In this article, I explored child’s mathematical thinking. I presented the development of this kind of thinking and the child’s play. Mathematical literacy is a part of a child since his birth. He slowly realizes that there are many things that can be counted or arranged by property. The child is in the prenumerical phase at that point. He likes to handle specific objects and discovers the world through them. He helps himself with graphic representations and also uses symbols. Around at the age of five the child already counts. All this happens in a mathematically stimulating environment prepared by the teacher in the kindergarten. She carefully equips the corners with interesting toys and places math in spontaneous or guided activities through the day. At the same time, she never forgets the child’s developmental stage, his abilities and, last but not least,his desires.
Key words: preschool child, mathematics, prenumerical period, development of counting.
The baby is like na unlisted sheet of paper at birth. He can develop his skills in a sufficiently stimulating environment. We adults are the ones who can strongly influence what the child will develop with appropriate stimulations. The stimulus isn’t necessarily the best toy or didactic aid, it is enough that the activity is adjusted in such a way to stimulate constructive thought processes in the child. Therefore, I can firmly say that the environment plays a very big role in a child’s learning. However, an important factor – heredity – cannot be ignored. ”What a child brings into the world” is the steel foundation on which a child builds his knowledge and develops his abilities. Mathematical abilities are classified as cognitive abilities which a child in the kindergarten will actively acquire through play and use them on a daily basis in school, and they will condition the child’s learning success. Therefore, it’s very important to pay attention to the development of mathematical thinking and problem solving in preschool.
Mathematical thinking in preschool and tools to encourage its development
Several different experts have studied the development of mathematical thinking in a child over the years. Piaget claims that a child trains this kind of thinking only through active handling of objects, that is, through research. He says we need to allow the child’s thinking to develop spontaneously and we have to wait. Bruner says it isn’t necessary to wait for the child ‘s readiness, but we can influence his development earlier and thus accelerate it. Vygotsky claims that teaching a child should be a step ahead of his stage of development. So, the child’s mathematical tasks shouldn’t be too easy and yet not too difficult, but in the area of his development (Lipovec and Antolin Drešar, 2019).
Mathematical contents in kindergarten are involved in planned and spontaneous activities. We first introduce them in activities based on a specific level, such as sorting cubes, differentation by size, observing shapes in place, playing shop…We increase the level of learning mathematics to a pictorial level, where we use various pictures, drawings, signs…Before entering school, we can already use symbolic level of learning. When there is a graphic representation of a certain number, for example, two drawn strawberries, we give the child a symbol of number 2 (Bohinc, 2014).
The child goes first through the prenumerical period phase. He observes, sorts and edits. He must acquire numerical concepts realted to quantity, develop relationships between the concepts of numbers and place mathematical thinking in different aspects of everyday life (Lipovec and Antolin Drešar, 2019). The forerunner of counting is therefore the perception of mathematics and numbers in specific situations. The child doesn’t count yet, but he perceives syllabels in the word, ticking the clock, notices that many things can be counted, such as, days of the week, months, fingers… (Ferbar, 1990).
Picture 1. Classifying by size
The child arranges and sorts very early. He first arranges the scattered things in the bin, later he sorts them according to a certain property. Therefore, the child urgently needs a crefully designed place that draws him to this type of activity. There have to be pots, boxes, shelves, drawers available…Such an environment is much more transparent and motivating for the child. The child can upgrade his knowledge of sorting and arranging through graphic representations (Kroflič idr, 2001).
Picture 2: Recording the presence of the children (the child is in kindergrten/ the child isn’t in kindergarten)
One of the interesting areas of mathematics is also geometry. There are many objects in the playroom, that remnid us of bodies and figures, such as clock on the wall, a calendar, cubes, different shapes of tables (Kroflič idr, 2001).
Picture 3. Sorting figures
The child needs the name of an individual group of objects, only then he will be able to compare and classify them. The activities of specific handling of objects can be taken to an even higher level and thus define their position (Kroflič idr, 2001).
Picture 4. Arranging coloured balls into sequences
The child doesn’t learn words to describe situations spontaneously, he needs someone to be his role model. When a child is looking for a certain toy, let’s not just say ”it’s there”. Let’s define its position with ”left of the table”, ”next to the table”, ”at the table”…The child learns to perceive perspective and orientation in space. When learning to measure, we offer the toddler various substances, such as sand, water, plasticine, salt dough…In this way, he will find out that all these things can be measured and also counted (Kroflič idr, 2001).
Different experts have researched how the concept of counting develops in a child. When the child counts things, he first uses his fingers, because they are always available. They also count objects by touching them (Manfreda Kolar, 2006).
Picture 5: Placemats in handbags marked with figures (eg: square – square table)
Only when the following four principles are fullfilled in a child, we can say that the process of correct counting has been established. This happens to a child at the age of five.
- When counting, the toddler doesn’t omit any numbers. The child is aware if this principle before the age of 3.
- The child always counts in the same order. 3-years-olds also have this ability.
- The child realizes that the number he pronounces is a property of the set.
- He is aware that the sequence of counted elements doesn’t change the final number of the set. The child becomes aware of the latter principle at about the age of five (Ferbar, 1990).
Picture 6. Counting autumn leaves
If we want to offer a child the best we can, we must first understand his development, his needs, identify strengths and weakness and build on them. Kindergarten education is child-centered education. It is necessary first to established a genuine personal contact with the toddler and gain his trust. Only then he wil be ready for work. He needs to be motivated through the game to think mathematically. A well-designed environment – a playroom that offers a variety of game options,is very important in promoting mathematical thinking. There must be different construction toys, puzzles, picture dominoes, board games…Personally, I have got a lot of ideas for making my own mathematical aids using various sources. However, learning and playing doesn’t end in the playroom. It’s also necessary to explore the outer world with the child. It offers us endless ideas for connecting mathematical content with the environment. Together with the child we can count cars, observe colours in nature, connect traffic signs with figures, determine the symmetry of butterfly wings, pay attention to the sequences of days of the week and months of the year… We can prepare the child for tomorrow. We give him interesting games he is experiencing today and connecting with the memories he got yesterday.
- Bohinc, A. (2014). Matematično znanje predšolskih otrok pred vstopom v šolo. Diplomsko delo, Ljubljana: Univerza v Ljubljani, Pedagoška fakulteta.
- Ferbar, Janez. (1990). Štetje. Novo mesto: Pedagoška obzorja.
- Lipovec, A., in Antolin Drešar, D. (2019) Matematika v predšolskem obdobju. Maribor: Univerza v Mariboru, Pedagoška fakulteta. https://www.dlib.si/details/URN:NBN:SI:DOC-9YIVXHGM
- Kroflič, R., Marjanovič Umek, L., Videmšek, M., Kovač, M., Kranjc, S., Saksida, I., idr. (2001). Otrok v vrtcu: Priročnik h kurikulu za vrtce. Ljubljana: Obzorja.
- Manfreda Kolar, V. (2006). Razvoj pojma število pri predšolskem otroku. Ljubljana: Pedagoška fakulteta.