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Implications for Mathematics Teaching and Learning Iman C. Chahine, Georgia State University, Atlanta, GA Delineating the Epistemological Trajectory of Learning Theories: Implications for Mathematics Teaching and Learning The purpose of this paper is to delineate the trajectory of fundamental learning theories and the way these theories have impacted the teaching and learning of mathematics over more than half a century. We argue that a critical examination of the depiction of learning theories and their inherent implications for the teaching of mathematics afford an understanding of the hierarchical evolution of the field of mathematics education. Needless to say, examining various learning theories in the mathematics education context unpacks epistemological and ontological core issues underlying the teaching and learning of vital topics that are assumed to account for the changes in global economics and business in a STEM world. Introduction fundamental problems facing education The quest to explore how people locally and globally. In a highly dynamic learn mathematics has been a perennial and versatile world, unfolding the best concern for decades. For some time now, practices particularly for teaching philosophers and learning theorists have mathematics and sciences instigates a been incessantly searching for optimal pressing need for consideration by educators conditions under which learning occurs. A and policy makers. For mathematics tremendous bulk of contesting theories has education, the push toward standards-based evolved, thriving to explain the roles of the curricula governed by accountability and learner and the teacher when engaged in acts teaching effectiveness dogmas juxtaposed of learning and teaching. Notwithstanding with policies to enact cutting edge the fact that many learning theories differ in educational interventions in an ever- their empirical manifestations, nonetheless changing economy command inevitable the underlying epistemologies are challenges that cannot be overlooked. The unequivocally analogous. highly political dynamics that depict the way At the turn of the 21st century, the standards are drafted and sanctioned in necessity to prepare children for a rapidly terms of content and pedagogy are changing world has been consistently determining the way educational policies are reiterated in the literature (Csikszentmihalyi institutionalized and eventually endorsed at & Schneider, 2000; Cornell & Hartman, the grass roots level. 2007; Drucker, 2010). With the tumultuous Nevertheless, recent studies on political and economic climate prevailing student motivation, attitudes and self- worldwide exacerbated by challenges efficacy have shown that unless students are emerging in the rapidly changing context of cognitively and emotionally invested in new technologies and globalization, there is what they are learning, little knowledge will an unprecedented need to capitalize on how be acquired (Friedman, 2006; Furner & best to educate future generations. A critical Gonzalez-DeHass, 2011). Naturally, examination of the trajectories that various designing learning environments that can theories of learning have taken since the last trigger students’ natural curiosity and century provides a clear explanation on the stimulate their interest will significantly 2013 Mathitudes 1 impact their learning. Thompson and thus provide sufficient support to students in Thornton (2002) found that when students learning the content. are intrinsically motivated they are eager to This leads us to the following learn. Yair (2000) argues that, “students’ questions: How did our understanding of interest in what they learn, and their sense of how students learn develop in light of enjoyment while learning, are highly widened exposure to subsequent research correlated with the outcomes of learning” (p. efforts in educational and cognitive 193). Furner and Berman (2003) found that psychology? And what are the major teachers need to do more in the way they learning theories that have impacted teach math to address attitudes toward math frequent paradigm shifts in the field of and mathematics anxiety in the classroom. mathematics education? However, research has suggested that The purpose of this paper is to motivation of adolescents decline as they delineate the trajectory of fundamental progress through junior and senior high learning theories and the way these theories school (Eccles, Midgley, et al., 1993; have impacted the teaching and learning of Gonzalez, 2002; Hidi & Harackiewicz, mathematics over more than half a century. 2000; Williams & Stockdale, 2004). We argue that a critical examination of the Additionally, the value children place on depiction of learning theories and their many academic activities, particularly inherent implications for the teaching of mathematics and their beliefs about the mathematics affords an understanding of the usefulness of school decline as they get hierarchical evolution of the field of older (Wigfield, Eccles, & Rodriquez, mathematics education. Needless to say, 1998). Today, students are more often examining various learning theories in the described as “physically present but mathematics education context unpacks psychologically absent” and thus are less epistemological and ontological core issues likely to actively and enthusiastically engage underlying the teaching and learning of vital in learning. Recently, student lack of topics that are assumed to account for the motivation in the mathematics classroom changes in global economies. has been a critical national concern in light Drawing on extensive literature of efforts to improve STEM (Science, related to learning theories that have Technology, Engineering, and Mathematics) emerged in the past two centuries, and education in the United States. One concern examining critically possible formulations in particular is that the pipeline of students on how mathematical knowledge and entering STEM does not meet the current problem solving activity can be constructed, demand for future scientists and engineers. we highlight important implications that, we One of the reasons attributed to the attrition argue, provide the most compelling rate of students embarking on a degree in explanation of how students learn STEM is students’ underperformance in mathematics. By virtually appealing to high school mathematics and their research on the cognitive as well as the inadequate preparation in rigorous social construction of mathematical mathematics content. Hence, addressing this knowledge, we explore various trends in national need requires research and teaching and learning practices proposed by development of the best pathways to each perspective and investigate their remediate the teaching of mathematics and practical significance and implications in the mathematics classroom. 2013 Mathitudes 2 We begin with a brief overview of completely characterized in terms of stimuli major “grand” theories of learning, namely and responses relations. Almost all those of Behaviorism, Cognitivism, behaviorists describe "knowledge" as simply Constructivism, and Social Constructivism. a succession of stimulus-response chain More concisely, we examine contributions acquired through conditioning. Behaviorists of cognitive and socio-cognitive theorists believe that learning is observable and is who advanced learning epistemologies that directly evidenced by a change in behavior. transformed mainstream perspectives on This theory has been criticized as being a learning mechanisms. We expand the theory of animal and human learning that argument further to discuss the implications only focuses on objectively observable of these theories with regards to addressing behaviors that discounts mental activities students’ attitudes and motivation in the (Tuckman, 1992). Attacked and refuted by mathematics classroom. Finally, we provide radical behaviorists, in particular by Skinner an account of possible contributions of (1938), behaviorism was abandoned in favor complexity science to the teaching and of operant conditioning where events in the learning of mathematics. environment determine and shape desired behavior (Post, 1988).Though this theory Theories of Learning was prevalent from the 1950’s through A handful of research studies 1970’s, it is still alive in the minds and classified learning theories according to practices of many educators in the 21st where these theories stand relative to four century. main categories: the nature of knowledge; In search for a more “humanistic” existence of mental representations; causal theory of learning, Neobehaviorism emerged relationship between mental relationships calling for some mental mechanism that and behavior; and the origin of knowledge mediates between situations that elicit (Illeris, 2004; Pritchard, 2005). Based on the behaviors i.e. stimuli and specific behaviors above-mentioned categories, Byrnes (2007) i.e. responses (Tuckman, 1992). In his book established three major groups that the conditions of learning, Gagné, a leading encompassed Meta-Theoretical Belief Neobehaviorist, explains “ the occurrence of Systems (MTBS): 1) Behaviorism, learning is inferred from a difference in Neobehaviorism, and Cognitivism; 2) human being’s performance as exhibited Structuralism and Functionalism; and 3) before and after being placed in a ‘learning Nativism, Empiricism, and Constructivism. situation’” (1965, p.20). Each of these groups comprises a spectrum When identifying the conditions of ideologies, perspectives and belief necessary for learning to occur, Gagné
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