مهارت های پیش نیاز جبر و تصورات غلط مربوط به دانش آموزان کلاس متوسط: بررسی

This article provides a comprehensive literature review related to prerequisite algebra skills and associated misconceptions of middle grades students as a means to draw together ideas for research and practice. Four algebra-related content domains (Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions) from the Common Core State Standards for Mathematics (CCSSM) were used as an organizing framework to examine findings that are linked to the need for greater student conceptual understanding as a priority in reaching algebra proficiency. By providing insights into prerequisite algebra skills and associated misconceptions of middle grade students, this manuscript has direct implications for classroom instruction and teacher education. This review of literature can serve as a comprehensive guide to a variety of stakeholders involved in the implementation of the middle grades algebraic content of the CCSSM ( CCSSO, 2010a).

The purpose of this article is to provide a review of the literature related to prerequisite algebra skills and associated misconceptions of middle grades students. We chose to focus on these skills and misconceptions because algebra often serves as a gatekeeper to success in high school, postsecondary education, and many career paths (Capraro and Joffrion, 2006, Edwards, 2000, Erbas, 2005 and Stephens, 2005). The emphasis is on middle school years as that time frame is critical in preparing students for Algebra I (Capraro & Joffrion, 2006) as they make the transition from concrete to more abstract mathematics. Additionally, by linking what is known about the need for greater student conceptual understanding to the priority placed on algebra proficiency, we can begin to see how the balance between relational understanding (conceptual) and instrumental understanding (procedural) fit within the Common Core State Standards for Mathematics (CCSSM) ( CCSSO, 2010a). Skemp (1976) brought the notion of relational understanding (conceptual) and instrumental understanding (procedural) to the forefront in his discussion of the difference between knowing how to do something and why (relational understanding) and knowing rules without reasons (instrumental understanding). He argued that relational mathematics was more advantageous because it was adaptable to new tasks, easier to remember over time, an effective goal in and of itself, and its relational schemas fostered mathematical growth. Nearly 35 years after Skemp's article on relational and instrumental understanding of mathematics, the recently released CCSSM (CCSSO, 2010a) state that a key point of the mathematics standards is to: