Assessment of a Problem-Centered Mathematics Program: Third Grade

Abstract

Six classes received problem-centered mathematics instruction for 2 years in second and third grade. This instruction was generally reflective of a socioconstructivist theory of knowing and compatible with recommendations for reform in mathematics education. A class-by-instruction factorial design was used to compare students in problem-centered classes for 2 years with students in problem-centered classrooms for 1 year, and with students in textbook classes for 2 years on a standardized achievement test. In addition, classes using problem-centered instruction for 2 years were compared with students in problem-centered classes for 1 year on an instrument designed to assess students' conceptual development in arithmetic and an instrument developed to examine personal goals and beliefs about reasons for success in mathematics. The results of the analyses indicate that significant differences exist in arithmetic learning for students in problem-centered classes for 2 years on the standardized achievement test and the arithmetic test. The results indicate that after 2 years of instruction in reform-based classes, students score significantly higher on standardized measures of computational proficiency as well as conceptual understanding. Additionally, these students hold stronger beliefs about the importance of finding their own or different ways to solve problems.

Reframing Teacher Professional Learning: An Alternative Policy Approach to Strengthening Valued Outcomes for Diverse Learners

“…In most of the studies with substantive effect sizes, there was an underlying assumption that students should be taught content at deep conceptual levels rather than more superficial factual-type knowledge. Indeed, in many of the mathematical and science studies, the shift from factual mastery to conceptual inquiry-based knowledge was particularly evident (see, e.g., Adey, 2004;Cardelle-Elawar, 1995;Carpenter, Fennema, Peterson, Chiang, & Loef, 1989;Cobb et al, 1991;Confrey, Castro-Filho, & Wilhelm, 2000;Fennema et al, 1993;Higgins, Irwin, Thomas, Trinick, & Young Loveridge, 2005;Kahle, Meece, & Scantlebury, 2000;McClain & Cobb, 2001;Palincsar, Magnusson, Marano, Ford, & Brown, 1998;Parke & Coble, 1997;Raghavan, Cohen-Regev, & Strobel, 2001;Saxe et al, 2001;Schorr, 2000;University of Hawaii Curriculum Research and Development Group, 2002;Wood & Sellers, 1996).…”

Experimenting With Teacher Professional Development: Motives and Methods

“…Group 2 PD activities also prescribed a set of generic teaching behaviors but were prescribed for use with one particular school subject (e.g., Good, Grouws, & Ebmeier, 1983). Group 3 PD activities provided general guidance on both curriculum and pedagogy for teaching a particular subject, and their recommended practices were justified with references to knowledge about how students learn this subject (e.g., Wood & Sellers, 1996). Finally, Group 4 PD programs provided knowledge about how students learn particular subject matter but did not provide specific guidance on the practices that should be used to teach that subject (e.g., Carpenter, Fennema, Peterson, Chiang, & Loef, 1989).…”