Chris L. Yuen, Ed.D . CLYUEN@buffalo.edu SUNY University at Buffalo

1. Authentic versus Contingent Knowledge: How Math-Anxious Adult Learners’ Engagement in Contingent Knowledge and Implications for Developmental Instruction Chris L. Yuen, Ed.D. CLYUEN@buffalo.edu SUNY University at Buffalo 2nd Untested Ideas International Research Conference June 27, 2014 Funding for this research project was generously provided by the American Mathematical Association for Two-Year Colleges (AMATYC) and from the General Research Grant awarded from the University of Phoenix.

2. Overview – What is Math Anxiety Learning Phenomenon (MALP)? [A] Before the learning process takes place, adult learners have sets of beliefs about the subject of mathematics, about their own abilities, and about certain attitudes toward learning. [B] The individual and social behaviors from [A] affect how learning takes place―i.e. learning what mathematical knowledge to memorize, learning how to survive school mathematics, and informing fellow learners of one’s past experience. [C] The individual and social behaviors from [B] serve as perceptions to reinforce or change the beliefs in [A]. [A], [B], and [C] altogether: How could the cycling learning phenomenon that is perpetuated in [A], [B], and [C] be sufficiently addressed (and perhaps be broken) in classroom instruction to optimize learning?

3. Theoretical Underpinning 1:What is Knowles’ Andragogy? Knowles’ andragogy as a set of assumptions on adult learning (Merriam & Caffarella, 1999, p. 272): • Self-Directedness: As a person matures, his or her self-concept moves from that of a dependent personality toward one of a self-directing human being. • Reservoir of Experience: An adult accumulates a growing reservoir of experience, which is a rich resource for learning. • Readiness to Learn: The readiness of an adult to learn is closely related to the developmental tasks of his or her social role. • Problem Centeredness: There is a change in time perspective as people mature—from future application of knowledge to immediacy of application. Thus an adult is more problem centered than subject centered in learning (Knowles, 1980, pp. 44–45). • Internal Motivation: Adults are motivated to learn by internal factors rather than external ones (Knowles & Associates, 1984, pp. 9–12).

4. Theoretical Underpinning 2 Wilber’s Integral Model: Individual-Interior (UL), Individual-Exterior (UR), Collective-Interior (LL), and Collective-Exterior (LR) Employ qualitative techniques from hermeneutic phenomenology to inquire the problem through the Integral Model’s fourfold “lens.”

5. Problem Statement and Research Questions As a practitioner who teaches developmental mathematics to adult learners who often experience mathematics anxiety, what characteristics of MALP could give insights that would influence instruction to optimize learning? • (UL) Personal beliefs and their manifestations on learning mathematics. • (UR) Roadblocks that prevent success in mathematics. • (LL) Cultural beliefs in MALP, how they are passed on to others, and how it is perpetuated within and outside of the classroom. • (LR) Social norms when learners are supporting each other and the identity and role of an adult learner in the mathematics education community. • (Integral Disclosure) Based on the above, the study aims to disclose an integral perspective to reveal truths about MALP.

6. Methods • Six participants each undergone a series of two unstructured interviews, and wrote three journal entries, highlighting their life history on math learning. • Interviews and journal focused on past and current math learning experiences, attitudes and beliefs toward the math subject, and the social learning experience, and the role and identity in the learning community and discourse • Analysis using hermeneutic techniques to develop themes for MALP, and how these themes relates to Knowles’ andragogy. Themes can be used to build upon Givvinet al.’s hypothetical model.

7. Major Themes and Findings of the Study

8. Theoretical Results • Self-Directedness: The six participants chose to continue their education by free will. • Reservoir of Experience: They showed that their past negative experience became a source for their anxiety, and indeed it was reinforced in subsequent learning experience through engagement of contingent knowledge. • Readiness to Learn: To cope with their anxiety, learners preferred formulaic procedures (surface learning) that could answer math questions efficiently. Sacrificing the logical reasoning (usually less time efficient) is acceptable.

9. Theoretical Results (Continued) • Problem Centeredness: Non STEM learners saw taking a college math course as a “problem”, and “jumping the hoops” for the course through a path of least resistance is a way to solve this immediate problem. As a result, learners focused on learning tasks that were contingent upon passing the course. • Internal Motivation: They were motivated to succeed in the math course, because it would lead to complete of the degree program and a career of choice Altogether:Anxious learners focus on the contingent knowledge as opposed to the authentic knowledge in order to complete learning tasks in a surface learning manner. Deep learning does not take place, and consequently MALP cycles and perpetuates.

10. Integral Approach to Instructional Implications • Five implications address from individualistic learners to the collectivistic social environment as an integral instructional approach to create more positive learning experiences in a mathematics anxious-friendly learning environment. These implications are: • Facilitating Active Control in the Learning Process. • Helping Learners to Reconceive Mathematics—A Dual Instructional Approach. • Fostering and Sustaining Positivity in the Learning Environment. • Creating a Parallel Context for Application. • Supporting Learners to Redefine Mathematics as a Subject for Logical Reasoning. More Individualistic More Collectivistic