The guiding question for this chapter is, “Recognizing that learning to teach is an ongoing process over many years, what are reasonable expectations for the most important knowledge, skills, and dispositions that beginning teachers of mathematics must possess to be effective?” This is a difficult question to answer, as some aspects of teaching are not going to be well learned initially, even though they may be critically important to student learning. This is also a significant equity issue, as students with the greatest needs are often taught by teachers with the least experience (Kalogrides, Loeb, & Béteille, 2012; Oakes, 2008).
Mathematics teachers, from the very beginning of their careers, must understand the mathematical content knowledge for the age groups or grades that they may teach, along with content that comes before and after those age groups or grades—and in a different and deeper way than often presented in textbooks, curriculum documents, or standards. Such knowledge impacts their students’ learning (e.g., Hill, Rowan, & Ball, 2005; National Mathematics Advisory Panel, 2008).
Well-prepared beginners must be ready to teach every child in their first classrooms. Although pedagogical skills develop over time, beginners must have an initial repertoire of effective and equitable teaching strategies; for example, in selecting tasks, orchestrating classroom discussions, building on prior knowledge, and connecting conceptual understanding and procedural fluency (National Council of Teachers of Mathematics (NCTM), 2014). All teachers, including well-prepared beginners, must hold positive dispositions about mathematics and mathematics learning, such as the notions that mathematics can and must be understood, and that all students can develop mathematical proficiency, along with a commitment to imbue their students with similar beliefs and dispositions.
Being able to teach effectively requires knowledge of learners and learning, both general pedagogical knowledge and knowledge specific to the learning and teaching of mathematics. Knowing learners includes knowing about their background, interests, strengths, and personalities, as well as knowing how students think and learn related to the mathematics they will be teaching, including possible misconceptions and creative pathways they may take in learning (Ball & Forzani, 2011; Clements & Sarama, 2014; Sztajn, Confrey, Wilson, & Edgington, 2012). Well-prepared beginners must understand—at least at an initial level—how to assess the understandings and competencies of their students and use this knowledge to plan and modify instruction using research-based instructional strategies (e.g., Ball & Forzani, 2011; Shulman, 1986).
Mathematics teaching and learning are influenced by social, historical, and institutional contexts. Beginning teachers must be aware of learners’ social, cultural, and linguistic resources; know learners’ histories; and recognize how power relationships affect students’ mathematical identities, access, and advancement in mathematics (e.g., Gutiérrez, 2013; Martin, 2015; Strutchens et al., 2012; Wager, 2012). For example, classroom dynamics and social interactions strongly influence students’ emerging mathematical identities, which in turn impacts the students’ learning opportunities. In short, well-prepared beginners must be ethical advocates for each of their students.