How Motivation and Emotion Affect Young Adolescent Girls Learning in Mathematics - Essay Example

How Motivation and Emotion Affects Young Adolescent Girls’ Learning in Mathematics Mathematics is one that unleashes deep-seated memories formany people. Most of these memories include the learning of mathematical concepts and skills. Such learning may either be fulfilling or frustrating for learners, as Math covers a wide variety of degrees of difficulty. A young lady pursuing an Engineering course may have been encouraged in her math subjects while she was in school even though her competency for the subject was average. On the other hand, a once-gifted Math whiz is currently taking up Culinary Arts instead of her dream course in Bachelors in Math because as a young girl, her high competence for Math was shunned and unappreciated by her male teachers and classmates. These examples show that there are psychological factors that affect one’s regard for Math as a subject. This paper shall be discussing the effects of motivation and emotion on adolescent girls’ learning of Math as well as how educators can support them to have a healthy attitude and regard for the subject to enable them to learn it more effectively. The study of Math incorporates the processes of questioning, reflecting, reasoning and proof. It is a powerful tool for solving familiar and unfamiliar problems both within and beyond mathematics. As such, it is integral to scientific and technological advances in many fields of endeavor. The inclusion of Mathematics in the curriculum is aimed at developing students’ mathematical thinking, understanding, competence and confidence in the application of mathematics, their own creativity, enjoyment and appreciation of the subject and their engagement in lifelong learning (Board of Studies New South Wales, 2002) Apart from the skills developed from the study of Math, values and attidudes are likewise emphasized. Students get to appreciate mathematics as an essential and relevant part of life. They show interest and enjoyment in inquiry and the pursuit of mathematical knowledge, skills and understanding. Children demonstrate confidence in applying mathematical knowledge, skills and understanding to everyday situations and the solution of everyday problems. Math also aims to develop and demonstrate perseverance in undertaking mathematical challenges. Students recognise that mathematics has been developed in many cultures in response to human needs (Board of Studies New South Wales, 2002). The literature provides several studies on the use of ability grouping in Mathematics. The experience of working with others and in teams can facilitate learning. Group work provides the opportunity for students to communicate mathematically with each other, to make conjectures, to cooperate and to persevere when solving problems and undertaking investigations. Motivation influences observational learning. It is expected that observing how others fare in the task is heightened, with the desire to make oneself at par or even go beyond the performance of others. Math lessons that reflect social cognitive theory collaborate that everyone learns from each other. The teacher teaches explicitly, feeding information to everyone, then they are asked to try out the solution together with her. This is within full view of everyone else, so if errors are made, then everyone learns from it too when teacher points it out. Provision of drills and practice exercise may be done within same ability groups so the students can support each other when one gets into a snag. If they are expected to work individually, they still learn with the group as their finished exercises are checked as a class. Cohen & Spenciner (2005) posit that group support and cooperation among students are essential in facilitating learning. In doing so, the classroom is transformed into a learning community that supports each member with the teacher as reference point. Harlen (1999) argues that ability grouping serves more relevance in the area of Math than other learning areas due to the huge range of abilities that are often exhibited within the same class. What makes it more complex is the fact that Mathematics is a hierarchical discipline where concepts build on previous concepts and more often than not, need full understanding before proceeding to the next, more complicated concept. (Ruthven, 1987). Hence, Math teachers are more likely to support homogeneous grouping than their colleagues in other subject areas. Cahan and Linchevski (1996) report from the UK where 80% of Mathematics teachers believe the inappropriateness of mixed ability teaching groups whereas, in contrast, only 16% of science teachers and 3% of English teachers believed the same. According to Ruthven (1987), similar trends are prevalent in primary schools where grouping was predominant in Math but not so in areas such as Science and Social Studies. He also believes that although ability grouping is consistent in Math, it diminishes in other subject areas as students move through the year levels.. The subject of math may be difficult for students of different cultures to learn because mathematical concepts may be interpreted differently, including terminologies. “If diverse learners are to fully benefit from the schooling experience, the teaching of mathematics needs to be linked to their lives and circumstances and in some respect, share their cultural norms.” (Ernst-Slavit & Slavit, 2007). This includes an understanding of the historical development of mathematics in the students’ country of origin, grounded in cultural heritage. The use of students’ cultural and linguistic backgrounds may be used as motivation in the classroom. It is heartening to note that “the ultimate reason for mathematics is, after all, not just to solve problems as presented in a text or worksheet but to solve problems that present themselves in many phases of life. The complexity of life today is many times greater than that in earlier centuries, and we are discovering that young children are capable of mathematical thinking that is much deeper and broader than we had ever before realized.” (Krogh, 1995, p.148) Motivations to learn math Hannula (2006) posit that emotions are the most direct link to motivation. Such can be manifested either in positive (joy, relief or interest) or negative (anger, sadness, frustration). Another strong motivator is need. In educational settings, students’ needs are often autonomy, competency and social belonging (Covington & Dray, 2002). Still another motivator is one’s goal, such as getting a good grade. The difference between needs and goals is in their level of specificity (Nuttin, 1984). As an example, a student might realize her need for competency as a goal to solve tasks well or at other times, as a goal to understand the particular lesson taught. Her social need might be realized as a goal to contribute to a group project, while her need for autonomy as a goal to challenge her teacher’s authority. Realizing her needs as goals in the mathematics classroom may be significantly influenced by her belief of her own competencies, mathematics and learning as well as school context, the social and sociomathematical norms in the class (Hannula, 2006). In a teacher-centered mathematics classroom where rules and routines as well as individual drilling are emphasized, students do not have much latitude to meet their needs for autonomy or social belonging within the context of mathematics learning (Hannula, 2006). However, in more student-centered classes where teamwork and meaning making are stressed, then they have many opportunities to meet various needs such as autonomy and social interactions (Hannula, 2006). With this knowledge in mind, Hannula (2006) defines motivation as a potential to direct behavior through the mechanisms controlling emotion. This potential is structured through needs and goals. As a potential, motivation cannot be directly observed but only as a manifestation of affect, cognition or behavior. For example, a motivated student in Math may show constant eagerness for the subject by always doing her homework, actively participating in class, doing well in her Math quizzes and exams and even goes out of her way to help out her less competent classmates. Such motivation is palpable in a positive class environment facilitated by an encouraging Math teacher. Frenzel, Pekrun & Goetz (2007) offer another view of motivation. They posit that value appraisals consider two categories. The first are beliefs regarding the intrinsic value of the domain under consideration and the second are the beliefs regarding the value of achievement outcomes in this domain. For example, a student may like Math because she appreciates its formal nature and dealing with numbers. This is her intrinsic domain value for Math. Another student may be more concerned with performing well in the subject in order to improve her career options, meet her parents’ expectation or attain personal achievement standards. This now becomes her achievement value for Math. The learning environment, teacher and student factors, have been identified to influence attitudes in learning Mathematics (Shaughnessy, Halaydyna and Shaughnessy, 1983). Evidence in a US cross-sectional study of 10-, 13- and 15-year-olds found that teacher factors such as quality of instruction; student factors such as fatalism affected students’ attitude towards math. Younger adolescents are predicted to be affected less than older ones when perceived learning environment factors such as whether other students in the class were satisfied with their lessons. This points to the possibility that when they perceive their math class as more supportive of their social relationships and personal development, then they are more likely to have higher self efficacy for learning behavior and learning intentions (Brahm, 1994). On a more practical note, Shaftel, Pass and Schnabel (2005) agree that students are more motivated to learn even difficult lessons in Math or other subjects through instructional games and simulations rather than traditional classroom instruction. Games have been found to result in improved content retention over time, possibly because of the opportunity for more participation. Math games improved on-task behavior and achievement even for students with mild intellectual disabilities (Beattie & Algozzine, 1982). What motivates students with math games is that it allows them many opportunities to reinforce current knowledge and to try out other strategies or techniques without fear of getting the wrong answer. Trial and error is always encouraged, making them more confident in taking risks (Shaftel, Pass and Schnabel, 2005). Math games provide students with an environment for experiencing incorrect answers not as mistakes but as necessary steps towards connecting pieces of knowledge together (Holton et al, 2001; Quinn et al, 1992). Practical games such as those involving knowledge about money should be tied to real-life experiences if mathematical learning is to be optimized. Simulations develop metacognitive skills for analyzing and organizing data, checking responses, justifying solutions to problems and applying mathematical knowledge to daily activities (Hopkins and Dorsey, 1992). Of course, it cannot be underestimated that an effective Math teacher greatly motivates her students to love the subject. She models to her students her enthusiasm for the discipline that she takes teaching it seriously while according due respect to her learners who may not exhibit the same level of competencies for the subject. Emotions That Mathematics Trigger Math triggers a variety of emotions – excitement, frustration, fulfillment, anxiety, among many others. However, it is mostly anxiety that it elicits in students (Ashcraft, 2002). Pekrun, Goetz, Titz, and Perry (2002) reported that emotions typically experienced by students include task- or activity-related feeling states such as task enjoyment, and emotions which relate to learning outcomes, such as pride, shame, anxiety, and hopelessness. Still, emotions other than anxiety have received conspicuously little attention in research on learning and achievement, with the exception of research on the attributional antecedents of achievement emotions (Weiner, 1985, 1994). Frenzel, Pekrun & Goetz (2007) suggest three reasons why studying emotions in learning and achievement is essential. One is that emotions are important dependent variables in their own right. They are key components of subjective well-being and psychological health. Another reason is that emotions impact students’ learning and achievement. Learners are more willing to invest time-consuming and effort-intensive work if the learning activities are emotionally rewarding. This means that they derive enjoyment and interest rather than anxiety or boredom. Emotions influence learning by triggering dopamine levels in the brain that affects long-term memory by directing attention processes and the use of cognitive resources; inducing and sustaining student interest in the learning material or activity; by setting up different modes of information processing and problem solving and by facilitating or hindering students’ self-regulation of learning and performance. Finally, when the subject becomes emotionally attractive to a student, it becomes a good predictor that he or she will engage in more future activities in it, such as enrolling in a college course related to it or follow a career in this domain (Frenzel, Pekrun & Goetz, 2007). Op’t Eynde, De corte and Verschaffel (2006) suggest that every emotion that students experience in the classroom has four characteristics. First, emotions are based on students’ cognitive interpretations and appraisals of specific events. Second, students create interpretations and appraisals based on their knowledge and beliefs, and thus, it varies with age, personal history and home culture. Third, emotions are contextualized because individuals have unique appraisals of similar events in different situations. Lastly, emotions are unstable because situations and even the individuals in the situations continuously develop. A study conducted by Op’t Eynde, De corte and Verschaffel (2006) indicates that negative emotions are usually experienced when students are not able to solve the problem as well as they expected. Feeling inadequate with the cognitive strategies used is an emotional as well as a metacognitive process. The study also found that the nature and intensity of the emotion experienced when confronted with a cognitive blockage significantly differed from one student to the next. For instance, when confronted with a difficulty in an early stage of the problem-solving process, one student becomes hopeless and quits while another, also got stuck at the same point, felt frustrated, but took it as a challenge and pushed forward with solving it. Most of the time, this shows the role of emotions in mathematical problem solving when the emotional experience triggers students to redirect their current behavior and look for alternative cognitive strategies to find either a way out of solving the problem, or a solution to it. Gender Differences in Math Competencies Gender differences in all aspects of behavior have been studied extensively. Studies on emotion-related differences especially in education and career choices have become relevant especially in Mathematics. Increasing the number of females in male-dominated fields would need interventions if women are to be placed in traditionally male, socially recognized and economically important jobs (Frenzel, Pekrun & Goetz, 2007) Stipek and Gralinsky (1991) studied gender differences in emotional responses to success and failure in mathematics and found that girls showed a “female” attribution bias by attributing failure to low ability and not attributing success to high ability. Girls likewise reported less feelings of pride after they succeeded in math tasks and more shame after failure. Results of the study suggested that girls have stronger tendencies to more negative emotional patterns in math. Frenzel, Pekrun & Goetz (2007) also conducted a study with adolescent students on gender differences in Math. They found that boys reported more enjoyment and pride in Math and less anxiety and hopelessness than girls. Boys likewise reported less shame with regards to their failures in Math, however, the difference was not very substantial. Student perceptions of their competence showed a big difference between boys and girls, with girls reporting less confidence in their math abilities. In relation to this, girls rated the domain value of math as being significantly lower than how boys rated it. However, both genders judged the importance of doing well in math as high. Even though both girls and boys achieved similar achievement levels in Math in their mid-term grades, gender discrepancies in emotional experiences were still found in the study. This suggests that apart from achievement in Math, there are still some factors responsible for boosting boys’ emotional experiences or harming girls’ feelings in this domain. One plausible reason may be gender stereotypes propagated through the ages that explain discrepancies between the genders. It has been believed that boys are wired to be more competent in Math than girls, and so, are expected to perform better than their female counterparts. Girls are also stereotyped to be more emotional, hence the self-fulfilling prophecy is lived out. Hence, it is most likely that girls often think they have to work harder than boys in order to achieve good results in Math (Lupart, Cannon & Telfer, 2004). Since women are often found to experience emotions more intensely than men (Barrett, Robin, Pietromonaco, & Eyssell, 1998; Larsen & Diener, 1987), especially true with negative emotions such as anxiety, sadness, shame and guilt. Thus, the higher levels of negative emotions towards math reported by the girls in the study may have been due to higher levels of self-reported negative emotions generally found in girls. The feelings of lack of competence paired with a lack of domain value of the subject, also hampers the experience of positive mathematics emotions for girls such as enjoyment or pride. (Frenzel, Pekrun & Goetz, 2007). One limitation of the study was the use of self-report scales to measure emotions. Instead of actually experiencing different emotional levels, the girls and boys in the study were limited to thinking about how they would feel, and may have differed in their capability and willingness to report their emotions. Their capability and willingness for emotional expression may also be influenced by social desirability and gender stereotyping (Eisenberg & Fabes, 1995; Grossman & Wood, 1993). The study of Frenzel, Pekrun & Goetz, (2007) concluded that gender differences in emotions towards math were likely due to differences in competence and values given to the subject domain rather than to gender differences in the relationships between beliefs and emotions. They suggest that if girls and boys held the same self-related beliefs in Math, then they would probably experience the same levels of positive and negative emotions for this subject. Effect of Emotions and Motivations on Adolescent Girls’ Math Learning For the past century, scholars have described adolescence as a period in girls’ development when many begin to devalue their thoughts, feelings, and perceptions, and, consequently, risk becoming repressed (Basow, 1999; Brown & Gilligan, 1992; Deutsch, 1944; Freud, 1905;). The study of Frenzel, Pekrun & Goetz (2007) on emotions and motivations towards Math showed that girls experienced significantly less enjoyment and less pride than boys. At the same time, they experienced more anxiety and more hopelessness related to mathematics. Further, girls reported slightly more shame than boys. This is echoed in the results of Spence et al’s (1975) experiment on the differences in math abilities of males and females. College students of equivalent math backgrounds took math tests. Half were told that the math test showed gender differences in the past and half were told that the test has been shown to be gender fair. As expected, among those who believed that the test was gender fair, there were no gender differences in performance, however, with those who believed it showed gender differences, women under-performed compared to men. This may be explained that stereotypes about women faring less than men in mathematics may have affected their performance. Such researches imply that stereotypes have the power to dictate how people may behave in certain situations. At the same time, it may be used as an excuse whenever people fail or succeed at one point or another, lessening accountability on the person himself. In the case of the experiment discussed, women may use the stereotype that they are weaker in math whenever they encounter difficult math problems. Sherman (1983) believes that in the study of mathematics as one of the most male-typed subjects, it is neither anxiety nor lack of ability that keeps women away from it but rather, a network of sex-role influences such as motherhood and being homemakers. Such roles appear incongruent with what math has to offer. However, she suggests that when girls see motherhood and demanding careers can be balanced effectively, then the resistance towards Math will disappear. Unless this belief is established and propagated, attempts to reduce sex-role stereotyping in mathematics will gain limited success if the ultimate goal is increasing the number of women representation in math-related careers. Understanding the nature of adolescent girls in terms of emotion and motivation, what can be done to support their learning of mathematical concepts and skills? Teachers should be adept with basic teaching approaches inspired by known theories and apply these to their classes, keeping in mind the gender differences in learning as motivated by emotions, needs and goals. Vygotsky (1978) came up with the concept of the zone of proximal development (ZPD). He defined the ZPD as the distance between a child’s independent problem-solving level and that obtained under adult guidance or in collaboration with more capable peers (Wertsch, 1985). Wells (1997) cautioned us, however, that a ZPD is formed not just within an individual learner, but in the interaction between the learner, coparticipants, and available tools during involvement in a common activity. ZPDs, therefore, depend on the quality of the total interactive context as well as individual learner capabilities. (Bonk & Cunningham, 1998). With young girls, they may not be so interested in Math especially if repeated on a regular basis. Teachers should challenge them learn a slightly more difficult concept to test their mettle in the skills they have gained, but with some guidance so they will feel success in their attempts. “Such cognitive apprenticeships are, of course, inherently reliant on a mentor or guide who effectively uses “scaffolded instruction.” (Bonk & Cunningham, 1998 p.40). As the term implies, scaffolds are temporary supports in the process of learning which are gradually taken away when the student is already capable of learning without them. The task would not have been completed without the help of scaffolds. As an example, the teacher helping young adolescent girls to do mathematical problem solving would first give them the very basic steps such as analyzing word problems for the unknown and given information and as they master the concept, the materials or “scaffolds” are slowly eased away until they can do the process mentally. “Examples of this support might include prompts, hints, comments, explanations, questions, counterexamples, and suggestions. A learning scaffold may be embedded in an explicit request to include additional information or a more general question or comment intended to spur new idea linkages or course connections. Of course, these learning aids are faded and removed as the learner assumes control over the activity. Through such assistance, the learner (or a team of learners) solves a problem, generates solutions, and gains insights that would ordinarily rest beyond or her independent abilities. (Bonk & Cunningham, 1998, p. 40-41) It is essential to strike a balance between giving the students sufficient challenge and taking care not to push them into a level they are not yet capable of. Research shows that when students are trained to learn mathematics above their reasoning level, there may be positive results at first but they are “rarely retained unless the child is already in transition from one level to another” (Suydam and Weaver, 1975, p. 47). The teacher should be discerning enough to know when to apply ZPD with her students and know the proper scaffolds to use. According to the behaviorist view, an individual is reinforced (positively or negatively) for responses to various stimuli, hence, the external environment plays a great part in the formation of behaviors. By administering positive reinforcement such as praising or smiling when a desired behavior occurs and administering negative reinforcement such as scolding or correcting when an undesired behavior occurs, one is assumed to encourage the desired behavior and make it more likely that that behavior will recur (Lindfors, 1987). Adolescent girls need a whole lot of positive reinforcement to boost their confidence in their mathematical abilities. The review of past lessons coupled with praise when the girls are successful in their recall moved towards the direction of more success in their present and future learning. More important than the lessons taught in the sessions are the interests of the adolescent girls themselves. The learning environment must be supportive of children’s ideas and feelings. In the stage of strengthening their identities, adolescents should be allowed to express themselves freely. Trafton (1975) suggests that individualization must include acceptance of each student as an individual worthy of adult respect. There must be an acceptance of the student’s ideas, a provision of opportunities for student input in developing and selecting learning experiences, a concern for the quality of the student’s intellectual development, and a willingness to take time to know the student as an individual. Conclusion In a world that keeps changing, old beliefs and values regarding gender differences must eventually die out to free people from the bondage of stereotypes. For young girls, particularly, the disadvantage of people’s expectations of their low competency in Math and their high emotionality can hamper their growth and development into adults who have optimized their potentials. Math has proven to be a powerful stressor. The mere mention of mathematical concepts and logical reasoning with numbers may be enough to send shivers to young girls who have been raised to believe they are not good enough to tackle Math challenges. The pathetic thing is that their natural emotionality towards stressors worsen how people perceive their competence, which in effect, worsens their own self-perception and self-esteem. The knowledge unearthed by numerous research on the links between Math, emotions and motivation should propel parents, relatives and educators to take a paradigm shift on their expectations of adolescent girls’ competencies in Math and other traditionally male-associated subjects and fields. Empowering young women by boosting their self esteem and actually believing that they can reach for the sky would do wonders for their self-image and abilities. Helping young women to set their goals would be a good start. Goals incrementally set and met become overwhelmingly reinforcing. For example, meeting small goals such as passing a Math test, then getting a high Math test score, then being able to excel in Math and join competitions would be an ideal path of goals to take. The happy emotions associated with small successes are enough to motivate an individual to stick to her goal plan. Handling emotional responses is a more difficult challenge for educators since it is not easy to predict how an individual will react with a learning material presented. However, the professional educator would know which strategies to use to make the introduction appealing to the learners. The teacher must also know how to present the lesson in such a way that it does not threaten the learner’s confidence to wane and instead challenge her to be able to understand and perform well. Supporting adolescent girls in their learning of Math may be a rewarding endeavor to educators because this particular stage has built-in challenges related to motivating them while being able to handle their emotions well. Achieving success in getting through those challenges ensures an educator that he or she has done her initial job well and is now ready to take the learners for Math adventures that would benefit as they grow up to be confident, competent and contributing women of society. References Ashcraft, M.H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science , Vol. 2, pp. 181-185 Barrett, L.F., Rohin, L., Pietromonaco, P., & Eyssell, K. (1998). Are women the over emotional sex? Evidence from emotional experiences in social context. Cognition and Emotion, 12, 555-578. Basow, S. A. (1999). Gender influences on adolescent development. In N. G. Johnson, M. C. Roberts, & J. 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