Indicator P.4.2. Sequence School-Based Experiences

The quality of school-based experiences is at least as important as the quantity of time in schools. Observations are ineffective for novices who have not been provided with a critical lens from which to gain insights into teaching. Scaffolded learning experiences of teacher candidates support movement toward classroom independence. Therefore, personnel in an effective mathematics teacher preparation program develop clear trajectories of school-based learning experiences focused on increasingly complex teaching practices (e.g., managing student mathematical discourse moving from individual to small group and then from small group to large group) and on learning through examination of student thinking and instructional practice (Smith, 2001). Mathematics teacher candidates must have multiple opportunities to practice the many skills that define them as well-prepared beginners (see Chapter 2).

An effective mathematics teacher preparation program includes opportunities for teacher candidates to engage in early clinical experiences to begin to shift their lenses from that of a student to that of a teacher and to gain insights into what grade level(s) they would like to teach. In such early experiences, effective programs provide strategies for helping the candidates to develop their mathematics-teaching identities. For example, candidates may be assigned in their field placements to reflect on how teacher-student interactions engage a student in productive struggle, observe or interview a student to understand which mathematical representations the student understands and uses to solve problems, or assist the classroom teacher during individual or small-group work by documenting students' ways of reasoning about the task. These early experiences help candidates determine whether they want to become teachers (and at what level), begin to focus on students’ mathematical thinking, and introduce basic ideas about effective instruction. In alternative pathways to teaching, wherein candidates are immediately hired into their own classrooms, strategies such as viewing videos, analyzing vignettes or cases, and comparing student-work samples serve to help candidates focus on student thinking and effective instruction.

When teacher candidates complete their mathematics methods course(s) or related professional learning experiences, their clinical experiences must provide varied and extensive opportunities to connect what they are learning in their coursework to authentic classrooms (see Standard P.3.4). In the case of alternative preparation programs, the candidates are teaching, so they are connecting what they are learning to actions in their own classrooms is even more critical. For example, during a middle school methods course, candidates may solve a proportional-reasoning task, consider ways students may reason about the task, implement the same task with middle school students, then return to the university classroom to discuss what they learned about proportional thinking, students, and their teaching. Candidates need multiple opportunities to teach or co-teach lessons, including opportunities to analyze student work and reflect on the effectiveness of teaching and classroom management in supporting the mathematics learning of each student in a group or class.

Student teaching or internship experiences (in which, over the duration of the placement, candidates take on the full responsibilities of the classrooms) must continue to include a range of activities and assessments that engage the candidate in planning, teaching, assessing, and reflecting on mathematics teaching, at increasingly sophisticated levels. These activities include candidates' focusing on culturally responsive instruction, in particular, identifying teaching practices that support or inhibit the learning of each of their students, noticing that some practices benefit some students but inhibit others. Such reflection by candidates requires significant, focused feedback from mentors who are themselves experienced and skilled at teaching mathematics effectively. Additionally, an effective mathematics teacher preparation program provides opportunities for candidates to co-teach, for example, with their mentor teachers or specialists (e.g., special education teacher or ESL specialist), reflecting on the ways in which such collaborations can effectively support and challenge each and every student without lowering expectations. Finally, internships provide opportunities for candidates to learn about, participate in, and reflect upon aspects of schooling beyond classroom teaching, such as after-school informal learning, record-keeping, engaging with parents, and analyzing school data.

Effective teacher preparation programs may vary widely in how they sequence experiences, but they have strategically organized a variety of experiences over time such that their candidates are able to develop the myriad of knowledge, skills, and dispositions to enter the workforce well prepared to support students’ mathematical engagement and understanding. For example, one field-experience model that fosters reflective and student-centered teaching practices is the paired-placement model in which two candidates are paired with a single mentor teacher. The mentor teacher provides purposeful coaching and mentoring; and the two candidates offer each other feedback, mentoring, and support (Goodnough, Osmond, Dibbon, Glassman, & Stevens, 2009; Leatham & Peterson, 2010). Another model found to help teacher candidates gain greater pedagogical content knowledge and knowledge of students is co-planning and co-teaching (CPCT). CPCT and the paired-placement model promote the collaboration and communication between teacher candidates and mentor teachers who share a common space in the planning, implementation, and assessment of instruction (Bacharach, Heck, & Dahlberg, 2010). Finally, a third model that has shown promise is the year-long-residency model, which enables teacher candidates to enact both their practicum and internship experiences in the same classroom. This model incorporates some of the same strategies as the co-planning and co-teaching models and has similar benefits.