As a professional community, mathematics teacher educators have begun to define, research, and refine the characteristics of effective teachers of mathematics and, in particular, the professional proficiencies of a well-prepared beginning teacher of mathematics. This document describes a set of proficiencies for well-prepared beginners and for programs preparing mathematics teachers. Although these proficiencies are grounded in available research, in many areas that research is not yet sufficient to determine the specific knowledge, skills, and dispositions that will enable beginning teachers to be highly effective in their first years of teaching. Hence, the standards presented in this document are intended to engage the mathematics teacher education community in continued research and discussion about what candidates must learn during their initial preparation as teachers of mathematics.

## Assumptions About Mathematics Teacher Preparation

The *Standards for Preparing Teachers of Mathematics* are centered on five foundational assumptions about mathematics teacher preparation. These assumptions reflect the emerging consensus of those involved in mathematics teacher preparation in response to the needs of both their teacher candidates and the students those candidates will teach. These assumptions underlie the standards presented in Chapters 2 and 3 as well as the grade-band elaborations in Chapters 4 through 7.

### Assumption #1. Ensuring the success of each and every learner requires a deep, integrated focus on equity in every program that prepares teachers of mathematics.

Over the past decades, the need for a central focus on issues related to equity in mathematics education has become clear in reflecting on the uneven performance of students by various demographic factors (AMTE, 2015; NCTM, 2000, 2014a, 2014b). Although equity, diversity, and social-justice issues need to be specifically addressed as standards, they must also be embedded within *all* the standards. Addressing these issues solely within the context of “equity standards” might be misinterpreted to imply that these issues are not important within the other standards; conversely, if they are not directly addressed in standards addressing equity, their centrality to the mission of mathematics teacher preparation can be overlooked. Thus, we believe that equity must be both addressed in its own right and embedded within every standard. Every standard must be built on the premise that it applies to each and every student, recognizing that equity requires acknowledging the particular context, needs, and capabilities of each and every learner rather than providing identical opportunities to students.

### Assumption #2. Teaching mathematics effectively requires career-long learning.

Experienced teachers reflecting on their first year of teaching mathematics have frequently described how much more they can now accomplish, given their current level of teaching competence and understanding of the mathematics and students they are teaching. Teachers improve through reflective experience and through intentional efforts to seek additional knowledge. They use that knowledge to build their understanding of the mathematics they teach and to support their improvement in supporting students’ learning of mathematics. This process must begin during their initial preparation and continue throughout their careers. Knowing that candidates will complete teacher preparation programs without the expertise they will later develop focuses attention on priorities for beginning teachers. Those priorities become the knowledge, skills, and dispositions of a well-prepared beginner.

### Assumption #3. Learning to teach mathematics requires a central focus on mathematics.

Teaching is often approached as a general craft that is independent of the content being taught. Effective mathematics teaching, however, requires not just general pedagogical skills but also content-specific knowledge, skills, and dispositions. To support student learning and develop positive dispositions toward mathematics, mathematics teachers at every level of instruction need deep and flexible knowledge of the mathematics they teach, of how students think about and learn mathematics, of instructional approaches that support mathematical learning, and of the societal context in which mathematics is taught and used in everyday life to effectively support student learning of, and positive dispositions toward, mathematics.

### Assumption #4. Multiple stakeholders must be responsible for and invested in preparing teachers of mathematics.

Preparing teachers to teach in ways that ensure that each and every student learns important mathematics requires the concerted effort of everyone who holds a stake in students’ future successes. Mathematics teacher educators and mathematicians; other teacher educators; program and school administrators; classroom teachers, including special education teachers; families and communities; policymakers and others in the educational system all play critical roles. When these groups send mixed messages about how mathematics is best taught and learned, beginning teachers receive incomplete and fragmented visions of how to enact effective mathematics learning environments for their students. Successful mathematics teacher preparation requires a shared vision of mathematics learning outcomes for students, of effective mathematics learning environments, and of the kinds of experiences that best support a mathematics teacher’s continuing growth and development. Moreover, stakeholders must feel both included in the development of that vision and accountable for enacting that vision.

### Assumption #5. Those involved in mathematics teacher preparation must be committed to improving their effectiveness in preparing future teachers of mathematics.

Mathematics teacher preparation program structures differ widely, as do the needs and backgrounds of teacher candidates. Additionally, mathematics teacher preparation occurs within a range of contexts; in the United States, hundreds of institutions as well as online and school district programs prepare teachers of mathematics, and each one is unique. Thus, program personnel need to discern how existing research might apply to their context and how they can respond to issues not yet addressed by research. Further, they must assess the relationship between their unique program and its effectiveness, sharing relevant findings with the broader mathematics teacher preparation community (e.g., through publications and presentations at conferences).

## A Well-Prepared Beginning Teacher of Mathematics

As stated in Assumption 2, the development of teachers’ content and teaching knowledge, skills, and dispositions occurs over a career-long trajectory. For example, InTASC developed learning progressions to describe “a coherent continuum of expectations for teachers from beginning through accomplished practice” (Council of Chief State School Officers, 2013, p. 6). Figure 1.1 depicts the career-long continuum of teacher development.

*Figure 1.1.* The teacher development continuum.

*Note*. Adapted from *Developing the Analytic Framework: A Tool for Supporting Innovation and Quality Design in the Preparation and Development of Science and Mathematics Teachers* (p. 9) by C. R. Coble, 2012. Washington, DC: Association of Public and Land-grant Universities. Copyright 2012 by APLU.

The standards in this document address primarily the initial preparation phase of the trajectory depicted in Figure 1.1, with some attention to the recruitment of teacher candidates. Chapter 2 provides clear expectations, based on the current knowledge base and national recommendations, for what a well-prepared beginning teacher of mathematics needs to know and be able to do as well as productive dispositions they need to develop, while Chapter 3 describes what programs need to provide to enable candidates to meet these expectations. Well-prepared beginning teachers of mathematics must be committed to supporting the mathematical success of each and every student, and with proper support from the mathematics teacher education community, they will continue to become more effective throughout their careers.