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Digital Games and Mathematics Learning pp 175–200Cite as

Mathematics and Educational Psychology: Construction of Learning Environments

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Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 4))

Abstract

When primary school children learn mathematics, highly complex phenomena occur. These phenomena have been studied in various disciplinary contexts and are organized in a complex and interdisciplinary synthesis, of which references can be found within the evolution of neurosciences, and the psychology of learning as well as experimental psychology. These disciplines are all valuable resources to refer to when researching and experimenting ways to create, plan and realize mathematics learning environments. Particularly for mathematics, these environments aim to facilitate the process of abstraction, stimulate the capacities and abilities that are necessary when entering the realm of mathematics, understand its characteristics, develop and make it possible to develop the skills required to be able to master its language and its uses, and, above all, the motivation to learn. Video games, if conveniently used, can represent learning environments. This essay proposes some reflections that are the result of research and experimentation based on the prerequisites described here. The central focus is mathematics, its prerogatives, and thought and action in teaching when it is integrated with the exploration of simulation games and video games, which are an integral part of a digital native’s daily life. Just as mathematics is embedded in real-life, art, and science, so are the laws of learning hidden in actions, thought and emotions. With careful observation of children playing video games, it was possible to discover a combination of abilities and skills which are made explicit and are described in this essay.

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Notes

  1. 1.

    Compared to Devlin (2005), p. 13.

  2. 2.

    Little more than half a century has passed since then, and the fact that these affirmations can still be applied to present-day students, leads one to wonder about the effectiveness of educational psychology research on the mathematics teaching-learning process.

  3. 3.

    Bruno D’Amore (1999) proposes an analysis of possible interpretations of mathematics teaching by moving in the direction of a theory of teaching mathematics itself.

  4. 4.

    Compared to previous paragraph.

  5. 5.

    Interesting applications of this research can be found in special teaching methods; in particular as an example of integrating the various disciplines (mathematics, psychology, neurosciences, teaching, anthropology). It could be interesting to consult the text by Biancardi et al. (2003), Franco Angeli, Milano.

  6. 6.

    With reference to the course Teaching mathematics for integration that the author holds at the Faculty of Primary Education Sciences at l’Università di L’Aquila for future, special education teachers who must plan individual courses for children with special needs. The aims of the course can be summed up as follows: to provide a program which integrates mathematical knowledge with disciplinary and pedagogical knowledge in mathematics, which can be applied to the principal difficulties in learning and various disabilities; to help teachers acquire a methodology which includes designing, planning, implementing, testing and evaluating mathematics teaching programs, characterized by a process of abstraction, representation and formalization with reference to a logical-mathematical language; and to cultivate an open attitude towards the mathematics teaching- learning process, by getting teachers to experience standard situations that follow the principles of graduality and transcoding, thus helping create learning environments for special needs cases and their teachers.

  7. 7.

    Mentioned here are some examples referring to themes that have already been intentionally implemented, which guide the process of didactic decision and the organization of the teaching-learning process: multiple intelligences diffusion; self-efficacy; the ego-states, the stimuli and psychology games in class; growth models; the attachment model.

  8. 8.

    In this regard compare <http://www.eatanews.org/wp-content/uploads/2012/09/ethics-code-feb-13th-edit.pdf>.

  9. 9.

    In this context, ‘pattern’ refers to Piaget’s use of the term. See Liverta Sempio (1998, p. 150).

  10. 10.

    An important program was left by the International Commission for the Study and Improvement of Mathematics Teaching (in French CIEAEM, Commission Internationale pour l’Etude et l’Amélioration de l’Enseignement des Mathématiques), founded in 1950, among whose members were the mathematician, educationalist and philosopher, Caleb Gattegno, from the University of London, the French mathematician Gustave Choquet (President) and the Swiss Jean Piaget (Vice-President), psychologist and epistemologist. Using updated teaching methods they attempted to establish a connection between three fields of knowledge which, at that time, were evolving rapidly, in the hope that this would contribute to, “creating a society where people would be able to use mathematical reasoning and its tools to act rationally and develop a capacity for critical thinking, both as citizens and future scientists. Such a humanistic perspective in mathematics education should have been a safeguard against both technocratic behaviour and ideological blindness” (50 anni di CIEAEM: dove siamo e dove andiamo? Manifesto 2000 per l’anno della matematica) (Fregola 2010a, p. 13).

  11. 11.

    Transactional Analysis (TA) is a humanistic-existential branch of psychology, introduced by Eric Berne in the 1950s–1960s. TA is a psychological and social theory based on the philosophy of mutual wellbeing and on a construct that involves studying three ego states of the personality, each of which is defined by Berne as a coherent system of thoughts, feelings and behaviours. The ego states are not roles; they are psychological and phenomenological realities. In every person there are three ego states that are defined as Parent, Child and Adult, which are recognizable according to distinct types of behaviour. Transaction is the unit of social exchange in communication that takes place between people’s ego states. The phenomena that emerge in the process of interaction can be read, partly recognized, and acted on with greater awareness and intention, thus leading to a more effective exchange based on the principle of expressing oneself in the best way possible when relating to another. The effectiveness of TA in education and learning is the subject of substantial research (Montuschi 1993, 1997; Fregola 2011). See also: <http://issuu.com/mathetica/docs/semestrale0>.

  12. 12.

    Research protocol can be found here: <www.mathetica.it>.

  13. 13.

    As regards to the content of this paragraph, it is worth noting Laura di Giovanni’s unpublished thesis: Videogames and learning environments, written for the Primary Education Sciences degree course (2010–2011).

  14. 14.

    In the introduction to their book, Pensare in Matematica, Isdrael and Millán Gasca (2012), write: “…teaching base concepts in elementary form requires mastering their subtleties and the countless difficulties that have been addressed over centuries of reflection and elaboration. What is directly taught to children may seem like nothing much in terms of the amount of concepts and methods used, but the clarity and effectiveness of the teaching comes from a background of in-depth understanding that, even though it remains behind the scenes, plays a decisive role”.

  15. 15.

    It is interesting observing that the Anglo-Saxon neologism edutainment is a fusion of the two words ‘educational’ and ‘entertainment’, and expresses the fundamental principle of video games that can enable learning through playing.

  16. 16.

    To study this interesting new field more deeply, compared to Aarseth (2001).

  17. 17.

    The Latin word Agon is the spirit of competition; Alea indicates the game of dice. The players are completely passive in that victory is only a matter of destiny; there is no ability skill, patience, or training involved. Mimicry (the mimicry of insects) for the author, this can be found in man’s love of disguising himself, dressing up, wearing a mask, and playing a part. Games involving illusion or an imaginary aspect come under this category. Ilinx is the last type of games which are based on the quest for a sense of vertigo.

  18. 18.

    Compared to Marrone (2009).

  19. 19.

    Some games have been included in an interesting paper Nesler (2007).

  20. 20.

    See, for example: < http://www.matematicamente.it/giochi_e_gare/gioca_con_la_matematica/lupo_e_lepre%3A_calcolo_mentale_rapido,_7%2B_anni_200804113058/>.

  21. 21.

    This refers, in particular, to the variables identified by Bloom (1972, 1979), when setting out his theory of scholastic learning: cognitive input capacities, affective characteristics and quality of education. The quality of education is the variable that is closely linked to teaching skills, which allow the teacher to contribute to and encourage learning by using the input variables and the capacity to analyze and plan the teaching.

  22. 22.

    Compared to Footnote 7.

  23. 23.

    Compared to Gagné (1973), from p. 193.

  24. 24.

    Compared to Gagné (1973), from p. 210.

  25. 25.

    Compared to Gagné (1973), from p. 249.

  26. 26.

    Compared to Gagné (1973), from p. 257.

  27. 27.

    A relevant contribution has been provided by Laura Di Giovanni and da Maria Eledia Mangia. The idea and the initial findings come from observations I made while watching my sons playing video games.

  28. 28.

    In this context, Frame of Reference is seen from a Transactional Analysis point of view. It is a construct introduced by Jaqui Schiff, written up by Viene, which is defined as a structure of associated responses that integrate the different ego states in response to specific stimuli. It provides a person with a perceptive, conceptual, affective system, as well as one of action, and is used to define the Self, Others, the World … the perception of the self that is learned.

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Authors and Affiliations

  1. Faculty of Primary Education, L’Aquila University, L’Aquila, Italy

    Cesare Fregola

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  1. Cesare Fregola
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Editors and Affiliations

  1. Faculty of Edu, Sci, Tech & Math, University of Canberra, Canberra, Aust Capital Terr, Australia

    Tom Lowrie

  2. Faculty of Edu, Sci, Tech & Math, University of Canberra, Canberra, Australia

    Robyn Jorgensen (Zevenbergen)

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Fregola, C. (2015). Mathematics and Educational Psychology: Construction of Learning Environments. In: Lowrie, T., Jorgensen (Zevenbergen), R. (eds) Digital Games and Mathematics Learning. Mathematics Education in the Digital Era, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9517-3_10

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