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Authors: Oksana G. Cherednichenko, Anastasia L. Pilyugina, Sergey N.Lukashenko, Elena G. Gubitskaya

Abstract:

The estimation of accumulated radiation doses in people professionally exposed to ionizing radiation was performed using methods of biological (chromosomal aberrations frequency in lymphocytes) and physical (radionuclides analysis in urine, whole-body radiation meter, individual thermoluminescent dosimeters) dosimetry. A group of 84 "A" category employees after their work in the territory of former Semipalatinsk test site (Kazakhstan) was investigated. The dose rate in some funnels exceeds 40 μSv/h. After radionuclides determination in urine using radiochemical and WBC methods, it was shown that the total effective dose of personnel internal exposure did not exceed 0.2 mSv/year, while an acceptable dose limit for staff is 20 mSv/year. The range of external radiation doses measured with individual thermo-luminescent dosimeters was 0.3-1.406 µSv. The cytogenetic examination showed that chromosomal aberrations frequency in staff was 4.27±0.22%, which is significantly higher than at the people from non-polluting settlement Tausugur (0.87±0.1%) (р ≤ 0.01) and citizens of Almaty (1.6±0.12%) (р≤ 0.01). Chromosomal type aberrations accounted for 2.32±0.16%, 0.27±0.06% of which were dicentrics and centric rings. The cytogenetic analysis of different types group radiosensitivity among «professionals» (age, sex, ethnic group, epidemiological data) revealed no significant differences between the compared values. Using various techniques by frequency of dicentrics and centric rings, the average cumulative radiation dose for group was calculated, and that was 0.084-0.143 Gy. To perform comparative individual dosimetry using physical and biological methods of dose assessment, calibration curves (including own ones) and regression equations based on general frequency of chromosomal aberrations obtained after irradiation of blood samples by gamma-radiation with the dose rate of 0,1 Gy/min were used. Herewith, on the assumption of individual variation of chromosomal aberrations frequency (1–10%), the accumulated dose of radiation varied 0-0.3 Gy. The main problem in the interpretation of individual dosimetry results is reduced to different reaction of the objects to irradiation - radiosensitivity, which dictates the need of quantitative definition of this individual reaction and its consideration in the calculation of the received radiation dose. The entire examined contingent was assigned to a group based on the received dose and detected cytogenetic aberrations. Radiosensitive individuals, at the lowest received dose in a year, showed the highest frequency of chromosomal aberrations (5.72%). In opposite, radioresistant individuals showed the lowest frequency of chromosomal aberrations (2.8%). The cohort correlation according to the criterion of radio-sensitivity in our research was distributed as follows: radio-sensitive (26.2%) — medium radio-sensitivity (57.1%), radioresistant (16.7%). Herewith, the dispersion for radioresistant individuals is 2.3; for the group with medium radio-sensitivity — 3.3; and for radio-sensitive group — 9. These data indicate the highest variation of characteristic (reactions to radiation effect) in the group of radio-sensitive individuals. People with medium radio-sensitivity show significant long-term correlation (0.66; n=48, β ≥ 0.999) between the values of doses defined according to the results of cytogenetic analysis and dose of external radiation obtained with the help of thermoluminescent dosimeters. Mathematical models based on the type of violation of the radiation dose according to the professionals radiosensitivity level were offered.

Keywords: Biodosimetry, chromosomal aberrations, ionizing radiation, radiosensitivity.

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

Abstract:

Creating favourable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. This paper describes a holistic approach to teaching mathematics designed to address the primary challenges of such teaching; specifically, the challenge of students’ comprehension. Essentially, this approach consists of (1) establishing links between the attributes of the notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience—value-based emotions, contextual, procedural and communicative—during the educational process; (3) linking together different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modelling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and techniques influence understanding of material used in teaching mathematics was the primary goal. The study included an experiment in which 256 secondary school students took part: 142 in the study group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics — “Derivative” and “Trigonometric functions”—was evaluated. Control group participants were taught using traditional methods. Students in the study group were taught using the holistic method: under teacher’s guidance, they carried out assignments designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as assignments that required the ability to operate with all modes of presentation. Identification, accounting for and transformation of subjective experience were associated with methods of stimulating the emotional value component of the studied mathematical content (discussions of lesson titles, assignments aimed to create study dominants, performing theme-related physical exercise ...) The use of techniques that forms inter-subject notions based on linkages between, perceptual real and mathematical conceptual spaces proved to be of special interest to the students. Results of the experiment were analysed by presenting students in each of the groups with a final test in each of the studied topics. The test included assignments that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion x2 was used to reveal statistics significance of results (pass-fail the modelling test). Significant difference of results was revealed (p < 0.001), which allowed to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. The total number of completed assignments of each student was analysed as well, with average results calculated for each group. Statistical significance of result differences against the quantitative criterion (number of completed assignments) was determined using Student’s t-test, which showed that students in the study group completed significantly more assignments than those in the control group (p = 0.0001). Authors thus come to the conclusion that suggested increase in the level of comprehension of study material took place as a result of applying implemented methods and techniques.

Keywords: Comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions.

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