Ïåäàãîãè÷åñêèå íàóêè/5.Ñîâðåìåííûå ìåòîäû ïðåïîäàâàíèÿ

Ñàäâîêàñîâà Ã. Á.

Øêîëà-ãèìíàçèÿ  ¹17 ã.Àñòàíà, Êàçàõñòàí

Ìåòîäèêà ðàáîòû íàä âíåòàáëè÷íûìè ñëó÷àÿìè óìíîæåíèÿ è äåëåíèÿ

Îäíà èç âàæíåéøèõ çàäà÷ îáó÷åíèÿ øêîëüíèêîâ ìàòåìàòèêå – ôîðìèðîâàíèå ó íèõ âû÷èñëèòåëüíûõ íàâûêîâ, îñíîâîé êîòîðûõ ÿâëÿåòñÿ îñîçíàííîå è ïðî÷íîå óñâîåíèå ïðèåìîâ óñòíûõ è ïèñüìåííûõ âû÷èñëåíèé.

Âû÷èñëèòåëüíàÿ êóëüòóðà ôîðìèðóåòñÿ ó ó÷àùèõñÿ íà âñåõ ýòàïàõ èçó÷åíèÿ êóðñà ìàòåìàòèêè, íî îñíîâà åå çàêëàäûâàåòñÿ â ïåðâûå 5-6 ëåò îáó÷åíèÿ.  ýòîò ïåðèîä øêîëüíèêè îáó÷àþòñÿ èìåííî óìåíèþ îñîçíàííî èñïîëüçîâàòü çàêîíû ìàòåìàòè÷åñêèõ äåéñòâèé (ñëîæåíèå, âû÷èòàíèå, óìíîæåíèå, äåëåíèå).  ïîñëåäóþùèå ãîäû,  ïîëó÷åííûå óìåíèÿ è íàâûêè ñîâåðøåíñòâóþòñÿ, çàêðåïëÿþòñÿ â  è ïðè èçó÷åíèè  äðóãèõ ïðåäìåòîâ [1].

Èìåííî â  íà÷àëüíûõ êëàññàõ  çàêëàäûâàþòñÿ îñíîâû îáó÷åíèÿ ìàòåìàòèêå. Íå íàó÷èì äåòåé ñ÷èòàòü â ýòîò ïåðèîä, â äàëüíåéøåì îíè áóäóò èñïûòûâàòü òðóäíîñòè.  Ïîýòîìó ó÷èòåëþ íåîáõîäèìî ôîðìèðîâàòü ó äåòåé âû÷èñëèòåëüíûå íàâûêè, èñïîëüçóÿ ðàçëè÷íûå âèäû óñòíûõ óïðàæíåíèé.

Î íàëè÷èè ó ó÷àùèõñÿ âû÷èñëèòåëüíîé êóëüòóðû ìîæíî ñóäèòü ïî èõ óìåíèþ ïðîèçâîäèòü óñòíûå è ïèñüìåííûå âû÷èñëåíèÿ, ðàöèîíàëüíî îðãàíèçîâûâàòü õîä âû÷èñëåíèé, óáåæäàòüñÿ â ïðàâèëüíîñòè ïîëó÷åííûõ ðåçóëüòàòîâ [2].

Êà÷åñòâî âû÷èñëèòåëüíûõ óìåíèé îïðåäåëÿåòñÿ çíàíèåì ïðàâèë è àëãîðèòìîâ âû÷èñëåíèé. Óìåíèÿ ôîðìèðóþòñÿ â ïðîöåññå âûïîëíåíèÿ öåëåíàïðàâëåííîé ñèñòåìû óïðàæíåíèé. Óìåíèå äîâîäèòñÿ äî íàâûêà. Âû÷èñëèòåëüíûå íàâûêè îòëè÷àþòñÿ îò óìåíèé òåì, ÷òî âûïîëíÿþòñÿ ïî÷òè áåñêîíòðîëüíî. Îáðàçîâàíèå âû÷èñëèòåëüíûõ íàâûêîâ óñêîðÿåòñÿ, åñëè ó÷àùèìñÿ ïîíÿòåí ïðîöåññ âû÷èñëåíèé è åãî îñîáåííîñòè  [3].

          ñâîåé ñòàòüå ÿ õîòåëà áû îñòàíîâèòüñÿ íà óñòíûõ ïðèåìàõ óìíîæåíèÿ è äåëåíèÿ â ïðåäåëàõ 100, îâëàäåíèå êîòîðûìè â äàëüíåéøåì îêàæóò íåîöåíèìóþ ïîìîùü ïðè âûïîëíåíèè ïèñüìåííûõ âû÷èñëåíèé â ïðåäåëàõ 1 000 000 â 4 êëàññå è ïðè èçó÷åíèè äðîáåé â 5 êëàññå.

         Âñå ýòè ïðèìåðû ìîæíî ñèñòåìàòèçèðîâàòü è äàâàòü çàó÷èâàòü èõ íàèçóñòü. Ïðè ýòîì, êîíå÷íî, îíè äîëæíû çíàòü è îáùåïðèíÿòóþ ìåòîäèêó. Íàïðèìåð, ÷òîáû 14 óìíîæèòü íà 3, íàäî 14 ðàçëîæèòü íà ðàçðÿäíûå ñëàãàåìûå 10 è 4, à ïîòîì êàæäîå ñëàãàåìîå óìíîæèòü íà    3, ÷òîáû 81 ðàçäåëèòü íà 27, ïîëüçóåìñÿ ìåòîäîì ïîäáîðà. Ïðè çàó÷èâàíèè ýòîé òàáëèöû äåòè ïîëüçóþòñÿ ñâÿçüþ êîìïîíåíòîâ ïðè óìíîæåíèè è äåëåíèè. Âàæíî è òî, ÷òî ê ïðîöåññó îáó÷åíèÿ àêòèâíî  ïîäêëþ÷àåòñÿ çðèòåëüíàÿ ïàìÿòü.

         Õî÷åòñÿ îòìåòèòü, ÷òî äàííàÿ ìåòîäèêà ðàáîòû íàä âíåòàáëè÷íûìè ïðèåìàìè óìíîæåíèÿ è äåëåíèÿ, èñïîëüçóåòñÿ ìíîþ íåñêîëüêî ëåò è ïðèíîñèò ïîëîæèòåëüíûå ðåçóëüòàòû.

1)

11 * 2 =                         22 : 2 =                          22 : 11 =              

11 * 3 =                         33 ; 3 =                          33 : 11 =

11 * 4 =                         44 : 4 =                          44 : 11 =

11 * 5 =                         55 : 5 =                          55 : 11 =

11 * 6 =                         66 : 6 =                          66 : 11 =

11 * 7 =                         77 : 7 =                          77 : 11 =

11 * 8 =                         88 : 8 =                          88 : 11 =

11 * 9 =                         99 : 9 =                          99 : 11 =

 

2)

12 * 2 =                         24 : 2 =                          24 : 12 =

12 * 3 =                         36 : 3 =                          36 : 12 =

12 * 4 =                         48 : 4 =                          48 : 12 =

12 * 5 =                         60 : 5 =                          60 : 12 =

12 * 6 =                         72: 6 =                           72 : 12 =

12 * 7 =                         84 : 7 =                          84 : 12 =

12 * 8 =                         96 : 8 =                          96 : 12 =

3)

13 * 2 =                         26 : 2 =                          26 : 13 =

13 * 3 =                         39 : 3 =                          39 : 13 =

13 * 4 =                         52 : 4 =                          52 : 13 =

13 * 5 =                         65 : 5 =                          65 : 13 =

13 * 6 =                         78 : 6 =                          78 : 13 =

13 * 7 =                         91 : 7 =                          91 : 13 =

4)

14 * 2 =                         28 : 2 =                          28 : 14 =

14 * 3 =                         42 : 3 =                          42 : 14 =

14 * 4 =                         56 : 4 =                          56 : 14 =

14 * 5 =                         70 : 5 =                          70 : 14 =

14 * 6 =                         84 : 6 =                          84 : 14 =

14 * 7 =                         98 : 7 =                          98 : 14 =

5)

15 * 2 =                         30 : 2 =                          30 : 15 =

15 * 3 =                         45 : 3 =                          45 : 15 =

15 * 4 =                         60 : 4 =                          60 : 15 =

15 * 5 =                         75 : 5 =                          75 : 15 =

15 * 6 =                         90 : 6 =                          90 : 15 =

6)

16 * 2 =                         32 : 2 =                          32 : 16 =

16 * 3 =                         48 : 3 =                          48 : 16 =

16 * 4 =                         64 : 4 =                          64 : 16 =

16 * 5 =                         80 : 5 =                          80 : 16 =

16 * 6 =                         96 : 6 =                          96 : 16 =

7)

17 * 2 =                         34 : 2 =                          34 : 17 =

17 * 3 =                         51 : 3 =                          51 : 17 =

17 * 4 =                         68 : 4 =                          68 : 17 =

17 * 5 =                         85 : 5 =                          85 : 17 =

8)

18 * 2 =                         18 : 2 =                          18 : 19 =

18 * 3 =                         54 : 3 =                          54 : 18 =

18 * 4 =                         72 : 4 =                          72 : 18 =

18 * 5 =                         90 : 5 =                          90 : 18 =

9)

19 * 2 =                         38 : 2 =                          38 : 19 =

19 * 3 =                         57 : 3 =                          57 : 19 =

19 * 4 =                         76 : 4 =                          76 : 19 =

19 * 5 =                         95 : 5 =                          95 : 19 =

10)

21 * 2 =                         42 : 2 =                          42 : 21 =

21 * 3 =                         63 : 3 =                          63 : 21 =

21 * 4 =                         84 : 4 =                          84 : 21 =

 

 

11)

22 * 2 =                         44 : 2 =                          44 : 22 =

22 * 3 =                         66 : 3 =                          66 : 22 =

22 * 4 =                         88 : 4 =                          88 : 22 =

12)

23 * 2 =                         46 : 2 =                          46 : 23 =

23 * 3 =                         69 : 3 =                          69 : 23 =

23 * 4 =                         92 : 4 =                          92 : 23 =

13)

24 * 2 =                         48 : 2 =                          48 : 24 =

24 * 3 =                         72 : 3 =                          72 : 24 =

24 * 4 =                         96 : 4 =                          96 : 24 =

14)

25 * 2 =                         50 : 2 =                          50 : 25 =

25 * 3 =                         75 : 3 =                          75 : 25 =

25 * 4 =                         100 : 4 =                        100 : 25 =

15)

26 * 2 =                         52 : 2 =                          52 : 26 =

26 * 3 =                         78 : 3 =                          78 : 26 =

16)

27 * 2 =                         54 : 2 =                          54 : 27 =

27 * 3 =                         81 : 3 =                          81 : 27 =

17)

28 * 2 =                         56 : 2 =                          56 : 28 =

28 * 3 =                         84 : 3 =                          84 : 28 =

18)

29 * 2 =                         58 : 2 =                          58 : 29 =

29 * 3 =                         87 : 3 =                          87 : 29 =

19)

31 * 2 =                         62 : 2 =                            62 : 31 =

31 * 3 =                         93 : 3 =                          93 : 31 =

20)

32 * 2 =                         64 : 2 =                          64 : 32 =

32 * 3 =                         96 : 3 =                          96 : 32 =

21)

33 * 2 =                         66 : 2 =                          66 : 33 =

33 * 3 =                         99 : 3 =                          99 : 33 =

22)

34 * 2 =                         68 : 2 =                          68 : 34 =

23)

35 * 2 =                         70 : 2 =                          70 : 35 =

24)

36 * 2 =                         72 : 2                             72 : 36 =

25)

37 * 2 =                         74 : 2 =                          74 : 37 =

26)

38 * 2 =                         76 : 2 =                          76 : 38 =

27)

39 * 2 =                         78 : 2 =                          78 : 39 =

28)

41 * 2 =                         82 : 2 =                          84 : 41 =

29)

42 * 2 =                         84 : 2 =                          84 : 42 =

30)

43 * 2 =                         86 : 2 =                          86 : 43 =

31)

44 * 2 =                         88 : 2 =                          88 : 44 =

32)

45 * 2 =                         90 : 2 =                          90 : 45 =

33)

46 * 2 =                         92 : 2 =                          92 : 46 =

34)

47 * 2 =                         94 : 2 =                          94 : 47 =

35)

48 * 2 =                         96 : 2 =                          96 : 48 =

36)

49 * 2 =                         98 : 2 =                          98 : 49 =

 

         Ïðè çàêðåïëåíèè äàííûõ ñëó÷àåâ óìíîæåíèÿ è äåëåíèÿ ìîæíî èñïîëüçîâàòü è ñëåäóþùèå óïðàæíåíèÿ:

- Ñîñòàâüòå ïðèìåðû íà óìíîæåíèå è äåëåíèå, èñïîëüçóÿ ÷èñëà

17, 8, 24, 13, 5, 85, 3, 72, 7, 91, 12,96

- Ïîëó÷èòå 72, 75, 96, 66, 88, 90, 78  ðàçíûìè ñïîñîáàìè.

- Íàéäèòå â ðÿäó «ëèøíåå» ÷èñëî.

91, 26, 52, 39,65, 96, 78

- Ïîñ÷èòàéòå ïî 12, 13, 14 è ò.ä.

 

Ëèòåðàòóðà

1.  Ì.È.Ìîðî, À.Ì. Ïûøêàëî. Àêòóàëüíûå ïðîáëåìû ìåòîäèêè îáó÷åíèÿ ìàòåìàòèêå â íà÷àëüíûõ êëàññàõ.— Ì.: Ïåäàãîãèêà, 1977.

2.  Èñòîìèíà Í.Á. Ìåòîäèêà îáó÷åíèÿ ìàòåìàòèêå â íà÷àëüíûõ êëàññàõ.

-  Ì., 1997.

3.  Ìåëüíèêîâà Í.À. Ðàçâèòèå âû÷èñëèòåëüíîé êóëüòóðû ó÷àùèõñÿ. Ìàòåìàòèêà â øêîëå.2010 - ¹ 18.