First grade children and their teachers participate in our research. Teachers participating in the experimental methodological work took part in the testing and implement and comment on the methodological materials. Teachers of the control groups participate only in the testing, they administer the tests, but proceed according to the usual methodologies. The third group teaches using the Chess Palace methodology developed by Judit Polgár.

The number of children of different test groups are the following:

1. 1. The experimental group participating in methodological development N= 443
2. 2. Control group not participating in methodological development N= 300
3. 3. The group studying with the Chess Palace method N= 307

Most of the children solved all the tasks of the test battery, and we got a complete set of indicators for a school-entry sensorimotor and cognitive profile. According to the age distribution, 94.57% of the children participating in the study are 6-7 years old.

Thanks to the competent cooperation of the teachers, we have a rare large database available for further research, in which we examine the development of children starting school. We can create a school-starting profile, which indicates the necessary sensorimotor and cognitive skills needed to acquire school skills.

Table 1 Number of children participating in the testing and number of completed tasks.

Group	Nr. of children	Completed tests	Completed tasks/children
Training	443	12602	28,45
Control	300	8317	27,72
Chess	307	8776	28,59
Sum	1050	29695	28,28

Table 2 Age of the children participating in the testing

Age	5	6	7	8	9	10	Sum
Children	1	387	606	43	12	1	1050
%	0,10%	36,86%	57,71%	4,10%	1,14%	0,10%	100,00%

Teachers receive statistical and visual feedback about each of the children and classes. We exchange information during joint and individual consultations. By this process we try to ground the data-based teaching. According to our assumption, teachers will be more aware of the data, and that way of their students’ abilities in the next year and when they choose teaching methods from our offer, they consider the development of the class.

The mobile application providing flashcards is ready to use. This is a part of our methodology unit called “Learning with games”. The learning card game is an excellent tool for developing thinking, it helps children succeed in school. Our flashcards contain tasks and questions that support children’s sensorimotor and cognitive development and/or the learning of the school material. Contact link: https://play.google.com/store/apps/developer?id=Tanul%C3%A1si+K%C3%B6rnyezet+Kutat%C3%B3csoport

The most exciting part of our research began on September 1, 2022, the 2-year methodological development in schools. The effect of this can only be shown if the students’ development is followed, examined both at the start and at the end of the development phase. The input testing has been completed at the end of October. Teachers did the testing of 441 students in the 20 developmental classes of the 19 schools undertaking methodological development, and 486 students in the 30 control groups. Plus, teachers using the Chess Palace Polgar Method joined and that way we have another control group using a well-researched method. The teachers examined a total of 1,050 children. The cleaning and aggregation of the received data has begun.

Our HAS-AVCC Learning Environment Research Group submitted its first annual report, which was accepted by the Academy. We have received the next year’s funding and we continue our work.

Here is the short version of the report:

1. Preparation period: 1 September 2021 – 28 February 2022.

The research team consists of 10 people, joined by an internal research team (4 people). This group’s research will focus on teachers’ social and mental characteristics. Our research involved 20 developmental and 21 control classes, and about a thousand first-graders.

2. Teacher preparation period: 1 March 2022 – 31 August 2022

We have developed 17 methodological units in three dimensions (development, spatial organization, and learning organization).

The topics of the methodological units are the following: listening to speech sounds, visualization, singing and music, sensory-motor skills, finger awareness, sayings, rhymes, gestures, relaxation by moving, use of algorithms, use of Mondrian Blocks, Mind Map, board games, and flashcards, free movement opportunities, free learning space, rotating classroom (comfort zone), clear rules, student activity, regular activities, mediated and self-directed learning.

Three-day teacher training was held online and in-person, plus two days, to train for the student testing. Also, detailed written instructions were given to the teachers.

Testing tools: Online Sensory and Cognitive Profile Test (https://kognitivprofil.hu), which can be used by teachers, and the Colour Raven Matrices. Teacher follow-up: Mental Health Test, Aspiration Index, Mini Oldenburg Burnout Questionnaire, Subjective Physical Symptom Scale, and a Socio-economic Status Questionnaire.

Applications: Learning card mobile app; online cognitive training based on Mondrian blocks.

Publication and dissemination of methodological materials:

(Eds.) Halbritter András Albert, Tamáska Máté (2022) Iskolakert, természet és közösség. Szociálpedagógia, 19. thematic issue  – it is entirely related to the work of the HAS-AVCC Learning Environment Research Group

Gyarmathy Éva, Kökényesi Imre (2022) Tapasztalat Alapú tudás I. TaníTani Online, https://www.tani-tani.info/tapasztalat_alapu_tudas_i

Gyarmathy Éva, Kökényesi Imre (2022) Tapasztalat Alapú tudás II. TaníTani Online, https://www.tani-tani.info/tapasztalat_alapu_tudas_ii

Fenyvesi K, Mérő, L., Kökényesi I, Brownell, C., & Stettner, N. (2022) Mondrian Blocks and Cognitive Training. Mondrian 150, Mondrian Day at National Museum of Mathematics, New York, 19 February.PI-Day, 2022.03.14: Transylvanian Maths Festival, School at Gyergyóremete, Apáczai Education and Spectrum Foundation – Digital Mondrian Blocks game with hundreds of schoolchildren. Fenyvesi K, Gyarmathy É., Kökényesi I, Brownell, C., & Stettner, N.; Maths Festival France – Digital games with Mondrian Blocks – by Fenyvesi K., Gyarmathy É., Kökényesi I, Brownell, C., & Stettner, N.; Peruvian Maths Festival – Maths and the Mondrian Blocks – by Fenyvesi K, Gyarmathy, É., Kökényesi I, Brownell, C., & Stettner, N.

Why should the learning environment be changed?

Development produces development. Each discovery leads to more discoveries and increases exponentially the rate of change. In a decade, we are experiencing more changes than people experienced in two centuries around the time of Gutenberg. The environment shapes the human brain, especially the brains of children. It means that with the extreme changes in the environment brain development changes extremely. Consequently, everything related to children’s brains, such as education, needs to change rapidly.

It is a frequent statement that education should prepare children for a future and for occupations we don’t even know about. However, the problem is more complex than that, because we don’t even know what kind of kids we want to prepare for the unknown future.

The nervous system is shaped by the environment and so far there is not much more that educators and specialists did than label a high percentage of children and called them special-need children.

The year 2020 gave a little insight into the future. The 21st century kicked the door with a pair of legs. Digital technology has suddenly become part of everyday teaching and learning. One day the responsible parents limit or even forbid the use of digital devices, the next day the kids have to sit in front of the computers all day. A parent mockingly asked that “does the school period count into the ’machine time’ or not?”

Humankind is facing a special situation which we can call a crisis. And such decision times will become more frequent. New inventions, as well as pandemics, can bring sudden changes. The situation is very much in line with the original meaning of the word „crisis” when the old solutions don’t work anymore, but the new ones are not developed properly, yet. Similar to any special situation, distance learning has widened the gap between those who were already at an advantage and could progress and those who couldn’t.

Stimulus richness increases the appearance of diversity. However, those who are less prepared can hardly gain, so, the differences increase and become significant. Any disadvantage causes an even greater disadvantage in a crisis. People experienced this condensed in 2020 during the restrictions because of the COVID pandemic. While about 10% of the children could progress better at home than in the classroom, the third of the student population, typically disadvantaged students lag significantly behind. Institutions and individuals who were more or less prepared for the 21st century were able to take advantage of the online situation.

Given that the 21st century is bringing explosive change at an ever-accelerating pace, institutions, educators, and parents have to be prepared for children with diverse development and have to provide them flexible learning environment. A methodological renewal is needed.

Mondrian Blocks as a cognitive training tool

“The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together harmoniously. Beauty is the first test: there is no permanent place in this world for ugly mathematics (Godfrey Harold Hardy, A Mathematician’s Apology, London 1941). The Hungarian mathematician Paul Erdős had an imaginary book in which God wrote down the most beautiful mathematical proofs. When Erdős wanted to express his particular appreciation of proof, he shouted, “This one’s from the Book!”.

Mathematics is a basic tool of knowledge and science, while it is an art motivated by beauty, and an integral part of music, dance, fine arts, architecture – patterns, symmetry-asymmetry, golden ratio, polygons, polyhedrons, fractals. Education treats arts and mathematics separately, though mathematics and art both are based on spatial abilities and develop the brain in terms of the most important functions of human thinking: sensorimotor and executive functions, symbolic and abstract thinking.

It is no coincidence that spatial skills are the foundation for later successful cognitive abilities and learning (Lubinski, Benbow, 2006; Wai, Lubinski, Benbow, 2009; Freeman, Marginson, Tytler, 2019).

However, spatial-visual skills, and thus development and learning methods in this area, have still not gained their rightful place in teaching, although there are increasing attempts to do so. Typically, creative activities such as exploring the symmetry of tapestries, cutting geometric shapes, arranging mosaics, mirroring, rotating, and translating pictures link mathematics to the arts in teaching.

Artistic activities develop mathematical and creative thinking, most often with a focus on the creative side. However, teachers do not provide many opportunities for students to think creatively in the practice of teaching mathematics. This is largely due to the highly structured curriculum and math textbooks, which leave little room for such opportunities (Schoevers, Leseman, Kroesbergen, 2020).

The Mondrian Blocks Cognitive Training combines the benefits of mathematics and art by providing systematic developmental material through an art-based mathematical problem. Indeed, the famous, coloured rectangles of the Dutch painter Piet Mondrian form the basis of an interesting mathematical problem, a puzzle, which mathematicians are still trying to solve (e.g. Basen, 2016; Dalfó, Fiol, López, 2021). Mondrian’s mathematical problem consists in dividing a grid of size n x n into rectangles and squares such that the difference between the area of the largest and the area of the smallest rectangle is as small as possible.

The Mondrian Blocks Cognitive Training is based on an art-mathematical problem, and its developmental impact is manifold. Quantities are tangible, and palpable, through the use of rectangles in a mathematically meaningful context, while their place in the given space has to be found. Magnitude and direction relationships, estimation of dimensions, spatial orientation, spatial translation, and recognition of visual shapes are required, while the concept of number is imperceptibly shaped in the mind of a child. Mondrian Blocks tasks are solved through a series of meaningful trials, which in addition to the above develop risk-taking, error detection, failure tolerance, creativity, and critical thinking.

We hypothesize that the basic functions required for mathematics and reasoning can be developed and tested in at least three main cognitive domains by using Mondrian Blocks:

• Sensory-motor function – Spatial orientation; Spatial memory; Eye-hand coordination; Tactile processing; Sequential processing; Processing speed.
• Cold executive functions – Cognitive control; Cognitive flexibility; Working memory; Rotation (spatial working memory); Error detection; Performance monitoring.
• Hot executive functions – Emotional regulation; Reward processing; Delay discounting; Risky decision making.
• Mathematical Thinking – Reasoning; Number concept.

Development and testing are particularly important given the steep increase in the rate of children diagnosed with mathematical difficulties. Research by Agostini, Zoccolotti, and Casagrande (2022) has shown that children with mathematical difficulties are impaired in cognitive areas such as executive functions, attention, and processing speed. The Mondrian Blocks cognitive training may benefit these children more than the average.

The training and testing of relevant cognitive functions can and should be incorporated into models of education and development to identify

• the cognitive functions behind the solution of “Mondrian Blocks” tasks;
• the role of Mondrian Blocks in the development of relevant cognitive skills;
• individual differences which may exist behind effective task solving;
• the ways cognitive training could be the most effective.

References

Agostini F, Zoccolotti P, Casagrande M. (2022) Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature. Brain Sciences. 12(2):239. https://doi.org/10.3390/brainsci12020239

Bassen H. (2016) Further insight into the Mondrian art problem.https://mathpickle.com/mondrian-art-puzzles-solutions/.

Dalfó, C., Fiol, M.A., López, N. (2021). New results for the Mondrian art problem. Discret. Appl. Math., 293, 64-73.

Freeman, B., Marginson, S., Tytler, R. (2019). An international view of STEM education. In: Sahin, A., Mohr-Schroeder, M. J. (eds.) STEM Education 2.0, Brill, 350–366 https://doi.org/10.1163/9789004405400_019

Lubinski, D., Benbow, C. P. (2006). Study of Mathematically Precocious Youth after 35 years: Uncovering antecedents for the development of math–science expertise. Perspectives on Psychological Science, 1, 316–345.

Schechter, B. (2000). My brain is open: The mathematical journeys of Paul Erdős. New York: Simon & Schuster. pp. 70–71. ISBN 0-684-85980-7.

Schoevers, E.M., Leseman, P.P.M., Kroesbergen, E.H. (2020).  Enriching Mathematics Education with Visual Arts: Effects on Elementary School Students’ Ability in Geometry and Visual Arts. Int J of Sci and Math Educ 18, 1613–1634 https://doi.org/10.1007/s10763-019-10018-z

Wai, J., Lubinski, D., Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835. https://doi.org/10.1037/a0016127