Justifying the Fraction Division Algorithm in Mathematics of the Elementary School
박중규 Park Jungkyu , 이광호 Lee Kwangho , 성창근 Sung Chang-geun
22(2) 113-127, 2019
DOI: JANT Vol.22(No.2) 113-127, 2019
The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.
An Analysis on the Contents of Fractional Operations in CCSSM-CA and its Textbooks
이대현 Lee Dae Hyun
22(2) 129-147, 2019
DOI: JANT Vol.22(No.2) 129-147, 2019
Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA.
As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.
Education of Primary School Mathematics
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"Kutumia algorithm ya ""kugawanya sehemu"" katika hisabati ya shule ya msingi Park Jung-kyu, Lee Kuan-hyo, Sung Chang-geun, 22 (2) 113-127 (JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JANU, JAN Kwanza, tulijifunza yaliyomo ambayo yanahitaji kuzingatiwa katika kufundisha mgawanyiko wa sehemu katika hisabati ya msingi na kupendekeza vigezo. Kwa kuzingatia utafiti huu, tulichunguza kama mbinu zilizopita ambazo hutumiwa kupata algorithm ya kawaida zinafaa kwa kozi ya kuanzisha mgawanyiko wa sehemu. "Kisha, tulijadili ""kugawanyika katika sehemu"" na tukapendekeza mfano wa mgawanyiko wa mduara wa kitengo na mfano wa mgawanyiko wa mraba ambao unaweza kuona ufafanuzi huo." Hatimaye, tulithibitisha kwamba kiwango algorithm ya mgawanyiko sehemu katika wote mgawanyiko na kipimo ni asili inayotokana kupitia mifano hii. Utafiti wa Maudhui ya Operesheni ya Fractional katika CCSSM-CA na Vitabu vyake vya Kielelezo Lee Dae-Hyun, 22 (2) 129-147 (DOI: JANT, Vol.22 No. 129, 147, 2019) Kwa sababu ya dhana na maana mbalimbali za Fractions na ugumu wa kujifunza, masomo ya kuboresha mbinu za kufundisha Fractions yamefanywa. Kwa sababu kuna mbinu mbalimbali za kufundisha kulingana na aina ya sehemu au mifano au mbinu kutumika kwa ajili ya kutatua tatizo katika shughuli sehemu, utafiti wengi wamekuwa kutekelezwa. Katika utafiti huu, mimi kuchambuliwa shughuli fractional ya CCSSM-CA na vitabu vyake vya Marekani. CCSSM-CA ilibadilishwa na kuwasilishwa huko California na vitabu vya Houghton Mifflin Harcourt Publishing Co, ambavyo vinaonyesha yaliyomo na mwelekeo wa CCSSM-CA. Kwa sababu ya uchambuzi, ingawa alama zilizowasilishwa katika CCSSM-CA na vitabu vya Kikorea vilikuwa sawa katika kuongeza na kuondoa sehemu, kuna sifa za kuelezea sehemu kwa jumla ya sehemu zenye jina moja au sehemu ya kitengo na tathmini ya usahihi wa jibu. Katika kuzidisha na kugawanya sehemu, kuna tofauti katika uwasilishaji kulingana na darasa. Kuna sifa za kulinganisha matokeo ya bidhaa kulingana na idadi ya sababu, kuwasilisha mgawanyiko ikiwa ni pamoja na sehemu ya kitengo kwanza, na kupendekeza kutatua matatizo ya mgawanyiko kwa kutumia njia mbalimbali. Shule ya msingi ya Hisabati ya Korea, Gwangju, Seoul, Korea, tarehe 8 Julai, 2018 na jina la kwanza, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho, jina la mwisho.