CHI TIẾT NGHIÊN CỨU …

Tiêu đề

Students connecting mathematical ideas: Possibilities in a liberal arts mathematics class

Tác giả

Glass B.

Năm xuất bản

2002

Source title

Journal of Mathematical Behavior

Số trích dẫn

DOI

10.1016/S0732-3123(02)00104-9

Liên kết

https://www.scopus.com/inward/record.uri?eid=2-s2.0-0036343965&doi=10.1016%2fS0732-3123%2802%2900104-9&partnerID=40&md5=812e126a515119d97b0c5b095ee71704

Tóm tắt

Problem solving and justification for a diversified group of 2-year college students enrolled in a mathematics course for liberal arts majors were studied as the students met in small groups to work on various non-routine problems. Several problems from the area of combinatorics were given during these problem-solving sessions. This paper focuses on one small group of students from this study. These students were engaged in thoughtful mathematics. They identified patterns, justified that their patterns were reasonable and recognized isomorphisms between the different problems. The findings support the importance of introducing rich problems to college students and encouraging them to explore solutions, explain their reasoning and justify their solutions. © 2002 Elsevier Science Inc. All rights reserved.

Từ khóa

Justification; Liberal arts mathematics; Problem solving; Reasoning

Tài liệu tham khảo

Adleman K.A., Problem-solving strategies of young children working on a combinatorics task in a computer environment, (1999); Burns M., The role of questioning, Arithmetic Teacher, 32, 6, pp. 14-17, (1985); Davis R.B., Learning mathematics: The cognitive science approach to mathematics education, (1984); Davis R.B., The role of representations in problem solving: Case studies, Journal of Mathematical Behavior, pp. 485-497, (1985); Davis R.B., Understanding 'understanding, Journal of Mathematical Behavior, 11, pp. 225-241, (1992); English L.D., Young children's competence in solving novel combinatorial problems, (1988); English L.D., Children's strategies for solving two- and three-dimensional combinatorial problems, Journal of Research on Computing in Education, 25, 3, pp. 339-346, (1993); English L.D., Children's construction of mathematical knowledge in solving novel isomorphic problems in concrete and written form, Journal of Mathematical Behavior, 15, pp. 81-112, (1996); Glass B.H., Problem solving and justification with community college students, (2001); Hiebert J., Carpenter T.P., Learning and teaching with understanding, Handbook of Research on Mathematics Teaching and Learning, pp. 65-97, (1992); Kiczek R.D., Maher C.A., Tracing the origins and extensions of mathematical ideas, 2, pp. 377-382, (1998); Maher C.A., Constructivism and constructivist teaching - Can they coexist?, Mathematics Teaching from a Constructivist Point of View, pp. 29-42, (1998); Maher C.A., Martino A.M., The development of the idea of proof: A five-year case study, Journal for Research in Mathematics Education, 27, 2, pp. 194-219, (1996); Maher C.A., Martino A.M., Conditions for conceptual change: From pattern recognition to theory posing, (1997); Maher C.A., Martino A.M., Brandon's proof and isomorphism. Can teachers help students make convincing arguments?, pp. 77-101, (1998); Maher C.A., Speiser R., How far can you go with block towers?, Journal of Mathematical Behavior, 16, 2, pp. 125-132, (1997); Maher C.A., Davis R.B., Alston A., Implementing a thinking curriculum in mathematics, Journal of Mathematical Behavior, 10, pp. 219-224, (1991); Muter E.M., The development of student ideas in combination and proof: A six-year study, (1999); Muter E.M., Maher C.A., Recognizing isomorphism and building proof: Revisiting earlier ideas, 2, pp. 461-467, (1998); Pirie S., Kieren T., Creating constructivist environments and constructing creative mathematics, Educational Studies in Mathematics, 23, pp. 505-528, (1992); Romberg T.A., Carpenter T.P., Research on teaching and learning mathematics: Two disciplines of scientific inquiry, Handbook of Research on Teaching, pp. 850-873, (1986); Schoenfeld A.H., What's all the fuss about metacognition, Cognitive Science and Mathematics Education, pp. 189-215, (1987); Wier D., The application of professional development in combinatorics and proof to classroom teaching, (1999)