For many years, learning the competences to teach mathematics in early education at university has been associated with the ability to reproductively apply methodological guidelines. Currently, however, the need to not only understand the mathematical meanings given by teachers, but also students of the specialty, are seen to be important. This article attempts to engage in an interpretive line of thinking with regard to mathematics education, coming from the perspective of students learning to be early education teachers. Their understanding of the contexts for learning mathematical concepts, as well as their sensitivity to the processes of constructing mathematical knowledge by very young pupils, being a way of predicting what educational activities will be undertaken in the classroom in the future. This text is the result of qualitative analyses of written essays of early education students, where respondents had to make conceptualizations of their beliefs by justifying the selection of particular declarative statements. Students’ mathematical meanings were also uncovered in their strategies for solving mathematical problems for very young pupils. Moreover, the results of this analyses provides a context for reading the students’ understanding of mathematics learning processes.

Among the big corpus of the commentaries over the Qur’an, one of the special developments was a genre of gloss (hāšiya). The study addresses main Ottoman glosses written to the Qur’anic commentaries, contextualizing it within the internal dimensions of the content transformations. It is argued that since the glosses were used as the textbooks in the Ottoman medrese, they could be considered as the “mainstream” Ottoman reading of the Qur’an. This reading was not merely one of the practices for approaching the Qur’an, but the kind of tradition with the related authorities and meaningful developments. The research covers these patterns of interpretations applied to the case of Āl ‘Imrān, 3: 7, showing the way of how the philology and theology interacted in the Ottoman tafsīr glosses.

Although currently pole dancing is growing in popularity due to its sport dimension, it seems that such a form of expression is still commonly associated with strip clubs and connotes above all the erotic performance of a woman in front of a male audience. And yet, as one can find by frequenting dance studios that teach pole dancing, it is practiced not only by women, but also by men and children. Thus keeping in mind the ambiguity that arises at the intersection of competing optics in decoding the pole dance—with regard to “perpetuate interpretation logic” and the everyday experience of people undertaking the activity—the aim of this paper is to reflect on the issue of constructing and interpreting the meanings of actions and processes within the context of pole dancing. These processes can be seen as a reflection of the everyday life in which they occur.

This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation(RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage(experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error(MSE) to compare the estimators. The errorswere juxtaposed with the Cramér–Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR > 25 dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.

The article shows that during the forming of grammatical category of gender in Indo-European languages, names of non-living objects and names of those animals whose sex is unimportant for humans were receiving grammatical meanings of gender on the basis of similarity or dissimilarity of designated objects with males or females. Such grammatical metaphors were based on the ideas of different peoples about some minor characteristics of persons of different sex, such as the difference between men and women with higher activity, greater size, strength and independence. By now, the metaphorical motivation of category of gender in the Russian language has survived only in certain nouns. These nouns are interrogative pronouns кто (masc.) ʻwhoʼ and что (neut.) ʻwhatʼ, paired nouns-synonyms, e. g. конь (masc.) ʻstrong horseʼ – лошадь (fem.) ʻordinary horseʼ, generic versions of nouns, e. g. ворон (masc.) ʻravenʼ – ворона (fem.) ʻcrowʼ, and nouns-occasionalisms used in speech oriented to expressiveness and creativity.

This paper aims to propose a new multi-attribute decision making (MADM) method in complicated and fuzzy decision-making environment. To express both decision makers (DMs’) quantitative and qualitative evaluation information comprehensively and consider their high hesitancy in giving their assessment values in MADM process, we combine q-rung dual hesitant fuzzy sets (q-RDHFSs) with uncertain linguistic variables and develop a new tool, called the q-rung dual hesitant uncertain linguistic sets (q-RDHULSs). First, the definition, operations and comparison method of q-RDHULSs are proposed. Second, given the interrelationship among multiple q-rung dual hesitant uncertain linguistic variables (q-RDHULVs) we introduce some aggregation operators (AOs) to fuse q-rung dual hesitant uncertain linguistic (q-RDHUL) information based on the Muirhead mean, i.e. the q-RDHUL Muirhead mean operator, the q- RDHUL weighted Muirhead mean operator, the q-RDHUL dual Muirhead mean operator, and the q-RDHUL weighted dual Muirhead mean operator. To cope with MADM problems with q-RDHUL information, we propose a new method based on the proposed AOs. Afterwards, we apply the proposed method to an enterprise informatization level evaluation problem to verify its effectiveness. In addition, we also explain why our proposed method is more powerful and flexible than others.