means of digital filters. The aim of analysis was to develop an algorithm for one-dimensional filtering of profiles using approximation by means of B-splines. The theory of B-spline functions introduced by Schoenberg and extended by Unser et al. was used. Unlike the spline filter proposed by Krystek, which is described in ISO standards, the algorithm does not take into account the bending energy of a filtered profile in the functional whose minimization is the principle of the filter. Appropriate smoothness of a filtered profile is achieved by selecting an appropriate distance between nodes of the spline function. In this paper, we determine the Fourier transforms of the filter impulse response at different impulse positions, with respect to the nodes. We show that the filter cutoff length is equal to half of the node-to-node distance. The inclination of the filter frequency characteristic in the transition band can be adjusted by selecting an appropriate degree of the B-spline function. The paper includes examples of separation of 2D roughness, as well as separation of form and waviness of roundness profiles.