Fostering mathematical creativity in the middle grades: Pedagogical and mathematical practices

摘要

Increased automation and outsourcing have increased the need for creativity in many domestic jobs, so the purpose of this study is to explore middle school students' opportunity to be mathematically creative. The process standards of the Texas Essential Knowledge and Skills (TEKS) and National Council of Teachers of Mathematics (NCTM) and the Standards for Mathematical Practice of the Common Core State Standards (CCSS) can be inferred to indicate that mathematics content should be taught in a way that develops mathematical creativity. A qualitative case study was done to describe ways that three teachers fostered mathematical creativity in the middle grades. Classroom observations were triangulated with teacher and student interviews, researcher's log, and documents. Transcripts for whole class discussions of 40 hours of observation and transcripts for teacher and student interviews were open coded initially before categories were standardized and themes emerged. The three themes that emerged were that the teachers helped the students make mathematics personally meaningful, the teachers helped create an environment where students were comfortable expressing their personally meaningful understanding of mathematics and making mistakes, and they maintained expectations of mathematics practices. The teachers helped students make mathematics personally meaningful by allowing students to make some choices in how they do mathematics (use alternative methods, use alternative answer forms, solve problems with multiple correct answers, and flexibility with creating graphs and tables), to use their own words to describe mathematical concepts rather than emphasizing memorization from a textbook, and to make connections (students' interests and experiences, school experiences and other content areas, and other real world experiences through the eyes of the teacher). A safe environment was created by allowing students adequate thinking time, making it clear that the students' voices were important (ask questions, share ideas and experiences, differentiate between off-task conversations and enthusiasm, insist students respect each other, and ensure all students participated in whole class discussion), promoting the idea that mistakes are okay (okay for students and teacher, provide a learning experience, and point out silver lining in incorrect or incomplete solutions), encouraging the use of resources, and emphasizing effort over perfection. Finally they maintained mathematics practices such as explaining reasoning, using appropriate terminology and notation, and using estimation to determine reasonableness of answers.