Anna Shvarts | Lomonosov Moscow State University (original) (raw)

Papers by Anna Shvarts

International Group for the Psychology of Mathematics Education, 2014

The aim of the research is to investigate the transformation of the perception process through ma... more The aim of the research is to investigate the transformation of the perception process through mathematics education, by an example of scanning the Cartesian coordinate system in order to locate a target point. We compared participants with different competence in mathematics. Historically, motion along axes appeared as a specific “theoretical” action that constituted the Cartesian coordinate system. We detected this specificity as a dominance of vertical and horizontal saccades of eye movements in perception processes of all groups of participants. Experts-novices differences dealt with an ability of experts to use additional essential information and to discard unnecessary data. Furthermore, a lot of evidences of shortening of the perception actions from novices to experts are presented.

As cognitive science reports joint action requiring tight intercorporeal coordination between two... more As cognitive science reports joint action requiring tight intercorporeal coordination between two partners, we aim to evaluate the role of this coordination in computer-supported instrumental genesis for mathematics. In our dual eye-tracking design study we developed an embodied activity that potentially contributes to technologically extended problem solving in trigonometry. We tested three versions of the design: (a) individual sensorimotor enactment only, (b) individual and then collaborative enactments, and (c) individual enactment and then collaborative description followed by enactment. As our first case showed, the required sensorimotor coordination was developed but never used in the following problem solving when a student worked alone. In contrast, in both collaborative cases the relevant sensorimotor coordination became a part of instrumented action scheme. Future research is needed to investigate if intercorporeal coordination with the other is crucial for the transfer o...

The article outlines the possibilities of extrafoveal analysis during a conceptual visual search,... more The article outlines the possibilities of extrafoveal analysis during a conceptual visual search, when the target stimulus represents a geometric concept with an unknown form. The previous works have shown that when the target and distractors are widely diverging, the very first saccade is headed towards the target or the answer is given without any saccades, suggesting that the target is recognized extrafoveally. Our experimental design and data analysis intend to reveal extrafoveal processing of visualized concepts while saccades planning. We made the stimuli harder varying two factors: the difficulty of the target shape and its similarity to the distractors to determine the limit of complexity when the stimulus becomes too complex to be processed extrafoveally. Twelve participants with normal or corrected-to-normal vision took part in Experiment 1 and eighteen in Experiment 2. Four images of stereometric shapes were spaced at an equal distance from the center. In the first experi...

Learning, Culture, and Social Interaction, 2019

The ‘theory working group’ (under various names) has been a feature of CERME since CERME4. An ear... more The ‘theory working group’ (under various names) has been a feature of CERME since CERME4. An early and constant focus has been ‘networking theories’, exploring ways of using different theories in mathematics education research (MER) into learning and teaching mathematics. The CERME9 ‘Call for papers’ included: — The need to go beyond a specific theory when researching a phenomena — Benefits and/or strategies and/or difficulties in connecting theories — Conditions for a productive dialogue between theorists — Difficulties and strategies when gathering results from different frameworks — Linking theoretical and methodological approaches — The epistemological dimension in theories — Steps towards (local/global) theoretical convergence in MER In our 12 hours together at CERME9 we discussed 19 research papers and two posters; our task in these five pages is to introduce you to the ones (almost all of them) which have been accepted for these Proceedings. We arrange the papers into five g...

In this chapter a review of the main features and difficulties of mathematics learning in Eastern... more In this chapter a review of the main features and difficulties of mathematics learning in Eastern European countries is provided. Setting out from historical, geographical, and political considerations about the definition of what Eastern Europe may mean in the context of mathematics education, we provide a general overview of curriculum shaping and the outcomes of these school systems. In Eastern European countries, there are some features of mathematics education that might be labeled as the heritage of “socialist mathematics education.” Among these features (and stereotypes), the role that mathematics plays in the system of school subjects, the characteristics of mathematics teacher education, and the importance of talent development are discussed.

Cognitive Science, 2021

The paper addresses the capabilities and limitations of extrafoveal processing during a categoric... more The paper addresses the capabilities and limitations of extrafoveal processing during a categorical visual search. Previous research has established that a target could be identified from the very first or without any saccade, suggesting that extrafoveal perception is necessarily involved. However, the limits in complexity defining the processed information are still not clear. We performed four experiments with a gradual increase of stimuli complexity to determine the role of extrafoveal processing in searching for the categorically defined geometric shape. The series of experiments demonstrated a significant role of extrafoveal processing while searching for simple two‐dimensional shapes and its gradual decrease in a condition with more complicated three‐dimensional shapes. The factors of objects’ spatial orientation and distractor homogeneity significantly influenced both reaction time and the number of saccades required to identify a categorically defined target. An analysis of ...

Signs of Signification

This study explores the coordination of several semiotic presentations in the process of the obje... more This study explores the coordination of several semiotic presentations in the process of the objectification of Cartesian coordinates by first grade children. By means of novel dual eye-tracking technology, I investigated the micro-dynamics of a child’s and her parent’s attentions as they were involved in the teaching-learning process. The analysis of the synchronized data that were retrieved from two eye-trackers and from an external video camera showed ambiguity, not only of verbal terms and visual inscriptions, but also of pointing gestures. It brought out the joint attention moments as crucial for acquiring the culturally adequate meaning of the Cartesian plane. The active disclosure of different presentations’ complementarity determined the moment when the child acquired some meaning, yet not always the cultural one. The joint attention (or the absence of it) allowed the adult to keep track of the understanding that was emerging in the child’s mind, to compare it with her own perception of the cultural representation, and to rectify the child’s perception.

Educational research is often of limited use to designers, as it typically offers descriptions of... more Educational research is often of limited use to designers, as it typically offers descriptions of or explanations for how education was or currently is. In this paper we argue that generalizability is not enough; what deserves more attention is generativity. Designers and educators need actionable knowledge on how education could be. To substantiate the criterion of generativity, we here develop the construct of a design genre—a theory-driven class of designs targeting a particular form of learning. As an example we discuss the evolution of an action-based genre of embodied design through iterative theory-design clarifications. Initially instantiated in the form of activities for promoting the understanding of proportional reasoning, the genre has been elaborated through the process of applying it to additional notions such as parabolas and trigonometry. We argue that this genre was generative for design, theory development, and methodological innovation.

ZDM Mathematics Education, 2020

As technologies that put the body at the center of mathematics learning enter formal and informal... more As technologies that put the body at the center of mathematics learning enter formal and informal learning spaces, we still know little about the teaching methods educators can use to support students' learning with these specialized systems. Drawing on ethnomethodology and conversation analysis (EMCA) and the CoOperative Action framework, we present three multimodal ways that educators can be responsive to learners' embodied ideas and help them transform sensorimotor patterns into mathematically significant perceptions. These techniques include (1) encouraging learners to use gesture to express and reflect on their ideas, (2) presenting multimodal candidate understandings to check comprehension of learners' embodied ideas, and (3) co-constructing multimodally expressed embodied ideas with learners. We demonstrate how these techniques create opportunities for learning and discuss implications for a multimodal, embodied practice of responsive teaching.

International Journal of Child-Computer Interaction

ZDM

Educational Studies in Mathematics

Recent developments in cognitive and educational science highlight the role of the body in learni... more Recent developments in cognitive and educational science highlight the role of the body in learning. Novel digital technologies increasingly facilitate bodily interaction. Aiming for understanding of the body’s role in learning mathematics with technology, we reconsider the instrumental approach from a radical embodied cognitive science perspective. We highlight the complexity of any action regulation, which is performed by a complex dynamic functional system of the body and brain in perception-action loops driven by multilevel intentionality. Unlike mental schemes, functional systems are decentralized and can be extended by artifacts. We introduce the notion of a body-artifact functional system, pointing to the fact that artifacts are included in the perception-action loops of instrumented actions. The theoretical statements of this radical embodied reconsideration of the instrumental approach are illustrated by an empirical example, in which embodied activities led a student to th...

Educational Studies in Mathematics

Learning, Culture and Social Interaction

Vygotsky conceptualized the teaching/learning process as inherently collaborative. We extend prio... more Vygotsky conceptualized the teaching/learning process as inherently collaborative. We extend prior evaluations of this claim by enlisting eye-tacking instruments to monitor the perceptual activity of four teacher-student dyads, as the student solves a challenging manipulation problem designed to ground the scientific notion of parabolas in their new sensorimotor routines. Analyzing each dyad's gaze paths led us to model the teaching/learning process as the emergence and dynamic transformation of intersubjective coupling between the student and tutor perception action systems. While the student's sensory-motor coordination gradually gravitates toward an effective routine, the tutor's perception is iteratively launched from the student's current action, until the tutor detects an optimal moment for verbal intervention. In this micro-zone of proximal development, the student's motor action comes to align with the tutor's cultural-perspective strategy. Our elaboration of the cultural-historical approach to teaching/learning draws on research on joint attention and joint action from the cognitive sciences as well as the embodied design approach from the educational sciences and demonstrates a compatibility of Vygotsky's heritage and complex dynamic systems theory. Finally, we discuss the educational value of the observed student-tutor intersubjective coupling phenomena, thus grounding the contribution of this multidisciplinary study within educational concerns. 1. Overview The objective of this study is to contribute to a better understanding of the teaching/learning process. Our approach is to evaluate and elaborate on Vygotsky's historical assertion that learning is a student and a teacher's irreducibly collaborative achievement, through which the student develops existing naive forms of perceiving and acting on the environment into cultural forms (Vygotsky, 1935/2001). One major challenge of this enduring effort to evaluate Vygotsky's model has been the lack of research instruments for making evident how the student and tutor are perceiving the world as they act upon it. Now, almost a century since Vygotsky first articulated his model, we are equipped with technological instruments and analytic methodology for tracking people's gaze direction at a high sampling frequency and searching for patterns in this sensory activity as they relate to co-performed physical actions. Recent

ZDM Mathematics Education, 2020

Mind, Culture, and Activity, 2019

Given the growing interest in the scaffolding process, it is worthwhile to address competing acco... more Given the growing interest in the scaffolding process, it is worthwhile
to address competing accounts about the origin of this term. The
concept was empirically introduced by Wood, Bruner, and Ross in
1976 and has often been associated with the “zone of proximal development”
in the writing of L.S. Vygotsky. We trace the origins of it in
instances of the term being used by Nikolai Bernstein and Alexander
Luria, as well as in Vygotsky’s notebooks. Our historical search helps to
highlight the theoretical connection between this metaphor and the
teaching/learning versus development opposition, and its relation to
motor control development.

The Russian Journal of Cognitive Science, volume 5, issue 3, pp. 4 - 17, 2018

The paper analyses the advantages and limitations of the current technical solutions for dual eye... more The paper analyses the advantages and limitations of the current technical solutions for dual eye-tracking (DUET) in relation to the research questions from educational science about joint attention in a multimodal teaching/ learning collaboration. The insufficiency of the current systems for the analysis of multimodal collaboration is stated as the reviewed systems do not allow researchers to relate a participant's eye movements to the video from their joint performance and accompanying gestures without time consuming manual coding. We describe a system of two low-cost Pupil-Labs eye-trackers and propose an open source utility DUET for Pupil that automatically produces synchronized gaze data in the shared system of coordinates. The data are available in the form of a video from the surface that is overlaid by gaze paths with supplementary sound waveforms and as textual data with synchronized coordinates of the two gazes. Our empirical evaluation of this technological solution reports 1.27 ° of visual angle as the spatial accuracy of the system after post-hoc calibration. The advantages, limitations, and further possible enhancments of the system are discussed.

Psychology Journal of Higher School of Economics, 2014

In this paper we explore the perceptual actions that allow one to perceive pictures as representi... more In this paper we explore the perceptual actions that allow one to perceive pictures as representing mathematical concepts. The research is based on the cultural–historical approach. Following V.V. Davydov’s ideas on theoretical and, particularly, mathematical thinking, we consider a mathematical concept as being based on a historically determined method of action. Using the eye-tracking system we analyzed the difference between school students, university students, and expert mathematicians in their perception of special pictures (so called ‘external visual representations of the theoretical concept’) when performing a set of tasks, namely choosing a point with given coordinates from a set of points. A standard expert-novice research analysis of dwell time in relevant and irrelevant areas of interest was used. We also compared the gaze paths, the number of visual fixations, and the time each group required to perform the tasks. The directions of the saccades were also analyzed, and our data showed that the vertical and horizontal saccades along the axes prevailed over saccades along other directions, a fact that may be considered as a trace of the ‘Cartesian plane’ concept. The data showed that experts performed the tasks faster and with fewer fixations and they also were able to use additional knowledge flexibly in organizing their perceptive actions. Our results show the fundamental interlacing of conceptual structures and visual processes, in which the latter are organized in accordance with prior knowledge. The specificity of the experts’ Cartesian plane perception corresponds to the late stages of the historical development of this concept. We consider this fact as an empirical confirmation of the relevance of the term “theoretical perception”.

International Group for the Psychology of Mathematics Education, 2014

Learning, Culture, and Social Interaction, 2019

Cognitive Science, 2021

Signs of Signification

ZDM Mathematics Education, 2020

International Journal of Child-Computer Interaction

ZDM

Educational Studies in Mathematics

Learning, Culture and Social Interaction

ZDM Mathematics Education, 2020

Mind, Culture, and Activity, 2019

The Russian Journal of Cognitive Science, volume 5, issue 3, pp. 4 - 17, 2018

Psychology Journal of Higher School of Economics, 2014

Our study concerns the advantages of dual theoretical analysis of teaching-learning processes, fr... more Our study concerns the advantages of dual theoretical analysis of teaching-learning processes, from the Husserlian phenomenological approach and Vygotsky's cultural-historical approach. The paper takes further Radford's 'poetic moment' (Radford, 2010) in merging opposed theoretical perspectives in the study of the emergence of mathematical perception. In particular, the focus of this research is the role of cultural means, namely verbal expressions and gestures, and of the intentionality of a child in the formation of joint attention and of theoretical perception of the Cartesian plane, by first grade children. For the closest possible understanding of the interaction between a child and a parent with gestures and verbal expressions we combine eye-tracking data with synchronised verbal protocols and video material. A unique feature of our research is that we have put two eye-trackers side by side and managed to calibrate two participants at the same monitor, so that they would both look at the same diagram; thus they had actual shared space, as is the case in common teaching processes. They were also able to manipulate a pointer, which allowed natural gesticulation. 5 pairs of a parent and a Grade 1 child participated in the research. The Cartesian coordinates were chosen as material within the zone of proximal development: the first grade children had never met the Cartesian plane before but they were able to solve the tasks with the parent's help. The 'moment' of shared understanding was achieved in each analysed case: we observed situations of joint attention as a crossing of a child's and an adult's gazes. The children were not simply 'following' the already enculturated adult but they were actively accepting and taking hold of the 'invitation' of culture themselves. Hence we tracked close encounters of the phenomenon of joint attention, as linked to the intersubjective, original intentional synthesis of the learner's intentionality (Husserl, 1970) and the adult's cultural practice. (Vygotsky, 2004). Thus, the analysis from the Husserlian phenomenological approach and Vygotsky's cultural historical approach demonstrated the dialectical synthesis of personal intentionality and cultural practice, and it accentuated their interplay as a principal source of learning.