Session Information
99 ERC SES 04 G, Mathematics Education Research
Paper Session
Contribution
Historically, school mathematics has been viewed as a complex and abstract subject with little relevance to daily life (Ernest, 2016). Eccles (1983) found that student negativity towards mathematics increases over time, mirroring a decline in self-belief and motivation. Eccles et al. (1993) subsequently investigated the causes of declining motivation, and found that getting older was not the primary driver; rather the decline was influenced by teachers exhibiting more control over students as they advanced through grades, restricting student decision-making and conveying lower expectations in students’ ability.
In their seminal report, Kilpatrick et al. (2001) identified five interconnected components that are necessary to learn mathematics successfully. One of these components is productive disposition, essentially a combination of self-efficacy and perceived usefulness for mathematics (Kilpatrick et al., 2001). Both self-efficacy and seeing that mathematics demonstrates utility (useful for future goals) are considered vital for motivation (Gafoor & Kurukkan, 2015).
For this study, Eccles & Wigfield’s (2020) Situated Expectancy-Value Theory will be used as a theoretical framework. The framework indicates primarily that expectancies and values drive future performance. Eccles (1983) found that motivation is boosted when students value the tasks that they are engaging with. Task values are a function of attainment values (Importance of succeeding), intrinsic values (Enjoyment), utility values (help with forthcoming goals) and cost(Eccles & Wigfield, 2020). In their framework, Eccles & Wigfield (2020) indicate that utility value is the most ‘malleable’ of task values. Utility value interventions have shown promise in improving student effort generally (Hulleman et al., 2008), but also specifically within mathematics (Liebendörfer & Schukajlow, 2020). However, despite evidence that utility value interventions positively impact student motivation, many teachers are unaware of its relevance (Hulleman & Barron, 2013).
While utility value interventions may improve motivation, what one person might see as useful another may not; it is important to remain cognisant of the fact that utility values are individual, and can be influenced by cultural differences. It is therefore worthwhile considering the potential of culturally responsive teaching as a method of enhancing students’ perceived utility values towards mathematics. Hunter et al. (2016) noted student reactions to culturally relevant interventions, citing comments such as “When the problems are about us you can see that maths is real and it’s useful……not just something random you do at school”. This demonstrates that relating mathematics to familiar contexts can impact utility value. Lowrie (2004) also highlights the benefits of using artefacts to make mathematical tasks more realistic, which may lead to students seeing increased utility value in mathematics.
Another approach that has been noted as supporting students to understand the relevance of more abstract mathematical concepts is mathematical modelling (Liebendörfer & Schukajlow, 2020). With mathematical modelling there is no definite answer; students take real-life scenarios, mathematise them, identify variables, make assumptions, generate initial solutions before iteratively reviewing the process (Sahin et al., 2019). By engaging with the process of modelling, students can reflect and generate further examples themselves. Regular Mathematical modelling tasks can enable students to encounter numerous concepts routinely in a variety of contexts, benefitting productive disposition and indeed all five components of mathematical proficiency (Kilpatrick et al., 2001).
The goal of this research is to draw together mathematical modelling and culturally responsive teaching in an approach to mathematics teaching that aims increase students’ perceived utility values, productive disposition and motivation, ultimately contributing to successful learning of mathematics. The overarching research question is: What impact does incorporating culturally relevant mathematical modelling tasks have on students’ utility value for mathematics?
Method
The research will be conducted via a mixed-methods case study, using Situated Expectancy-Value as a theoretical framework. The intervention will be conducted over the course of two academic years, with students and teachers from a single school. Quantitative data in relation to utility values of students - will be generated by way of a questionnaire administered at various points throughout the research. Qualitative data from both teachers and students via focus group discussions and exit tickets throughout will be collected. The sample of students will be age ~12-13 at the beginning of the intervention (ISCED 2) and three of their teachers. The choice of conducting this intervention with this age group (first year, lower secondary in Ireland) is due to the recent addition of mathematical modelling to the Irish curriculum for this cohort ("Junior Cycle Mathematics," 2024). In addition to teaching students, training for teachers will be provided, where eventually they will be facilitating mathematical modelling lessons. If successful, the intervention will be expanded to more schools. In terms of professional development for teachers, the principles of ‘Experiential Learning Design’ will be followed. Participants will have opportunities to teach in the manner that the training has suggested. They can then reflect on the teaching and learning of students, abstract their reflections and embed this into their practice going forward. This form of professional development is participant-centred and, while quite intensive, it has been shown to be very beneficial for participants (Girvan et al., 2016). Research Questions: 1. Does incorporating culturally relevant artefacts into task designing mathematical modelling tasks increase student utility value for mathematics? 2. Does engaging with mathematical modelling tasks increase student’s conceptual understanding of abstract mathematical concepts? 3. Does incorporating culturally relevant artefacts into task designing mathematical modelling tasks increase student performance in Mathematical Investigation assessment (2nd year Classroom Based Assessment in Ireland, (ISCED 2)) Data 1. Quantitative data from student surveys. 2. Students will complete reflective exit tickets following lessons. 3. Focus group discussions will be conducted with both teachers and students. They will allow for capturing of real-life complexities that quantitative data may not (Zainal, 2007). Focus group discussions topics will include task values, expectations, attributions of past performance and self-concept of ability (Eccles & Wigfield, 2020). 4. A thorough analysis will then be compiled of both qualitative feedback from students and teachers and quantitative data from student utility values and in-class assessments.
Expected Outcomes
Ultimately, the goal is for students to be successful. Motivation is strongly correlated with future success (Amrai et al., 2011), however, research has shown that motivation, tends to decline as students get older ((Parsons), 1983). Many factors contribute to this decline, but one that has been noted by some authors is the lack of perceived relevance of the subject. However, it is hoped that by situating the mathematics in situations that are relevant to the students, it may be possible to slow, or even halt, this decline (Eccles et al., 1993). The Situated Expectancy-Value theory provides a useful framework through which to explore the effect of the kinds of teaching and learning promoted by this study. Students may identify increased cultural relevance in their mathematics due to culturally relevant artefacts being the basis for mathematical modelling tasks thereby increasing utility value. In sum, this research aims to investigate whether incorporating culturally relevant mathematical modelling tasks leads to increased utility values as outlined in Eccles & Wigfield (2020) and improved academic performance for students.
References
(Parsons), J. E. (1983). Expectancies, Values and Academic Behaviours. In J. T. Spence, Achievement and Achievement Motives (pp. 75-146). San Francisco: W.H. Freeman and Company. Amrai, K., Motlagh, S. E., & Parhon, H. A. (2011). The relationship between academic motivation and academic achievement students. Procedia Social and Behavioural Sciences, 399-402. An Roinn Oidicheas agus Scileanna. (2024, January 31). Junior Cycle Mathematics. Retrieved from curriculumonline.ie: https://www.curriculumonline.ie/Junior-cycle/Junior-Cycle-Subjects/Mathematics/ Eccles, J. S., & Wigfield, A. (2020). From expectancy-value theory to situated expectancy-value theory: A developmental, social cognitive, and sociocultural perspective on motivation. Contemporary Educational Psychology, 1-13. Eccles, J. S., Wigfield, A., Midgley, C., Reuman, D., MacIver, D., & Feldlaufer, H. (1993). Negative Effects of Traditional Middle Schools on Students' Motivation. The Elementary School Journal, 554-574. Ernest, P. (2016). The Collatoral Damage of Learning Mathematics. Philosophy of Mathematics Education Journal, 13-55. Gafoor, K. A., & Kurukkan, A. (2015, August 18). Why High School Students Feel Mathematics Difficult? An Exploration of Affective Beliefs. Retrieved from https://files.eric.ed.gov: https://files.eric.ed.gov/fulltext/ED560266.pdf Girvan, C., Conneely, C., & Tangney, B. (2016). Extending experiential learning in teacher professional development. Teaching and Teacher Education, 129-139. Hulleman, C. S., & Barron, K. E. (2013, May 1). Teacher Perceptions of Student Motivational Challenges and Best Strategies to Enhance Motivation. Charlotsville, Virginia, United States of America: American Educational Research Association. Hulleman, C. S., Durik, A. M., Schweigert, S. A., & Harackiewicz, J. M. (2008). Task Values, Achievement Goals, and Interest: An Integrative Analysis. Journal of Educational Psychology, 398-416. Hunter, J., Hunter, •. R., Bills, T., Cheung, I., Hannant, B., Kritesh, K., & Lachaiya, R. (2016). Developing Equity for Pa¯sifika Learners Within a New Zealand Context: Attending to Culture and Values. NZ J Educ Stud, 197-209. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it Up; Helping Children Learn Mathematics Successfully. Washington D.C.: National Academy Press. Liebendörfer, M., & Schukajlow, S. (2020). Quality matters: how reflecting on the utility valu of mathematics affects future teachers' interest. Educational Studies in Mathematics, 199-218. Lowrie, T. (2004). Making mathematics meaningful, realistic and personalised: Changing the direction of relevance and applicability. Towards Excellence in Mathematics (p. 10pp). Brunswick, Australia: The Mathematics Association of Victoria. Sahin, S., Dogan, M., Cavus Erdem, Z., Gurbuz, R., & Temurtas, A. (2019). Prospective Teachers’ Criteria for Evaluating Mathematical Modeling Problems. International Journal of Research in Education and Science, 730-743. Zainal, Z. (2007). Case study as a research method. Jurnal Kemanusiaan, 1-6.
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