Problem-based Learning in Mathematics(2)

Problem-Based Learning (PBL) describes a learning environment where problems drive the learning. That is, learning begins with a problem to be solved, and the problem is posed is such a way that students need to gain new knowledge before they can solve the

ERIC/CSMEE Problem-based Learning in Mathematics Page 2tasks for nurturing student problem-solving strategies, nor plan appropriate problem-based classroom activities (Prawat, 1997; Smith III, 1997). Furthermore, it is important that teachers in PBL environments develop a broader range of pedagogical skills. Teachers pursuing problem-based instruction must not only supply mathematical knowledge to their students, but also know how to engage students in the processes of problem solving and applying knowledge to novel situations. Changing the teacher role to one of managing the problem-based classroom environment is a challenge to those unfamiliar with PBL (Lewellen & Mikusa, 1999). Clarke (1997), found that only teachers who perceived the practices associated with PBL beneficial to their own professional development appeared strongly positive in managing the classroom instruction in support of PBL. Mathematics teachers more readily learn to manage the PBL environment when they understand the altered teacher role and consider preparing for the PBL environment as a chance to facilitate professional growth (Clarke, 1997). ConclusionsIn implementing PBL environments, teachers instructional abilities become critically important as they take on increased responsibilities in addition to the presentation of mathematical knowledge. Beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999). Preparing teachers for their roles as managers of PBL environments presents new challenges both to novices and to experienced mathematics teachers (Lewellen & Mikusa, 1999). ReferencesBoaler, J. (1998). Open and closed mathematics: student experiences and understandings. Journal for Research on Mathematics Education, 29 (1). 41-62.Carpenter, T., Ansell, E. Franke, M, Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children s problem solving processes. Journal for Research in Mathematics Education, 24 (5). 428-441.Clarke, D. M. (1997). The changing role of the mathematics teacher. Journal for Research on Mathematics Education, 28 (3), 278-308.Erickson, D. K. (1999). A problem-based approach to mathematics instruction. Mathematics Teacher, 92 (6). 516-521.Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The Case of Mathematics. Educational Researcher, 12-18.Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26 (2). 24-26.Krulik, S., & Rudnick, J. A. (1999). Innovative tasks to improve critical- and creative-thinking skills. In I. V. Stiff (Ed.), Developing mathematical reasoning in grades K-12. Reston. VA: National Council of Teachers of Mathematics. (pp.138-145).Lewellen, H., & Mikusa, M. G. (February 1999). Now here is that authority on mathematics reform, Dr. Constructivist! The Mathematics Teacher, 92 (2). 158-163.Lubienski, S. T. (1999). Problem-centered mathematics teaching. Mathematics Teaching in the Middle School, 5 (4). 250-255.Prawat, R. S. (1997). Problematizing Dewey s views of problem solving: A reply to Hiebert et al. Educational Researcher, 26 (2). 19-21.Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press. Smith, C. M. (1998). A Discourse on discourse: Wrestling with teaching rational equations. The Mathematics Teacher, 91 (9). 749-753.Smith III, J. P. (1997). Problems with problematizing mathematics: A reply to Hiebert et al. Educational Researcher, 26 (2). 22-24.Selected ERIC ResourcesThe ERIC database can be electronically searched online at: http://www.eric.ed.gov/searchdb/index.html. To most effectively find relevant items in the ERIC database, it is recommended that standard indexing terms, called ERIC Descriptors, be used whenever possible to search the database. Both problem based learning and problem solving are ERIC descriptors, so these would be good terms to use in constructing an ERIC search. Following are some sample items that are included in the ERIC database:Delisle, R. (1997) How to use problem-based learning in the classroom. Alexandria, VA: Association for Supervision and Cur-riculum Development. [ED 415 004]This book shows classroom instructors how to challenge students by providing them with a structured opportunity to share information, prove their knowledge, and engage in independent learning. Ulmer, M. B. (2000). Self-grading: A simple strategy for formative assessment in activity-based instruction. Paper pre-sentated at the Conference of the American Association for Higher Education, Charlotte, NC. [ED 444 433]This paper discusses the author's personal experiences in developing and implementing a problem-based college mathematics course for liberal arts majors. The paper addresses concerns about increased faculty workload in teaching for critical thinking and the additional time required for formative assessment. van Biljon, J. A., Tolmie, C. J., du Plessis, J. P.. (1999, January). Magix-An ICAE System for problem-based Learning. Computers & Education, 32 (1), 65-81. [EJ 586 410]Discussion focuses on Magix, a prototype ICAE system for use in problem-based learning of linear mathematics for 10- to 12-year olds. The system integrates the principles of constructivism, user-driven interaction, knowledge-based systems, and metacognition. Erickson, D. K. 1999, September). A problem-based approach to mathematics instruction. Mathematics Teacher, 92 (6), This article describes preparation for instruction using a problem-based approach as part of a teaching-strategy repertoire. Suggestions of ways that mathematics teachers can get assistance in successfully implementing a problem-based teaching approach are included. Research results indi-cate what students are likely to accomplish in such classes.SE 068 409 This digest is in the public domain and may be freely reproduced. This digest was funded by the Office of Educational Research and Improvement, U.S. Department of Education, under contract no. ED-99-CO-0024. Opinions expressed in this digest do not necessarily reflect the positions or policies of OERI or the U.S. Department of Education.EDO-SE-03-07The Educational Resources Information Center is a nationwide information system initiated in 1966 by the U.S. Department of Education. 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