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Early Childhood :(prosperity) Making it Count

October 2017

(introduction) (by) (goals)An increasing body of in early childhood mathematics, Sandra M. Linder, Ph.D. defi ned as mathematics for children from birth to age Associate Professor eight, has continually shown that early experiences in mathematics of Early Childhood can support children as they transition from informal schooling Mathematics Education, (i.e. child care or home-based environments) to formal schooling Clemson (i.e. ).1 Early mathematics skills are shown to be a predictor of academic success in both and mathematics as children progress from prekindergarten to kindergarten, and as they progress through the elementary years.2 Yet, across the world of early childhood care and education, there is signifi cant misunderstanding regarding the importance of these skills as well as uncertainty as to how to best incorporate them into classroom experiences.

This brief addresses the crucial role of early mathematics, the importance of both content and processes related to early math, and what research indicates on the barriers and opportunities for math in early childhood classrooms. The primary audience is early childhood teachers and administrators but recommendations are also made for family and community stakeholders, to build awareness and understanding to the challenges present in eff ective math instruction.

(why early math?) Young children are entering more rigorous school settings where an emphasis on accountability and standards is often prioritized over developmental needs. Kindergartners today experience more academic content than ever before, sometimes at the expense of developmentally appropriate practices that focus on social and emotional growth and contextual experiences. Unfortunately, if children enter kindergarten at a disadvantage, the resulting early achievement gaps in literacy and mathematics tend to be sustained or widen over time.3

In 2008, the National Mathematics Advisory Panel (NMAP) highlighted early mathematics by including PreK in all statements related to curriculum and standards.4 NMAP examined over 16,000 research articles to make recommendations for mathematics education in the . As part of their central fi ndings, the NMAP highlighted early childhood,

“Most children acquire considerable knowledge of numbers and other aspects of mathematics before they enter kindergarten. This is important, because the mathematical knowledge that kindergarteners bring to school is related to their mathematics for years thereafter.” – Foundations for Success: The Final Report of The National Mathematics Advisory Panel, National Mathematics Advisory Panel.

These fi ndings confi rm the increasing prominence of early childhood mathematics in the past two decades. The growth of this fi eld is also clear in increased funding opportunities; revisions of early learning standards to focus on mathematical thinking in lieu of ; and recognition of

1 the importance of early childhood mathematics in promoting cognitive development by national education organizations In 2010, the National Council of Teachers of Mathematics (NCTM) and the National Association of Educators of Young Children (NAEYC) updated a collaborative position statement stressing the importance that children under the age of six should receive high-quality, research-based instruction in mathematics. Experiences in early mathematics not only ensure “a sound mathematical foundation for all members of our society,”5 but also “prepare increasing numbers of young people for work that requires a higher proficiency level.”6

Best practices in early math experiences are often play-based and contextualized to connect with children’s experiences. Early mathematics should not be described as young children “doing worksheets” or “memorizing flash cards,” common visuals that many associate with math in the classroom. With increased emphasis on the role of mathematics in early childhood education, particularly in contexts prior to kindergarten, it is critical to understand trends in research in this relatively new field of study.

In short, what should schools, early learning centers, teachers, and the systems training these professionals, be doing to promote mathematics understanding in young children?

This issue brief focuses specifically on two constructs related to early childhood mathematics:

• Curriculum in Early Mathematics, and • Instructional Practices in Early Mathematics.

Examining both curriculum and teaching provides an overview of current issues that pervade early childhood mathematics education through the lens of the teacher.

(curriculum in early mathematics: content and processes) Mathematical instruction can be considered as two parts: the content and the processes. Curriculum can be conceptualized as programs that can be readily purchased to be implemented in a classroom context, or the content to be taught in the classroom. This issue brief broadens curriculum on a larger scope to include the concepts that are taught to young children in relation to early mathematics, including both content and the processes behind the content.

Mathematical Content The content is the what of math; it is the counting, adding, measuring, identifying shapes, and organizing of data. There are five specific content strands as defined by the National Council of Teachers of Mathematics and refined within early learning standards across the country:

2 Content Strand: What is Taught:

Numbers and Operations Counting, composing, decomposing, , subtracting

Geometry Two- and three-dimensional shapes, spatial awareness

Measurement Length, weight, time, temperature, money

Data Analysis Sorting, graphing

Algebra Repeating and growing patterns7

7

Mathematical Processes The processes of mathematics are the how of mathematics; they are the ways that children should be engaging in mathematical thinking. While content is important, it is through the mathematical processes that young children are best able to gain a sophisticated understanding of mathematics.8 To learn math in a child-centric and developmentally appropriate manner, early childhood teachers teaching must teach both content and process.

Teaching the mathematical processes behind the content offer increased opportunities for:

• Communication, • Representing ideas in multiple ways through pictures, symbols, words, or additional mediums, • Engaging in tasks that encourage logical thought and the use of reasoning and proof, and • Creating connections between mathematics and children’s everyday lives.

Process-oriented tasks promote self-regulatory behaviors (often connected to the development of executive ) and mathematics interest in young children.9 Additionally, process-oriented mathematics tasks support learning for students with social or emotional concerns.10 These process-oriented tasks also tend to be culturally responsive, in that teachers are making intentional connections to children’s lives, which can be beneficial for English Language Learners.11

What Research Tells Us There is limited research in regard to the specificmathematical content that should be taught in the early years. The majority of research from 2000 to the present examines content related to numbers and operations with as a distance second. A recent literature review of 1,133 empirical articles related to early mathematics from 2000-201512 found that articles focused on numbers and operations accounted for 44% of the total identified articles, while the other content areas were much less represented (See Figure 1).

3 Figure 1: Types of Early Math Content Researched

(types of early math content researched)

39% 44%

2% 4% 4% 7%

n Numbers & Operations n Geometry n n Measurement n Data Analysis n No content Focus

Source: Linder, S.M. & Simpson, A. (In Press). Connecting the mathematics identity of early childhood educators to classroom experiences for young children. In Forging connections in early mathematics teaching and learning.

What explains this relative lack of focus on four out of five mathematical content areas? It could relate to the structure of most pre-K and Kindergarten readiness assessments (with items focusing mainly on counting or early number concepts and shape identification) as these readiness assessments are often used as a benchmark for effectiveness. A second possibility might be related to limitation in how the general public perceives and often describes early mathematics (i.e. simple counting and shapes).

Despite these limitations, recent research provides some insight regarding early mathematics in connection to school readiness:

One study on the use of numerical board games in classroom environments found that the numerical ability of children from affluent families was significantly better than the numerical ability of children from impoverished families prior to the study; however, the gap between groups in their understanding of numerical magnitude was closed because of the experiment.13 Following this study, the same researchers found that linear numerical board game play in home environments had an impact on numerical ability.14

Building spatial sense through block play has also been established as a predictor of success in terms of school achievement in the elementary years and beyond. Researchers identified a significant relationship between block play at the level and later ability, though no significant relationships were identified between block play and later math achievement. Higher levels of sophistication in young children’s representations through block construction led to higher levels of success in reading during the early elementary years.15

4 While block play may not be a predictor of mathematics success at the early elementary level, it has been found to be a predictor of success for later school achievement in mathematics. One study reported the positive predictive relationship of levels of preschool block play and middle and high school mathematics achievement. Similar findings were again reported by the authors when examining the relationship between construction-type play with LEGOs and later school achievement.16 The reason why has not been confirmed in the research literature, but one could posit the problem solving and reasoning necessary in block play supports self-regulatory behaviors needed for later school success.

(instructional practice in early mathematics) How math is taught in the early years is as important as what is taught. The ideal role is for teachers to promote mathematical processes by acting a facilitator rather than transmitter of knowledge. This is described by Jonda, a teacher of four-year-olds in a Head Start center in upstate South Carolina:

My role throughout the day as the teacher is to encourage them [the children] to ask more questions. My goal is not to necessarily answer all of their questions. My role is to make them more curious. Make them want to go to the next steps. So my goal is to always be able to ask an open-ended question that will leave them wanting more or lead them to discover something on their own because the more they discover on their own, the more they will remember it. They will remember what I say, but if they do it hands-on, it seems to work better (Jonda, Head Start Teacher).

Jonda recognizes the need to promote children’s curiosity through open-ended questioning. While Jonda represents the ideal for how early childhood educators should approach mathematics instruction, she is not necessarily representative of the current state of instructional practices.

What Research Tells Us It is widely accepted in the research literature that mathematics instruction, at all levels, should focus on building conceptual understanding through student-centered tasks that are structured through the process standards (problem solving, reasoning and proof, communication, connections, representation). Many studies promote a play-focused approach to mathematics instruction in early childhood settings. Children in all early childhood settings should be engaged in mathematical thinking and talk throughout the day, whether during play in centers, during indoor and outdoor free play, during transitions or informal activities (i.e. snack time, handwashing), or during formal tasks (whole group or small group) structured within the classroom context.17 Early childhood educators need to increase connections throughout the day by encouraging ‘math talk’ (e.g. asking children open-ended questions while they are playing in the house area about how they can best the table for dinner if they have a certain number of guests coming over). Interactive peer play encourages deeper mathematical outcomes, especially when teachers were also involved in play- based scenarios.18

The role of the teacher in early childhood mathematics instruction is to promote problem solving and reasoning through open-ended tasks that encourage communication and collaboration, thereby creating an effective early childhood mathematics environment. The crux of an effective mathematics

5 environment lies within the symbiosis between people and space. Whether in a childcare or home-based setting, (early math builds critical certain components are necessary to develop math-rich environments: executive function skills) Executive Function skills – the brain’s • Having readily available tools and materials (e.g. ability for self-regulation, mental blocks, concrete manipulatives, scales and balances, flexibility, and working memory standard and nonstandard tools for measurement, – are developed throughout early etc.) throughout the space that are useful in engaging childhood. Strong Executive Function young children in mathematical tasks; development helps children’s school success academically, behaviorally, • Encouraging mathematical discourse and and health-wise. communication between all members of the classroom or home by understanding and making Executive Function skills are linked connections to young children’s interests and current to mathematical process and learning schema about the world around them and can strengthen one another. Establishing foundational neural • Modeling positive dispositions and promoting the connections early in life builds value of mathematics. the brain’s ability for higher order • Strategically increasing formal opportunities thinking, complex problem solving, (circle time, small group time, etc.) related to early and critical thinking skills, skills mathematics. necessary for a competitive workforce.

Source: Harvard Center on the Developing Child, • Capitalizing on informal learning opportunities Executive Function: Skills for Life and Learning; (center time, outdoor/indoor play, snack/lunch, etc.) Cragg and Gilmore, Skills Underlying Mathematics: The Role of Executive Function in the Development related to early mathematics. of Mathematics Proficiency.

Implementation Challenges Exist Many early childhood teachers (whether in informal or formal education settings) hold dominant cultural views of what it means to teach and learn mathematics, which can influence instruction in a negative manner. These include:19

• Mathematics (even for young children) is a static body of knowledge in which memorizing mathematical facts and procedures are considered more powerful than understanding mathematical concepts • The teacher (not the student) is deemed as the expert of the classroom.20

Often these beliefs about mathematics instruction are based on their experiences as a mathematics student.21 Many early childhood teachers enter into the profession with negative attitudes toward mathematics.22 In fact, a study of Head Start teachers found that the majority of teachers studied did not have positive experiences with mathematics while in school and, as a result, did not feel confident in teaching mathematics to their students.23

Center directors, principals, and policymakers can help combat this math anxiety and improve classroom instruction of math by improving math education in teacher preparation programs and providing quality professional development to teachers already in the classroom. However, as noted in the joint NAEYC-NCTM position statement, simply requiring additional math coursework or

6 mandating hours of in-service will not remedy these issues. Rather, NAEYC-NCTM report that “[e]ffective professional programs weave together mathematics content, pedagogy, and knowledge of child development and family relationships.”24 The goal of improved math preparation and in-service is to develop deep understanding of mathematical concepts; demonstrate the type of interactive teaching styles that will work best with children; and help teachers understand how to ask questions to encourage children’s mathematical thinking.25

(implications for south carolina classrooms and beyond) We know that early childhood mathematics should focus on mathematical processes, best taught through play-based experiences connected to children’s everyday contexts.26 Many early childhood teachers use traditionally oriented approaches to mathematics instruction (e.g. rote counting as a whole group, completing worksheets as a small group) and not teaching in a child centric manner through the mathematical processes.27 These practices are not isolated to South Carolina.

To maximize learning and skill-building, early childhood educators across the country need to abandon the instructional practices they experienced as children to adopt student-focused practices that emphasize the role of the teacher as a facilitator, rather than a transmitter, of knowledge. In addition to altering instructional practices, we must also consider the sheer amount of time spent throughout the day on encouraging mathematical thinking. Children can make mathematical connections in every aspect of their day, from getting dressed in the morning, to handwashing or informal times within the classroom (e.g. snack, lunch, transitions, outdoor play), to free or structured play within centers, and during formal mathematics lessons. To move towards this child centric, process-oriented vision of early childhood mathematics environments, childcare teachers require effective, continual professional development focused on building their knowledge and understanding of what it means to build mathematical awareness in young children and addressing their own “math anxiety.” Childcare teachers across South Carolina are typically required to take a certain number of hours of professional development annually to obtain licensure, but only a small amount of this professional development relates to mathematics education.28 Concerted efforts are required to reform current professional development initiatives to spend increased time on promoting effective mathematical practices in early childhood settings, which, in turn, can lead to increased success in terms of school readiness.

For teachers and administrators, early math plays an important role in Kindergarten readiness broadly, particularly in the growing use of Kindergarten Readiness Assessment (KRAs). KRAs are a useful tool in determining developmental stages, child’s readiness to learn kindergarten-level curriculum. They can be used to design instructional practice and ensure children are on track developmentally. It is recommended that KRAs assess a child’s five developmental domains of learning:

• physical well-being and motor development; • social and emotional development; • approaches toward learning; • language development; and • cognition and general knowledge, including mathematics.

7 KRAs are not an appropriate instrument for teacher or classroom accountability purposes. However, they are strong drivers of the conversation on what children should learn, when they should learn it, and how. While early childhood teacher should not be driven to “teach to the test,” KRAs present an opportunity to align what children need to know in early math to succeed in Kindergarten and beyond with the content and processes addressed in early childhood classrooms. That being said, the KRA items should be process-oriented rather than skill-based to best determine pathways of instruction for young children.

While this brief has focused on challenges and opportunities for classroom teachers, children and their early math experiences exist in the broader world in which they live.

Families play a tremendous role in shaping early math experiences for children but often do not know how to incorporate early math into their daily lives. Schools again play a role in providing parents with resources and techniques to infuse math into home life. Community-based programs and organizations (such as home-visiting and literacy programs) can also contribute to their clients. One review of math promotion in family engagement programs recommends teaching caregivers to make small changes in their everyday activities, such as running errands, reading books, and playing with a child, to infuse more mathematical content; this can be as simple as counting throughout the day and identifying shapes. Additionally, adults in a child’s life can foster mathematical thinking, without addressing math content explicitly, by “asking children open-ended questions that involve real-life problems and…giving children enough time to think about and respond to a question regardless of whether they answer it correctly.”29 Programs should work to include families in early math activities in the classroom and provide skills and resources they can utilize at home.

Home-based care providers, including “kith and kin” child care providers, are often locked out of the formal systems of professional development that classroom teachers access. While most professional development systems must revise how they address early math, it is essential that providers outside of public pre-K and Head Start are able to access quality resources as well. Whether through inviting local providers to district-operated trainings, creating separate sessions for home- based providers to address their unique needs, or utilizing virtual trainings and resources, investing in these providers creates a tremendous opportunity for the children in their care. Involving these providers is important to fostering “coherence and continuity for teachers and for children’s mathematical experiences.”30

Business: Investing in early math can help put children on track not only for academic success but also for a STEM-focused career in the future. The current US economy is shifting towards a base of higher-skilled jobs that require a greater supply of workers with advanced math skills. In response to this uptick in workforce demand, the U.S. Chamber of Commerce’s Institute for a Competitive Workforce encourages members to promote high quality early educational experiences in their communities, noting the strong social, academic, and economic returns on investment yielded from ECE programs. The business community can promote early math skill-building by partnering with local early childhood advisory groups to better understand the importance of ECE, promoting ECE as a means for economic development, and by creating policies that support the needs of working parents and by extension, the developmental needs of their children.31

8 (conclusion and next steps) Research makes clear that early mathematics experiences play an important role in the academic and social-emotional development of children, yet many early childhood settings face barriers to implementing best practices. While mathematical content is important for young learners, early childhood settings also need to embrace a play-based, whole child approach to math. Moving the field in this direction will require the collaboration of teachers, administrators, and institutes of higher education. Additionally, families and community-based resources play an important role in children’s development both within and outside the classroom. While this brief focused primarily on the classroom experience, future research briefs should further examine developmentally appropriate mathematical content for young children, home and school connections in early mathematics, student achievement and/or understanding in mathematics, and student dispositions towards mathematics.

About the Author

Sandra M. Linder is an Associate Professor of Early Childhood Mathematics Education in the College of Education at Clemson University. Her research centers on supporting and sustaining teacher quality in early childhood mathematics through professional development. She has taught in a variety of early childhood and elementary settings and have worked intensively with in-service and pre-service mathematics educators from infant settings through fifth grade. Recently, she examined the impact of mathematics professional development on the early care workforce (birth to age 5) in South Carolina through Project BEEMS (Building Environments for Early Mathematics Success) funded through PNC Foundation. Currently, Dr. Linder is investigating the role of the parent/caregiver in promoting mathematics understandings in young children through the use of a take-home math bag intervention. Most importantly, Dr. Linder has three beautiful children (Bella: age 6, AJ: age 5, and Clara: age 4) so she is immersed in early childhood 24 hours a day!

9 (notes) 1 Hanline, M. F., Milton, S., & Phelps, P. C. (2008). A longitudinal study exploring the relationship of representational levels of three aspects of preschool sociodramatic play and early academic skills. Journal of Research in Childhood Education, 23(1), 19-28. 2 NICHD Early Child Care Research Network. (2002). Early childcare and children’s development prior to school entry: Results from the NICHD study of early childcare. American Journal, 39, 133-164. 3 Linder, S.M., Ramey, M.D., & Zambak, S. (2013). Predictors of success for school readiness: A selective review of the literature. Early Childhood Research and Practice. 15(1); McLoyd, V. C., & Purtell, K. (2008). How childhood poverty and income affect children’s cognitive functioning and school achievement. In S. Neuman (Ed.), Educating the other America: Top experts tackle poverty, literacy, and achievement in our schools (pp.53-72). Baltimore, MD: Paul H. Brookes Publications.; NICHD Early Child Care Research Network. (2002). Early childcare and children’s development prior to school entry: Results from the NICHD study of early childcare. American Educational Research Journal, 39, 133-164. 4 National Mathematics Advisory Panel (NMAP). (2008). Foundations for success: The final report of the national mathematics advisory panel. U.S. Department of Education. Washington, DC. 5 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 6 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 7 National Council of Teachers of Mathematics (NCTM). (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: NCTM. 8 Benoit, L., Lehalle, H., Molina, M., Tijus, C., & Jouen, F. (2013). Young children’s mapping between arrays, number words, and digits. Cognition, 129(1), 95-101.; De Haan, A. K., Elbers, E., & Leseman, P. P. (2014). Teacher-and child-managed academic activities in preschool and kindergarten and their influence on children’s gains in emergent academic skills. Journal of Research in Childhood Education, 28(1), 43-58.; National Council of Teachers of Mathematics (NCTM). (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: NCTM. 9 Dobbs-Oates, J., & Robinson, C. (2012). Preschoolers’ mathematics skills and behavior: Analysis of a national sample. Review, 41(4), 371-386.; Fisher, P. H., Dobbs-Oates, J., Doctoroff, G. L., & Arnold, D. H. (2012). Early math interest and the development of math skills. Journal of , 104(3), 673-681.; Montroy, J. J., Bowles, R. P., Skibbe, L. E., & Foster, T. D. (2014). Social skills and problem behaviors as mediators of the relationship between behavioral self-regulation and academic achievement. Early Childhood Research Quarterly, 29(3), 298-309. 10 Dobbs, J., Doctoroff, G. L., Fisher, P. H., & Arnold, D. H. (2006). The association between preschool children’s socio-emotional functioning and their mathematical skills. Journal of Applied Developmental Psychology, 27(2), 97-108.; Fantuzzo, J., Bulotsky-Shearer, R., McDermott, P., McWayne, C., Frye, D., & Perlman, S. (2007). Investigation of dimensions of social-emotional classroom behavior and school readiness for low-income urban preschool children. School Psychology Review, 36(1), 44-62.; Vitiello, V. E., Moas, O., Henderson, H. A., Greenfield, D. B., & Munis, P. M. (2012). Goodness of fit between children and classrooms: Effects of child temperament and preschool classroom quality on achievement trajectories. Early Education and Development, 23(3), 302-322. 11 Burchinal, M., Field, S., López, M. L., Howes, C., & Pianta, R. (2012). Instruction in Spanish in pre-kindergarten classrooms and child outcomes for English language learners. Early Childhood Research Quarterly, 27(2), 188-197. 12 Linder, S.M. & Simpson, A. (In Press). Connecting the mathematics identity of early childhood educators to classroom experiences for young children. In Forging connections in early mathematics teaching and learning. 13 Siegler, R. S., & Ramani, G. B. (2008). Playing linear board games—but not circular ones—improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545–600. 14 Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79, 375–394. 15 Hanline, M. F., Milton, S., & Phelps, P. C. (2010). The relationship between preschool block play and reading and maths abilities in early elementary school: a longitudinal study of children with and without disabilities. Early Child Development and Care, 180, 1005-1017. 16 Wolfgang, C., Stannard, L., & Jones, I. (2001). Block play performance among preschoolers as a predictor of later school achievement in mathematics. Journal of Research in Childhood Education, 15, 173–180. 17 Brendefur, J., Strother, S., Thiede, K., Lane, C., & Surges-Prokop, M. J. (2013). A professional development program to improve math skills among preschool children in head start. Early Childhood Education Journal, 41(3), 187-195.; Hanline, M. F., Milton, S., & Phelps, P. C. (2010). The relationship between preschool block play and reading and maths abilities in early elementary school: a longitudinal study of children with and without disabilities. Early Child Development and Care, 180, 1005-1017. 18 Bulotsky-Shearer, R. J., Bell, E. R., Carter, T. M., & Dietrich, S. L. (2014). Peer play interactions and learning for low-income preschool children: The moderating role of classroom quality. Early Education and Development, 25(6), 815-840. 19 National Council of Teachers of Mathematics (NCTM). (2014). Principles to action: Ensuring mathematical success for all. Reston, VA: NCTM. 20 Löfström, E., & Pursiainen T. (2015). Knowledge and knowing in mathematics and pedagogy: a of mathematics student teacher epistemological beliefs. Teachers and Teaching: theory and practice, 21(5), 527-542.

10 21 Bekdemir, M. (2010). The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students. Educational Studies in Mathematics, 75(3), 311-328.; Lortie, D. C. (2002). Schoolteacher: A sociological study (2nd ed.). Chicago, IL: University of Chicago Press. 22 Brady, P., & Bowd, A. (2005). Mathematics anxiety, prior experience and confidence to teach mathematics among pre‐service education students. Teachers and Teaching, 11(1), 37-46.; Zacharos, K., Koliopoulos, D., Dokimaki, M., & Kassoumi, H. (2007). Views of prospective early childhood education teachers, towards mathematics and its instruction. European Journal of , 30(3), 305-318. 23 Linder, S.M. & Simpson, A. (2017) Towards an understanding of early childhood mathematics education: A systematic review of the literature focusing on practicing and prospective teachers. Contemporary Issues in Early Childhood, DOI: 10.1177/1463949117719553; Simpson, A. & Linder, S.M. (2016). The indirect effect of children’s gender on early childhood educators’ mathematical talk. Teaching and Teacher Education, 54, 44-53. 24 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 25 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 26 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 27 National Research Council. (2001). Adding it up: Helping children learn mathematics. J.Kilpatrick, J. Swafford, and B.Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. 28 Simpson, A. & Linder, S.M. (2014). An examination of mathematics professional development opportunities in childcare settings. Early Childhood Education Journal, 42 (5), 335-342. 29 Harris, B., Peterson, D., & Smither Wulsin, C. (2017). Integrating Mathematical Thinking into Family Engagement Programs. Mathematica Policy Research and Heising-Simons Foundation. 30 National Association for the Education of Young Children (NAEYC). (2002). Early childhood mathematics: Promoting good beginnings. Retrieved from http://www.naeyc.org/files/naeyc/file/positions/psmath.pdf 31 Institute for a Competitive Workforce. (2010). Why Business Should Support Early Childhood Education.

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