A Curriculum Focus Intervention's Effects on Prealgebra Achievement.

(ProQuest: . denotes formulae omitted.)Though the phrase a "mile wide and an inch deep" was coined to describe school mathematics (Schmidt, McKnight, & Raizen, 1997), it is also very descriptive of many ist-year college courses. Postsecondary developmental algebra sequences - pre or introductory algebra and intermediate algebra - are often dense with topics, push students at a breath-taking pace, and cover many of the same topics in both courses, as if closure is neither expected nor achieved.This curriculum issue was noted by Steinfort (1996) who reported on a collaborative effort by 14 Michigan community colleges to reform dieir developmental algebra curricuIums. Steinfort wrote that one of the problems motivating the reform was that "as mathematics educators, we were racing through material with lack of realistic applications, and there was too much course content for effective conceptual understanding. In addition, many of us were re-teaching Elementary Algebra topics in Intermediate Algebra" (p. 2). More recently, Epper and Baker (2009) criticized current best-selling community college developmental mathematics textbooks and software packages, asserting they replicate K-12 curriculums by presenting long lists of seemingly unrelated topics.Yet textbooks and software packages that are packed with topics do not appear to reflect the curriculum desires of college developmental mathematics teachers. As reported in the ACT National Curriculum Survey 2005-2006 (ACT, 2007), which asked teachers what they find to be important about curriculum, "postsecondary mathematics teachers of entry-level and remedial courses agree in favoring 'depth' and rigorous understanding of fundamental skills, whereas high school mathematics instructors more highly value 'breadth'" (ACT, p. 20). In this study, remedial mathematics teachers "consistently rated understanding of fundamental mathematics as more important than exposure to more esoteric mathematics content topics for success in their courses" (ACT, p. 19). However, the ACT survey fell short of identifying exactly which topics are important enough to be called fundamental by developmental mathematics teachers. As Epper and Baker (2009) point out, "while there is broad agreement on the importance of both computation fluency and conceptual understanding, the issue of which skill should be taught, and in what order, has not been resolved" (p. 4). Thus, there is a need for research that identifies the most important concepts and skills for each course in the developmental algebra sequence and that also examines the achievement effects for students who master those topics. This article serves as a starting point for such research by reporting a pilot study which shows that when a small subset of high priority learning objectives for a prealgebra course is identified and agreed upon by the faculty at an institution, it is reasonable to expect students to master these objectives completely (in terms skill proficiency and standards-based proficiency such as students' abilities to structure and communicate their responses), not simply come close. It is also shown that students who do achieve mastery on these high-priority learning objectives display a measureable positive effect in their mathematical achievement as measured by the course's common final exam and their mathematics selfefficacy beliefs.This research differs from traditional mastery learning research in that it focuses on a subset of high priority learning objectives, as opposed to the entire curriculum, and focuses on assessing students' ability to structure, represent, and communicate their processes and thinking skills, as opposed to assessing only whether the solution and process are correct.Mastery Learning and Feedback ResearchThe concept of mastery learning is not new to education. The 1920s and 1930s saw several systems of instruction requiring mastery on formal assessments before students were moved to new material (Bloom, 1968; Kulik, Kulik, & BangertDrowns, 1990). …