Operationalizing Levels of Academic Mastery Based on Vygotskys Theory: The Study of Mathematical Knowledge
The present study tested the possibility of operationalizing levels of knowledge acquisition based on Vygotskyђs theory of cognitive growth. An assessment tool (SAMMath) was developed to capture a hypothesized hierarchical structure of mathematical knowledge consisting of procedural, conceptual, and functional levels. In Study 1, SAM-Math was administered to 4th-grade students (N = 2,216). The results of Rasch analysis indicated that the test provided an operational definition for the construct of mathematical competence that included the three levels of mastery corresponding to the theoretically based hierarchy of knowledge. In Study 2, SAM-Math was administered to students in 4th, 6th, 8th, and 10th grades (N = 396) to examine developmental changes in the levels of mathematics knowledge. The results showed that the mastery of mathematical concepts presented in elementary school continued to deepen beyond elementary school, as evidenced by a significant growth in conceptual and functional levels of knowledge. The findings are discussed in terms of their implications for psychological theory, test design, and educational practice.
One merit of Trends in International Mathematics and Science Study (TIMSS) is that apart from a direct school students cognitive appraisal, it enables to collect information on teachers of these students, on their education, work experience and teaching practices. The first difference method was used to determine how teachers characteristics were associated with students achievements and to overcome restrictions of TIMSS correlation design. In addition, effects of teachers characteristics were evaluated by the conventional regressions method. The discovered associations differed across subject areas, and the first difference method results differed from the conventional correlation analysis results. For mathematics the first difference method revealed negative association of reproductive tasks and collaborative learning with achievements, and tasks aimed at comprehension and development of metasubject skills showed positive association. For natural science reproductive tasks showed, on the contrary, positive association, while tasks aimed at comprehension and development of metasubject skills either did not produce any effects, or they were negative. Also, for natural science, unlike mathematics, a teachers experience considerably influenced students achievements.
Lev Semyonovich Vygotsky (real name Lev Simkhovich Vygodsky; Orsha 1896–Moscow 1934) was a Russian psychologist who created cultural-historical theory, which proved influential in developmental psychology and other psychological disciplines. Vygotsky characterized his approach as “height psychology” (as opposed to “depth psychology”) and posited that the higher forms of mind should be the starting point for the study of human development. In his view it was essential to study psychological processes in their historical dynamics; these dynamics could be unraveled with the causal-genetic approach he developed, which involved the guided formation of mind in the course of its study or the experimental unfolding of ontogeny. Vygotsky claimed that the mechanisms of human development are not genetically determined and that we must find its source in culture and the social environment. Human development is mediated by cultural artifacts and sign systems, which are mastered in a dialogue with other people in spontaneous or guided interaction, which stimulates development by creating a zone of proximal development. The major means of the transformation of innate mind into higher mind is language, which enables us to preserve and transmit the experience of generations. In this process of cultural development the person develops a system of higher psychological functions that are social in origin, voluntary and mediated in nature, and form part of a systemic whole. The process of ontogeny goes through a series of stable periods and crises that correspond with specific conditions of the social situation of development and the developmental tasks. Age periods are completed with the development of neoformations, which do not just form results but are also prerequisites for further development. With the development of verbal thinking and the mastery of cultural means of behavior the person masters her/his innate mind and becomes a personality, whose main characteristic is freedom of behavior.
This article consider The project of the scientific and educational Center for integration of multimedia technologies in science, education and culture, as space-technological environment for the implementation of innovative scientific and educational projects of the 21st century, which should become the support for the master's programs, especially interdisciplinary; at the intersection of science, art and information technologies, and implementation of innovative scientific and commercial projects, which are to become a master's thesis.
The three already traditional volumes of the WDS Proceedings you are holding in the hands are composed of the contributions which have been presented during the 21st Annual Conference of Doctoral Students that was held in Prague, at Charles University, Faculty of Mathematics and Physics from May 29 to June 1, 2012. In this year, 100 student manuscripts were submitted to publishing and 88 were accepted after the review process.
The paper discusses in detail the scale of translation of primary points scored by school graduates in the unified state exam in mathematics, used from 2013 to the present time. Based on the analysis of the dynamics of these scales, a conclusion is made about the annual increase in the "average" 100-point result, as well as the presence of a significant increase in the final grade compared with the linear scale. Additionally, the authors describe the effect of reducing the value of primary points as they approach the maximum.
This article presents the results of a pilot study assessing the level of formation of a stochastic competence among teachers of mathematics. Besides, the indicators that reflect the competence of formation of stochastic students are identified and ranked in order of importance. Different instruments (questionnaires, tests, assignments) have been used to solve the problem under study.
The distractive effects on attentional task performance in different paradigms are analyzed in this paper. I demonstrate how distractors may negatively affect (interference effect), positively (redundancy effect) or neutrally (null effect). Distractor effects described in literature are classified in accordance with their hypothetical source. The general rule of the theory is also introduced. It contains the formal prediction of the particular distractor effect, based on entropy and redundancy measures from the mathematical theory of communication (Shannon, 1948). Single- vs dual-process frameworks are considered for hypothetical mechanisms which underpin the distractor effects. Distractor profiles (DPs) are also introduced for the formalization and simple visualization of experimental data concerning the distractor effects. Typical shapes of DPs and their interpretations are discussed with examples from three frequently cited experiments. Finally, the paper introduces hierarchical hypothesis that states the level-fashion modulating interrelations between distractor effects of different classes.