Academic Success Skills: Beliefs about Mathematics
Students often view mathematics as a disconnected set of procedures. It is common for them to believe that mathematical proficiency is most clearly evidenced by one’s ability to solve problems quickly. Students’ beliefs about mathematics influence the ways they engage with it and, consequently, their educational outcomes. For example, students who believe all problems can be solved in under five minutes or less (Schoenfeld, 1988) are unlikely to persevere to solve novel problems and thus fail to benefit from potentially valuable learning opportunities.
Faculty at the MIP Academic Success Skills Initiation Workshop in May, 2019 recommended that instructional resources developed by CoRDs and ARCs addressing Beliefs about Mathematics for success in the Oklahoma entry-level college math pathways should:
1. Review and synthesize the literature about students’ beliefs about mathematics, including any relevant findings about the origins of those beliefs.
2. Develop a list of beliefs we, as mathematicians and mathematics educators, would like students to hold about mathematics and describe how they contribute to students’ engagement in mathematical inquiry.
3. Develop recommendations for instructional and curricular design that foster the development of the beliefs identified in (2).
4. Describe the potential affordances of the MIP focus on promoting students’ active engagement and leveraging meaningful applications for supporting students’ development of productive beliefs about mathematics.
Suggested Resources
Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman mathematics attitudes scales.
This spreadsheet, available upon request (allison.j.dorko@okstate.edu), is a Likert-scale survey that can be employed to lend insight into students’ attitude toward success in mathematics, beliefs about mathematics, confidence about their ability to do mathematics, and usefulness about mathematics. It could be useful to prompt CoRD developers in imagining what students believe about mathematics and what we want them to believe.
Kerins, B., Yong, D., Cuoco, A., & Stevens, G. (2015). Famous functions in number theory. PREFACE:
https://bookstore.ams.org/sstp-3/~~FreeAttachments/sstp-3-pref.pdf
This book preface explains the design principles behind task sequences that engage students in learning significant mathematics through inquiry. For example, the same problem shows up in multiple task sequences, allowing students to explore it repeatedly and make some progress while, throughout the other tasks in the sequences, they build the tools to eventually solve the problem. This design supports persistence in problem solving and helps counter the belief that any problem can be solved very quickly. The book’s task sequences are from intensive workshops aimed at practicing high school math teachers. We suggest this resource not for the mathematical content, but as an example of how tasks can be designed and sequenced in ways which support students’ mathematical inquiry as well as their beliefs about what it means to do mathematics.
Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of ‘well-taught’ mathematics courses. Educational psychologist, 23(2), 145-166.
This resource contains a list of students’ beliefs about mathematics that the CoRD might take as a starting point for (1).
Carlson, M. (1999). The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success. Educational Studies in Mathematics, 40(3), 237-258.
This paper explored the characteristics and experiences of mathematics graduate students that contributed to their development and success.