International Journal on New Trends in Education and Their Implications April 2014 Volume: 5 Issue: 2 Article: 19 ISSN 1309-6249 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org 209 MATHEMATICAL KNOWLEDGE AND THE COGNITIVE AND METACOGNITIVE PROCESSES EMERGED IN MODEL-ELICITING ACTIVITIES Dr. Juhaina Awawdeh SHAHBARI Al-Qasemi Academic College of Education The College of Sakhnin Cana- ISRAEL Assoc. Prof. Dr. Wajeeh DAHER Al-Qasemi Academic College of Education Nazareth- ISRAEL Dr. Shaker Rasslan Al-Qasemi Academic College of Education Ibilline- ISRAEL ABSTRACT The study investigates the relationship between mathematical knowledge and cognitive and metacognitive processes exhibited by 83 students from Grades 6, 7, and 8 who engaged in a set of model-eliciting activities in groups of 4-5 students each. The data sources include audiotapes of their group work, worksheets, and notes. The findings indicate that the groups in each grade use different mathematical concepts. While they employed cognitive and metacognitive processes, these differed in number and distribution. The highest percent of cognitive processes and lowest percent of metacognitive processes occurred amongst the Grade 6 students. The lowest percent of cognitive processes and highest percent of metacognitive processes occurred amongst the Grade 8 students. The Grade 6 students’ metacognitive processes indicate that they exhibited greater awareness than regulation and evaluation skills. Conversely, the Grade 7 and 8 students employed more regulation and evaluation processes. Key Words: Cognitive processes, metacognitive processes, model-eliciting activities. INTRODUCTION Cognitive and metacognitive thinking processes—such as translation, organizing, prediction, and evaluation— are essential components of today’s dynamic and technological age. Modeling activities give students an opportunity to put these processes into practice (Lesh & Zawojewski, 2007). Although broad studies have examined cognitive and metacognitive thinking processes and model-eliciting activities, little is still known about the interaction between mathematical knowledge and the nature of the cognitive and metacognitive thinking processes employed in model-eliciting activities. The present study seeks to explore this area by comparing how students from different grades and with different mathematical knowledge dealt with a specific set of model-eliciting activities. THEORETICAL BACKGROUND Cognitive and metacognitive processes Cognition is a mental process or representation that manifests itself in such things as problem solving, learning memory, and reasoning (Dunlosky & Metcalfe, 2009). The first to define metacognition was Flavell—who identified as referring to “one’s knowledge concerning one’s own cognitive processes and products or anything