Assessment is a cornerstone for all educational endeavors, the means by which those striving to support learning come to know the knowledge, skills, and dispositions of those whose learning they are supporting. This information is crucial for a myriad of reasons, including, but not limited to the design of learning experiences, the development of curriculum and programs, and reflections of learners and their teachers. Assessment in mathematics teacher preparation is purpose driven, and those purposes are summarized in Table 8.1.
Table 8.1. Purposes for Assessment of Mathematics Teacher Preparation

Formative Assessment 
Summative Assessment 
Assessment of Candidates 
Provides information on candidates' progress toward becoming wellprepared beginning teachers of mathematics 
Determines candidates’ readiness to begin practice as beginning teachers of mathematics (credentialing or licensing) 
Assessment of Programs 
Elucidates program’s strengths and weaknesses to improve the program 
Determines whether standards are met for program accreditation 
These purposes are served through sound and efficient assessments designed to provide information, support interpretation, and spur action. Assessments necessarily appraise mathematics teacher candidates and elements of the mathematics teacher preparation programs that support their professional growth, providing timely formative information needed to provide ongoing feedback to candidates and to tailor learning experiences that support their growth. Assessments also provide summative information on the outcomes of teacher preparation, most crucially providing information on the quality of the knowledge, skills, and dispositions of mathematics teaching candidates and the candidates’ proficiencies in supporting mathematical learning as well as the quality of a program.
AMTE is committed to promoting the improvement of mathematics teacher preparation. Therefore, this chapter is focused on formative, improvementoriented uses of assessment that are aligned with the teacher preparation standards described in earlier chapters. Chapters 2 and 3 of this document set forth standards for what candidates should know and be able to do (Candidate Standards) as well as what programs must provide to support their candidates in achieving those standards (Program Standards). Effective programs need assessments that provide useful information about their candidates, both individually and collectively, to identify areas in which programs can better support their candidates’ growth toward becoming wellprepared beginning teachers of mathematics.
Although we choose to focus on assessing these standards for purposes of ongoing improvement, we acknowledge that the standards could at some points and in some ways inform summative purposes. For example, these standards are not designed to establish minimum benchmarks that candidates must meet before beginning their careers as mathematics teachers. However, these standards provide important descriptions of knowledge, skills, and dispositions to be considered in devising such benchmarks. Such an emphasis on program quality and improvement is consistent with Standard 5 of the accreditation standards put forward by the Council for the Accreditation of Educator Preparation (CAEP, 2013b).
This chapter begins with recommendations about general features of effective assessments used in mathematics teacher preparation; these recommendations are abbreviated AF (Assessment Features). The recommendations for features of effective assessments should guide assessment decisions of instructors and programs when they select, design, and use assessments.
The second section of the chapter includes recommendations for assessments designed to determine progress toward attaining the Candidate Standards in Chapter 2; these recommendations are abbreviated AC (Assessment of Candidates). Finally, recommendations are given for assessments designed to determine progress toward attaining the Program Standards in Chapter 3; these recommendations are abbreviated AP (Assessment of Programs). Together these recommendations should be used to effectively guide efforts to support candidate growth and improve mathematics teacher preparation programs. A summary of the recommendations follows in Table 8.2.
Table 8.2. Recommendations About Assessing Mathematics Teacher PreparationFeatures of Effective Assessments Used in Mathematics Teacher PreparationRecommendation AF.1. Focus on Mathematics Teaching in AssessmentsEffective assessments are tailored to provide information relevant to the development of mathematics teacher candidates. Recommendation AF.2. Promote Equity and Access in AssessmentsEffective assessments are designed, implemented, interpreted, and used to advance equity and access. Recommendation AF.3. Embody Openness in AssessmentsEffective assessments are part of a transparent process in which those assessing, those being assessed, and other stakeholders know the assessment focus, the nature of assessment methods and criteria, and the uses of the information gathered. Recommendation AF.4: Support Valid Inferences and Action Based on AssessmentsEffective assessments appropriately include multiple measures that are well suited to gather the types and amounts of information needed to make valid inferences and take action. Recommendation AF.5: Embody Coherence and Sustainability in AssessmentsEffective assessments are aligned with teacher preparation goals, opportunities to learn, and intended uses of the information they generate. They are designed and enacted in ways that can be sustained over time. Assessing Quality of Mathematics Teacher CandidatesRecommendation AC.1. Assessment of Mathematical Knowledge Relevant to TeachingEffective assessments of mathematics knowledge incorporate attention to candidates’ development of mathematical knowledge relevant to teaching, including processes and practices. Recommendation AC.2. Assessment of Mathematics Teaching PracticeEffective 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. Recommendation AC.3. Assessment of DispositionsEffective 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. Assessing Quality of Mathematics Teacher Preparation ProgramsRecommendation AP.1. Assessment of Stakeholder EngagementEffective mathematics teacher preparation programs assess the degree to which a broad range of stakeholders are meaningfully engaged in the program and involved in its ongoing improvement. Recommendation AP.2. Assessment of Program Curriculum and InstructionEffective mathematics teacher preparation programs assess the effectiveness of courses or equivalent professionallearning opportunities they offer in promoting their candidates’ progress and work to improve them. Recommendation AP.3. Assessment of Effective Clinical ExperiencesEffective mathematics teacher preparation programs assess and work to improve the quality of the clinical experiences they provide mathematics teacher candidates. Recommendation AP.4. Assessment of Recruitment and RetentionEffective mathematics teacher preparation programs assess and work to improve their success in recruiting prospective teachers, in retaining candidates in the program, and in supporting beginning teachers’ continued professional growth, with a focus on developing a mathematics teacher workforce that reflects the diversity of the student population in the region. 
Note that the match between these recommendations for assessment and the Candidate and Program Standards in Chapters 2 and 3 is not one to one. The features of effective assessments apply to all assessments of both candidate and program quality. Table 8.3 illustrates the relationships between the recommendations for assessing mathematics teacher candidate quality and the Candidate Standards; the checked cells indicate that the recommendation should particularly inform assessment of the given standard.
Table 8.3. Relation of Assessment Recommendations to the Candidate Standards

Candidate Standards 

Assessment 
C.1. Mathematics Concepts, Practices, and Curriculum 
C.2. Pedagogical Knowledge and Practices for Teaching Mathematics 
C.3. Students as Learners of Mathematics 
C.4. Social Contexts of Mathematics Teaching and Learning 
AC.1. Assessment of Mathematical Knowledge Relevant to Teaching 
✔ 



AC.2. Assessment of Mathematics Teaching Practice 

✔ 
✔ 
✔ 
AC.3. Assessment of Dispositions 
✔ 
✔ 
✔ 
✔ 
Table 8.4 illustrates the relationships between the recommendations for assessing program quality and the Program Standards; checked cells indicate the recommendation should particularly inform assessment of the given standard. In addition, given that candidate outcomes are essential components of program success, the recommendations for assessing mathematics teacher quality also inform assessment of Program Standards.
Table 8.4. Relation of Assessment Recommendations to Program Standards

Program Standards 

Assessment 
P.1. Partnerships 
P.2. Opportunities to Learn Mathematics 
P.3. Opportunities to Learn to Teach Mathematics 
P.4. Opportunities to Learn in Clinical Settings 
P.5. Recruitment and Retention of Teacher Candidates 
AP.1. Assessment of Stakeholder Engagement 
✔ 




AP.2. Assessment of Program Curriculum and Instruction 

✔ 
✔ 


AP.3. Assessment of Effective Clinical Experiences 



✔ 

AP.4. Assessment of Recruitment and Retention 




✔ 
AC.1. Assessment of Mathematical Knowledge Relevant to Teaching 

✔ 

✔ 

AC.2. Assessment of Mathematics Teaching Practice 


✔ 
✔ 

AC.3. Assessment of Dispositions 

✔ 
✔ 
✔ 

Closing Remarks
The standards in Chapters 2 and 3 of this document set aggressive targets for the knowledge, skills, and dispositions of wellprepared beginning teachers of mathematics as well as for the qualities of effective mathematics teacher preparation programs. These standards are intended to guide efforts to support the development of wellprepared beginning teachers of mathematics and to improve mathematics teacher preparation programs. However, improvement is not possible without assessment. Evidence is necessary in identifying areas in which improvement is needed. Evidence also is needed to guide the process of improvement to ensure that changes are actually improvements (Bryk, Gomez, Grunow, & LaMahieu, 2015). Thus, seeking effective ways to assess the quality of candidates and of the program itself is central to attaining the goals set forth in this document. Indeed, when priorities for program improvement are considered, identifying or creating and implementing a more effective assessment system might be an important first step for a program to consider so that progress toward meeting the Candidate and Program Standards can be tracked.