Paths to learning ten-structured understandings of teen sums: Addition solution methods of Japanese grade 1 students

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students moved through all the levels of conceptions of quantities as previously reported in the U.S. and European literature over the period. Individual student paths were varied, and some students used methods based on their transitional understanding between the levels as they gained experiences. They gradually came to use the culturally valued break-apart-to-make-ten method of making, while counting and visual grouping supported the process. Classroom instruction that supported the development of their conceptual structure is also summarized and discussed.