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Acquaintance with geometry as one of the main goals of teaching mathematics to preschool children

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Раздел: Тарелки

MI IS RY OF EDUCA IO OF HE REPUBLIC OF BELARUS EDUCA IO AL ES ABLISHME “ BELARUSIA S A E PEDAGOGICAL U IVERSI Y AMED AF ER MAXIM A K” FOREIG LA GUAGES DEPAR ME ACQUAI A CE WI H GEOME RY AS O E OF HE MAI GOALSOF EACHI G MA HEMA ICS O PRESCHOOL CHILDRE Execu ed by: s ude of magis racy depar me Yulia А dreev a Du ai ( el.: 8-029-3468595) Scie ific Supervisor: Professor Doc or of pedagogical scie ce, I.V. Zhi ko E glish Supervisor: Doc or of Psychology Associa e Professor . G. Olov ikova Mi sk, 2009 CO E S I RODUC IO I. HIS ORICAL PA ER S A D PERSPEC IVES OF EACHI G MA HEMA ICS I PRIMARY SCHOOL II. HE PURPOSES A D CO E OF MODER MA HEMA ICAL EDUCA IO I PRIMARY SCHOOL III. HE ME HODS OF CHILD’S ACQUAI A CE WI H GEOME RIC SHAPES CO CLUSIO CO E S REFERE CES I RODUC IO You g childre &quo ;do&quo ; ma h spo a eously i heir lives a d i heir play. Ma he­ma ical lear i g for you g childre is much more ha he radi io al cou i g a d ari hme ic skills. I i cludes a varie y of ma hema ical sec io s of amo g which he impor a place belo gs o geome ry. We've all see preschoolers explori g shapes a d pa er s, drawi g a d crea i g geome ric desig s, aki g joy i recog izi g a d ami g specific shapes hey see. his is geome ry — a area of ma hema ics ha is o e of he mos a ural a d fu for you g childre . Geome ry is he s udy of shapes, bo h fla a d hree dime sio al, a d heir rela io ships i space. Preschool a d ki dergar e childre ca lear much from playi g wi h blocks, ma ipula ives (Je se a d О' eil), differe bu ordi ary objec s ( Julie Sarama, Douglas H. Cleme s), boxes, s acks a d meal (Elle Boo h Church). Also card games, compu er games, board games, a d o hers all help childre lear geome ry. his problem is releva because he geome rical co cep s should be formed si ce early childhood. Geome rical co cep s help childre o perceive he world. Also i will provide fu ure success i academic achieveme : as he rudime s , childre lear i primary school, from he basis for fur her lear i g of geome ry. Game me hods help childre o u ders a d some complex phe ome a i geome ry. hey also are ecessary for he developme of emo io ally-posi ive a i udes a d i eres o he ma hema ics a d geome ry. I. HIS ORICAL PA ER S A D PERSPEC IVES OF EACHI G MA HEMA ICS I PRIMARY SCHOOL hroughou his ory, ma hema ical co cep s a d sys ems have bee de­veloped i respo se o real-life problems. For example, he zero, which was i ve ed by he Babylo ia s arou d 700 в.с, by he Maya s abou 400 a.d., a d by he Hi dus abou 800 a.d., was firs used o fill a colum of umbers i which here were o e desired. For example, a 8 a d a 3 ex o each o her is 83; bu if you wa he umber o read 803 a d you pu some hi g be wee he 8 a d 3 (o her ha emp y space), i is more likely o be read accura ely (Baroody, 1987). Whe i comes o cou i g, allyi g, or hi ki g abou umerical qua i y i ge eral, he huma physiological fac of e fi gers a d e oes has led i all ma hema ical cul ures o some sor of decimal sys em. His ory's early focus o applied ma hema ics is a viewpoi we would do well o remember oday.

A few hu dred years ago a u iversi y s ude was co sidered educa ed if he could use his fi gers o do simple opera io s of ari hme ic (Baroody, 1987); ow we expec he same of a eleme ary school child. he amou of ma hema ical k owledge expec ed of childre oday has become so ex e sive a d complex ha i is easy o forge ha solvi g real-life problems is he ul ima e goal of ma hema ical lear i g. he firs grad­ers i Suza e Colvi 's classes demo s ra ed he effec ive ess of lyi g i ­s ruc io o mea i gful si ua io s. I ’s possible o recall ha more ha 300 years ago, Come ius poi ed ou ha you g childre migh be augh o cou bu ha i akes lo ger for hem o u ders a d wha he umbers mea . oday, classroom research such as Su­za e Colvi 's demo s ra es ha you g childre eed o be give mea i g­ful si ua io s firs a d he umbers ha represe various compo e s a d rela io ships wi hi he si ua io s. he i flue ces of Joh Locke a d Jea Jacques Rousseau are fel oday as well. Locke shared a popular view of he ime ha he world was a fixed, mecha ical sys em wi h a body of k owledge for all o lear . Whe he ap­plied his view o educa io , Locke described he eachi g a d lear i g pro­cess as wri i g his world of k owledge o he bla k-sla e mi d of he child. I his ce ury, Locke's view co i ues o be a popular o e. I is especially popular i ma hema ics, where i ca be more easily argued ha , a leas a he early levels, here is a body of k owledge for childre o lear . B. F. Ski er, who applied his view o a philosophy of behaviorism, re­ferred o ma hema ics as &quo ;o e of he drill subjec s.&quo ; While Locke recomme ded e er ai i g games o each ari hme ic fac s, Ski er developed eachi g machi es a d accompa yi g drills, precursors o oday's compu erized ma h drills. O e cri ic of his approach o ma hema ics lear i g has said ha , while i may be useful for memorizi g umbers such as hose i a elepho e lis i g, i has failed o provide a powerful expla a io of more complex form: of lear i g a d hi ki g, such as memorizi g mea i gful i forma io or problem solvi g. his approach has, i par icular, bee u able o provide a sou d descrip io of he complexi ies i volved i school lear i g, like he mea ­i gful lear i g of he basic combi a io s or solvi g word problems (Baroody, 1987). Rousseau's views of how childre lear were qui e differe , reflec i g his prefere ce for a ural lear i g i a suppor ive e viro me . Duri g he la e eigh ee h ce ury as oday, his view argues for real-life, i formal ma hema ­ics lear i g. While his approach is more closely alig ed o curre hi ki g abou he way childre lear ha is he Locke/Ski er approach, i ca have he u desired effec of givi g childre so li le guida ce ha hey lear almos o hi g a all. he view ha seems mos sui able for you g childre is ha i spired by cog i ive heoris s, primary amo g hem Jea Piage . hree ypes of k owledge were ide ified by Piage (Kamii a d Joseph, 1989), all of which are eeded for u ders a di g ma hema ics. he firs is physical, or empirical, k owledge, which mea s bei g able o rela e o he physical world. For example, before a child ca cou marbles by droppi g hem i o a jar, she eeds o k ow how o hold a marble a d how i will fall dow ward whe dropped.

he seco d ype of k owledge is logico-ma hema ical, a d co cer s rela­ io ships as crea ed by he child. Perhaps a you g child holds a large red marble i o e ha d a d a small blue marble i he o her. If she simply feels heir weigh a d sees heir colors, her k owledge is physical (or empirical). Bu if she o es he differe ces a d similari ies be wee he wo, she has me ally crea ed rela io ships. he hird ype of k owledge is social k owledge, which is arbi rary a d desig ed by people. For example, ami g umbers o e, wo, a d hree is social k owledge because, i a o her socie y, he umbers migh be ichi, i, sa or u o, dos, res. (Keep i mi d, however, ha he real u ders a di g of wha hese umbers mea belo gs o logico-ma hema ical k owledge.) Co s a ce Kamii (Kamii a d DeClark, 1985), a Piage ia researcher, has spe ma y years s udyi g he ma hema ical lear i g of you g childre . Af er a alyzi g eachi g ech iques, he views of ma h educa ors, a d Ameri­ca ma h ex books, she has co cluded ha our educa io al sys em of e co fuses hese hree ki ds of k owledge. Educa ors e d o provide childre wi h ple y of ma ipula ives, assumi g ha hey will i er alize ma hema i­cal u ders a di g simply from his physical experie ce. Or educa ors ig ore he ma ipula ives a d focus i s ead o pe cil-a d-paper ac ivi ies aimed a eachi g he ames of umbers a d various ma hema ical erms, assumi g ha his social k owledge will be i er alized as real ma h lear i g. Some­ hi g is missi g from bo h approaches, says Kamii. radi io ally, ma hema ics educa ors have o made he dis i c io amo g he hree ki ds of k owledge a d believe ha ari hme ic mus be i er alized from objec s (as if i were physical k owledge) a d people (as if i were social k owledge). hey overlook he mos impor a par of ari hme ic, which is logico-ma hema ical k owledge. I he Piage ia radi io , Kamii argues ha &quo ;childre should rei ve ari h­me ic.&quo ; O ly by co s ruc i g heir ow k owledge ca childre really u der­s a d ma hema ical co cep s. Whe hey permi childre o lear i his fash­io , adul s may fi d ha hey are i roduci g some co cep s oo early while pu i g o hers off oo lo g. Kamii's research has led her o co clude, as Su­za e Colvi did, ha firs graders E d sub rac io oo difficul . Kamii argues for savi g i u il la er, whe i ca be lear ed quickly a d easily. She also poi s o s udies i which place value is mas ered by abou 50 perce of four h graders a d 23 perce of a group of seco d graders. Ye place value a d regroupi g are regularly expec ed of seco d graders! As a example of wha childre ca do earlier ha expec ed, Kamii (1985) poi s o heir discovery (or rei ve io ) of ega ive umbers, a co ­cep ha does ' eve appear i eleme ary ma h ex books. Based o her experie ces wi h you g childre , Kamii argues ha i is impor a o le chil­dre hi k for hemselves a d i ve heir ow ma hema ical sys ems. Wi h Piage , she believes ha childre will u ders a d much more, developi g a be er cog i ive fou da io as well as self-co fide ce: childre who are co fide will lear more i he lo g ru ha hose who have bee augh i ways ha make hem dis rus heir ow hi k­i g.

A hacker working on some programming language or operating system might likewise be able to get a day job using it. When I say that the answer is for hackers to have day jobs, and work on beautiful software on the side, I'm not proposing this as a new idea. This is what open source hacking is all about. What I'm saying is that open source is probably the right model, because it has been independently confirmed by all the other makers. It seems surprising to me that any employer would be reluctant to let hackers work on open source projects. At Viaweb, we would have been reluctant to hire anyone who didn't. When we interviewed programmers, the main thing we cared about was what kind of software they wrote in their spare time. You can't do anything really well unless you love it, and if you love to hack you'll inevitably be working on projects of your own. Because hackers are makers rather than scientists, the right place to look for metaphors is not in the sciences, but among other kinds of makers. What else can painting teach us about hacking? One thing we can learn, or at least confirm, from the example of painting is how to learn to hack

1. Перевод реферата "Acquaintance with geometry as one of the main goals of teaching mathematics to preschool children"

2. The main fault of The 70s or the years of “might-have-been hopes”

3. Working out of the search algorithm of failures of Air Conditioning System of TU-154

4. The history of England can be defined as the gradual process of Parliament asserting its authority over the monarchy

5. Rise of sociology as an intellectual tradition. Classical tradition in sociology of the XIX century

6. International Combating The Crimes Harming The Economic Development Of States
International Combating The Crimes Harming The Economic Development Of States
7. Comparison of the Renaissance and Enlightenment (Сравнение Ренессанса и Просвещения)
8. On the problem of crystal metallic lattice in the densest packings of chemical elements
On the problem of crystal metallic lattice in the densest packings of chemical elements

9. Project of decoding of "The Stermer Effect" (Сигналы из космоса, серии Штермера)

10. The conflicts of the modern world. A competitive society

11. The Impact of the Afghan War on soviet soldiers

12. Geometrization of the Fundamentals of Chemistry

13. The Queen of the UK

14. The United Kingdom of Great Britain and Northern Ireland

15. History of `The Beatles` and biographies of members in english

16. The Consequences of the Soviet-Afghan War

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17. Geometrization of the Fundamentals of Chemistry

18. Redesigning the Dragon Financial Reform in the Peoples Republic of China

19. The dark side of the moon

20. The United States of America

21. Polysemy In The Semantic Field Of Movement In The English Language

22. The United States of America
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23. THE Growing Influence of English Mass Culture
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24. The United States Of America
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25. Discovery of the New World

26. Use of the Topical Project Work “My Body” for Developing All Language Skills in Form 4

27. Cities of the USA

28. The United Kingdom of Great Britain and Nothern Ireland. The land and the people.

29. Washington is the capital of the USA

30. The pride of the nation

31. The political system of Great Britain

32. Eyck, Jan van: The Adoration of the Lamb

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33. Category of number of the noun

34. Historical Background of the Middle English Period

35. Lexicology of the English Language

36. Regional variation of pronunciation in the south-west of England

37. The Comparative Analysis Of The History Of The Computer Science And The Computer Engineering In The USA And Ukraine

38. The war of the roses
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39. A Brief History of the Internet and Related Networks
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40. Henry Wadsworth Longfellow: Most Popular Poet of the Nineteenth Century
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41. Problems of the youth (friendship, love, conflicts)

42. The making of the collection

43. For the Beauty of the Earth

44. London city - Capital of the United Kingdom

45. Giza, Wonder of the World

46. The development of the Tower

47. Second period of the Renaissance.

48. The Taming of the Shrew

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49. Population of the UK

50. Economy of the Republic of Ireland

51. A (Very) Brief History of the English Language

52. Of the Polish political parties and organizations in Vilnius (1919 - 1922 gg.)

53. Algorithmic recognition of the Verb

54. Incorporation of [2,3,4,5,6-2H5]Phenylalanine, [3,5-2H2]Tyrosine, and [2,4,5,6,7-2H5]Tryptophan into the Bacteriorhodopsin Molecule of Halobacterium halobium
55. The United States of America
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56. Comparative Analysis of the Compound Words
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57. Creation of control system by a personnel how to begin with a zero

58. Emblems of the UK

59. Role of the interpreter in the modern world

60. Sport in different countries of the world

61. Stylistic Classification of the English Vocabulary

62. The comparative typology of English, Russian and Uzbek languages

63. The explaining of the meaning of neologism

64. The Heraldic Symbolism of the Unicorn on the British Coat-of-Arms

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65. The marking of the Russian Revolution

66. The origin and history of the English language

67. The outline of the period

68. The political thinking of Hobbes, Locke and Rousseau decisively shaped the western intellectual tradition

69. The selection and adaptation of the material on the topic "Towns and places"

70. The theoretical basis for the international trade. The modern trends of the international trade development
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71. The War of the Roses: the Historical Facts of the Tudor Myth (Shakespeare’s Histories)
72. Lectures in Contrastive Lexicology of the English and Ukrainian Languages

73. Division of the sentence into phrases

74. Intellectual history of the Europe

75. The impact of the French Revolution on the European system

76. The Radicalism of the American Revolution

77. Analysis of Sufism Through Art of Sufi Poetry

78. Jealousy as the cause of internal self-destruction in "Kreutzer Sonata" by Leo Tolstoy (Ревность как причина внутреннего самоуничтожения в "Крейцеровой сонате" Льва Толстого)

79. The manager as a teacher: selected aspects of stimulation of scientsfsc thinking

80. The effect of light intensity on the amount of chlorophyll in “Cicer arietinum”

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81. The Economy of Great Britain

82. Роль СМИ в современном мире (The mass media in the life of Society)

83. The history of railways (История железных дорог)

84. Alaska’s Wildlife: on the Verge of Extinction (Живая природа Штата Аляска на грани исчезновения)

85. Motivation: Reward system and the role of compensation

86. The Proverbs Are Children Of Experience (Пословицы - Дети Опыта)
87. The Tower of London
The Tower of London
88. Water World as Another Home for English Nation Reflected in the English Folklore
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89. The face of every city is different. Washington D.C.

90. The New-York City, Places of interest

91. Династия Тюдоров (essay the house of Tudor)

92. Raskolnikov and Svidrigailov: on the brink of suicide. Ф.М. Достоевский, Преступление и наказание

93. The history of Old English and its development

94. Consequence of building the National Missile Defense

95. The house of my dream

96. The History of Alaska (история Аляски)

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97. The role of art in our life

98. Raskolnikov and Svidrigailov: on the brink of suicide. Ф.М. Достоевский, Преступление и наказание

99. The History of Alaska (история Аляски)

100. “The Role of Smallpox Vaccination in Mortality Decline in the Great Britain through Eradicating the Disease between XVIII-XX centuries – Facts or a Political Arithmetick?”


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