Well-prepared beginning teachers of mathematics at the early childhood level demonstrate positive attitudes toward mathematics as a discipline and productive dispositions toward the teaching and learning of mathematics. [Elaboration of C.1.3]
For positive dispositions toward mathematics to be cultivated during the mathematical preparation of early childhood teachers is particularly important because teachers’ beliefs and affect toward mathematics (see Vignette 4.1) influence what children come to believe and feel toward mathematics (Tsamir & Tirosh, 2009; White, Perry, Way, & Southwell, 2006), and teachers’ beliefs influence the opportunities they provide for children to engage in significant mathematical thinking (Staub & Stern, 2002). Children’s early experiences with mathematics form the foundation for their future success as mathematics learners. That foundation includes not only the development of mathematical knowledge but also the establishment of productive dispositions toward mathematics. Productive dispositions are defined as the “habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy” (NRC, 2001a, p. 116). When teachers make decisions about the mathematical tasks, tools, and discourse within the learning environment, they influence the mathematics content knowledge that children develop as well as children’s identities as mathematics learners (Aguirre et al., 2013).
The mathematical preparation of teachers plays a critical role in developing productive beliefs and attitudes toward mathematics (Philipp, 2007; Swars, Smith, Smith, & Hart, 2009). Prospective elementary school teachers’ attitudes toward mathematics are affected at two key points (Jong & Hodges, 2015). First, positive shifts in attitudes toward mathematics occur as a result of mathematics methods experiences, and, second, further positive shifts occur as a result of clinical experiences. Throughout the effective mathematical preparation of early childhood teachers, increased attention is given to the development of positive dispositions toward mathematics as a necessary requirement for the teaching of rigorous mathematics, including to our youngest learners in preschool and primary settings.
Each semester on the first day of my mathematics methods course, I ask my candidates to reflect on their memories of learning mathematics in elementary school, middle school, and high school. For about 10 minutes, they write about memories of their own mathematical experiences (e.g., people, activities, topics, expectations for learning). I encourage them to include not only specific examples of what they remember doing but also descriptions of how they felt in those mathematical situations.
Needless to say, the memories and stories are not all positive. Next the candidates form small groups and share their memories. We then discuss and chart common themes as a whole group, including both positive and negative memories. When memories are shared, I often ask candidates to comment on feelings about themselves as learners of mathematics and about the expectations for understanding or making sense of the mathematics in each situation shared. Unfortunately, over the years, far too few prospective early childhood teachers have shared positive memories. Mathematics was, for many, just something they had to do, and it was not a favorite subject. For others, those reflections evoke bad memories, generate tears, and raise anxieties. Whether the memories were positive or negative, a common theme surfaces that mathematics was for most something to memorize and not something to understand or enjoy.
To close the session, I have the candidates reflect and write once again. This time, I ask them to write about how they would like to be remembered as a teacher of mathematics. As the instructor, I then collect, read, and respond to their writing. This initial experience serves as a backdrop for our work together throughout the semester while each candidate delves more deeply into what being an effective teacher of mathematics at the early childhood level entails.
See Guillaume and Kirtman (2005) and McCulloch, Marshall, DeCuir-Gunby, and Caldwell (2013) for additional resources.
 This chapter includes a number of vignettes meant to bring to life the recommendations put forward. The vignettes serve a number of purposes, including proposing tasks that may be used with candidates for particular purposes, providing example interactions from mathematics or mathematics methods courses to exemplify effective instruction, or describing the experiences of a teacher candidate. Each vignette was chosen to highlight a particular point, but use of an isolated vignette may require surrounding context to preserve the spirit intended by the use of the vignette.