# Preschool mathematics: An examination of one program's alignment with recommendations from NAEYC and NCTM

iv TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ............................................................................................... iii

LIST OF TABLES ............................................................................................................vi

LIST OF FIGURES ..........................................................................................................ix

Chapters

1. INTRODUCTION ....................................................................................... 1 Problem ........................................................................................... 2 Purpose ........................................................................................... 2 Research Questions ........................................................................ 3 Working Assumptions ..................................................................... 3 Methodology ................................................................................... 3 National Council of Teachers of Mathematics (NCTM) ................... 4 Definitions ..................................................................................... 15 Limitations of the Study ................................................................. 16 Summary ....................................................................................... 17

2. REVIEW OF LITERATURE ..................................................................... 18 Historical Perspective .................................................................... 18 Research Related to NCTM Standards ......................................... 32 Research Supporting Recommendations ...................................... 33 Early Childhood Mathematics Curricula ........................................ 48 Summary ....................................................................................... 56

3. METHODOLOGY .................................................................................... 57 Setting ........................................................................................... 57 Population ..................................................................................... 58 Sample .......................................................................................... 58 Classrooms ................................................................................... 60 Question 1: Preschool Teachers’ Instructional Practices .............. 64 Question 2: Preschool Program’s Curriculum ............................... 72

v Data Analysis ................................................................................ 75 Summary ....................................................................................... 79

4. RESULTS ................................................................................................ 80 Organization of Data Analysis ....................................................... 80 Descriptive Statistics ..................................................................... 81 Analysis of Data ............................................................................ 84

5. DISCUSSION ........................................................................................ 155 Summary of Study ....................................................................... 155 Discussion of Findings ................................................................ 156 Significance of Study ................................................................... 161 Limitations ................................................................................... 161 Suggestions for Future Research................................................ 162 Conclusion .................................................................................. 164

Appendices

A. KEY QUOTATIONS FROM “EARLY CHILDHOOD MATHEMATICS: PROMOTING GOOD BEGINNINGS” (2002) ......................................... 166

B. INTERVIEW QUESTIONS ..................................................................... 170

C. LIST OF CODES ................................................................................... 174

D. VISUAL REPRESNTATION OF RECOMMENDATIONS....................... 177

REFERENCES ............................................................................................................ 179

vi LIST OF TABLES Page

2.1 Curriculum Alignment with NAEYC and NCTM Recommendations .................... 55 3.1 Teachers’ Educational Background, Teaching Experience, and Membership in Professional Organizations ................................................................................. 59 3.2 Sample Schedule ............................................................................................... 61 3.3 Topics for Themes .............................................................................................. 63 3.4 Evaluation Criteria for COEMET ......................................................................... 65 3.5 COEMET’s Alignment with “Early Childhood Mathematics: Promoting Good Beginnings”......................................................................................................... 68 3.6 Observation Minutes ........................................................................................... 69 3.7 Codes for Recommendation 6 ............................................................................ 77 4.1 Number of Math Activities ................................................................................... 81 4.2 Number of Math Activities for Math Focus Days and Language Focus Days ..... 82 4.3 t-Tests for Number of Math Activities on Math Focus Days and Language Focus Days ................................................................................................................... 83 4.4 Teacher Involvement During Classroom Observations ...................................... 84 4.5 COEMET Averages for Items Aligned to Recommendation 1 ............................ 86 4.6 Teachers’ Comments about Connecting Mathematics to the Real World ........... 89 4.7 Teachers’ Comments about Developing Children’s Interest in Mathematics ...... 90 4.8 Lesson Plan Activities Aligned with Recommendation 1 .................................... 91 4.9 Real World Connections in Curriculum Materials ............................................... 92 4.10 Modifications Observed ...................................................................................... 94 4.11 Math Vocabulary Observed ................................................................................ 95 4.12 Learning Styles Discussed during Interviews ..................................................... 96 4.13 Teachers’ Comments Relating to Children’s Differences ................................... 96

vii 4.14 Teachers’ Comments Relating to Designing Activities for Different Learners ..... 97 4.15 COEMET Average for Items Aligned to Recommendation 3 ............................ 100 4.16 Developmental Considerations Mentioned by Teachers During Interviews ...... 102 4.17 COEMET Averages for Items Aligned to Recommendation 4 .......................... 106 4.18 SMA Addressing Multiple NCTM Standards ..................................................... 108 4.19 Teachers’ Comments about Problem Solving Activities ................................... 110 4.20 Teachers’ Views of Major Math Skills ............................................................... 114 4.21 Children’s Math Participation ............................................................................ 117 4.22 Time Spent on Mathematics ............................................................................. 118 4.23 Math Topics Addressed during SMAs .............................................................. 119 4.24 COEMET Averages for Items Aligned to Recommendation 7 .......................... 124 4.25 Frequency of Mathematics during Daily Routines ............................................ 125 4.26 Integration of Mathematics with Other Content Areas During Observations ..... 126 4.27 Teachers’ Comments about Math Integration ................................................... 127 4.28 Integration of Mathematics with Other Content Areas in Lesson Plans ............ 128 4.29 Integration of Mathematics with Other Content Areas in Curriculum Materials . 129 4.30 COEMET Averages for Items Aligned to Recommendation 8 .......................... 133 4.31 Percentage of SMAs Identified as Play ............................................................ 134 4.32 Children’s Mathematical Activity Without Teacher ............................................ 135 4.33 Play Opportunities Encouraging Mathematical Thinking in Planned Center Activities ........................................................................................................... 137 4.34 COEMET Averages for Items Aligned to Recommendation 9 .......................... 139 4.35 Organization Used By Teachers During Observations ..................................... 141 4.36 Math Concepts Revisited in Lesson Plans ....................................................... 143 4.37 Types of Mathematical Assessments Identified by Teachers During Interviews ......................................................................................................................... 146

viii 4.38 Instructional Practices’ Alignment with NAEYC and NCTM Recommendations (2002) ............................................................................................................... 151 4.39 Curriculum’s Alignment with NAEYC and NCTM Recommendations (2002) .... 153

ix LIST OF FIGURES Page

3.1 Sample classroom floor plan. ............................................................................. 62 4.1 Organization of data analysis. ............................................................................ 85

1 CHAPTER 1 INTRODUCTION Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. Innumeracy deprives them not only of opportunity but also of competence in everyday tasks. All young Americans must learn to think mathematically, and they must think mathematically to learn. National Research Council, 2001

Many adults indicate their dislike for mathematics or their lack of ability to complete simple tasks such as calculating the tip for a server at a restaurant. Sometimes, these feelings develop after a frustrating experience when learning math in school (Carroll, 1994). Low-achieving students as early as third grade, show a dislike for mathematics (Kloosterman & Clapp Cougan, 1994). Providing high-quality mathematical learning experiences may help to build a foundation to prevent these outcomes. Research supports the benefits of early learning opportunities (Barnett, Lamy, & Jung, 2005; Campbell, Ramey, Pungelllo, Sparling, & Miller-Johnson, 2002; Ou & Reynolds, 2006; Schweinhart, 2005). Variance is present in programs for young children, so it is important to insure that these early learning opportunities are high quality (Bracey & Stellar, 2003; Neuman, 2003; Varol & Farran, 2006). To help improve the instructional practices in the classrooms of young children, many national and state organizations have provided teachers with indicators or guidelines for high quality learning experiences (Bordova, Leong, & Shore, 2004). Forty-six states have comprehensive learning standards for preschool children (Barett et al., 2008). Furthermore, national organizations such as the National Association for the Education of Young Children (NAEYC) and National Council of Teachers of Mathematics (NCTM)

2 have created specific recommendations related to high quality mathematics instruction in the early childhood classroom (NAEYC & NCTM, 2002; NCTM, 2000; NCTM, 2006). Once these recommendations or standards are disseminated to the public it is important for researchers to determine whether teachers understand these guidelines and how they are being used in the classroom.

Problem In early childhood education, there are different types of programs such as privately funded preschools, state funded prekindergarten programs, and federally funded Head Start programs. With this variety, come issues with the quality of individual programs (McMullen & Alat, 2002). For instance, some early learning programs do not focus on high quality mathematics instruction (Rudd, Lambert, Satterwhite, & Zaier, 2008) despite research supporting early mathematics experiences influencing mathematical outcomes later in school (Lopez, Gallimore, Garnier, & Reese, 2007; Slaby, Loucks, & Stelwagon, 2005) and promoting school readiness skills in mathematics (Gormley, Gayer, Phillips, & Dawson, 2005; Magnuson, Ruhm, & Waldfogel, 2005). In addition, teachers’ misconceptions of appropriate high-quality mathematical learning opportunities for young children may hinder their ability to incorporate new mathematical standards (Lee & Ginsburg, 2009).

Purpose The purpose of this study was to determine the extent to which a preschool program followed the recommendations outlined in the National Association for the

3 Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics’ (NCTM) position statement Early Childhood Mathematics: Promoting Good Beginnings (2002).

Research Questions 1. To what extent do the preschool teachers’ instructional practices follow the recommendations outlined in NAEYC and NCTM’s position statement Early Childhood Mathematics: Promoting Good Beginnings (2002)? 2. To what extent does the preschool program’s curriculum align with the recommendations outlined in NAEYC and NCTM’s position statement Early Childhood Mathematics: Promoting Good Beginnings (2002)?

Working Assumptions 1. Teachers will show a limited implementation of the recommendations outlined by NAEYC and NCTM (2002). 2. This preschool program’s adapted curriculum will align with the recommendations outlined by NAEYC and NCTM (2002).

Methodology The sample for this study consisted of 6 teachers from a preschool program in an urban area in Texas. To determine the extent the preschool teachers followed the suggestions provided by NAEYC and NCTM (2002), I observed each teacher 6 times using the Classroom Observation of Early Mathematics—Environment and Teaching (COEMET) (2007) protocol. To provide support for the data collected using the COEMET, I wrote field notes of items observed during my observations. To gain an understanding of the teachers’ perspectives, I interviewed each teacher 3 times. To

4 determine how the curriculum aligned with the recommendations outlined by NAEYC and NCTM (2002), I collected weekly lessons plans from teachers each time I went to observe them. In addition, I had access to all the preschool program’s math curriculum materials for the purpose of document analysis.

National Council of Teachers of Mathematics (NCTM) To provide the context for this study, it is important to provide a brief overview of some of the documents published prior to NAEYC and NCTM’s (2002) position statement. These publications presented an articulated list of standards influencing educational practices. In addition, they laid the foundation to the ideas expressed in Early Childhood Mathematics: Promoting Good Beginnings (NAEYC & NCTM, 2002).

Standards Movement In 1989 NCTM published Curriculum and Evaluation Standards for School (CESS), considered one of the first documents of the standards or reform movement (Herrera & Owens, 2001). This publication, along with Professional Standards for Teaching Mathematics (PSTM, 1991) and Assessment Standards for School Mathematics (ASSM, 1995) influenced mathematics education in the 1990s. CESS (1989) provided K-12 educators guidelines for what mathematical concepts teachers should focus on in the classroom. The organization of the document included three grade groupings (K-4, 5-8, 9-12) of standards. PSTM (1991) presented guidelines to help teachers create mathematical environments to support children’s understandings of these standards. NCTM (1995) developed ASSM to help guide teachers’

5 development of new assessment strategies to support the evaluation of these standards.

Principles and Standards for School Mathematics (PSSM) To develop a better understanding of NAEYC and NCTM’s (2002) position statement Early Childhood Mathematics: Promoting Good Beginnings, it is important to understand NCTM’s (2000) latest standards document, Principles and Standards for School Mathematics (PSSM). The following paragraphs include a description of the development of this document and a description of the key elements.

Development of PSSM In response to concerns about the clarity and currency of previous standards documents, NCTM decided to create a new coherent document (Herrera & Owens, 2001). In 1995 NCTM created the Commission on the Future of the Standards to oversee this process. By spring 1997, the writing group was formed and was composed of a variety of members, including teachers and researchers in the field of mathematics education. The goal of this group was to develop a document with a revised set of standards that included selections from previous NCTM writings: CESSM (1989), PSTM (1991), and ASSM (1995). In addition, this new document would include four grade groupings (Prek-2, 3-5, 6-8, and 9-12) (NCTM, 2000). The writing group met during the summers of 1997, 1998, and 1999. “The writers had access to collections of instructional materials, state and province curriculum documents, research publications, policy documents, and international frameworks and

6 curriculum materials” (NCTM, 2000, p. x). In addition, throughout the creation of this document, the Commission on the Future of the Standards facilitated a review of the document. Members of the Conference Board of the Mathematical Sciences participated in this process by responding to a variety of questions about the document. Their answers helped to shape the format and content of the new standards (NCTM, 2000). To help support the writing team, NCTM’s Research Advisory Committee developed white papers (NCTM, 2000, p. x) or research summaries on eight major topics related to high quality mathematics education. Papers presented at the Conference on Foundations for School Mathematics provided additional information for the writing team. All of these documents are complied in the book A Research Companion to NCTM Standards (NCTM, 2000). Close to 30,000 copies of the completed draft were distributed for review. NCTM made the draft available online to allow interested parties to critique the ideas outlined in the new document. Six hundred fifty individuals and 70 groups submitted comments. Using qualitative analysis methods, these submissions were coded and given to the writing group. During the summer of 1999, the writing group used these suggestions to make necessary modifications or adjustments to the document (NCTM, 2000).

PSSM Description Principles. NCTM (2000) identifies six principles of high-quality mathematics instruction: equity, curriculum, teaching, learning, assessment, and technology. Although, these principles are described separately, NCTM (2000) emphasizes that all

7 must be in place to lay the foundation for creating mathematical environments that are challenging and supportive for all children. Equity focuses on the importance of all students having access to quality mathematics environments. Three components of this principle are outlined in PSSM (2000). First, all students should have teachers who create learning environments in which high expectations and quality learning opportunities are central to every mathematics lesson. Second, teachers should develop modifications to provide all children access to learning materials. Lastly, PSSM emphasizes the importance of all children having the necessary resources to create high-quality learning opportunities (NCTM, 2000). The second NCTM principle relates to the importance of the mathematics curriculum. Curricula should be coherent so that mathematical ideas build on previous learning experiences. In addition, it is pertinent that the curriculum focuses on key mathematical ideas children need to learn to be successful and understand the world around them. Alignment among the grade levels provides teachers with an understanding of the foundational skills children need to learn to be ready to understand more complex mathematical thinking. Furthermore, it prevents unnecessary repetition of material. The next principle, teaching, emphasizes the teacher’s role in high quality mathematical learning environments. Teachers need to understand children’s prior knowledge about a concept and connect these experiences to new ideas. Instructors should have a thorough understanding of the math concepts children need to learn at a

8 particular grade level. Furthermore, teachers need to support children’s learning while providing challenging activities (NCTM, 2000). Learning, the fourth principle focuses on the importance of children developing more than a superficial understanding of mathematical concepts. Students need to have opportunities to create a deep understanding of new ideas that go beyond memorization of facts or strategies. Learning environments that connect children’s natural inquisitiveness about mathematics to new ideas help to encourage positive experiences. In addition, students should have opportunities to communicate with others about various mathematical ideas and strategies (NCTM, 2000). The next principle, assessment, focuses on the importance of monitoring a student’s mathematical development. NCTM (2000) emphasizes that assessment should focus on more than end of unit tests. Assessment is an integral part of the mathematics classroom, which includes helping to inform which mathematical activities to include. Assessments provide teachers, as well as students, with a wealth of knowledge about a student’s mathematical development. A variety of types of assessments should be used including observations, portfolios, and performance-based activities. The last principle addressed in PSSM is technology. NCTM (2000) encourages teachers to use computers, calculators, and other forms of technology to support and enhance mathematical understanding. Teachers need to select appropriate learning opportunities to include technology that will allow children to access meaningful mathematical material.

9 Standards. The next section of the document describes the five content standards (number and operations algebra, geometry, measurement, and data analysis and probability) and the five process standards (problem solving, reasoning and proof, communication, connections, and representation). In addition, at the beginning of each grade grouping there is an introductory section that gives the reader a general overview of mathematics learning during that stage. Suggested concepts for the PreK-2 group for the number and operations standard include: understanding a variety of problems involving addition and subtraction situations, developing foundational notions of the base ten system, and building a strong number sense. One of the key concepts addressed in the algebra strand for this age range is patterning. NCTM (2000) emphasizes the importance of children creating and extending a variety of patterns with sounds, shapes, and numbers. For the geometry standard, children should begin to develop an understanding of 2 and 3- dimensional shapes including opportunities to create and to sort by characteristics. When considering the measurement standard, young children should have chances to work with a variety of units, including nonstandard and standard, and measure different attributes of an object (e.g., length, weight, area). The last standard focuses on data analysis. NCTM (2000) recommends that children have opportunities to collect and analyze data using graphs to organize this information. The final section of the document addressed the five process standards: problem solving; reasoning and proof; communication; connections; and representation. These elements are key to high-quality learning environments and children should have opportunities to engage in these types of activities across all five content standards.

10 Young children should have chances to solve meaningful problems that challenge them to develop understanding of their mathematical world. When solving these problems, students should share their strategies and provide reasons to support why they selected a given approach. High-quality mathematics environments provide children time to discuss these ideas with the teacher as well as with peers. In addition, mathematics should be connected to children’s daily routines and other areas of study to help them deepen their understanding of various concepts. Mathematical activities should provide students with a variety of ways to show their mathematical understanding through pictures, words, and numbers.

“Early Childhood Mathematics: Promoting Good Beginnings” To support the National Council of Teachers of Mathematics’ (NCTM) inclusion of prekindergarten in its Principles and Standards for School Mathematics (PSSM, 2000), NCTM and the National Association for the Education of Young Children (NAEYC) published a joint position statement in 2002 titled Early Childhood Mathematics: Promoting Good Beginnings. In this document, NAEYC and NCTM (2002) outlined 10 recommendations to help teachers provide high-quality mathematics instruction for children ages 3 to 6 years old. The recommendations suggested by NAEYC and NCTM (2002) include: 1. Enhance children’s natural interest in mathematics and their disposition to use it to make sense of their physical and social worlds.

2. Build on children’s experience and knowledge, including their family, linguistic, cultural, and community backgrounds; their individual approaches to learning; and their informal knowledge.

11 3. Base mathematics curriculum and teaching practices on knowledge of young children’s cognitive, linguistic, physical and social-emotional development.

4. Use curriculum and teaching practices that strengthen children’s problem solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas.

5. Ensure that the curriculum is coherent and compatible with known relationships and sequences of important mathematical ideas.

6. Provide for children’s deep and sustained interaction with key mathematical ideas.

7. Integrate mathematics with other activities and other activities with mathematics.

8. Provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest.

9. Actively introduce mathematical concepts methods, and language through a range of appropriate experiences and teaching strategies.

10. Support children’s learning by thoughtfully and continually assessing all children’s mathematical knowledge, skills, and strategies. (p. 3)

In addition, this document provides four recommendations for early childhood education advocates in leadership positions such as policymakers and program leaders. Recommendation 1 focuses on a child’s early mathematical experiences prior to formal instruction. According to NAEYC and NCTM (2002), teachers should tap into these prior experiences by creating activities that will “cultivate and extend children’s mathematical sense and interest” (p. 4). These positive experiences will help children gain confidence in their emerging mathematics ability as well as foster in them mathematical dispositions “such as curiosity, imagination, flexibility, inventiveness and persistence” (NAEYC & NCTM, 2002, p. 4).

12 Recommendation 2 indicates to teachers the importance of understanding various aspects of each child’s background and how their experiences might influence their understanding of mathematical concepts. The NAEYC and NCTM (2002) document acknowledges, “Young children have varying cultural, linguistic, home, and community experiences” (p. 4). Teachers should be aware of children’s different learning styles and provide students with a variety of modalities to learn mathematical concepts. Taking these differences into consideration, educators should connect children’s prior knowledge to new mathematical experiences in the classroom, which include making connections to the formal vocabulary of mathematics. Recommendation 3 addresses the need of developing mathematics activities that take into consideration not only the cognitive development of the child but also other areas such as linguistic, physical, and social-emotional development. Looking at the whole child will help the teacher create developmentally appropriate activities. In connection with these ideas, NAEYC and NCTM (2002) hold that due to, “. . . enormous variability in young children’s development, neither policymakers nor teachers should set a fixed timeline for children to reach each specific learning objective” (p. 5). Rather, it is more important for children to build a strong conceptual understanding of ideas independently of a fixed timeline. Recommendation 4 focuses on the importance of problem solving in the mathematics classroom. As part of this process, children should have opportunities to participate in mathematical conversations and to represent mathematics in a variety of ways. In addition, NAEYC and NCTM (2002) address providing children occasions to make connections among different mathematical concepts. “When children connect

13 number to geometry…they strengthen concepts from both areas and build knowledge and beliefs about mathematics as a coherent system” (NAEYC & NCTM, 2002, p. 6). Children should also connect mathematical concepts to other content areas as well. Recommendation 5 discusses the importance of developing a mathematics curriculum that is coherent. “To create coherence and power in the curriculum, however, teachers also must stay focused on the ‘big ideas’ of mathematics and on the connections and sequences among these ideas” (NAEYC & NCTM, 2002, p. 6). Educators should also be aware of how concepts are developed throughout the first several years of schooling. Recommendation 6 suggests that teachers need to provide children with a mathematics curriculum that allows them to develop a depth of understanding of the concepts. In order to have these meaningful learning opportunities, teachers need to formally introduce a variety of mathematical ideas to students. In addition, children need opportunities to engage with these ideas at home with their families. Recommendation 7 addresses the importance of integrating mathematics with other content areas as well as children’s daily routines. NAEYC and NCTM (2002) suggest developing integrated projects that will allow children to make connections between mathematics and the different subject areas. “Extended investigations offer children excellent opportunities to apply mathematics as well as to develop independence, persistence, and flexibility to making sense of real-life problems” (NAEYC & NCTM, 2002, p. 7). Recommendation 8 encourages teachers to provide children with opportunities to play. When playing, children discuss mathematical ideas about the world around them

14 and develop various strategies for solving problems. Teachers can support these emerging ideas by asking children questions to “provoke clarifications, extensions, and development of new understandings” (NAEYC & NCTM, 2008, p. 8). NAEYC and NCTM (2002) recommend the use of block play as one way for children to develop a variety of mathematical ideas such as sorting, seriating, and patterning. In addition, teachers should use their observations of children’s play to help guide the mathematics activities in the classroom. Recommendation 9 focuses on the importance of introducing mathematical concepts to young children. These activities can occur in large group or small group settings; however, it may be easier to focus children’s attention and to make observations with a smaller number of children. Teachers should plan meaningful activities that allow children to connect prior experiences to new ideas. Part of this planning includes deciding which materials are developmentally appropriate. Recommendation 10 discusses the use of assessment in the mathematics classroom. Assessment provides teachers with vital information about children’s mathematical understandings. NAEYC and NCTM (2002) suggest using a variety of types of assessment including observations, portfolios, and performance assessment while cautioning the use of “single group-administered test[s]” (p. 10). Teachers should take into consideration differences among individual children and make modifications to assessments when necessary. This study investigated the extent to which teaching practices align with these recommendations (NAEYC & NCTM, 2002) in a metropolitan preschool program. These findings provide information related to teachers’ use of these recommendations and

15 possible areas for professional development. In addition, an analysis of the curriculum materials indicates any alignment with the recommendations (NAEYC & NCTM, 2002). This information provides details pertaining to possible gaps in mathematics curricula for young children.

Definitions • Classroom Observation of Early Mathematics—Environment and Teaching (COEMET) – Observation protocol designed to identify the quality of mathematics teaching in early childhood programs (Kilday & Kinzie, 2009; Sarama & Clements, 2007). • Early Childhood Mathematics: Promoting Good Beginnings – Position statement from NAEYC and NCTM that outlines 10 recommendations for high-quality mathematics learning environments for children ages 3-6 years old • Expanded protocol – Term to describe when the observer completed all items on the specific math activity (SMA). • Head Start – A federally funded early childhood program for children 3-5 years old. Most children who qualify for this program come from families living below the poverty line. In 2009, the poverty guideline for a family of four was $22,050 (U.S. Department of Health and Human Services, 2010). • Mini specific math activity (mSMA) – A type of math activity identified on the COEMET in which the teacher does not address the mathematics in the learning experience (Sarama & Clements, 2007)

16 • National Association for the Education of Young Children (NAEYC) – A professional organization for early childhood professionals working with children from birth to age 8. • National Council of Teachers of Mathematics (NCTM) – A professional organization for mathematics educators. • Principles and Standards of School Mathematics (PSSM) – NCTM document that provides guidelines for high-quality mathematics instruction for PreK-12 grade. • Program – Term used to describe all the preschool locations that are part of this population. • Site – Term used to describe one of the schools that is part of this preschool program. • Specific math activity (SMA) – A type of math activity identified on the COEMET in which the teacher addresses the mathematics in the learning experience (Sarama & Clements, 2007)