In effective mathematics teacher preparation programs, assessments of the quality of mathematics teacher candidates are selected or developed to provide insight into the knowledge, skills, and dispositions of the candidates. Providing such insight requires that assessments are sensitive to the mathematical and pedagogical dimensions of quality mathematics teaching. The features of effective assessments discussed in the first section guide the selection and use of assessments in an effective program. Effective assessments are accessible and promote equity, both in the sense of equitably appraising the mathematics teacher candidates themselves and assessing the ability of candidates to engage in teaching practices that promote the mathematical achievement of all their students. Every mathematics teacher candidate is fully aware of the assessments, products, criteria, and potential consequences of the assessments in which they engage. Those assessing the quality of mathematics teacher candidates draw on assessments and develop systems that are valid, coherent, and sustainable.

Assessments of candidate teachers' quality can be used in several ways to improve mathematics teacher preparation. Candidates can be positioned to learn from video and other records of their own teaching experiences and to apply criteria reflectively to their performance. Mentor teachers and field supervisors can analyze appraisals of teacher candidates’ teaching with an eye toward providing opportunities to further hone particular teaching practices or to expand knowledge of children’s thinking and learning. Course instructors can look across reflections of teacher candidates to notice areas in which they could raise awareness of bias that might be interfering with their abilities to formulate productive next steps in teaching. Content course instructors could look at student work that is collected by teacher candidates to prioritize which mathematical understandings, principles, or practices to bring to the fore. Program administrators could look at the performance of teacher candidates at a particular point in the program and marshal resources that could expand or deepen work on a particular teaching practice.

This section provides recommendations for how effective assessments can be used to gather information about mathematics teacher candidate quality to support candidate growth toward meeting the standards from Chapter 2, as outlined in Table 8.3.

### Recommendation AC.1. Assessment of Mathematical Knowledge Relevant to Teaching

Effective assessments of mathematics knowledge incorporate attention to candidates’ development of mathematical knowledge relevant to teaching, including processes and practices.

Effective mathematics teacher preparation programs include a variety of assessment methods to assess the (a) mathematical and statistical content knowledge including both conceptual and procedural knowledge, and (b) knowledge and use of mathematical and statistical practices and processes of teacher candidates. Effective programs use more than tests embedded in coursework or a mandated, external test to assess prospective teachers’ knowledge of mathematics. Courses in effective programs include assessment strategies in alignment with approaches that prospective teachers will be expected to enact as future teachers (cf. NCTM, 2014a). This practice aligns with the increasing attention mathematicians are giving to the failure to connect what is valued and what is assessed (Tallman, Carlson, Bressoud, & Pearson, 2016). In an effective program, in addition to tests, other measures, such as projects and performance-based assignments, are used. Self-assessment is also a regular part of coursework, and formative assessment is an integral part of instruction and is used to make instructional decisions (AMTE & NCSM, 2014).

Beyond assessment within courses or equivalent professional-learning experiences, effective programs assess candidates’ progress across courses. Quality assessment is more than an accumulation of individual course grades and includes assessment of dispositions, agencies, and understandings of the nature of mathematics. For example, tests of mathematical knowledge relevant to teaching—such as the Learning for Mathematics Teaching (2011) assessment or the Diagnostic Mathematics Assessments for Middle School Teachers (Peters et al., 2016a, 2016b; Ronau et al., 2016a, 2016b)—or assessments of dispositions toward mathematics might be incorporated at critical points in the program or as a requirement prior to student teaching. An effective program might also use a candidate-created work sample or electronic portfolio as an overall assessment of the depth and soundness of the candidate's knowledge of mathematics content and use of mathematical practices and processes.

### Recommendation AC.2. Assessment of Mathematics Teaching Practice

Effective assessments of mathematics teaching practice include observations of teaching focused on how well the teaching supports learning of important mathematical content, processes, and practices by each and every student.

Effective mathematics teacher preparation programs offer candidates ongoing feedback from mentors and supervisors who know and have taught mathematics. These observers benefit from training and calibration using tools that are specific to the effective planning, teaching, and assessment practices highlighted in standard C.2, such as the Mathematics Classroom Observation Protocol for Practices (Gleason, Livers, & Zelkowski, 2015) and Student Discourse Observation Protocol (Weaver, Dick, & Rigelman, 2005). The observation cycle is most powerful when it includes preobservation discussion, focused observation of a lesson, data-based discussion following the lesson, and follow-up that holds candidates responsible for and supports their continued growth. The preobservation can engage the candidates in articulating their learning goals for students as well as potential foci for the observation (e.g., student engagement at various points in the lesson, responsiveness to student thinking/ideas, teacher questioning and wait time, student mathematical discourse, student use of mathematical tools). In the debrief of the lesson, participants use the data gathered by the observer to inform progress toward the learning goals and growth in instructional practice. Finally, following the observation cycle, the observer follows up with the candidate by checking on progress and providing resources to support continued development of teaching practice.

### Recommendation AC.3. Assessment of Dispositions

Effective assessments provide data on a range of dispositions related to mathematics teaching, including dispositions toward engaging in mathematics, identity as a mathematics teacher and learner, and commitment to support the mathematics learning of each and every student.

Although candidates' reflections on their dispositions provide useful information and can serve as starting points for their continued growth, effective mathematics teacher preparation includes assessments of dispositions beyond candidates' self-assessment. Combining self-assessments with assessments from those working most closely with the candidates (i.e., advisers, faculty, mentor teachers, supervisors) can provide more powerful indications of their dispositions than self-assessments alone and can serve as points of reflection and growth for candidates. Dispositions can be further assessed when candidates reflect upon ways they support each of their students in developing productive mathematical identities.