This study discussed the representation method of unknowns from the perspective of multi-dimensional curriculum. For this, The elementary mathematics curriculum revised in 2015 as the intended curriculum was compared and analyzed from the 7th curriculum to the curriculum revised in 2009. The mathematics textbooks of 5th and 6th grade of curriculum revised in 2015 as the written curriculum were compared and analyzed with the 5th and 6th grade textbooks for each curriculum. For elementary school teachers, a survey study was conducted regarding the representation method of teaching unknown concepts as an implemented curriculum. A survey was conducted on elementary students' understanding of the unknown concepts as an accomplished curriculum. As a result, first, it is necessary to actively discuss the representation method of unknowns so that early algebra education can be effectively performed in the upper grades of elementary school. Second, when introducing unknown concepts, it is necessary to consider a step-by-step instructional method of using character symbols in elementary school, in order to help understand the concept using shape symbols and ultimately to connect with secondary mathematics. Third, in terms of strengthening the connection between elementary mathematics and secondary mathematics, early algebra education in elementary schools linked to full-scale algebra education in secondary schools can be pursued through the introducing the unknown representation method using character symbols in the 5th grade and 6th grade of elementary school mathematics.
This study discusses including concave polygons in teaching polygon concepts from the perspective of a series of multi-dimensional curriculum. The elementary mathematics curriculum revised in 2015 as the intended curriculum was compared and analyzed from the primary curriculum to the curriculum revised in 2009. The elementary mathematics textbooks of the curriculum revised in 2015 as written curriculum were compared and analyzed. For elementary school teachers, a survey study was conducted regarding the use and method of concave polygons when teaching polygon concepts as an implemented curriculum. A survey was conducted on elementary students' understanding of polygonal concepts as an accomplished curriculum. As a result, first, in consideration of the developmental characteristics of elementary school students, it is necessary to suggest clear limitations related to the polygon concept map in textbooks which is the intended curriculum and written curriculum. Second, since the teachers' PCK has significant impact on the students' mathematical concept formation, teacher training programs and pre-service teacher education should be strengthened to enable teachers to form accurate PCK on polygonal concepts. Third, teaching polygonal concepts by presenting concave polygons in accordance with the definition of polygons in the written curriculum, which can facilitate students' learning and understanding precise polygonal concepts, prevents the formation of misconceptions.
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