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Where’s the Math?: Books, Games, and Routines to Spark Children's Thinking (2019)

by Mary Hynes-Berry (Author), Laura Grandau (Author)

Over the past two decades, a quiet revolution in developmental psychology and related fields has demonstrated that children have skills and concepts relevant to mathematics learning that are present early in life, and that most children enter school with a wealth of knowledge and cognitive skills that can provide a foundation for mathematics learning. At the same time, these foundational skills are not enough- children need rich mathematical interactions, both at home and at school in order to be well prepared for the challenges they will meet in elementary school and beyond.
— National Research Council, Mathematics Learning in Early Childhood: Paths Towards Excellence and Equity, 2009


  • The early years significantly affect mathematics learning and attitudes. (NAEYC & NCTM, 2002)

  • Students entering Kindergarten with a strong foundation in math were more likely to be successful students.

  • A strong foundation in math before Kindergarten entry was the strongest predictor of math achievement and reading ability. (Duncan et al., 2007)

  • Students with strong kindergarten math skills had better social skills- less physical aggression, better attention, less anxiety/depression, and less hyperactivity/impulsivity in third grade. (Romano, Babchishin, Pagani, & Kohen, 2010)

  • Children with early mathematical abilities were found to have more creative accomplishments and leadership roles in adulthood (Lubinski, Benbow, & Kell, 2014).


  • American students achieve in mathematics at a mediocre level by comparison to peers worldwide. (National Mathematics Advisory Panel, 2008)

  • There are large, persistent disparities in mathematics achievement related to race and income (National Mathematics Advisory Panel, 2008)

  • Children who enter kindergarten with fewer math skills typically do not catch up, and those same children continue to lag behind their better prepared peers into 8th grade (Schoenfeld & Stipek, 2011).

  • Adults lack confidence in teaching math due to personal insecurities about math, a misconception that math learning occurs naturally through play, a lack of overall math knowledge and limited resources for teaching. (NAEYC & NCTM, 2002)


National Association for the Education of the Young Child & National Council of Teachers of Mathematics, 2002

  • National Research Council, 2009

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National Council of Teachers of Mathematics, 2013

"Early childhood educators should actively introduce mathematical concepts, methods, and language through a variety of appropriate experiences and research-based teaching strategies. Teachers should guide children in seeing connections of ideas within mathematics as well as with other subjects, developing their mathematical knowledge throughout the day and across the curriculum. They must encourage children to communicate, explaining their thinking as they interact with important mathematics in deep and sustained ways."




Math Resources:

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Erikson Institute’s Early Math Collaborative (2014). Big Ideas of Early Mathematics. Boston, MA: Pearson Education.

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Geist, E. (2001). Children are born mathematicians: Promoting the construction of early mathematical concepts in children under five. YC Young Children, 4(12).

Gennarelli, C. & DeBlasio, M. (2017). Big questions: Using questions and selecting materials to promote math thinking. Teaching Young Children, 11(1).

Ginsburg, H. (2014). Young children’s mathematical minds. In H. Ginsburg, M. Hyson, & T.A. Woods, (Eds.), Preparing early childhood educators to teach math: Professional development that works. (53-74). Baltimore: Brookes.

Ginsburg, H., & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29(4), 274-285.

Ginsburg, H., Hyson, M., & Woods, T. A. (2014). Preparing early childhood educators to teach math: Professional development that works. Baltimore: Brookes Publishing.

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Gunderson, E.A., & Levine, S.C. (2011). Some types of parent number talk count more than others: relations between parents- input and children’s cardinal number knowledge.Developmental Science, (5), 1021. 

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Heddens, J. W. (1986b). Improving mathematics teaching by using manipulatives. Kent State University, Retrieved from:

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Kanter, P. F., Darby, L., & Toth, R. (1999). Helping your child learn math. Washington,DC: U.S. Dept. of Education Office of Educational Research and Improvement.

Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children's mathematical knowledge: The effect of teacher "math talk". Developmental Psychology, 42(1), 59-69.

Laski, E.V., Jor’dan, J.R., Daoust, C., & Murray, A. K. (2015). What makes mathematics manipulatives effective? Lessons from cognitive science and Montessori education. SAGE Open, 5(2).

Linder, S., Powers-Costello, B., & Stegelin, D. (2011). Mathematics in early childhood: Research-based rationale and practical strategies. Early Childhood Education Journal, 39(1), 29-37.

Lubinski, D., Benbow, C. & Kell, H. (2014). Life paths and accomplishments of mathematically precocious males and females four decades later. Psychological  Science, 25(12), 2217-2232.

Malaguzzi, L. (1998). History, ideas, and basic philosophy: An interview with Lella Gandini. In C. Edwards, L. Gandini & G. Forman (Eds.), The Hundred Languages of Children.(pp. 49-97). Westport, CT: Ablex Publishing. 

Master, A. (2017). Teachers' mindsets about math (and why they matter). Teaching Young Children, 11(1), 22-23.


McCray, Chen, Eisenband-Sorkin. (2019). Growing Mathematical Minds: Conversations between Developmental Psychologists and Early Childhood Teachers. New York, NY: Routledge.McLennan, D. P. (2014). Making math meaningful for young children. Teaching Young Children, 8 (1), 3.

Mononen, R., Aunio, P., Koponen, T. & Aro, M. (2014). A review of early numeracy interventions for children at risk in mathematics. International Journal of Early Childhood Special Education. 6(1), 25-54.

Moomaw, S. (2011). Teaching mathematics in early childhood: Baltimore, MD: Brookes Publishing.

Moore, A. M., vanMarle, K., & Geary, D. C. (2016). Kindergartners' fluent processing of symbolic numerical magnitude is predicted by their cardinal knowledge and implicit understanding of arithmetic 2 years earlier. Journal Of Experimental Child Psychology, 150, 31-47.

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National Association for the Education of Young Children. (2017). NAEYC Early Learning Standards and Accreditation Criteria & Guidance for Assessment. Washington,DC: NAEYC. Retrieved from

National Association for the Education of Young Children. (2018). NAEYC Early Learning Program Accreditation Standards and Assessment Items. Washington, DC: NAEYC. Retrieved from

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2003). Mathematics in Early Childhood Learning.Reston, VA: Author.

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: Author.

National Council of Teachers of Mathematics. (2014a). Access and Equity in Mathematics Education. Reston, VA: Author.

National Council of Teachers of Mathematics. (2014b). Principles to actions: Ensuring Mathematical success for all. Reston, VA: Author.

National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards for mathematics: Kindergarten   introduction. Retrieved from

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National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity.C. T. Cross, T. A. Woods, & H. Schweingruber (Eds.). Washington, DC: National Academies Press.

Nelson, G. (2014). Fostering children’s number sense in grades K-2: Turning math inside out. Upper Saddle River, NJ: Pearson.

Nemeth, K. (2017). Make math meaningful for diverse learners. Teaching Young Children, 11(1), 4-6.

Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Childhood Research Quarterly, 36, 550-560.

Ontario English Catholic Teachers’ Association. (2016). Encouraging math learning at home: A guide for parents. Retrieved from

Platas, L.M. (2017). Three for one: Supporting social, emotional, and mathematical development.Young Children, 72 (1) 33-37. **This article has a list of math vocabulary and questions that support mathematical thinking.

Reed, K.E. & Young, J.M. (2017). Games for young mathematicians: Shape cards about the math. Waltham, MA: Education Development Center, Inc.

Romano, E., Babchishin, L., Pagani, L. S., & Kohen, D. (2010). School readiness and later achievement: Replication and extension using a nationwide Canadian survey. Developmental Psychology, 46(5), 995-1007.

Rudd, L., Lambert, M., Satterwhite, M., & Zaier, A. (2008). Mathematical language in early childhood settings: What really counts? Early Childhood Education Journal, 36(1), 75-80.

Rushton, S. (2011). Neuroscience, early childhood education and play: We are doing it right!, Editorial. Early Childhood Education Journal,pp. 89-94. Retrieved from

Schaefer, R. (2016). Teacher inquiry on the influence of materials on children’s learning. YC Young Children, 71(5), 64-73.

Schiller, P., & Willis, C. A. (2008). Using brain-based teaching strategies to create  supportive early childhood environments that address learning standards. YC Young Children, (4),52.

Schoenfeld, A. H., & Stipek, D. (2011, November 7 & 8). Math matters: Children’s mathematical journeys start early. Conference proceedings. Berkeley, CA.

Seo, K. (2003). What children’s play tells us about teaching mathematics. YC Young Children, 58(1), 28–33.

Sousa, D. A. (2006). How the brain learns: a classroom teacher's guide. Thousand Oaks, CA: Corwin Press.

Sparks, S. D. (2017). Do parents see math as 'less useful' than reading? Survey finds parents rank subject lower. Education Week, 36 (30), 9.

Stipek, D. (2013). Mathematics in early childhood education: Revolution or evolution?. Early Education and Development, (4). 431.

Stipek, D., Schoenfeld, A.H., & Gomby, D. (2012). Math matters, even for little kids. Education Week, 31(26), 27.

Swartout-Corbeil, D.M. (2017). Early childhood education. Retrieved from

Trawick-Smith, J., Oski, H., DePaolis, K., Krause, K., & Zebrowski, A. (2016). Naptime data meetings to increase the math talk of early care and education providers. Journal of Early Childhood Teacher Education, 37(2), 157-174. 

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Van Voorhis, F. L., Maier, M. F., Epstein, J. L., & Lloyd, C. M. (2013). The impact of family involvement on the education of children ages 3 to 8: A focus on literacy and math achievement outcomes and social-emotional skills. Retrieved from

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Weisberg, D.S., Hirsh-Pasek, K., Golinkoff, R.M., Kittredge, A.K., & Klahr, D. (2016). Guided play: Principles and practices. Current Directions in Psychological Science, 25(3), 177-182.

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Natural Materials Resources:

Bailie, P.E. (2010). From the one-hour field trip to a nature preschool: Partnering with environmental organizations. Young Children.65(4), 76-82.

Banning, W., & Sullivan, G. (2011). Lens on outdoor learning. St. Paul, MN: Redleaf Press.

Cain-Chang, & Veselack. (2017, November 15–18). Outdoor classrooms.NAEYC national conference, Atlanta, GA.

Daly, L., & Beloglovsky, M. (2015). Loose parts: Inspiring play in young children. New York: Redleaf Press.

Johnson, G. G., & Wilson, R. W. (2016). Nature as a path to early math. Exchange, 19460406 (227), 3.

Kemple, K. M., Oh, J., Kenney, E., & Smith-Bonahue, T. (2016). The power of outdoor play and play in natural environments. Childhood Education, (6), 446.

Louv, R. (2008). The last child in the woods: Saving our children from nature-deficit disorder. (1st ed.). Chapel Hill, NC: Algonquin Books of Chapel Hill.

Louv, R. (2011). The nature principle: human restoration and the end of nature-deficit disorder. Chapel Hill, NC: Algonquin Books of Chapel Hill.

McLennan, D.P. (2017). Math learning—and a touch of science—in the outdoor world. Teaching Young Children, 10(4), 19-22.

Nicholson, S. (1972). The theory of loose parts: An important principle for design methodology. Studies in Design Education Craft & Technology, 4(2).

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Ruzzi, B. L. & Eckhoff, A. (2017). STEM resources and materials for engaging learning experiences. YC: Young Children, 72(1), 90-93.

Sear, M. (2016). Why loose parts? Their relationship with sustainable practice, children's agency, creative thinking and learning outcomes. Educating Young Children: Learning & Teaching in the Early Childhood Years, 22(2), 16-19.

Selly, P. B. (2017). Teaching STEM outdoors: Activities for young children. St. Paul, MN: Redleaf Press.

Spencer, A.M. (2013). Loose parts and learning on the playground. Exchange, 19460406 (211), 70-71.

Torquati, J., Cutler, K., Gilkerson, D., & Sarver, S. (2013). Early childhood educators' perceptions of nature, science, and environmental education. Early Education & Development, 24(5), 721-743.

Resources for effective teaching :

NAEYC. (n.d.) 10 effective DAP teaching strategies. Retrieved from

Stewart-Henry, K. and Friesen, A. (2018). Promoting powerful interactions between parents and children. Teaching Young Children. 11(5), 24-27.

Open-ended Questions:
Strasser, J. (2018). Conversations with children! Questions that spark conversations and deepen understanding open-ended questions. Teaching Young Children. 11(4).

Strasser, J. and Maiorana, E., (2018). Conversations with children! Big questions lead to math adventures. Teaching Young Children. 12(1).

Strasser, J. and Bresson, L.M. (2017). Big questions for young minds: Extending children’s thinking. Washington, DC: NAEYC.

Open ended questions. Retrieved from

Georgia’s Pre-K Program. (2014). Open-ended questions to help children think. Retrieved from