| This paper examines metacognition--students' knowledge about their own cognition and their control of their cognitive processes (Garofolo and Lester, 1985) --in mathematics education. Specifically it examines the effects of a log in which students record their errors and comments about these errors (the Bogus Log). This paper's central question is: Does the use of the Bogus Log improve the learning of Algebra?;The instrument used to provoke metacognitive reflection--the Bogus Log--was the object of a pilot study. This study, also described in this paper, established that the Log does foster metacognitive reflection in students.;The bulk of this paper centers around a field study examining the effects of the Bogus Log. Roughly 250 students from ten Algebra classes were divided into control and treatment groups. Five teachers were involved. Each teacher had one average level Algebra class using the Log and another class not using the Log. These classes are examined quantitatively--through pretests and posttests--and qualitatively--through observations and interviews.;The January pretest and the June posttest scores were practically identical--around 32% correct--for both treatment and control classes. Not only did the Log appear to have had no statistically significant effect, but the test scores were considerably lower than expected and demonstrated no improvement after five months of teaching.;The analysis begins with a critical review of metacognition and student error analysis in math problem solving. The review contains not only research but also some of my personal experiences teaching secondary mathematics as a reflective practitioner.;Numerous possible reasons for these low test scores and the lack of test gains are examined. There were students who lacked motivation. There were teachers who taught in ways that mirror research documented examples of boring courses. The main conclusion drawn, however, is that this low level of Algebra achievement is not enough for students to perform adequate error analysis. This is unfortunate because the errors they made do not necessarily fit into the known error patterns that teachers and researchers usually caution against. |
