초록
본 연구는 초등학생의 수학적 창의성을 함양하기 위한 교육적 시사점을 도출하고자 비례배분 문제를 다중해법과제로 제시하여 초등학교 6학년 학생 100명을 대상으로 수학적 창의성 평가 관점에서 개별 문제해법공간을 분석하고, 집단적 해법공간의 특징을 도출하였다. 연구 결과, 교사는 집단적 해법공간의 수학적 창의성에 중요한 영향을 미치는 것으로 나타났으며, 교사에 따라 유창성과 독창성에서 유의미한 차이가 있었다. 수학적 창의성 수준이 높은 집단의 해법공간은 공식 활용 비율이 낮고, 다양한 유형의 해법과 표현을 제시한 반면, 수학적 창의성 수준이 낮은 집단의 경우 식 표현이 전체 응답 중 91.9%를 차지했다. 또한 식 표현에 의존하는 문제 해결은 수학적 창의성으로 자연스럽게 이어지지 않으므로, 수학적 창의성 함양을 위해서는 학생들이 다양한 수학적 표현을 시도할 수 있는 기회를 제공하는 것이 중요함을 확인하였다.
This study aims to derive educational implications for fostering mathematical creativity in elementary students. To achieve this, proportional distribution problems were presented as multiple-solution tasks, and students' problem-solving processes were analyzed from the perspective of mathematical creativity. The study involved 100 sixth-grade elementary students who were given proportional distribution problems as multiple-solution tasks to analyze their problem-solving methods. The students were grouped based on teacher variables, and the groups were assessed in terms of fluency, originality, and flexibility in mathematical creativity. The characteristics of the collective solution spaces were identified by comparing the frequency of various problem-solving strategies and representation types. The study found that teachers significantly influence mathematical creativity within collective solution spaces. Depending on the teacher, differences in fluency and originality were observed. Collective solution spaces with less reliance on formulaic approaches and higher use of diverse representations scored higher in creativity. Conversely, heavy reliance on symbolic representations was associated with lower creativity. These findings highlight the importance of encouraging various problem-solving strategies and representations within collective solution spaces to foster creativity. The study confirms that teachers play a crucial role in fostering mathematical creativity. Differences in creativity between groups based on teacher variables indicate that teachers impact students' problem-solving approaches. Additionally, relying solely on symbolic representations does not naturally lead to mathematical creativity, underscoring the need to provide students with opportunities to explore diverse mathematical representations. Creating an educational environment that encourages students to experiment with various strategies and representations is essential for nurturing their creativity.