Pages: 282-300
Published: 30.06.2024
Abstract: A cognitive model of a teacher's pedagogical skills has been developed. Sense and numeric variables have been introduced. Numerical coefficients that measure the magnitude of the strength of relationships between variables have been introduced. The numerical values of deviations from 0 to the right/left of the variability of zik z-variables, multiplied by the “weights” сkj, were found (modeled). The sum of the products zikсkj , k=1,…, 9, forms a new y-variable; for j=1,…, 9, the y-variables form an uncorrelated set of y-variables.The meanings of these y-variables, which are extracted hidden knowledge about the factors of the pedagogical skill of a teacher teaching students within the framework of the original 9 z-events, were found. The model added (cognized) another 9 z-events to them. Newer y-events are quantitatively and meaningfully substantiated. The manifestations of events are realized, their formulaic, phraseological, visualized on graphs descriptions of curve behavior are justified and correspond to the expected. A system of 9 semantic equations with 18 semantic variables has been developed: meaning(y1),..., meaning(y9), meaning(z1),..., meaning(z9). Nine semantic solutions-knowledge (new extracted knowledge), cognize the meanings, pairwise connections, and strengths of manifestations of 13 semantic variables. Visualization of the mutual dynamics of curves (variability values of z-, y-variables from matrices Zm9,Ym9) of knowledge about “weights” (from C99) and z-, y-variabilities in a model with 9 z-variables, 9 y-variables showed the dynamics of the model values of unmeasured indicators of manifestations of teacher skill. The variables introduced into the model are endowed with mathematical and statistical properties, and the parameters are constant. They are modeled in the Optimization Problem and depend on the number of variables and on the values of 3 indicators. Both uncorrelated (y-) and correlated (z-) variability are multiplied by their “weights” - the strength of the factor manifestation. Interesting knowledge was gained after visualization. The most informative is the found event y4. Meaning (y4) = “presentation of new educational material (with force c244=1.0000)2), carried out by the teacher with the attention of the student (with force c214 =0.35482).” 3 more events are informative: meaning (y3)= “repetition of already studied material (with strength c233 = 0.60002), carried out by the teacher with a decrease in the strength of manifestation of 3 factors: a) information about learning goals (with strength (-0.7165 )2), b) presentation of new educational material (with force c243 = (-0.1248)2)"; meaning (y2) = “attracting the student’s attention (with strength c212 =0.35022), explaining learning goals (with strength c222 = (0.3502)2) and repeating already studied material (with strength c232 = 1.0000)2)"; meaning (y1) = “the teacher’s efforts to attract the attention of students, shown (with force c211 = (+0.5000)2) reduce the amount of information for learning purposes (with force c221 = (-0.1735)2)”. The presented structure of situations in which the model has learned unknown hidden knowledge can be applied to subjects (professor, student) if the initial data is changed - z-situations for the teacher are replaced with z-situations inherent in universities.
Key words: multisense equation with known and unknown semantic variables, Cognitive Model of teacher pedagogical skill.
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