by Kenneth Butler

I am a cognitive scientist who is interested in how and why people learn mathematics, and in alignment with the National Council of Teachers of Mathematics (NCTM) access and equity principle (NCTM, 2014), I believe all students should have access to mathematics that is rich in content and engaging. Unfortunately, too many students believe they are being forced to participate in mathematics, they do not believe they are competent participants in mathematics classrooms, and they do not see success in mathematics as something attained by people who are similar to them.  This lack of the basic psychological needs of autonomy, competence, and relatedness in many current mathematics environments forces some of the brightest students to cede their opportunity to learn and to abandon any aspirations of a career path rich in mathematics. I see this lack of motivation for mathematics as one of the biggest challenges facing educators in the United States today, and it is the impetus for much of my research.

My interest in cognition and the desire to measure motivation led me to consider issues surrounding the measurement of motivational constructs, and therefore as a PhD candidate, I acquired a strong foundation in quantitative measurement. My dissertation (Butler, 2016) involved the development and validation of an abbreviated instrument to measure motivation as framed by self-determination, self-efficacy, achievement goal theory, and expectancy-value. This study involved the development of a structural equation model and was motivated by recent research looking across these traditional theories on motivation (Friedel, Cortina, Turner, & Midgley, 2007; Murayama, Pekrun, Lichtenfeld, & vom Hofe, 2013). The use by these studies of a myriad of psychometric surveys highlighted the need for an abbreviated combined instrument that parallels these theoretical constructs defining motivation.

My dissertation was framed by the Standards for Educational and Psychological Testing (AERA, 2014), and it directly addressed three of the five sources of validity evidence. The resultant instrument –the Motivation for Mathematics Abbreviated Instrument (MMAI)– has a factor structure that parallels theory, and for the population being measured, it has strong internal convergent and discriminant validity. I am currently publishing research that was conceived in this dissertation and is associated with relationships between gender and achievement goals, and with both theoretical and experimental sources of evidence for validating content.

Research utilizing the MMAI has provided insight into the fluid relationship between gender, achievement goals, and mathematics achievement. I recently explored this relationship when a path analysis provided significant evidence that mastery orientation in males was inversely related to achievement, and that performance orientations in females were directly related to achievement. To reconcile these relationships, I relied on cognitive interviews. Data from these interviews revealed that some of the students in the study felt they were in a situation where course pacing made it impossible to understand the material being presented. This situation produced anxiety in a mastery oriented male. Alternatively, a performance oriented female stopped trying to understand everything and instead focused solely on her grades. This coping strategy may have explained why performance orientation in females improved achievement. Notice, the quantitative analysis revealed a relationship, but I relied upon qualitative data for interpretation.

This reveals my inclination towards mixed methods research. Being fluent in quantitative methods opens many paths to further the science of education; however, numbers should not become bludgeons. In educational settings numbers represent people. Therefore, it is often necessary to rely on qualitative analyses to interpret quantitative data, or to rely on quantitative analyses to help understand and organize qualitative codes. As a mixed methods researcher, I see benefits in triangulating quantitative findings with interviews and observations of participants, and when qualitative data is obtained, in quantifying relationships by creating intra-respondent matrices (Onwuegbuzie, 2003) and calculating qualitative effect sizes.

Recently, through a collaboration with a colleague I reworked an article associated with improving engagement by adding situational content to word problems with spatial content. This added situational content created a potential for causation and then provided agency to the reader for finding a resolution to conflict. Using path analyses, we revealed that seventh grade females who were better in language arts were more successful at solving mathematical word problems with included situational content. This led to the conclusion that situational content was motivational for some students as it gave them agency and helped them form relationships.

This study aligned with my focus on developing a theoretical framework associated with relatedness in mathematics education, and I am currently reviewing this framework using an ecological model for situational grounding. Constructivist theories on education foster peer-to-peer as well as student-teacher relationships. Project based instruction and model eliciting activities encourage family and community relationships, and social justice issues and culturally relevant pedagogy provide students a lens to critically view controversial social issues and culture. In this process, I am dedicated to fostering relationships between student interests and mathematical content, because I believe this is the best way to improve student motivation. Through improving motivation we can improve student engagement in a mathematically rich, logical, and fact based society.

 

References

American Educational Research Association, American Psychological Association, National Council on Measurement in Education, Joint Committee on Standards for Educational, & Psychological Testing (2014). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.

Butler, K. (2016). Motivation for mathematics: The development and initial validation of an abbreviated instrument. Dissertation University of South Florida.

Friedel, J. M., Cortina, K. S., Turner, J. C., & Midgley, C. (2007). Achievement goals, efficacy beliefs and coping strategies in mathematics: The roles of perceived parent and teacher goal emphases. Contemporary Educational Psychology, 32, 434-458.

Murayama, K., Pekrun, R., Lichtenfeld, S., & vom Hofe, R. (2013). Predicting Long‐Term Growth in Students’ Mathematics Achievement: The Unique Contributions of Motivation and Cognitive Strategies. Child Development, 84, 1475-1490.

National Council of Teachers of Mathematics (2014). Principles to actions: ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

Onwuegbuzie, A. J. (2003). Effect sizes in qualitative research: A prolegomenon. Quality & Quantity: International Journal of Methodology, 37, 393-409.