Approximately Research Articles

On approximate equality of Z-values of the statistical tests for win statistics (win ratio, win odds, and net benefit)

ABSTRACT Dong et al. (2023) showed that the win statistics (win ratio, win odds, and net benefit) can complement each another to demonstrate the strength of treatment effects in randomized trials with prioritized multiple outcomes. This result was built on the connections among the point and variance estimates of the three statistics, and the approximate equality of Z-values in their statistical tests. However, the impact of this approximation was not clear. This Discussion refines this approach and shows that the approximate equality of Z-values for the win statistics holds more generally. Thus, the three win statistics consistently yield closely similar p-values. In addition, our simulations show an example that the naive approach without adjustment for censoring bias may produce a completely opposite conclusion from the true results, whereas the IPCW (inverse-probability-of-censoring weighting) approach can effectively adjust the win statistics to the corresponding true values (i.e. IPCW-adjusted win statistics are unbiased estimators of treatment effect).

Anchor-guided global view reconstruction for multi-view multi-label feature selection

In multi-view multi-label learning (MVML), the accuracy of feature weights is pivotal for establishing feature order. However, conventional MVML methods often struggle with integrating distinct information from multiple views effectively, leading to unclear segmentation and potential noise introduction. To address this challenge, this paper proposes an anchor-based latent representation method for global view learning in MVML. Specifically, we encode inherent information from each view to derive a candidate multi-view representation. Anchors extracted from both the candidate view and the global view are then constrained to approximate equality in the latent space. Furthermore, a carefully designed view matrix serves as supplement, seamlessly integrated into the reconstruction process to augment information. The convergence of results is subsequently validated using multiplicative update rules. Experimental findings showcase the superior performance of our proposed method across various multi-view datasets.

Approximate equality for two sums of roots

In this paper, we consider the problem of finding how close two sums of mth roots can be to each other. For integers m≥2, k≥1 and 0≤s≤k, let em(s,k)>0 and Em(s,k)>0 be the largest exponents such that for infinitely many integers N there exist k positive integers a1,…,ak≤N for which two sums of their mth roots ∑j=1sajm and ∑j=s+1kajm are distinct but not further than N−em(s,k) from each other, or they are distinct modulo 1 but not further than N−Em(s,k) from each other modulo 1. Some upper bounds on em(s,k) and Em(s,k) can be derived by a Liouville-type argument, while lower bounds are usually difficult to obtain. We prove that em(s,k)≥min⁡(2s,k−1,2k−2s)−1/m for 1≤s<k and that Em(s,k)≥min⁡(2s,k−2,2k−2s)+2−1/m for 0≤s≤k. Very recently, Steinerberger managed to show that E2(k,k)≥ck3, where c>0 is a small absolute constant. This seems to be the first result when the bound for s=k is increasing in k. By an entirely different argument, for any integers m≥2, k≥1 and s in the range 0≤s≤k, we show that Em(s,k)≥(k−2)/m+1. In particular, for m=2 and any non-negative integer s≤k, this yields the bound E2(s,k)≥k/2, which is much better than ck3. We also prove that e2(2,4)=7/2, which settles a problem raised by O'Rourke in 1981. These problems can be also considered for non-integer m. In particular, we show that 1≤E3/2(1,1)≤4/3, and that E3/2(1,1)=1 under assumption of the abc-conjecture.

An analysis of the stability and bifurcation of a discrete-time predator-prey model with the slow-fast effect on the predator.

In many environments, predators have significantly longer lives and meet several generations of prey, or the prey population reproduces rapidly. The slow-fast effect can best describe such predator-prey interactions. The slow-fast effect ε can be considered as the ratio between the predator's linear death rate and the prey's linear growth rate. This paper examines a slow-fast, discrete predator-prey interaction with prey refuge and herd behavior to reveal its complex dynamics. Our methodology employs the eigenvalues of the Jacobian matrix to examine the existence and local stability of fixed points in the model. Through the utilization of bifurcation theory and center manifold theory, it is demonstrated that the system undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at the positive fixed point. The hybrid control method is utilized as a means of controlling the chaotic behavior that arises from these bifurcations. Moreover, numerical simulations are performed to demonstrate that they are consistent with analytical conclusions and to display the complexity of the model. At the interior fixed point, it is shown that the model undergoes a Neimark-Sacker bifurcation for larger values of the slow-fast effect parameter by using the slow-fast effect parameter ε as the bifurcation parameter. This is reasonable since a large ε implies an approximate equality in the predator's death rate and the prey's growth rate, automatically leading to the instability of the positive fixed point due to the slow-fast impact on the predator and the presence of prey refuge.

STUDY ON THE ACTUAL SITUATION OF DOMESTIC WATER IN 24 MILITARY UNITS IN THE NORTHERN REGION IN 2022

Purpose: Study on the actual situation of domestic water in some military units in the Northern region in 2022. Subjects and Methods: A cross-sectional descriptive study with analysis and evaluation of seven basic physical, chemical and microbiological indicators on 113 samples of domestic water collected at 24 military units stationed in the Northern Region from July to October, 2022. Results: The water used for consumption and daily activities in the studied units accounted for 58.4% from drilled wells and dug wells and 35.4% from water supplied by factories, in which 61.1% of the water was untreated before use. The proportion of water sources that did not meet the standards according to QCVN 01:2018/BYT for pH indicator was 29/113 samples (25.7%), and for turbidity was 10/113 samples (8.8%). A comparison of nitrite and ammonia standards between treated and untreated water sources showed approximate equality. The difference in permanganate criteria between treated and untreated water sources and the proportion of samples meeting standards according to QCVN 01-1: 2018/BYT was statistically significant with p &lt; 0.05.

Expectation-maximization vector approximate message passing-based frequency-domain turbo equalization for underwater acoustic communications.

Channel equalization plays a crucial role in single-carrier underwater acoustic (UWA) communications. Recently, a frequency-domain turbo equalization (FDTE) scheme enabled by the vector approximate message passing (VAMP) algorithm, was proposed, and it outperformed classic linear minimum mean square error FDTE at acceptable complexity cost. The operation of the VAMP-FDTE requires knowledge of noise power, which is predetermined before the equalization starts. In practice, however, it is difficult to obtain prior knowledge of noise power due to factors of unknown channel estimation errors and dynamic underwater environments. Motivated by this fact, we propose an enhanced VAMP-FDTE scheme, which learns the noise power knowledge during the equalization process via the expectation-maximization (EM) algorithm. The EM-based noise power estimation makes use of intermediate results of the VAMP-FDTE and, thus, only incurs a small extra computational overhead. The improved VAMP-FDTE, named EM-VAMP-FDTE, was tested by experimental data collected in shallow-sea horizontal UWA communication trials with MIMO configuration. It showed better performance than the existing VAMP-FDTE scheme, attributed to the online noise power learning.

Critical Discourse Analysis of Gender Equality in English Textbooks

Textbooks are recognized worldwide as one of the most widely used and important teaching materials in formal instruction. In alignment with their significance, they are often evaluated and examined in terms of many elements such as content, method, achievements, and skills. Recently, they have also been scrutinized from a more socio-cultural perspective, considering gender representations, equity, racial inclusivity, and cultural diversity. Within this tendency, this study aimed to investigate the status of gender and gender equality in two English textbooks used in tertiary-level English courses offered for the first-year students of a state university in Turkey within quantitative and qualitative perspectives by using Fairclough’s (1989) model of critical discourse analysis. Of the two English textbooks, one was published by a national publishing house and the other by an international one. Female and male representations in visuals and written texts were investigated and the equality of genders was analyzed with a critical viewpoint. The results indicated that there exists approximate equality in gender representation in visuals and texts of the textbooks within a quantitative perspective; however, the qualitative analysis of gender representation according to the values of firstness, titles, and occupational roles yielded a gender bias in favor of men. Consequently, this study made suggestions for enhancing gender equality within English language textbooks.

Methods of the “New Division of the Empire”: The Reforms of Administrative Division in Vyatka Rеgion from Catherine the Great to Paul I

This article examines the territorial transformations carried out in Vyatka Region in the 1780s–1810s. As is known, before the last quarter of the eighteenth century, the system of administrative-territorial division of the country was based on the historically established system of uyezds. However, in 1775–1802, two major reforms were carried out, which rebuilt the administrative-territorial division following qualitatively new principles – approximate equality of the population of provinces and uyezds and transport accessibility of administrative centres for the population. These changes largely determined the outlines of the social structure of the Russian Empire over the next century, and changes in the management system and social structure naturally attract researchers’ attention today. With the help of a detailed reconstruction (based on maps of the time, both printed, from national atlases of 1792 and 1800, and handprinted, from the collections of several archives) and comparison of the boundaries of provinces in the middle of the eighteenth century, in 1792, in 1792, 1800 and 1805–1806, the author reveals the redistribution of territories between urban centres. It transpires that the system of territorial relations in this region during the reform of Catherine II changed more decisively than in the central regions of the country, and the new borders were initially drawn without a survey of the situation on the ground, in some cases – in the form of straight lines on the map. The correction of inconveniences caused by such a manner of reform was delayed and was completed already during the administrative reforms of Paul I, which, unlike most regions, were not cancelled there in the first decade of the nineteenth century.

Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach

Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach

Uncertainty measurement for single cell RNA-seq data based on class-consistent technology with application to semi-supervised gene selection

Because of the high cost of label collection, people are now faced with a large number of partially labeled gene expression data (plge-data). Single cell RNA-seq data (scrs-data) are a kind of important plge-data and reflect the abundance of gene transcript mRNA measured directly or indirectly in cells. For convenience, a decision information system (DIS) based on scrs-data is called a single cell gene decision space (scgd-space). Due to the high dimensionality of scrs-data, feature selection must be done before clustering and classification. The existing feature selection methods based on equivalence relation are ineffective for the scgd-space owing to the strictness of equality between information values. To solve the above problems, this paper studies the uncertainty measurement of the scgd-space based on class-consistent technology and considers its application to semi-supervised gene selection. Class-consistent technology replaces equality with approximate equality between two expression values at a gene. Based on the proposed technology, class-consistent and non-class-consistent relations on the cell set of the scgd-space are established first. Then, the scgd-space (O,A,d) is divided into labeled space (Ol,A,d) and unlabeled space (Ou,A,d). Next, four metrics of importance on each gene subset of (O,A,d) are defined. They are the weighted sum of (Ol,A,d) and (Ou,A,d) determined by the missing rate of labels and the established relations and can be used to measure the uncertainty of (O,A,d). In addition, as an application of four metrics to the scgd-space, a semi-supervised gene selection algorithm is designed. Finally, the experimental results and statistical tests on 16 large-scale scrs-data sets show that the defined metrics can effectively measure the uncertainty of the scgd-space. The designed algorithm with a high reduction rate outperforms some state-of-the-art feature selection algorithms in terms of eight performance evaluation indicators.

Age and sex structure of the population of the Srubnaya culture in the late bronze age (on the materials from the Samara Volga region)

The demographic structure of the population is reconstructed on the basis of 866 sex and age definitions of the skeletons of the late Bronze Srubnaya culture of the Samara Volga region. The historiographical information on this aspect of paleopopulations life in the region is given. The analysis of the materials of the early and developed stages of this culture is carried out both on the basis of traditional approaches and using the principal component analysis of multidimensional statistics. There is a high mortality rate of the childrens share of the population of the Srubnaya culture, approximate equality in the maintenance of representatives of both sexes, a somewhat longer life expectancy of the male part of the population. These characteristics are relatively close to those of the carriers of the Potapovka culture type who lived in the region in the previous time and sharply differ from the demographic indicators of the Yamnaya culture tribes of the early and Middle Bronze Age, leading a mobile cattle-breeding type of economy. In this line of historical ties, the early Srubnaya culture groups by gender and age structure, taking into account the presence of their settlement monuments, already represent a relatively settled population, with the development of domestic cattle breeding. At the developed stage of the existence of the Srubnaya culture, there is a slight decrease in the overall infant mortality, and especially among adolescents, the overall demographic indicators are more stable. Apparently, this is the time of the maximum adaptation to the natural conditions of the forest-steppe Volga region, the time of the use of their resources for the life support of the population.

Minimization of the Land Right-of-Way During The Landscape Design of a Road

Purpose. The main purpose of this work is to solve the problem of designing a longitudinal profile, provided that the volume of earthworks is rationally distributed and the width of the right-of-way is reduced when designing a road on the ground in conjunction with the landscape. Methodology. The study was conducted in accordance with the requirements of SBS B.2.3–4:2015 regarding the need to comply with the principles of landscape design and the use of rational combinations of plan elements and longitudinal profile to ensure the smoothness of the road, as well as its relationship with the environment to reduce destruction and preserve the existing landscape in each case. Findings. The paper considers two options for drawing the design line relative to the ground line: in the first option, the design line is drawn based on the condition of approximate equality of the volumes of excavations and embankments, in the second – on the condition of designing the longitudinal profile with the maximum permissible slopes to reduce the value of the working elevations. The research confirms that designing the longitudinal profile with maximum slopes leads to a decrease in the working elevations of embankments and excavations. This, in turn, leads to a reduction in the width of the road right-of-way. In the case of a balanced distribution of embankment and excavation volumes, the width of the right-of-way increased by 1.6 times. However, the use of soil from the excavations for embankment filling (the so-called longitudinal dumping) reduced the total cost of earthworks by 27%, despite the increase in the width of the right-of-way. Originality. Methodological approaches to determining the scope of work and cost of subgrade construction are proposed, provided that the width of the right-of-way is minimized during the design of the road. The cost of the subgrade is represented by two components – the cost of soil development and transportation and the cost of land occupation. Practical value. The results obtained in the course of the research work indicate that the task of determining the scope of work and cost of the subgrade construction, while minimizing the width of the right-of-way during the construction of the road, has been solved. The provided recommendations will contribute to the effectiveness of design solutions, determine the quality of the road project in general and the feasibility of its implementation in particular.

ИЗМЕНЕНИЯ ГРАНИЦ РЕГИОНОВ ЦЕНТРАЛЬНОЙ РОССИИ В XVIII-XX ВВ

The article discusses the administrative-territorial division of Central Russia (within the modern Central Federal District) over the past three centuries. The purpose of the study was to find out how the composition of regional centers and the territories of the regions associated with them have changed during this time. There are two periods of the most active transformations - the provincial reform of Catherine II, 1775-1785, and a series of Soviet reforms of 1917- 1970, - between which the borders of the regions in the center of the country were stable. Based on a wide range of cartographic sources (both published and archival), accurate maps of the borders of the regions for 1760 (provinces and governorates) and 1792 (governorates) were compiled; then they were compared with each other and with the borders of modern regions. Based on this comparison, it was shown that the composition of regional centers in Central Russia was significantly stable: 13 of the 17 modern regional centers were previously the centers of provinces, and 12 of them were provinces even earlier. On the contrary, the borders changed significantly at each of the stages of transformation, which is related to specific circumstances: the provincial reform of Catherine II was carried out based primarily on the principle of approximate equality of the population of provinces and counties; Soviet transformations were based on the logic of industrial development. The historical ties of the territories in both cases were little taken into account, and as a result, in most cases the core of the region is surrounded by the periphery, which in the past changed its administrative registration. The work contains maps of the historical borders of each of the regions, which have independent scientific and practical significance.

Tachocline Alfvén waves manifested in stellar activity

Context. The short-time (&lt; 700 days) periodicities of both the stellar and solar activity that controls space weather are usually are discussed as manifestations of Rossby modes in tachoclines. Various interpretations of this phenomenon that have been proposed, in particular for the Sun, can be verified by considering the broad population of nonsolar-type stars. Aims. We look for surface stellar activity features, drifting in longitude, and compare their drift rates with those predicted for different low-frequency waves in stellar photospheres and tachoclines. Methods. Analogously to the Hovmöller diagrams in meteorology, we constructed a dynamic diagram of stellar activity pattern (DDSAP) to visualize the rotational variability of the stellar radiation flux as a function of rotation phase and time. We used the high-precision light curves of the fast-rotating main sequence stars, with rotation periods of 0.5 to 4 days, from the Kepler mission database. Results. We found quasi-periodic drifting lanes (DLs) of various durations and intensities in the DDSAPs for 108 stars. In the course of analysis, we carried out a correction of the stellar rotation periods by nullifying the drifts of the longest-lasing DLs that are presumably related to the long-lived starspot complexes co-rotating with the star. We discovered a clear elongated cluster of the absolute values of the DLs’ drift rates versus the stellar effective temperatures. This cluster cannot be attributed to any accidental contaminations of the light curves or manifestation of waves in the stellar photospheres, because of their extremely short timescales. An approximate equality of the absolute values of positive and negative drift rates of the considered DLs makes it impossible to interpret them in terms of Kelvin and/or magneto-Rossby waves in the stellar tachoclines. It is only global kink-type Alfvénic oscillations of the tachocline as a whole that allow us to interpret the estimated drift rates forming the above-mentioned cluster, as well as the related activity periodicities and turnover times in the convective zones. The corresponding magnetic field strength appears to be about 50 kG, which is approximately in the middle of the range of assumptions discussed in the literature. Conclusions. Alfvén waves are an important, albeit commonly ignored factor in stellar interiors. Apparently, the global tachocline’s Alfvén waves ought to play a role in triggering emergence of the magnetic flux tubes. Their manifestation in stellar activity opens up a unique way of probing the magnetic field strength in tachoclines of individual stars. Since the investigations of the tachocline waves performed thus far have been based on the shallow-fluid approximation, and also assuming a rigid fixed bottom of the tachocline layer, the global kink-type Alvénic disturbances of the whole tachocline layer have not been considered. The reported observational detection of signatures of such waves, manifested in specific longitude drifts of the stelar surface activity pattern, calls for a more detailed theoretical study.

On the Changes in Administrative Boundaries during the Paul I’s Provincial Reform

The article is devoted to the study of the restructuring of provincial and uezd borders carried out during the transformations of Paul I in 1796—1797, in 25 central provinces of European Russia. Based on cartographic sources, primarily atlases of 1792 and 1800, electronic maps of administrative border systems were created at the end of the reign of Catherine II and at the end of the reign of Paul I. The study and correlation of the received multi-time electronic maps of the administrative division showed that the transformations covered all regions of the country, but to varying degrees. In the interior of the country, only two governorships were abolished, and, with this exception, the borders of the provinces did not undergo significant changes. However, the situation was different at the uezd level. In each province (except Arkhangelsk), cities were abolished and their uezds were dismantled. The study showed that mainly &amp;quot;new&amp;quot; administrative centers, which received city status during the reform of 1775, were subject to abolition. The territories of the abolished counties were distributed among neighboring ones. Although the population was not taken into account when determining which counties would be abolished, in many regions administrators sought to preserve the approximate equality of counties by residents, and other parts were often cut off from counties that acquired large plots in order to even out the resulting imbalance.

Words with Value Semantics in the Language Consciousness of Generation «Y» Representatives

The author analyzes the composition of the associative content and the semantic areas behind the signs that convey values in the linguistic consciousness of native 30-40 years old speakers of the Russian language. Responding to incentives of family, work, money etc. revealed the types of speech action in the situation of a free and directed associative experiment. The actualization of meanings in the process of responding to value-significant stimuli established the uniformity of cognitive mechanisms, the absence of complexity in the cognitive structure of associative fields, the prevalence of semantic areas representing socially and personally significant intangible objects - family, love, morality, ethics, a person that should be stored, developed, transmit. Most of the cases of directed association are associated with the unambiguous nature of the response, clear boundaries of the stereotype area, a low level of emotion and evaluation, the frequency of complex reactions (series of enumerations, for example, values - security, comfort, stability, family, one’s job, country). The concentration of stereotypical meanings (the area of frequency reactions of the core of associative fields) is higher when responding to stimuli What kind of work …, Work requires what …, What kind of family …. The remaining stimuli cause an approximate equality of stereotyped and individual ways of responding. The life experience of the respondents had a significant impact on the choice of the type of speech action and the method of response.

Moral Foundations for the Feelings of Shame and Pride Regarding the Native Country

The feelings of shame and pride regarding the native country are important in the context of the problem of civic identity; therefore, they are of growing interest on the part of sociologists and psychologists. Given the moral nature of these emotions, their analysis based on one of the most authoritative approaches in the psychology of morality, moral foundations theory, seems relevant and justified. The purpose of this study was to analyze the moral foundations for the feelings of shame and pride regarding the native country. The online survey involved 752 subjects (49.9% men) aged 16-73 (mean age M = 42, SD = 10.87). A new version of the Moral Foundations Questionnaire (MFQ-2) was used to assess the moral foundations. The feelings of shame and pride regarding the native country were assessed using a questionnaire tested in previous sociological and psychological studies. Data processing was carried out using exploratory factor analysis, linear regression analysis and analysis of variance (ANOVA). The results of the regression analysis on the factors of shame and pride regarding the native country showed that the moral foundations play an important role in these feelings among the inhabitants of Russia. However, a specific set of predictors is determined by what exactly is the subject of pride or shame. In general, the moral foundations of loyalty and authority are of the greatest importance for pride, while liberty and equity are most important for shame regarding the native country. Using the latent profile analysis, we identified typical profiles of moral foundations associated with age. A small group (14% of the sample) of relatively young respondents with an individualistic profile of moral foundations demonstrated a significant predominance of shame over pride regarding their native country. The other two groups with a traditionalist and a moderate profiles of moral foundations were characterized by a balance (or approximate equality) of pride and shame regarding their native country. The results of the study contribute to a deeper understanding of the role of the moral factors of patriotic education based on the formation of a feeling of pride in the country.

Experimental investigation of flow pattern over a fully developed bed at a 60° river confluence in large floods

River confluences have a complex flow and sedimentation pattern that have vital influences on the hydraulic and bed morphology of river reach and the surrounding area. Confluences can be observed in waterways with various situations such as live bed conditions. This condition is a hydro-morphological situation with a high densimetric Froude number, i.e., bed load transport is supplied from upstream. According to the literature review, most of the experimental studies investigate the flow pattern on the flatbed and not on the developed riverbed, or/and in the low densimetric Froude number, or/and without supplying the sediment from upstream. Therefore, in the present study for the quantification of the flow pattern under these conditions, each developed bed was fixed with the cement blanket method in the laboratory. Then, the 3D velocity was measured at specific points at the confluence. The current study was designed to understand the flow pattern corresponding to the river bed behavior in the case of large floods. It is expected that the morphological features downstream of the confluence have a different pattern than the ones in the condition described in other literature. Thus, this paper describes briefly what are the different bed features and investigates the corresponding flow pattern. The results of the flow pattern on the developed bed show that all zones at the river confluence can be observed except the point bar due to the approximate equality of the mean longitudinal velocity of the separation zone and the main channel upstream of the confluence. Moreover, results show that by increasing the bedload ratio (sediment discharge to water discharge of the main channel of upstream of the confluence) from 0 to 3 × 10−4, flow deflection to the outer bank of the channel decreased down to 45%, the stagnation equivalent area decreased down to 2.5 times, and bed shear stress decreased down to 40%. Hence, the momentum of lateral flow decreased with increasing bedload. Besides, the recovery zone occurred at a longer distance after the confluence compared to the case without bedload. Hence, the location of the maximum velocity zone, vortices, and secondary flows changed downstream of the confluence, by changing the bed load value.

Reading and writing, a window to the universe of children

El proyecto de lectura y escritura en el preescolar constituye un ejercicio de investigación orientado a identificar el proceso pedagógico para conducir el aprestamiento a estas operaciones en niños de cuatro a seis años, que asisten a algunas instituciones educativas públicas y privadas del área metropolitana de Bucaramanga. Además de precisar la ruta pedagógica que más se acerca a las necesidades de la población, este proyecto busca proponer unas orientaciones básicas dirigidas a maestros sobre el aprestamiento al proceso de lectoescritura. La propuesta surge de inquietudes sentidas por los autores, después de realizar unos estudios de investigación que les permitieron conocer y comprender prácticas pedagógicas y necesidades educativas de la población infantil, y que necesariamente deben ser atendidas, para fortalecer los procesos propios del desarrollo de los niños antes de llevarlos a la lectura y escritura formal. Con el estudio investigativo se pudo establecer diferentes acciones que promueven el aprestamiento y por tanto conforman la ruta pedagógica: acciones del campo cognitivo; acciones del campo socioafectivo; acciones del campo comunicativo y, por último, acciones del campo psicomotor. El proyecto se desarrolló bajo el enfoque cualitativo, diseño de investigaciónacción. Consideramos que esta forma de indagación ha permitido acercarnos de una manera natural a los centros educativos y aulas de clase, y construir conocimiento situado mediante la práctica pedagógica analizada y reflexionada de manera permanente. Así mismo podemos concluir insistiendo en la necesidad de fortalecer los proyectos educativos institucionales de los centros escolares en cuanto a diseños curriculares activos, creativos, innovadores y lúdicos.