MINISTRY OF EDUCATION OF THE REPUBLIC OF BELARUS
EDUCATIONAL ESTABLISHMENT "BELARUSIAN STATE
PEDAGOGICAL UNIVERSITY NAMED AFTER MAXIM TANK "
FOREIGN LANGUAGES DEPARTMENT
ACQUAINTANCE WITH GEOMETRY AS ONE OF THE MAIN GOALS OF TEACHINGMATHEMATICS TO
PRESCHOOL CHILDREN
Executedby:
studentof magistracy department
YuliaАndreevna Dunai
(tel.: 8-029-3468595)
ScientificSupervisor:
Professor
Doctorof pedagogical science,
I.V.Zhitko
EnglishSupervisor:
Doctorof Psychology
AssociateProfessor
N.G. Olovnikova
Minsk, 2009
CONTENTS
INTRODUCTION
I. HISTORICAL PATTERNS AND PERSPECTIVES OF TEACHINGMATHEMATICS IN PRIMARY SCHOOL
II. THE PURPOSES AND CONTENT OF MODERNMATHEMATICAL EDUCATION IN PRIMARY SCHOOL
III. THE METHODS OF CHILD'S ACQUAINTANCE WITHGEOMETRIC SHAPES
CONCLUSION
CONTENTS
REFERENCES
INTRODUCTION
Young children "do"math spontaneously in their lives and in their play. Mathe-matical learning foryoung children is much more than the traditional counting and arithmeticskills. It includes a variety of mathematical sections of among which the important place belongs to geometry. We've allseen preschoolers exploring shapes and patterns, drawing and creating geometricdesigns, taking joy in recognizing and naming specific shapes they see. This isgeometry - an area of ​​mathematics that is one of the most natural and fun foryoung children.
Geometry is the study ofshapes, both flat and three dimensional, and their relationships in space.
Preschooland kindergarten children can learn much from playing with blocks,manipulatives (Jensen and О'Neil), different but ordinary objects (Julie Sarama, Douglas H. Clements),boxes, snacks and meal (Ellen Booth Church). Also card games, computer games,board games, and others all help children learn geometry.
Thisproblem is relevant because the geometrical concepts should be formed since earlychildhood. Geometrical concepts help children to perceive the world. Also itwill provide future success in academic achievement: as the rudiments,children learn in primary school, from the basis for further learning ofgeometry. Game methods help children tounderstand some complex phenomena in geometry. They also are necessaryfor the development of emotionally-positive attitudes and interest to themathematics and geometry.
I. HISTORICAL PATTERNS ANDPERSPECTIVES OF TEACHING MATHEMATICS IN PRIMARY SCHOOL
Throughout history,mathematical concepts and systems have been developed in response to real-lifeproblems. For example, the zero, which was invented by the Babylonians around700 В.С, by the Mayans about 400 ad, and by the Hindus about 800 ad, was firstused to fill a column of numbers in which there were none desired. For example,an 8 and a 3 next to each other is 83; but if you want the number to read 803and you put something between the 8 and 3 (other than empty space), it is morelikely to be read accurately (Baroody, 1987). When it comes to counting,tallying, or thinking about numerical quantity in general, the human physiologicalfact of ten fingers and ten toes has led in all mathematical cultures to some sort of decimal system.
History'searly focus on applied mathematics is a viewpoint we would do well to remembertoday. A few hundred years ago a university student was considered educated ifhe could use his fingers to do simple operations of arithmetic (Baroody, 1987);now we expect the same of an elementary school child. The amount of mathematicalknowledge expected of children today has become so extensive and complex thatit is easy to forget that solving real-life problems is the ultimate goal ofmathematical learning. The first grad-ers in Suzanne Colvin's classesdemonstrated the effectiveness of lying instruction to meaningful situations.
It'spossible to recall that more than 300 years ago, Comenius pointed out thatyoung children might be taught to count but that it takes longer for them tounderstand what the numbers mean. Today, classroom research such as Su-zanneColvin's demonstrates that young children need to be given meaningfulsituations first and then numbers that represent various components andrelationships within the situations.
The influences of John Lockeand Jean Jacques Rousseau are felt today as well. Locke shared a popular viewof the time that the world was a fixed, mechanical system with a body ofknowledge for all to learn. When he ap-plied this view to education, Lockedescribed the teaching and learning process as writing this world of knowledgeon the blank-slate mind of the child. In this century, Locke's view continuesto be a popular one. It is especially popular in mathematics, where it can bemore easily argued that, at least at the early levels, there is a body ofknowledge for children to learn.
B. F. Skinner, who applied thisview to a philosophy of behaviorism, referred to mathematics as "one ofthe drill subjects. "While Locke recommended entertaining games to teacharithmetic facts, Skinner developed teaching machines and accompanying drills,precursors to today's computerized math drills. One critic of this approach tomathematics learning has said that, while it may be useful for memorizingnumbers such as those in a telephone listing, it has failed to provide apowerful explanation of more complex form: of learning and thinking, such asmemorizing meaningful information or problem solving. This approach has, inparticular, been unable to provide a sound description of the complexitiesinvolved in school learning, like the meaningful learning of the basiccombinations or solving word problems (Baroody, 1987).
Rousseau's views of howchildren learn were quite different, reflecting his preference for naturallearning in a supportive environment. During the late eighteenth century astoday, this view argues for real-life, informal mathematics learning. Whilethis approach is more closely aligned to current thinking about the waychildren learn than is the Locke/Skinner approach, it can have the undesiredeffect of giving children so little guidance that they learn almost nothing atall.
The view that seems mostsuitable for young children is that inspired by cognitive theorists, primary amongthem Jean Piaget. Three types of knowledge were identified by Piaget (Kamii andJoseph, 1989), all of which are needed for understanding mathematics. The firstis physical, or empirical, knowledge, which means being able to relate to thephysical world. For example, before a child can count marbles by dropping theminto a jar, she needs to know how to hold a marble and how it will fall downwardwhen dropped.
The second type of knowledge islogico-mathematical, and concerns relationships as created by the child.Perhaps a young child holds a large red marble in one hand and a small bluemarble in the other. If she simply feels their weight and sees their colors,her knowledge is physical (or empirical). But if she notes the differences andsimilarities between the two, she has mentally created relationships.
The third type of knowledge issocial knowledge, which is arbitrary and designed by people. For example,naming numbers one, two, and three is social knowledge because, in anothersociety, the numbers might be ichi, ni, san or uno, dos, tres. (Keep in mind,however, that the real understanding of what these numbers mean belongs tologico-mathematical knowledge.)
Constance Kamii (Kamii andDeClark, 1985), a Piagetian researcher, has spent many years studying themathematical learning of young children. After analyzing teaching techniques,the views of math educators, and American math text...
