99. Emerging Researchers' Group (for presentation at Emerging Researchers' Conference)
Paper
The Effect of Visual Reasoning on Arithmetic Word Problem Solving
Ana-Maria Purcar1, Mușata-Dacia Bocoș2, Alexandra-Lucia Pop3
1Babeș-Bolyai University, Romania; 2Babeș-Bolyai University, Romania; 3College of Tourism Services “Napoca”
Presenting Author: Purcar, Ana-Maria
Problem-solving is an important part of the primary school mathematics curriculum. The purpose of problem-solving activities in the classroom is to apply abstract mathematical concepts to real-world situations. (Verschaffel et. al, 2000; Mellone, et. al, 2014) Riley et. al (1983) described the conceptual knowledge required to solve simple addition or subtraction word problems in terms of semantic relations residing between quantitative information existing in problem text: compare, combine and change.
For primary school pupils, comprehending word problems at the early stages of learning to read, is a difficult task. Despite their lack of understanding, some pupils still engage in the solving process, employing arbitrary strategies, such as randomly combining numbers existing in the problem into mathematical operations suggested by specific keywords in the problem i.e. “more” for addition and “less” for subtraction (Schoenfeld, 1991).
Research on mathematical reasoning evidenced that mental representations of abstract mathematical concepts appear to be visual, originating in one's visually sensed experiences. (Bishop, 1989) Arcavi (2003) described visualization as the ability, process and product of creation, interpretation, use and reflection upon pictures, images, and diagrams in our minds or paper or with other technological means to describe and communicate information, develop thinking, and advance understanding of new ideas. Dreyfus (1991) described visual reasoning in mathematics as a process of expressing verbal information in concrete visual representations that illustrate the relationships between mathematical expressions and concepts. By advancing the use of visual reasoning in mathematics learning, comprehension is translated into one's ability to use the given information to solve problems. (Mayer, 1989)
To improve pupils' problem-solving abilities, recent studies explored different methods of facilitating the understanding of mathematical relations in word problems. In his research, Glenberg et al. (2012) improved elementary school pupils' problem-solving performance by having them physically manipulate objects that recreated the problem situation, which supported forming accurate mental representations of the relations between quantitative information in the problem. Dewolf et. al (2017) investigated the effect of representational illustrations that accompanied problematic word problems in solving process, expecting to help pupils mentally imagine the situation and solve the problems more realistically by employing everyday life knowledge. The findings evidenced no positive effect on realistic problem-solving.
Research question/ hypothesis
The current study investigates the effect of visual reasoning on the solving process of a mathematical word problem which involves part-whole relations between sets of elements. To test our hypothesis, we worked on word problems commonly encountered in the first-grade mathematics curriculum, which required addition and subtraction operations to determine the problem solution. We also aimed to investigate and describe the correlation between students' reading comprehension abilities and their visual and mathematical reasoning performances.
We expect that visual reasoning will help pupils form accurate mental representations of the mathematical relations in the problem, improving their comprehension of the problem situation and increasing the number of correct problem solutions afterwards.
- Is it possible to improve first-graders' word problem comprehension by asking them to create visual representations of the problem situation by drawing?
- Will the number of correct problem solutions increase if pupils create correct visual representations of the problem situation, by drawing?
- Will pupils with average reading comprehension abilities create accurate visual representations of the problem situation, by drawing and determining the correct problem solution afterwards?
We hypothesized that asking first-grade pupils to create visual representations of the problem situation by drawing will improve comprehension, determining an increased number of correct problem solutions.
We also predicted that pupils with average reading comprehension abilities would create correct visual representations of the problem situation leading them to perform the appropriate operations to determine the correct problem solution.
Methodology, Methods, Research Instruments or Sources UsedDesign: quasi-experiment, one group pretest-post-test.
Participants: 45 first-grade pupils (22 boys and 23 girls) with ages of 7 and 8 years old (mean age 7.13). The pupils belonged to two first-grade classes from the same urban primary school in Cluj-Napoca, Romania. The pupils were assigned to each class randomly, following the Romanian class formation legislation in 2021.
At the beginning of the experiment, pupil's mathematics performances and reading comprehension abilities (RCA) were globally assessed by their teacher, by completing an individual form. The individual mathematical abilities (IMP) ranged from very good (= 27 participants, 15 boys and 12 girls), good (= 10 participants, 2 boys and 8 girls); sufficient (= 6 participants, 4 boys and 2 girls), to insufficient (= 2 participants, 1 male and 1 female). The reading comprehension abilities ranged from 1 (poor) to 5 (high) as follows: 1 (= 5 participants, 3 boys and 2 girls), 2 (= 3 participants, 1 boy and 2 girls), 3 (= 8 participants, 3 boys and 2 girls), 4 (= 16 participants, 8 boys and 8 girls), to 5 (= 13 participants, 7 boys and 6 girls).
The participants were tested in two different contexts:
In normal context, pupils received the following word problem, containing compare and combine semantic relations between sets of objects, in an individual paper-and-pencil task during a usual mathematics class: Radu has 3 pencils, and Tudor has 4 more pencils than Radu. How many pencils do children have altogether? The problem was read aloud once by the teacher. Pupils were instructed to read the problem again and solve it independently, writing down the solution procedure and the answer on paper.
In visual context, a similar word problem was given during another regular mathematics class: 5 frogs are sitting on a water lily leaf and 3 less frogs are sitting on the leaf nearby. How many frogs are sitting on the lily leaves altogether?
The problem was written on the board and read aloud once, by the teacher. The pupils were instructed to individually read and illustrate the problem situation by drawing, following the information in the problem statement. Afterwards, they were required to perform the mathematical operations and determine the numerical solution of the problem, on the back of the page.
Conclusions, Expected Outcomes or FindingsProblem solutions and visual representations were categorised as follows::
Correct Problem Solution (= CPS): participants determined the number of elements required by the problem statement, performing one or two operations;
Solution Error (= SE/ pSE): participants only performed subtraction 5–3=2 (=partial solution error, pSE) or provided other numeric solution than CPS;
No Answer (= N/A)
Correct Visual Representation (= CVR): accurate illustration of numeric information and of the relations between the two sets of elements;
Representation Error (= RE): incorrectly illustrates the sets of elements that must be combined to determine the whole value.
In normal context, we assumed that understanding the problem situation was associated with the amount of CPS. Solving problems in visual context revealed increased comprehension of the problem situation, reflected by the amount of CVR. Data analysis in SPSS revealed a significant correlation (p=0.044<0.05) between the problem solutions determined in normal context and the problem solutions determined in visual context. Findings evidenced significantly improved problem solutions when pupils solved the problem in visual context compared to problem solutions determined in normal context. Pupils with higher RCA and IMP levels who determined CPS in normal context maintained their performance in visual context. About a third of pupils that provided pSE in normal context, most of them with very good IMP and medium RCA, determined CPS in visual context.
Despite the positive effect of using visual reasoning in solving problems, about half of the participants with CVR couldn’t determine CPS. Participants with CVR who provided SE couldn’t associate mathematical operations required to determine the numeric solution and combined numbers in the problem into a subtraction suggested by the keyword “less”. Therefore, illustrating the problem situation by drawing can be a helpful tool in current teaching practice because of its positive effect on problem comprehension and solving process.
ReferencesArcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241. https://doi.org/10.1023/A:1024312321077
Bishop, A. J. (1988). A review of research on visualization in mathematics education. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference (vol. 1, pp. 170–176). OOK Printing House.
Dewolf, T., Dooren, W., & Verschaffel, L. (2017). Can visual aids in representational illustrations help pupils to solve mathematical word problems more realistically? European Journal of Psychology of Education, 32(3), 335–351. https://doi.org/10.1007/s10212-016-0308-7
Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 1, 33-48.
Glenberg, A., Willford, J., Gibson, B., Goldberg, A., & Zhu, X. (2012). Improving Reading to Improve Math. Scientific Studies of Reading, 16(4), 316–340. 10.1080/10888438.2011.564245
Riley, M. S., Greeno, J. G., & Heller, I. J. (1983). Development of Children’s Problem-Solving Ability in Arithmetic. In H. P. Ginsburg (Ed.), The Development of Mathematical Thinking (pp. 153–196). Academic Press.
Mayer, R. E. (1989). Models for Understanding. Review of Educational Research, 59(1), 43–64. https://doi.org/10.3102/00346543059001043
Mellone, M., Verschaffel, L., & Van Dooren, W. (2014). Making sense of word problems: The effect of rewording and dyadic interaction. In P. Liljedahl, S. Oesterle, C. Nicol & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 4, (pp. 201‒208). https://www.pmena.org/pmenaproceedings/PMENA%2036%20PME%2038%2020
14%20Proceedings%20Vol%204.pdf
Schoenfeld, A. H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311–343). Lawrence Erlbaum Associates.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets and Zeitlinger.
99. Emerging Researchers' Group (for presentation at Emerging Researchers' Conference)
Paper
The Amsterdam Model of Learning Environments (AMOLE) – A conceptual approach for linking pedagogy and architecture
Michelle Laux
University of Ed. Freiburg, Germany
Presenting Author: Laux, Michelle
The question of how an optimal learning environment should be designed is probably as old as the building task itself. It has always been and continues to be a reflection of constantly changing educational, social, and technological conditions. Despite the small field of research, the scientific debate on the subject has gained attention since its beginnings in the 1920s, especially in the past decade. The fact that physical space can influence learning has already been proven several times (e.g. Rance et al., 2023; Baloch et al. 2021; Barrett et al., 2015; Walden, 2008). However, there is still no theoretical model that takes a holistic view of the architectural aspects of a learning environment and at the same time addresses current research and school development.
Today, we are faced with a fundamentally changed pedagogical understanding, even if some demands in this respect were already made at the beginning of the 20th century by the New Education Movement (Renz, 2016). Findings from educational research have influenced teaching methods and goals of education in the last decades: Lessons should include different social forms, be skills-oriented, and take individualised learning into account (Saalfrank, 2017; Corno, 2008; Helmke, 2007; Weinert, 2001). In addition, the role of schools has changed since the Emotional Turn in the 1990s, meaning the topic of well-being is receiving increasing attention (Hascher & Balloid, 2000). This also raises the question of social responsibility: to what extent can schools respond to the challenges of our time, such as inclusion, division of society, strengthening democracy, and the climate crisis? In addition to these pedagogical and social demands, however, there are also changing technological and construction-specific conditions (digitalization, climate-neutral buildings, resource conservation, etc.), which on the one hand call for increased responsibility, but also open up opportunities to find answers for the school building question.
In construction practice, this is usually based on the orientation of positive examples and building guidelines, but also increasingly through participation processes in which, for example, teachers and pupils are involved in the concept planning (Montag Stiftungen Jugend und Gesellschaft, 2017). Although this is fundamentally a positive development, it is also associated with the problem that this approach is tailored to the personal needs of individual groups at a specific point in time and therefore does not represent the whole. To date, an orientation towards Evidenced Based Design in (school) construction is hardly common (Hamilton & Watskin, 2009), which is due on the one hand to the common professional practice of architects, but also to the small field of research. Even here, the presentation of positive examples takes up a large space, and empirical research methods are still only used sporadically. What is more, the knowledge that has already been gained is seldom bundled and prepared for practical use – as a result, there is hardly any scientific communication. In addition to the problem of the very limited number of studies, there is also little cooperation between the various scientific disciplines, which means that architecture, educational science, and architectural psychology (which is generally underrepresented) usually act separately from each other.
This results in the need for an interdisciplinary approach that, on the one hand, maps the different aspects of a learning environment as comprehensively as possible and, at the same time, takes current pedagogical, social, and technological developments into account. It raises the question of how architectural-psychological and pedagogical requirements of the school learning environment can be mapped in a theoretical model – and thus serves as a basis for empirical research, as a planning aid, and for the evaluation of school buildings.
Methodology, Methods, Research Instruments or Sources UsedIn the course of a metatheoretical reorientation in empirical social research, a plea is made for multiple modes of representation that place theories and conceptual models consequently in the centre of attention (Renkl, 2022; Dreier, 2013). To present the complex relationships between teaching/learning and architectural psychology coherently, a multi-layered theoretical model has been designed as follows:
Initially, innovative new and existing school buildings (N=42), mainly in the Netherlands, but also in Germany, and Austria were inspected using the environmental psychology observation method Casual Observation with the purpose “to inform the direction of a possible future study“ (Sussman, 2016, p.13) to obtain a practical, up-to-date approach to the topic. In addition, a literature review was carried out, focusing on conceptual models for the built (learning) environment (Preiser, 1983; Vischer, 2005; Walden, 2008; Gifford, 2014; Barrett et al., 2015; Seidel, 2023). While being flexible to be applied to different typologies that are currently being pursued (e.g. classroom plus, cluster, learning studio), social changes that are already increasingly being integrated into current pedagogy (inclusion, digitalization, sustainability, etc.) are mapped with an architectural reference on a theoretical level. As the model focuses on environmental psychology, the central concepts of privacy, personal space, territory, crowding (Altman, 1975), and environmental control (Walden, 2008) are taken into account.
This systematic analysis is followed by a conceptualisation of the new model in terms of content and graphics (although the visualisation cannot be attached here, it will form the basis of the explanation during the presentation). Subsequently, a literature review is now being conducted to re-examine each of the aspects of the model in terms of their organisation into sub-groups and the current state of research from different perspectives (environmental psychology, architecture, and teaching/learning research). Finally, based on this analysis, hypotheses about correlations within the model will be formulated.
Conclusions, Expected Outcomes or FindingsThe literature review has shown that no model exists to date that takes pedagogical, architectural, and environmental psychological aspects into account and can be applied to new learning environments at the same time. Taking into account the fragmented nature of previous research, the aim was to develop a basic theoretical framework that would allow for the elaboration of interrelationships: The AMOLE is divided into two main areas: On the left are the General Requirements, including Basic, Physical, and Aesthetical Aspects – i.e. components that every type of building should fulfill. On the right are the Specific Requirements, including Functional and Pedagogical Aspects – i.e. aspects that are particularly relevant to learning environments. Both areas are not strictly separated but must be considered with flowing transitions. At the same time, the individual components of the aspects influence each other (size/openness, for example, significantly determines acoustics). The different zones of a learning environment with their Transition Requirements (Activity Setting, School Building, School Grounds, Neighborhood) represent the question of how connections are created – spatially and in terms of cooperation. All in all, the areas are enclosed by the Ethical Requirements, thus: What is the message that a school should send in terms of social issues (inclusion, diversity, sustainability)?
Focusing on Environmental Psychology, the presented model aims to provide a foundation for practice and research upon which further work can be built. It does not claim to be complete but provides a framework for development. As a next step, it could serve as a basis for a generally applicable Post-Occupancy Evaluation (POE) survey tool. In addition, the model may be used in the future to look more closely at individual areas, such as those of Educational Aspects to derive recommendations in the sense of an Evidenced Based Design.
ReferencesAltman, I. (1975). The Environment and Social Behavior. Privacy, Personal Space, Territory, Crowding. Books/Cole Publishing Company.
Baloch, R. M., Maesano, C. N., Christofferson, J., Mandin, C., Csobod, E., De Oliviera Fernandes, E., Annesi-Maesano, I. (2021). Daylight and School Performance in European Schoolchildren. International Journal of Environmental Research and Public Health, 18, 258.
Barrett, P., Fay, D., Zhang, Y., Barrett, L. (2015). The impact of classroom design on pupils’ learning: Final results of a holistic, multi-level analysis. Building and Environment 89, 118–133.
Corno, L. (2008). On Teaching Adaptively. Educational Psychologist, 43(3), 161–173.
Dreier, V. (2013). Modelle, Theorien und empirische Daten. zum Beitrag der modernen Wissenschaftstheorie für eine metatheoretische Neuorientierung in der empirischen Sozialforschung. Zeitschrift für Theoretische Soziologie 1, 116–134.
Gifford, R. (2014). Environmental Psychology: Principles and Practice (5th Edition). Optimal Books.
Hamilton, D. K. & Watskin, D. H. (2009). Evidence-based Design for Multiple Building Types. John Wiley & Sons.
Hascher, T., Balloid, J. (2000). Auf der Suche nach dem Wohlbefinden in der Schule. Schweizer Schule, 87(3), 3–12.
Helmke, A. (2007). Was wissen wir über guten Unterricht? Wissenschaftliche Erkenntnisse zur Unterrichtsforschung und Konsequenzen für die Unterrichtsentwicklung. Bildung. koeln.de/imperia/md/content/selbst_schule/downloads/andreas_helmke_.pdf
Montag Stiftungen Jugend und Gesellschaft (2017). Schulen planen und bauen 2.0. (2. Aufl.). Jovis.
Preiser, W. F. E. (1983). The hability framework: a conceptual approach towards linking human behaviour and physical environment. Design Studies 4(2), 84–91.
Rance, G., Dowell, R. C. & Tomlin, D. (2023). The effect of classroom environment on literacy development. npj Science of Learning, 8(9).
Renz, K. (2016). Testfall der Moderne. Transfer und Diskurs im Schulbau der 1950er Jahre. Wasmuth.
Renkl, A. (2022). Meta-analyses as a privileged information source for informing teachers’ practice? Zeitschrift für Pädagogische Psychologie 36(4), 217–231.
Saalfrank, W.‐T. (2012). Differenzierung. In E. Kiel (Hrsg.), Unterricht sehen, analysieren, gestalten (2. Aufl.). UTB GmbH.
Seidel, O. (2023). Anforderungen an ein Schulgebäude. Lernräume – Arbeitsräume – Lebensräume. Klett Kallmeyer.
Sussman, R. (2016). Observational Methods: The First Step in Science. In R. Gifford (Ed.), Research Methods for Environmental Psychology (pp.9–28). John Wiley & Sons.
Vischer, J. C. (2005) Space meets status: Designing workplace performance. Taylor and Francis/ Routledge.
Walden, R. (2008). Architekturpsychologie: Schule, Hochschule und Bürogebäude der Zukunft. Pabst Science Publishers.
Weinert, F. E. (2001) (Ed.). Leistungsmessungen in Schulen. Beltz
99. Emerging Researchers' Group (for presentation at Emerging Researchers' Conference)
Paper
In the Sign of Dialogue. Traces of Creativity Teaching in Primary School
Sofia Marina Antoniello
University of Padova, Italy
Presenting Author: Antoniello, Sofia Marina
The development of creative skills (UNESCO, 2006) appears to be one of the most urgent challenges in today's complex (Morin, 2017) and 'fluid' (Bauman, 2007) society, characterized by uncertainty and instability. This is because creativity is not an adaptive response to needs and difficulties but an exactive (Vrba & Gould, 1982) opportunity to be in relation to the context. In fact, the concept of creativity has multiple definitions: it is a performative skill, a transformative process (Edwards, Grandini & Forman, 2017; Munari, 2017; Rodari, 2010), an improvisational attitude (Zorzi, 2020), a generative capacity (Tiozzo Brasiola, 2020), a political condition and a dimension of complex thinking (Lipman, 2005). Moreover, creativity is a higher psychic function present in all human beings since childhood (Vygotsky, 2010) and a process historically and culturally mediated. Creativity is a necessary educational condition to imagine otherness, to think in terms of differences, and to welcome the thought of the other (Santi, 2006a) to nurture open and democratic societies. Hence, schools are in charge of cultivating it, so that it becomes a different opportunity to relate with others and with the world.
If and how can creativity be taught? In the Italian language, the word "teach" comes from the Latin word "insignare" and means to put things into signs, to leave a mark. According to Peirce (1980), sign is a dialogical relationship between three semiotic entities: object, representamen and interpreter. The transition between them occurs through a creative mediation, which is possible only when the sign participates in the nature of thought. For this reason, creative mediation allows signs to always have other interpretations thus inserting them into a process of unlimited semiosis. What results is the generativity of the sign through thought. In this sense, sign, like creativity, is also uncertain, indefinite, never completely clear. As a result, teaching creativity understood as putting creativity into signs can only involve the dimension of thought.
According to Lipman (1988, 2005), creativity is one of the dimensions of complex thinking that can be finds expression in Philosophy for Children (P4C), an educational practice characterized by the dialogic-argumentative method and the didactic model of the research community (Santi, 2005). In the literature, there are many researches aimed at investigating creative thinking through P4C (De Puig, 2003; Sátiro, 2006, 2019; Santi, 2007), but no studies highlighting the possible link between generativity and creative thinking through signs in the perspective of complex thinking. Therefore, mobilizing generativity as an interpretative model to read an empirical investigation of creativity promoted through P4C can open a new pedagogical and didactic view of what has already been explored. The research aspires to give a generative reading of creativity, as an object of teaching, by investigating the horizon of generative didactics of creativity through PhilosophArt.
PhilosophArt is an educational-didactic practice that aims to generate creativity through art and dialogue in the community, taking into account the complexity of thought. It combines the dialogical-discursive method and the research community of P4C with the realization of community works of art through graphic signs (Kandinsky, 1968, 2005). P4C develops creative, critical and free minds in community members so that they can live in today's complex, unstable and uncertain society.
Methodology, Methods, Research Instruments or Sources UsedThe research questions are:
1. How can the complex thinking approach be reinterpreted through a generative outlook in order to redefine the concept of creativity at school?
2. What is generative creativity didactics?
3. Can PhilosophArt be an educational-didactic activity that moves creative-generative thinking?
3.1 What signs of creative-generative thinking are moved through PhilosophArt?
The research involved the entire school community of a primary school in the Veneto Region, Italy. More specifically, 120 students and 13 teachers. This school was chosen because it is a small public school, located on the outskirts of the city and with a school timetable suitable for hosting a medium-term research project. Furthermore, the teachers decided to join the research by highlighting the urgency of promoting creativity education in their school.
In line with the participants and the research topic, the Participatory Art-Based Research has been chosen for this exploratory study (Barone & Eisner, 2012; Lenette, 2022). The use of arts-based participatory research methods fosters research practices that are more collaborative, creative, and respectful of co-researchers' perspectives (Lenette, 2022).
The research design involves three phases.
The first phase (October 2022) was an exploration of the structural, organizational, and methodological-didactic aspects of the school context. This has been done through a community of inquiry with all teachers in the school. The macro-topics of the focus group refer to an INDIRE questionnaire on creative practices and they concern 1) the concept of creativity, 2) didactics and creativity, and 3) creativity space.
The second step (October 2022-February 2023) of the research was an experimental phase: PhilosofArt sessions were proposed in each classroom of the school.
In the concluding phase (March 2023), we did a community of inquiry with the teachers of the school complex around the macro-topics investigated in phase 1 in the light of the observed PhilosophArt experience and its reflections on everyday teaching.
The collected data were analyzed with the video-analysis software "Transana." The dialogue between the collected data and Kandinsky's theory brought out the meanings the community attributed to the abstract graphic signs used in the PhilosophArt sessions. A possible model of thinking in signs emerged.
Conclusions, Expected Outcomes or FindingsThis research is part of a national and international overview that strongly believes in creativity as the key to 21st-century education (UNESCO, 2006, OCSE, 2022). There are many meanings that psychology and pedagogy have been attributing to creativity for years, but few of them are their educational nuances. On this gap in the literature, the research intends to fit.
The educational and pedagogical value of research on creative and generative thinking in the historical, social and cultural context of today's schools shows how it can be an opportunity to cope with the uncertainty and instability of today's society. In this horizon, PhilosophyArt can be an opportunity to promote creative thinking through its signs. Indeed, in this educational practice, the conceptual indefiniteness of creativity is reflected in all the meanings that are attributed by the community to signs. Signs suggest, invite, evoke something that is never certain, clear and equal for all. This uncertainty that inhabits meaning also encroaches on gesture, on the way of leaving a graphic and verbal trace. In addition, in PhilosophyArt, the cultural diversity of creativity promotes inter-subjective exchange, growth of knowledge and openness to different perspectives also through different languages of communication. Finally, this educational practice fosters the contextual diversity of creativity, as artistic and dialogical signs do not have value in themselves but in relation to others and the world (Lotman, 2022). The questioning of the sign and the discussion about the sign thus create a habit of uncertainty in the community of enquiry.
A school that creates the conditions for creativity to reproduce itself becomes a school that generates different opportunities for all in relation to others, the world, and culture.
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Lipman, M. (1988). Philosophy goes to school. Temple Univ Pe
Lipman, M. (2005). Educare al pensiero. Vita e Pensiero
Lotman, J. M. (2022). Il girotondo delle muse: Semiotica delle arti. Milano: Bompiani
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Santi, M. (2007). How students understand art: a change in children through Philosophy. Childhood & Philosophy, 3, n.5, 19-33
Sátiro, A. (2006). Pensar creativamente. III Seminario Iberoamericano
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Vygotskij, L. (2010). Immaginazione e creatività nell’età infantile. Editori Riuniti university press
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