Study Choice
Mathematics self-concept, attitude and achievement are emphasized as motivational factors in science, technology, engineering, and mathematics (STEM) fields. As a mathematics teacher of middle school students, it seems only natural to have an interest in these factors.
Research on attitude is driven by the belief that it plays a crucial role in learning mathematics. Ma and Kishor (1997) define one’s attitude towards mathematics “as an aggregated measure of liking or disliking of mathematics, a tendency to engage in or avoid mathematical activities, a believe that one is good or bad at mathematics, and a belief that mathematics is useful or useless” (p. 27). Neal (1969) defines attitude towards mathematics as “an aggregated liking or of disliking mathematics, a tendency engage in or avoid mathematical activities, a belief that one is good or bad at mathematics, and a belief that mathematic is useful or useless"(p. 632). Mathematical attitude where behaviors do not appear explicitly are defined as a pattern of beliefs and emotions associated with mathematics leading from a motivation view to one that is based on self-concept; a student’s perception or belief in ability (Daskalogianni & Simpson, 2000).
Research by Wang, Osterlind, and Bergin (2012) emphasizes self-concept of ability as one of the major predictors of achievement making it an essential concept in mathematic education. Self-concept of ability is argued as having a direct impact on a student’s attitude and achievement making the connectivity amongst the constructs apparent (Möller, Pohlmann, Köller & Marsh, 2009; Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005; Wilkins, 2004).
At the preliminary stages, it has been suggested that as students progress in years of schooling, negative attitudes towards mathematics increase, and self-concept of ability in mathematics decrease (Wilkins, 2004). This happens to coincide with the dip in mathematical achievement seen at the middle school level and a reason why the three constructs have been researched in depth for several years. Research by Yilmaz, Altun and Olkun (2010) suggests a successful student has a positive attitude. On the other hand, Bouhlila (2011) suggests some of the highest scoring countries have the greatest number of students with negative attitudes in mathematics. According to Bouhlila (2011), the Middle East and North African (MENA) countries that rank high in attitude and self-concept show low mathematical performance. Conversely, countries such as Japan, Korea and China who rank low in positive attitudes, and self-concept are some of the higher scoring countries in mathematics. In the U.S. negativity towards mathematics becomes prominent around the middle school years.
According Hassan, Ching, and Hamizah (2012), interventions such as teacher support, cooperative learning, classroom materials, modeling, and self-efficacy have direct effects on the intrinsic motivation; related to the attitudes of students. With such interventions having an impact on attitude, one can consider these interventions to further have an impact on self-concept and achievement. However, this is unclear.
The review of current literature supports the interdependence of attitude, achievement, and self-concept. The relationships are supported by the findings of researchers however there is a lacking in causal delineations. Few studies examine the impact of support and interventions on self-concept of ability. Essentially, the literature fails to discuss collaborative efforts and the potential impacts such efforts could have on a student’s sense of self-concept.
The goal is to look globally for factors and influences, which have a positive effect on middle school students’ mathematical attitudes and self-concept to provide supports and interventions. There is little perspective on specific supports and interventions which have a positive effect on middle school students’ mathematical attitudes and self-concept. The hierarchal or causal relations of supports and the role which they play in the development of self-concept in the middle school mathematic student is an area which is lacking. As a researcher a gap in knowledge has been identified which helps to support my interests as a middle level math teacher.
Theories and Authors
The perspective of my work thus far relies on the psychology theory of academic self-concept. Self-concept is defined as “an individual’s perception or belief in their ability to do well in an academic domain” (Wang et al., 2012, p. 1215). Self-concept explains an individual’s belief to learn and do well in. Research endorses the importance of a positive self-concept to achievement, emphasizing self-concept enhancement (McInerney, Cheng, Mok, & Lam, 2012). Self-concept has an important effect on the way student’s “feel about themselves, their accomplishments, persistence and educational decisions” (Möller et al., 2009, p. 1130).
Academic self-concept of ability is of significance in understanding mathematics achievement defined as an explanatory variable in mathematics achievement and as a controlling variable in initial achievement (Valentine, Dubois & Cooper, 2004; Wang et al., 2012). Academic self-concept is argued to be one of the strongest predictors of mathematics achievement in both the near and distant future of students (Valentine et al., 2004). This advances self-concept as a fundamental attribute in understanding the mathematical achievement in students but also provides a lens for achievement in mathematics.
At this point in research there is a scattering of research related to self-concept, attitude and achievement in mathematics with a few authors appearing as prevalent within academic self-concept theories.
Jacquelynne Eccles, Allan Wigfield and associated colleagues have significance in the presentation of their expectancy value model. The expectancy-value model is a model that concentrates on students’ beliefs in their own ability and competence (Denissen et al., 2007). According to this model there are two key predictors of achievement; self-concept of ability and subjective task values. Subjective task values are strong predictor of future choices (Wilkins, 2004; Wang et al., 2012). Where as, self-concept of ability is a stronger predictor of achievement of self-concept (Wilkins, 2004; Wang et al., 2012). This model tends to put a focus on self-concept for those concerned with immediate achievement. Authors such as Marsh, Trautwein, Lüdtke, Köller, and Baumert (2005) confirm the relationship between academic self-concept and achievement but extend the relationship to include academic interest adding a new branch when considering achievement.
According to the internal/external frame of reference model, students compare their abilities using two frames. The external frame of reference is explained by students who make social comparisons such as comparing math performance to their peers. The internal frame of reference refers to instances when students compare their achievement in one subject to that of another subject. These external and internal elements are considered crucial in the development of self-concept and can be found in much of the work of Marsh and colleagues, making Marsh a key researcher in this area.
Good and Useful Theory
Good, and useful theory contributes to research. According to Anfara and Mertz (2006) theory provides a simple explanation of relations, is consistent with observed relations and previously established knowledge, is a means of verification, and inspires further research (p. xvii). In essence it is the theory which provides a "lens that can be applied to understand phenomena” (Anfara & Mertz, 2006, p. xxvii). Good theory affects research as it allows the researcher “to present a unique view of the phenomenon being studied” (Anfara & Mertz, 2006, p. xiv). It is good and useful theory that provides a support to “shift in one’s mental structure” to discover a different way of thinking (Anfara & Mertz, 2006, p. xxvii). Through the application of good and useful theory, the researcher has the provisions to see and understand aspects of phenomena beyond the ordinary bringing about new insights to research.
References
Anfara, V. A., & Mertz, N. T. (2006). Theoretical frameworks in qualitative research. Thousand Oaks, Calif: SAGE Publications.
Bouhlila, D. S. (2011). The quality of secondary education in the Middle East and North Africa: what can we learn from TIMSS’ results? Compare: A Journal of Comparative and International Education, 41(3), 327–352. doi: 10.1080/03057925.2010.539887
Daskalogianni, K., & Simpson, A. (2000). Towards a definition of attitude: The relationship between the affective and the cognitive in pre-university. Proceedings of PME Conference, 24(2), 2-217.
Denissen, J. J. A., Zarrett, N. R., & Eccles, J. S. (2007). I like to do I, I’m able, and I know I am: Longitudinal couplings between domain-specific achievement, self-concept, and interest. Child Development, 78(2), 430–447. doi:10.1111/j.1467-8624.2007.01007.x
Hassan, N., Ching, K. Y., & Hamizah, N. N. (2012). Gifted students’ affinity towards mathematics. Advances in Natural & Applied Sciences. 2012, 6(8), 1219–1222. 4p. 3 Charts. Retrieved from: http://www.researchgate.net/publication/235631140_Factors_That_Influence_Gifted_Students_Attitude_against_Mathematics
Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics education, 28(1), 26-47. doi:10.2307/749662
Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O., & Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76(2), 397–416. doi:10.1111/j.1467-8624.2005.00853.x
McInerney, D. M., Cheng, R. W., Mok, M. M. C., & Lam, A. K. H. (2012). Academic self-concept and learning strategies: Direction of effect on student academic achievement. Journal of Advanced Academics, 23(3), 249–269. doi: 10.1177/1932202X12451020
Möller, J., Pohlmann, B., Köller, O., & Marsh, H. W. (2009). A meta-analytic path analysis of the internal/external frame of reference model of academic achievement and academic self-concept. Review of Educational Research, 79(3), 1129–1167. doi:10.3102/0034654309337522
Neale, D. C. (1969). The role of attitudes in learning mathematics. The Arithmetic Teacher, 16(8), 631-640.
Valentine, J., Dubois, D. L., & Cooper, H. (2004). The relation between self-beliefs and academic achievement: A meta-analytic review. Educational Psychologist, 39(2), 111–133. doi:10.1207/s15326985ep3902_3
Wang, Z., Osterlind, S. J., & Bergin, D. A. (2012). Building mathematics achievement models in four countries using TIMSS 2003. International Journal of Science and Mathematics Education, 10(5), 1215–1242. doi: 10.1007/s10763-011-9328-6
Wilkins, J. L. M. (2004). Mathematics and science self-concept: An international investigation. The Journal of Experimental Education, 72(4), 331–346. doi: 10.3200/JEXE.72.4.331-346
Yilmaz, C., Altun, S. A. & Ollkun, S. (2010). Factors affecting students‟ attitude towards math: ABC theory and its reflection on practice. Procedia Social Science and Behavioural Sciences, 2(2), 4502-4506. doi: 10.1016/j.sbspro.2010.03.720
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