Art education – which engages multiple layers of the personality and keeps intellectual and emotional processes, as well as voluntary and involuntary reactions, in motion – became the subject of increasing research in the 20th century. The concept of visual education has become intertwined with self-expression and the creation of experiences; the need to navigate the increasingly complex everyday elements of visual perception, cognition and communication – which have come to the fore in contrast to verbal expression – has placed the development of visual thinking and creative imagination at the centre of attention (Feuer, 2000; Bodóczky, 2009; Horányi, 2003). The development of visual perception refines observational skills, whilst visual creation provides a means of making one’s individual, inner world visible. Visual education is not merely about drawing, but involves the understanding and active use of visual language; in the process, not only do manual skills develop, but problem-solving, critical thinking and innovative abilities are fundamentally restructured (Tóth 2008; Kárpáti and Gaul, 2011). Consequently, visual education plays a central role in the development of creative thinking.
Visual education is of fundamental importance in the realisation of creative potential; we highlight four areas in particular. These areas are linked to mathematical competence.
1. The foundations of divergent thinking
Creative thinking is not a single, isolated ability, but a complex cognitive (cognitive) system comprising several sub-processes, elements of thought and mental strategies (Pásztor . Creative thinking consists of the rhythmic, successive alternation (known as dynamic oscillation) between these two modes of thinking: divergent (branching) thinking and convergent (focusing) thinking. Divergent thinking enables us to find several different solutions to a problem and to view it from multiple perspectives.
• Artistic tasks rarely offer a single ‘correct’ answer. Through visual arts education, pupils learn how to express the same theme in countless ways and to seek out alternatives.
• Visual creation provides a safe learning environment in which to experiment. In this learning space, a ‘mistake’ is not a failure, but can mark the beginning of a new direction or structure. This develops the ability to take risks.
2. Visual literacy and cognitive flexibility
According to Kepes (1979), visual language is more effective at disseminating knowledge than any other means of communication. The integration of elements of visual culture into our everyday lives has become radicalised as a result of digitalisation. Technological progress not only influences our daily lives but also has a significant impact on the processes of education, assessment and evaluation (Mitra, 2013; Brown, 2005; Csapó, Molnár and R. Tóth, 2008; Jensen, 2003; Duchowski, 2007). Visual education fosters the ability to decode and critically analyse images.
• Non-verbal processing helps to give form to mental images and abstract concepts that are difficult or impossible to express in words.
• Visual education develops the ability to transcend schemata. It enhances one’s repertoire of forms and helps break away from stereotypical modes of representation, which forms the basis for flexible thinking that goes beyond schemata.
3. Problem-solving
Throughout the creative process, from planning to execution, there are constant decision-making situations and technical obstacles. The creative process functions in a very similar way to the design thinking approach and the algorithm used in mathematical problem-solving.
• When a student works out how to turn corrugated cardboard or clay into a three-dimensional structure, they are in fact solving engineering and spatial problems.
• Synaesthesia is typically present in art education; this is particularly characteristic of methodologies based on contemporary art. In synaesthesia, the various senses (touch, sight) and inner intuition are linked to rational decisions.
4. Transfer effects
Visuality acts as a link to other academic disciplines. Visual education is not an isolated subject, but has significant transfer effects on other areas (for example, within the STEAM – Science, Technology, Engineering, Arts, Mathematics – educational model) (Eisner 2002).
• An understanding of geometric shapes, perspective and spatial relationships directly supports mathematical and engineering skills and develops spatial intelligence.
• Visual education also plays a role in developing innovation skills. Design thinking is based on combining visual aesthetics with function, which is the most important element of modern product development.
The Guilford–Torrance model of creative thinking in visual education
We align the exercises and tasks of this methodology with the structure of creative thinking, as well as with mathematical abilities and domains, and match them accordingly. When measuring or developing creative thinking, we examine the following four core abilities:
• Fluency (Smoothness / Abundance of Ideas): The ability to generate a certain number of ideas or answers within a given time frame.
• Flexibility: The ability to switch between categories. A flexible thinker does not get stuck on a single approach. (For example, if we ask about ways to use a brick, and the student says: to build a house, to build a fence, to build a pavement – this shows high fluency but low flexibility, because they are all forms of construction. If they say: ‘to use as a paperweight, to crack nuts with it, to prop open a door’ – that shows greater flexibility, because these are completely different categories).
• Originality (Uniqueness): The ability to generate ideas that are statistically rare, unusual and unconventional. The idea that no one else in the group had thought of.
• Elaboration (Detailed Development): Refining the details of the basic idea, developing it in rich detail and structuring it. It is this ability that enables a working prototype, a finished painting or a precise mathematical derivation to emerge from a flash of genius.
In addition to the four basic elements, further higher-level cognitive components and mental mechanisms are also required for creative thinking to function:
• Problem sensitivity (Problem Finding): The ability to identify shortcomings, errors or opportunities for improvement even where others believe ‘everything is fine’.
• Re-definition: Breaking away from the familiar functions of known objects, concepts or mathematical formulas (overcoming functional rigidity) and placing them in a completely new context.
• Remote associations: Linking areas, pieces of information or images that appear to be completely unrelated.
Visual education and mathematics intersect directly in that both operate within the following structure: from problem recognition (how to represent space / how to model a process) through brainstorming (fluency, flexibility) to precise, elegant elaboration (elaboration) (Gaul, Szepesi, 2025). The connection between visual education and creative thinking in mathematics is deep and bidirectional. Cognitive research and modern pedagogy demonstrate that both fields utilise the same brain structures and mental processes. (Boaler, Munson, Williams, 2017; Tokuhama-Espinosa, 2010; Blakemore, Frith, 2005; Csépe, 2006; Csapó, 2003)
We are developing the methodology for the 14–16 age group, when young people reach a milestone in their cognitive development: according to Jean Piaget’s theory, the formal operational stage stabilises by this point. This means that pupils are now able to think in abstract terms, formulate hypotheses and understand systemic relationships.
At this age, the transfer effects between visual education and mathematics no longer manifest merely at the level of basic skills (e.g. measuring with a ruler), but develop into high-level cognitive strategies.
At this age, visual education is neither fine-motor development nor aesthetic education, but rather a visual laboratory. The essence of the transfer effect is that the abstract, dry system of symbols in mathematics becomes visible, manipulable and emotionally accessible through visual culture or art lessons. A pupil who understands structures visually does not simply memorise formulas in maths lessons, but can see the path leading to the solution.
The visual methodology is linked, on the one hand, to areas of creative thinking and, on the other, to mathematical competence and content. We examined several areas of competence, on the basis of which we selected our points of connection (Kónya, Kovács, 2009; OECD 2022). Below, we list the most characteristic areas for which we are developing the visual methodology.
1. Spatial Reasoning
The ability to visualise and manipulate internal, mental images is essential for mathematical creativity – particularly in geometry, topology and complex calculus. This is the most direct and most extensively researched area of transfer. Abstract geometric concepts become tangible experiences in the art room.
The essence of mathematical competence: recognising the properties of spatial figures, mental rotation (imagining the rotation of shapes), identifying views and projections, and plane and spatial transformations (reflection, translation, scaling).
Link to visual arts education:
• Mental rotation: When a pupil designs a three-dimensional clay sculpture or creates a perspective drawing in a visual arts lesson, they are using precisely the same spatial rotation and transformation skills required for the creative solution of spatial geometry problems.
• Sense of proportion and changes of scale: Cropping images, scaling up or down, and applying the golden ratio in practice teach the logic of mathematical pairs of ratios and fractions.
Examples:
• Perspective and axonometry: Linear perspective (the representation of spaces with one, two or three vanishing points) is essentially the projection of a 3D coordinate system onto a 2D plane.
• Sculpting (modelling with clay, making models): When a pupil creates a sculpture, they constantly switch between different viewpoints (plan view, front view, side view). This activity directly develops mental rotation, which is essential for solving spatial geometry problems.
• Origami (paper folding): Three-dimensional shapes are constructed from flat sheets of paper. When unfolded, the fold lines reveal complex geometric networks, axes of symmetry and angle bisectors.
2. Pattern recognition, the logic of functions and algebraic competence
Mathematics is, in essence, the science of patterns and relationships. The visual arts are also based on patterns (rhythm, repetition, symmetry). The essence of algebra lies in recognising patterns and expressing them in abstract form. Visual rhythm serves as a gateway to this. In the first years of secondary school, transformations (shift, stretch) of mathematical functions (linear, quadratic, periodic, e.g. sine) are central topics.
The essence of mathematical competence: recognising patterns and sequences, continuing them, understanding periodicity (repetition), and the transformations of functions.
Connection to visual education:
• Perception of structure: Visual education teaches pupils to see the underlying geometric structures behind complex visual scenes (e.g. breaking down the human body into cylinders and spheres). This kind of abstract thinking is crucial in mathematical modelling, where reality must be reduced to equations.
• Fractals and tessellations: The prints of Maurits Cornelis Escher or Islamic decorative art (mosaics, coverings) are perfect examples of where visual creativity and advanced mathematical group theory are completely intertwined.
• Understanding the principles of visual rhythm, densification, thinning and repetition provides a direct analogy for the behaviour of functions. When pupils understand how the undulation of a graphic pattern creates dynamism, they intuitively connect this to the mathematical logic of trigonometric or exponential changes.
Examples:
• Sequences and rhythm: Folk motifs, textile design and the creation of mandalas are based on strict algorithms (e.g. two blue triangles are followed by a red circle, after which the pattern is mirrored). This is a clear visual equivalent of mathematical sequences and algorithmic thinking.
• Tessellation (plane tiling): Following the example of M. C. Escher, pupils design shapes that cover the plane seamlessly and without overlap (like tiling). To do this, they must apply – even unconsciously – the sum of the interior angles of polygons and the logic of group theory.
3. Proportions, measurement and numerical skills
In the visual arts, mathematical pairs of proportions almost always underpin harmony and aesthetics.
The essence of mathematical competence: understanding fractions, pairs of ratios, changes in scale (reduction, enlargement), the ability to estimate, and the practical application of units of measurement.
Links to visual arts education:
• Proportions and scale: Measuring the proportions of the human body, the golden ratio, reduction and enlargement, perspective, comparisons
• Measurement and accuracy: Proficiency in using tools, spatial modelling
• Numerical competences: Patterns and rhythm, colour mixing and fractions.
• Digital art: The use of pixels, resolutions and coordinate systems in digital drawing programmes.
Examples:
• Proportional freehand drawing (e.g. still life, portrait): Pupils use their pencils as measuring tools to calculate ‘visual fractions’: ‘How many times does the length of the head fit into the full body?’, ‘Is the width of the vase half its height?’. This is an intuitive, experiential understanding of divisibility and proportionality.
• The golden ratio and composition: Classical rules of composition (the rule of thirds, the golden ratio) are linked to the Fibonacci sequence and the ratio systems of irrational numbers.
• Design and packaging design: Designing the flat-pack pattern for a box requires measurements accurate to the millimetre, surface area calculations and estimates of material requirements.
4. Non-linguistic (visual) problem-solving, mathematical modelling and the ability to think abstractly
Mathematical creativity does not mean the mechanical application of formulas, but rather the search for new ways to solve a problem.
The essence of mathematical competence lies in: problem sensitivity, identifying key points, abstraction, translating a real-life situation into mathematical language, and then placing the resulting solution back into its context. The most important aim of modern mathematics is to be able to strip down the chaotic problems of reality to clear models (equations, graphs). Non-verbal, or visual, problem-solving is a fundamental mathematical competence in which thinking takes place through images, shapes and spatial relationships rather than words. It helps us to quickly grasp complex relationships and find solutions to problems with the aid of drawings, models or mental images. (Csíkos, Szitányi, Kelemen, 2010; Arnheim 1979)
Link to visual education:
• Visual representation: Drawings that schematically model mathematical quantities and relationships play an important role in the mental processes accompanying mathematical problem-solving. This is particularly significant for pupils who learn using visual learning strategies when solving word problems.
• Recognising structures: Visual thinking is a fundamental pillar of rule-making and rule-following.
• Abstraction: The ability to transform real objects into simple symbols and shapes forms the basis for geometric constructions and for solving problems based on real-world situations.
• Visual proofs: Many mathematical theorems (such as the Pythagorean theorem) are much easier to understand and can be developed more creatively through visual diagrams and the manipulation of areas than by purely algebraic means.
• The ‘thinking hand’ principle: During creative activities, pupils experiment with material properties (e.g. how to create load-bearing structures by folding paper – origami). This kind of experimental visualisation can be directly applied to formulating and testing mathematical conjectures.
Examples:
• Visual abstraction: When pupils study and apply 20th-century abstract art (e.g. the Bauhaus, Malevich or Mondrian), they learn to strip back the complex visual reality to pure colours, lines and basic geometric shapes. This ability to distil the essence is exactly the same as what a mathematician does when they filter out unnecessary information from a word problem and write down the pure equation.
• Digital and parametric design (vector graphics): In modern digital drawings, shapes are not drawn freehand but are constructed using mathematical curves (Bézier curves), unions and intersections (Boolean operations on shapes). This is a direct, interactive laboratory for set theory and coordinate geometry.
• Geometric abstraction (Kandinsky method): Pupils must depict a story or an emotion (e.g. ‘a tense argument’ or ‘a peaceful Sunday’) using only geometric shapes (circles, triangles, parallel and perpendicular lines) and colours. This develops an understanding of the dynamics of shapes.
Tünde Simon
Hungarian University of Fine Arts