Modeling learning and teaching interaction by a map with vanishing denominators: Fixed points stability and bifurcations

Merlone, Ugo; Panchuk, Anastasiia; Geert, Paul van

doi:10.1016/j.chaos.2019.06.008

Cited by 9 publications

(5 citation statements)

References 30 publications

(47 reference statements)

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“…The dynamics of these processes have been amply discussed in earlier publications [20,21]. A detailed study of the properties of a dynamic systems model based on Vygotskyan principles of learning reveals a rich landscape of possible outcomes (for a mathematical analysis, see [22]).…”

Section: Figurementioning

confidence: 99%

Some thoughts on dynamic systems modeling of L2 learning

Geert

2023

Front. Phys.

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The aim of this article is to present a very basic dynamic systems model of L2 learning based on a number of basic principles 1) at any moment in time, a learner’s L2 proficiency is a distribution of potentialities (possible levels of L2 production), 2) the distribution changes as a result of experienced L2-events such as conversations, 3) L2 proficiency and L2 events are represented on the same underlying array of linguistic proficiency (from 0, i.e., inexistent, to 1, i.e., maximal under the currently available linguistic resources); 4) learning processes are “normative” in the sense that they are governed by a process of convergence on the language spoken by a particular L2 community, this process depends on an optimum between familiarity and novelty; 5) the parameters governing the systems dynamic differ among individual learners and L2 learning contexts (e.g., highly adaptive versus non-adaptive communicative interactions with native L2 speakers).

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Section: Figurementioning

confidence: 99%

Some thoughts on dynamic systems modeling of L2 learning

Geert

2023

Front. Phys.

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“…Iterative functions, such as those formalized by logistic equations, have proven particularly useful for modeling the dynamics of such phenomena as personality development (Nowak et al, 2005), language development ( van Geert, 1991), cognitive development ( van Geert, 1998), talent development (Den Hartigh et al, 2018Den Hartigh, van Dijk et al, 2016), and social development (Steenbeek & van Geert, 2008). Relatedly, differential equations and difference equations have made it possible to model many psychological phenomena in areas such as motor coordination (Haken et al, 1985), visual perception (Fajen & Warren, 2003;Warren, 2006), emotions (Hoeksma et al, 2007), interpersonal relationships (Gottman et al, 2002;Steele et al, 2013), and learning-teaching interaction (Merlone et al, 2019).…”

Section: Formally Modeling Intrinsic Dynamics and Their Signaturesmentioning

confidence: 99%

How the Complexity of Psychological Processes Reframes the Issue of Reproducibility in Psychological Science

Gernigon

Hartigh

Vallacher

et al. 2023

Perspect Psychol Sci

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In the past decade, various recommendations have been published to enhance the methodological rigor and publication standards in psychological science. However, adhering to these recommendations may have limited impact on the reproducibility of causal effects as long as psychological phenomena continue to be viewed as decomposable into separate and additive statistical structures of causal relationships. In this article, we show that (a) psychological phenomena are patterns emerging from nondecomposable and nonisolable complex processes that obey idiosyncratic nonlinear dynamics, (b) these processual features jeopardize the chances of standard reproducibility of statistical results, and (c) these features call on researchers to reconsider what can and should be reproduced, that is, the psychological processes per se, and the signatures of their complexity and dynamics. Accordingly, we argue for a greater consideration of process causality of psychological phenomena reflected by key properties of complex dynamical systems (CDSs). This implies developing and testing formal models of psychological dynamics, which can be implemented by computer simulation. The scope of the CDS paradigm and its convergences with other paradigms are discussed regarding the reproducibility issue. Ironically, the CDS approach could account for both reproducibility and nonreproducibility of the statistical effects usually sought in mainstream psychological science.

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“…High school ideological and political classrooms should pay full attention to the students' personalized hobbies and constantly encourage students to actively integrate into the classroom atmosphere so as to cultivate their interest in accepting new knowledge and correct learning attitude and then gradually develop into independent learning, independent construction of knowledge system of new skills [1][2][3]. Civics teachers should take active means to guide students to develop positive interaction between students, clarify the difference and internal correlation between moral education and theoretical knowledge, and pay attention to the cultivation of students' independent thinking and independent learning ability so that students can learn new knowledge independently and autonomously under the active guidance of teachers [4][5]. From the perspective of psychology, interaction is reflected in the thoughts, psychology and behavior of teachers and students with each other for the enhancement and exchange of their feelings [6].…”

Section: Introductionmentioning

confidence: 99%

Using Game Theory to Analyze the Interaction between Teachers and Students in the Teaching of Civics in College Courses

Yin

2023

Applied Mathematics and Nonlinear Sciences

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In this paper, firstly, on the basis of Marx’s theory of intersubjectivity, we use the concept of teachers and students as the main body of each other to construct the interactive teaching mode and mechanism of teachers and students in Civics courses and actively explore the path and prospect of interactive teaching of Civics in courses in the new era. Then we use the pure strategy game in game theory to determine the performance production function, and then we use Nash equilibrium to obtain the teacher utility function and student utility function on the basis of the performance production function so as to further construct the game model of teacher-student behavior in the teaching process of Civics courses, and analyze the teacher-student interaction in the Civics of higher education courses by using the game model. The results show that in the pure strategy game analysis of teacher-student behavior, 0.3872 teachers will choose to reduce teaching inputs, while the other 0.6128 teachers will choose to reduce teaching inputs to “almost no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”. The optimal choice strategy is “no reduction in instructional inputs”. In the Nash equilibrium analysis of teacher-student behavior, the equilibrium value of the teacher-student behavior game is (42.22% and 64.59%), and teachers and students need to continuously improve their behavioral strategy choices in order to achieve the maximum utility value of each other. This study improves the quality of teaching and ultimately achieves the objective of Civic Education.

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Modeling learning and teaching interaction by a map with vanishing denominators: Fixed points stability and bifurcations

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Cited by 9 publications

References 30 publications

Some thoughts on dynamic systems modeling of L2 learning

Some thoughts on dynamic systems modeling of L2 learning

How the Complexity of Psychological Processes Reframes the Issue of Reproducibility in Psychological Science

Using Game Theory to Analyze the Interaction between Teachers and Students in the Teaching of Civics in College Courses

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