## Figures

- Figure 1.1. The teacher development continuum 3
- Figure 2.1. Fraction-bar representation of the problem 3 ÷ 1/5
- Figure 2.2. Sample task for Pre-K–5 teacher candidates.
- Figure 2.3. Sample task for middle level teacher candidates.
- Figure 4.1. A learning trajectory for recognition of number and subitizing.
- Figure 9.1. The ongoing and cyclic nature of improving mathematics teacher preparation programs.

## Tables

- Table 0.1. Standards and Reports Related To Preparing Teachers of Mathematics.
- Table 2.1. Standards and Related Indicators For Well-Prepared Beginning Teachers of Mathematics.
- Table 2.2. Mathematics Teaching Practices.
- Table 3.1. Standards and Related Indicators for Effective Programs for Preparing Beginning Teachers of Mathematics.
- Table 3.2. Minimum Mathematics Content Preparation for Teacher Candidates.
- Table 4.1. Elaborations of Selected Candidate and Program Standards for Early Childhood Teachers of Mathematics.
- Table 4.2. Connections to
*MET II*(CBMS, 2012) Related to Number and Numeration in Early Childhood. - Table 4.3. Connections to
*MET II*(CBMS, 2012) Related to Operations and Algebraic Thinking in Early Childhood. - Table 4.4. Connections to
*MET II*(CBMS, 2012) Related to Geometry, Measurement, and Data in Early Childhood. - Table 4.5. Research-based Developmental Learning Trajectories.
- Table 5.1. Elaborations of Candidate and Program Standards for Teachers of Mathematics for Upper Elementary Grades.
- Table 5.2. Connections to
*MET II*(CBMS, 2012) Related to Multiplicative Structures in the Upper Elementary Grades. - Table 5.3. Connections to
*MET II*(CBMS, 2012) Related to Fractions and Decimals in the Upper Elementary Grades. - Table 5.4. Connections to
*MET II*(CBMS, 2012) Related to Geometry and Measurement in the Upper Elementary Grades. - Table 5.5. Connections to
*MET II*(CBMS, 2012) Related to Algebraic Thinking in the Upper Elementary Grades. - Table 6.1. Elaborations of Candidate and Program Standards for Middle Level Teachers of Mathematics.
- Table 6.2. Connections to
*MET II*(CBMS, 2012) Related to Ratios and Proportional Reasoning at the Middle Level - Table 6.3. Connections to
*MET II*(CBMS, 2012) Related to the Number System at the Middle Level - Table 6.4. Connections to
*MET II*(CBMS, 2012) Related to Expressions, Equations, and Functions at the Middle Level - Table 6.5. Connections to
*MET II*(CBMS, 2012) Related to Geometry at the Middle Level - Table 6.6. Connections to
*MET II*(CBMS, 2012) and SET (Franklin et al., 2015) Related to Statistics and Probability at the Middle Level - Table 6.7. Interdisciplinary Modeling Task for the Middle Grades.
- Table 7.1. Elaborations of Candidate and Program Standards for High School Teachers of Mathematics.
- Table 8.1. Purposes for Assessment of Mathematics Teacher Preparation.
- Table 8.2. Recommendations About Assessing Mathematics Teacher Preparation.
- Table 8.3. Relation of Assessment Recommendations to the Candidate Standards.
- Table 8.4. Relation of Assessment Recommendations to Program Standards.
- Table 8.5. Mathematics Teacher Preparation Quality: Attributes and Evidence.
- Table 9.1. Assumptions About Preparing Teachers of Mathematics.

## Vignettes

- Vignette 4.1. Examining Memories of Learning Mathematics.
- Vignette 4.2. Building From What Children Understand Mathematically
- Vignette 4.3. Collaborative Sense Making of Children’s Mathematical Thinking.
- Vignette 4.4. Solving 21 + 32.
- Vignette 5.1. Measuring Angles.
- Vignette 5.2. Students’ Use of a Key-Words Strategy to Solve Word Problems.
- Vignette 6.1. A Sequence of Course Activities Focused on Proportional Reasoning and Student Thinking.
- Vignette 6.2. Co-planning and Co-teaching to Support Every Student
- Vignette 6.3. Attending to Algebra Content and Language in a Classroom With Emergent Multilingual Students.
- Vignette 7.1. Meaningful Algebraic Expressions.
- Vignette 7.2. Providing Opportunities to Learn.
- Vignette 7.3. Mathematical Identity.
- Vignette 7.4. A Student Teacher’s Revelation Related to Emergent Multilingual Students.
- Vignette 7.5. The Importance of Coherent and Consistent Program Components.
- Vignette 7.6. Helping Candidates Consider Ethical Decisions They May Face.