Abstract:

Earlier research with younger students finds considerable diversity in the in-the-moment motivating desires that occur during mathematical problem solving. These evoke differing patterns of engagement. This study uses survey, individual interview, and focus group techniques to explore prospective K-12 teachers’ motivating desires as they work in groups to solve mathematical problems in university methods courses.

We address the following research questions in a qualitative, phenomenological investigation involving 72 participants enrolled in elementary and secondary mathematics teaching methods courses: What motivating desires do prospective K-12 teachers of mathematics report as present during problem solving? Which of the in-the-moment motivating desires identified in earlier studies occur in the present context? What additional motivating desires are reported?

Mathematical engagement is widely regarded as essential to effective learning (Middleton, Jansen and Goldin, 2017; Goldin, Epstein, Warner and Schorr, 2011). Studies of social, affective and cognitive interactions of students have led to a series of research papers addressing in-the-moment engagement and motivating desires that appear to occur in students (for more details see Goldin, Epstein, Schorr & Warner, 2011). Some examples are “Check this Out” (with a motivating desire to have an intrinsic or extrinsic payoff); “Get the Job Done” (a desire to complete the work); “I’m Really Into This” (an experience of “flow” where the mathematical activity becomes so intriguing that one tunes out his/her surroundings) and “Let Me Teach You” (a desire to teach someone something he/she doesn’t know).

Findings from the present study confirm that several of the motivating desires mentioned above were found to occur frequently among the prospective K-12 teachers. We found that the motivating desires described above were, in this context, likely to result in actions leading to problem-solving success and a productive experience both cognitively and affectively

We found evidence for the occurrence of two motivating desires not previously identified in the literature. The first, which we term “Carry My Weight”, involves the desire to be part of and contribute productively to the group effort – a “team” impulse. The second, “Don’t Let My Group Down”, involves avoiding an outcome where one may disappoint others in the group.

This study’s significance lies not only in identifying, confirming, and describing motivating desires present during problem solving, but also in its potential to help researchers, teacher educators and teachers better address mathematical engagement. Our observations lend concreteness and specificity in the domain of collaborative mathematical problem solving to more general psychological models of motivation, such as the self-determination theory of Ryan and Deci (2000).

Keywords:

Mathematical engagement, student motivation, mathematical problem solving.