Mathematics and pre-school children
Development of mathematic notions and mathematics thinking starts much before enrolment in school. In the first years of life, children explore space and numbers in its environment. They learn that some things fall, roll, and some not. They learn about big and small. They learn to share on equal parts. They notice that someone get more or less then them etc.
Unlike the verbal development, beginnings of mathematics development very often is unseen by parents and educators because of prejudicing that mathematics is learned only in school – if we do not write numbers we do not learn mathematics. The truth is that before writing numbers, child gain notions about the world and its objects based on multiplex experience. They are the base of mathematic intuition that parents and educators can and should encourage. Mathematics in pre-school education contributes to intellectual development of child, to development of creative potential and to development of child personality as whole. It is the tool for development of thinking. It enables the child for symbolic presentation of reality, which is foundation for logical-mathematical thinking. Although the possibilities of pre-school child are very limited for development of mathematic notions, since without development of notion conservation (around year 6) there is no real mathematical thinking, and none of mathematical notions could be develop fully, that should not influence intensive work on development of logical-mathematical thinking at this age. With development and enrichment of children pre-school experience and thinking, we create good and necessary base for development of abstract thinking on later stage. Process of abstraction and speculative extraction of object attributes from the object itself that is also happening at this age is extremely important for development of mathematical concepts. The task of mathematic in pre-school education is not to gain mathematical knowledge, but to use mathematic content to encourage development of logical-mathematical structures, which are in the phase of intensive development in that age.
How we learn mathematics?
Mathematic education goes parallel with other segments of child development. It goes parallel with familiarizing with objects and appearances they are surrounded with, development of speech, familiarizing with social relations, sport education.
First mathematic notions could be formed only with practical and cognitive activities of the child itself. Child has to pass through the process of practical and manipulative activities with concrete objects, the process through which child experience properties of objects (colour, shape, size, type, purpose, type of material etc.), perceive similarities and differences among them and do the practical activities of grouping, classification, association and sequencing.
Only through the number of activities, first on practical, and later on cognitive level with usage of work sheets, the child will understand that the number does not depend on the shape, size or distribution of objects in space. It is the fact that picture can never replace child practical manipulative activities and relations that child of this age experience through direct relation with the object. Usage of picture has to be based on the rich experience with concrete objects. She is transition from concrete to abstract, from practical to conceptual thinking.
Manipulating with various objects and materials, child gradually perceive that different objects has common properties. Naturally, only manipulative activities would leave the child on lower phase of development if we do not encourage verbalisation. With verbalisation of activities we step up upper types of cognition. Word encourage process of generalisation. Children remember better the names of objects and their characteristic if during the manipulation they use speech. Content and abet for learning, at pre-school age, need to be find in the life context of children themselves, family, kindergarten. Activities need to be develop in the context that has sense for children, for which they are personally interested, and which are not artificially created and imposed to them as mathematical knowledge they have to accept.
Educators have to be models of mathematic thinking and to pay attention on mathematical characteristic and relations that the children themselves would not notice.
Naturally and spontaneously introducing mathematical symbols and terminology they will help children to notice mathematical characteristic, as well as the way of collecting necessary information about objects, relations and events in space and time in their environment. Educators should encourage the child to do the cognitive strain. Possible questions for that are: What do you think? How would you solve that? Do you have an idea? Why? How? What would be if…? What will be when…?
When math is done in a relaxed way, a child develops into a curious and interested mathematician.
Integration of mathematic in daily schedule of kindergartens
Mathematics can and should be integrated in daily schedule in kindergartens. The life in kindergarten gives many samples for concrete mathematic experiences. Time when children arrive in kindergarten, making records for present and absent children, breakfast, playing time, making diary etc. All of it is concrete mathematic experiences, of course, if educator sees them as such and use for development of mathematical notions at children.
Hanging the clothe can give a sample for correspondence one to one, the same as breakfast (one child-one plate-one chair). Making evidence about present and absent children is connected with numbering and calculating. Being in the yard is connected with physical activities of child. Rhythmic movement of the body connected with the number (each step or each kicking of the ball – one number etc.) contributes to the importance of the meaning of each number. Mechanical numbering and identification of numbers do not have any sense without this concrete experience. Keeping weekly diaries about the weather gives possibility for calculation of the number of sunny and cloudy days etc.
Mathematic practice in three kindergartens
Although there is numerous samples for integration of mathematic in daily schedule of kindergartens and activity centres, it depends on educators awareness if he/she is going to use it. Partial answer on this question gives a mini research conducted couple years ago in three kindergartens in Zenica town (Bosnia and Herzegovina). Partial answer because the sample is small! Still, the results call for thinking!
Educators were asked to extract all activities they consider contribute development of mathematic notions, and which they conduct during the period of 3 months. Here is what they did!
In younger group it was mainly grouping of objects from their surrounding and naming the shapes, but without comparison. As they did not do comparing of sets with 3 elements, it was not possible to do adoption of notions “equal” and “more-less”.
In the middle group the work was based on sets and comparing of objects according high and size, whereas other properties were neglected. Geometric shapes (ball and square), are only named without spotting and comparison of properties.
Although orientation in time and space was not evidenced from educator’s side, it is to believe that it happen in everyday communication, but not on deliberate level of educators.
Older group of children was not familiar with the notion subset, nor they were given possibilities to work with work sheets which contribute transition from practical to the conceptual thinking. Since they named geometric figures, mainly without analyse and description, they worked as in younger and middle group, only on developing academical skills of memorizing and reproduction. They did not work on abetment of further phase of child development, logical-mathematic thinking.
Activities in block centre rarely happen. In younger group only 2 times during three months, in older group 5 times, and never in the middle group! Block centre enable children, by making its own structures, to experience mathematical and geometrical relations on intuitive level, that make foundation on which abstract algebra concept and pure mathematic would be built. Centre for manipulative games, and also the table for sand and water, that gives most possibilities for gaining mathematical concepts, was also rarely used.
Experiences from these three kindergartens tell us about absence of educators awareness for overall presence of mathematic and about its roll in child development. If opposite, they would integrated mathematic in kindergarten’s daily schedule, and also in activity centres. There are possibilities that some activities were conducted in centres, but educators do not connect them with development of mathematical notions. Absence of that awareness deprive possibilities that educators find contents and abets for teaching in the life context of children themselves and kindergartens. That is very important, as activities need to happen in the context that have sense for children, for which they show interest, not in the ones that are created artificially and imposed as mathematic knowledge they have to adopt.
It could be said that realisation of mathematic context, in these kindergartens, is abandon to accident, and that is why it does not have efficiency as designed and planned support to the children to construct and awake certain mathematic concepts.
Still, it is to believe that positive samples exist. Here we think on educators who have conscience about overall presence of mathematic, who have knowledge about developing possibilities and needs of the pre-school children, who use their creativity to conduct mathematic on relaxed and child acceptable way, and on that way they contribute to the development of logical-mathematical structures which are, at the pre-school children, in the phase of intensive development and who support child to become interested and curious mathematician.
Hansen, K., Kaaufmann, R. K., Walsh, K. B. (2000). Creating the classrooms in which child have central roll, 3-6 years. Sarajevo: Centre for educative initiative «Step by Step»
Polonssky, L., Freedman, D., Lessher, S., Morrison, K. (2002) Math for the youngest ones. Beograd
Group of authors. (2000). Step by step 2. Beograd: Creative centre
Marendi?, Z. (1998). Mathematic on pre-school age: magazine Family and child no.3