Developing students' universal competencies in working with mathematical texts and symbols based on the technology of semantic reading and annotation

Abstract

This article examines the development of students' universal competencies in working with mathematical texts and symbols in the context of the increasing role of information translation activities in learning. Students' difficulties stem not so much from computational deficiencies as from an inability to relate natural language to formalized sign systems and to grasp logical connectives, quantifiers, and the high information density of mathematical discourse. Mathematical text is interpreted as a semiotically heterogeneous structure requiring a hermeneutic «unfolding» of meanings, and semantic reading is viewed as a meta-subject mechanism for reducing cognitive load when switching codes between text, formulas, graphs, and tables. This paper describes the piloting of a methodology on a sample of 482 junior students enrolled in various faculties of a pedagogical university over two academic years. The methodology relies on systemic activity logic and the step-by-step development of mental actions in combination with a semiotic approach. The study included tests of mathematical text comprehension, analysis of educational materials, participant observation, interviews, and statistical analysis (correlation analysis, chi-square test). The diagnostics revealed the dominance of the reproductive level of decoding (approximately half of the students) and a persistent gap between the semantics and syntax of mathematical speech. The implementation of active annotation modules (infographic marking of conditions, structuring of evidence, glossaries of symbols, «translation» between languages) was accompanied by a significant reduction in semantic, logical, and syntactic errors in the experimental groups (up to 45,56%, 39,52%, and 33,49%, respectively), while in the control groups the changes were weak (approximately 8%). A strengthening relationship was demonstrated between meaningful reading and academic performance in mathematical disciplines (algebra, geometry, mathematical analysis, probability theory, etc.): the correlation coefficient in the experimental group increased to 0.82 by the end of the second year, with moderate values in the control group (up to 0.47). The adequacy of self-assessment of the complexity of mathematical texts has significantly increased (index up to 0.815), which is interpreted as the development of metacognitive regulation and resistance to long formulations due to the mastery of decomposition and structural analysis tools.