METHODOLOGY OF LEARNING OF ADDING AND SUBTRACTING NUMBERS UP TO 20 IN THE NEW BULGARIAN MATHEMATICS FOR THE FIRST GRADE
Journal Title: Knowledge International Journal - Year 2018, Vol 26, Issue 2
Abstract
Over the last three years, educational reform has taken place in Bulgaria. It also affects the mathematics curriculum in the first grades. The curriculum for mathematics for the first grade was approved by Order of the Minister of Education and Science No RD 09-1857 dated 17.12.2015. It came into force in the school year 2016/2017. One of the areas of mathematical competence in the first grade curriculum is “Numbers”. It is basic. In this area of competence, students are expected to build up their knowledge of the numbers up to 10 that they have from the preparatory group/class. Students should understand concepts for numbers up to 10, up to 20 and numbers 30, 40, 50 ... 100. It is intended that they master adding and subtracting the numbers up to 10 to automatism. With numbers up to 20, pupils in the first grade have to master adding and subtracting without carrying over the ten to automatism. At the end of the school year, students study adding and subtracting with the numbers 10, 20, 30, 40, 50 ... 100. During the second semester of the first grade, they mainly study to add and subtract the numbers up to 20 by carrying over the ten. These are tasks of type 8 + 5, 11- 4. These tasks are of great importance as they are the basis of the adding and subtraction with carrying over the ten with larger numbers – up to 100, up to 1000 and over 1000 (like 48 + 25; 328 + 535; 234,158 + 413,625). If children do not master the adding and subtraction with numbers up to 20 with carrying over the ten to automatism, they have no chance to learn to add and subtract the larger numbers with carrying over. That is why, in textbooks, most time of the learning process and most topics of this learning content are allocated to this content of mathematics for the first grade. For this reason, for me it is of scientific interest how this learning content is covered in the new mathematics training kits. Nine first-grade mathematics training sets received approval of the Ministry of Education and Science and of the teachers in Bulgaria. This article is devoted to the issue of clearing the addition and subtraction of numbers up to 20 with the carrying over the ten in the new first grade mathematics kits. I present a comparative analysis of the methodological approaches that the different authors’ groups have used in their textbooks under the “Adding and Subtracting Up to 20 with Carrying over the Ten” section. Interesting results were achieved. The number of lessons foreseen in this section in the different syllabi varies greatly from 20 to 38. When subtracting numbers up to 20 with carrying over the ten, two different approaches are known in the methodology of the mathematics training: subtraction is based on the “subtract a sum from number” (11 - 4 = ? 4 = 1 + 3; 11 - (1 + 3) = (11 – 1) - 3 = 10 – 3 = 7; 11 - 4 = 7) and on the basis of the “subtract a number from sum” (11 - 4 = ? 11 = 10 + 1; (10 + 1) - 4 = (10 - 4) +1 = 6 +1 = 7; 11 - 4 = 7). These two approaches are not represented in all nine textbooks. Explaining how to add and subtract with numbers of up to 20 with carrying over, visualization plays an important role. The best tool to illustrate this is the abacus. Other possible ways to illustrate are schematic models and visualization using the numerical axis. It is best to use all three types of visualization in the lessons of acquiring new knowledge. Some of the training kits presented here lack adequate visualization. This speaks of a lack of a systemic methodical approach in compiling the mathematics training kits. Conclusions are drawn on the advantages and disadvantages of compared textbooks. Conclusions can serve the authors of mathematics training kits in their future work, as well as primary school teachers in choosing training set to teach mathematics.
Authors and Affiliations
Gabriela Kirova
Keywords
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