Nav: Home

Symmetry, a resource that children spontaneously use to draw the plant world

February 06, 2019

This study shows that children up to the age of 7 spontaneously use symmetry in their drawings to express their knowledge about plant life. In the sample analysed, this is a very frequent strategy and becomes more complex with the education level, as highlighted by the researchers in the Faculty of Education - Bilbao (José Domingo Villarroel and Álvaro Antón) and the Faculty of Science and Technology (María Merino).

"The fact of establishing that, well before the age of 7, children display drawing skills that include the spontaneous depiction of symmetries, should exert a significant influence on infant teaching and learning processes, not only with respect to the sphere of comprehension of biological phenomena but also with respect to the development of geometrical thinking," said the Professor of the Department of Mathematics and Experimental Sciences Didactics, José Domingo Villarroel.

The results of this research have been published in the international scientific journal Symmetry that includes articles on symmetry in Mathematics and in the rest of the sciences. This journal is indexed in the Science Citation Index Expanded (Web of Science) with an impact factor of 1.256.

The research method

Prof Villarroel explains that "a highly significant factor related to teaching and learning processes is about being able to determine the pupils' abilities and knowledge so as to be able to adapt didactic activities to these prior determinants. This is one of the golden rules in education".

In this respect, the lecturer in the same department, Álvaro Antón, points out that "knowing that children spontaneously use symmetry provides an opportunity to explore graphical expression in childhood and use this resource in the teaching activities relating to biological phenomena and geometrical knowledge".

To conduct their analysis the research team worked with a sample of 116 drawings produced by 65 girls and 41 boys from three schools in Pre-primary and Primary Education located in the Uribe-Kosta district in Bizkaia during the 2012-2013 academic year. They were spontaneous drawings, without any knowledge or instructions beforehand relating to symmetry.

The researchers selected plant life as the subject for pictorial expression, a subject that a priori has no apparent link with geometry and symmetry. With the help of a puppet, the children were encouraged to produce a drawing that would explain to the puppet what plants are like, where they live and what is good for them. The individual activity took about ten minutes.

These representations are the ones that were analysed by the research team and they found that the girls and boys used two types of symmetry. As the lecturer in the area of Statistics and Operations Research María Merino explained, "they use cyclic symmetry (which presents rotational symmetry around a central point), for example, when they depict the sun; and dihedral symmetry (which includes both rotational symmetry and reflection symmetry) when depicting the human shape, for example. Of the two, the most common is dihedral symmetry which they use to draw the plant world, people and their environment or decorative elements such as stars or hearts".

At the same time the researchers saw that the complexity in depicting dihedral symmetries is greater than that corresponding to cyclic symmetries, and that at higher levels of education, when children need to express more in-depth knowledge, they also draw more complex symmetrical pictorial items. From the gender perspective, girls use complex symmetries more frequently than boys.

This study is a first step towards finding out the connection existing between children's knowledge about the plant world and the images they produce; the aim is to find out what relationship exists between geometrical thinking and the graphical expression of this thinking. "The study of these connections is hugely interesting, because," asserts Villarroel, "scientific activity is always linked to Mathematics. Scientific thinking is inevitably linked to mathematical thinking and that is why it is important to understand how relations begin to be established during childhood between both types of thinking, that relating to the explanation of biological phenomena and geometry".
-end-
Authors of the research

José Domingo Villarroel holds a PhD from the UPV/EHU and is a lecturer and researcher in the Faculty of Education - Bilbao (UPV/EHU) in the Department of Mathematics and Experimental Sciences Didactics. https://orcid.org/0000-0003-4108-6122

Maria Merino-Maestre holds a PhD from the UPV/EHU and is a lecturer and researcher in the Faculty of Science and Technology (UPV/EHU) in the Department of Applied Mathematics and Statistics and Operations Research.

Álvaro Antón-Baranda holds a PhD in Sciences from the UPV/EHU and is a lecturer and researcher in the Faculty of Education - Bilbao (UPV/EHU) in the Department of Applied Mathematics and Statistics and Operations Research. https://orcid.org/0000-0003-4108-6122

Bibliographical reference

José Domingo Villarroel, María Merino, Álvaro Antón
Symmetrical Motifs in Young Children's Drawings: A Study on Their Representations of Plant Life
Symmetry 2019, 11(1), 26; https://doi.org/10.3390/sym11010026

University of the Basque Country

Related Mathematics Articles:

More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.
How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.
Mathematics supports a new way to classify viruses based on structure
New research supports a structure-based classification system for viruses which could help in the identification and treatment of emerging viruses.
US educators awarded for exemplary teaching in mathematics
Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.
Authors of year's best books in mathematics honored
Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.
The mathematics of coffee extraction: Searching for the ideal brew
Composed of over 1,800 chemical components, coffee is one of the most widely-consumed drinks in the world.
Even physicists are 'afraid' of mathematics
Physicists avoid highly mathematical work despite being trained in advanced mathematics, new research suggests.
Mathematics and music: New perspectives on the connections between these ancient arts
World-leading experts on music and mathematics present insights on the connections between these two ancient arts, especially as they relate to composition and performance, as well as creativity, education, and geometry.
Kindergarteners' mathematics success hinges on preschool skills
In a study funded by the National Science Foundation, researchers at the University of Missouri discovered that preschoolers who better process words associated with numbers and understand the quantities associated with these words are more likely to have success with math when they enter kindergarten.
First international mathematics research institute launched in Australia
World leaders in the mathematical sciences are visiting Melbourne for a series of research programs at Australia's first international research institute for mathematics and statistics.

Related Mathematics Reading:

Best Science Podcasts 2019

We have hand picked the best science podcasts for 2019. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.
Now Playing: TED Radio Hour

Digital Manipulation
Technology has reshaped our lives in amazing ways. But at what cost? This hour, TED speakers reveal how what we see, read, believe — even how we vote — can be manipulated by the technology we use. Guests include journalist Carole Cadwalladr, consumer advocate Finn Myrstad, writer and marketing professor Scott Galloway, behavioral designer Nir Eyal, and computer graphics researcher Doug Roble.
Now Playing: Science for the People

#529 Do You Really Want to Find Out Who's Your Daddy?
At least some of you by now have probably spit into a tube and mailed it off to find out who your closest relatives are, where you might be from, and what terrible diseases might await you. But what exactly did you find out? And what did you give away? In this live panel at Awesome Con we bring in science writer Tina Saey to talk about all her DNA testing, and bioethicist Debra Mathews, to determine whether Tina should have done it at all. Related links: What FamilyTreeDNA sharing genetic data with police means for you Crime solvers embraced...