Mariya A. Yanishevskaya

Background. The formation of multiplicative concepts of complex structure is a challenge for educational design. Students’ typical mistakes and strategies spontaneously obtained through hands-on trials in solving balance scale problems have been at the center of many studies within this trend. However, the consideration of relevant concept-mediated actions based on Learning Activity Theory (Davydov) remains a relevant problem.

Objective. We aimed to develop a feasible framework for digital support of students’ learning actions in this domain. The productiveness of individual and joint forms of work with dynamic objects in a digital environment, mediated with conceptual modeling tools, was compared.

Design. The participants were 181 fifth-grade students (11–12 years old). The first group (123 students) was taught a special procedure of modeling, which they then could test during individual computer-supported problem-solving. The second group (58 students) worked in pairs (jointly), using the same procedure. The pre- and post-tests included challenging problems on prediction of the balance state and ways to regain equilibrium.

Results. Comparison of the pre- and post-test results of the joint computer-supported activity instruction revealed students’ progress in solving critical tasks as guided by the conceptual modeling procedure of load evaluation instead of “empirical” correlations of weights and distances. The individual computer-supported work, however, failed to overcome the belief of some students in the efficacy of trial-and-error methods as applied to the digital simulation with instant feedback.

Conclusion. The special organization of the computer-supported concept-mediated joint activity may promote multiplicative concept formation.

Background. Using the Activity Theory of education (Galperin, 1992; Talyzina, 2018), this article examines the students’ actions that constitute the early stages of forming the concept of ratios. The psychological analysis of mastery of this concept shows that it essentially depends on understanding the coordination of the changes of two independent values (area, velocity, density, etc.).

Objective. The present research considers differences in students’ operations with numbers on various tasks, based on their comprehension of ratio relations (direct and inverse proportions); these differences are revealed through posing certain modified tasks, but may stay unnoticed in regular tasks. The goal of the study was to identify the criteria for adequate assessment of the sustainability of the students’ orientation in modified tasks.

Design. A test of 15 tasks was designed based on Galperin's classification of task variations: domain specific, logical, and psychological. The formulation of the tasks disguised the operations needed to achieve the right answer, and sometimes even prompted the wrong solution. There were 12 tasks on direct proportions – four sample and eight modified; and three inverse proportion tasks: one sample and two modified. One hundred sixty (160) students (5^th-6^th grade, 11-13 years old) took the test in writing.

Results. The comparison of students’ performance on the sample and modified tasks showed significant differences. Modifications impaired the students' performance on both types of proportion problems (direct and inverse). Logical and psychological modifications had the most impact on the quality of the students' orientation and thus proved to be most indicative in terms of students’ orientation quality assessment.

Conclusion. The data suggest the following: 1) that the concepts of proportionality which the students acquired from a regular school curriculum lack "generalization," and 2) that students’ ability to apply the ratio concept is very sensitive to the way the word problem is presented. These findings are essential for evaluating students’ multiplicative thinking: their actual level of comprehension cannot be revealed through their performance on regular tasks.

Background. This paper addresses the issue of educational text comprehension, which is one of the major problems in secondary schools, especially when such texts are introduced in the natural sciences. Studies on text comprehension often regard reading as a standalone skill: its mechanisms are discussed from leading theoretical approaches (cognitivism, constructivism, etc.), and variables are distinguished and evaluated. Most of the researchers consider text comprehension to be active reconstruction of the meaning which the text delivers, and regard the application of the information retrieved from the text to problem-solving as the indicator for a deep comprehension level. Since we work within the framework of Cultural-Historical Activity Theory (CHAT), we consider educational text comprehension to be mediated through special content-related models which students have to acquire. Unfortunately, there are no studies which have directly linked reading, corresponding problem-solving, and working with content-related models (symbolic means, schemes); hence, with this research, we are seeking to fill in the gap.

Objective. Our goal is to elaborate the perspective on educational text comprehension as mediated through mastering special modeling (symbolic) means. In this article we illustrate this approach with the “Moon test” – an assessment procedure which we designed to materialize the components of orientation of students’ action as they succeed or fail to solve problems by relying on the educational text provided.

Design. We conducted the “Moon test” among the fifth graders (10-12 years old). The text, which told the students how to use the moon’s visual transformations as a calendar, was followed by 12 tasks on the topic. The tasks required using the text to master the model provided, and then solve challenging tasks which only referred to the model implicitly.

Results. To analyze the results, we grouped the tasks in four blocks: 1) model acquisition; 2) mastering; 3) application; and 4) experience. The results showed a statistically significant decrease in the students’ performance on tasks of the third and the fourth blocks, which required reasonable application of the models. Further analysis of individual patterns of performance allowed us to distinguish clusters of students with different levels of success in each block.

Conclusion. Our results attest to the importance of model mediation for reading comprehension and the development of scientific literacy.

Background. We apply the theory of step-by-step concept formation (Galperin) and the theory of learning activity (Davydov) to the practice of education and teacher training.

Objective. This paper describes a feasible way to teach the basics of Galperin’s theory to students studying pedagogical psychology, by involving them into an exemplary educational module on combining chemical formulas according to the elements’ valency values.

Design. We suggested that our students participate in an educational module which was designed as an example of how to materialize orientation components of action as the basis of concept formation. The “practical” action for mastering the valency concept was to combine the correct formula for a pair of elements, whose valency was provided, and correct the formulas made by someone else. However, the core “orientation” required an extended procedure of building a “molecule” structure with a special construction kit. The key challenge for the students was to coordinate their calculation of the number of bonds needed for the molecule, and name the exact total before they would receive their atom-tokens for constructing the model.

Results. Our workshop participants took on the role of students facing their first encounter with chemistry, and embarked on the formation sequence. At the same time they analyzed the mistakes they had made by ignoring some procedural steps. Considered through the lens of Galperin’s theory, these “adult” mistakes proved how vital his theoretical principles are for educational design.

Conclusion. Our workshop thus illustrated that the search for the proper action for concept formation within Galperin’s theory framework is a challenging task. The difficulties that our participants experienced while they worked as pupils revealed the divergence of didactic approaches. The effectiveness of the concept formation approach, even within our small exemplary educational module, once again confirmed the practical value of pedagogical psychology in general, and Galperin’s theory in particular.