NEW RESOURCES

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

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

**Research **

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).

**Problem**

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)

**Recommendations**

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

**National Research Council, 2009**

**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."

**Websites:**

### Standards and Publications:

http://www.corestandards.org/Math/Practice/

**Sample Assessments:**

http://program.yourschools.ca/early-numeracy-assessment-portfolio/

**Open Ended QUestions:**

http://www.decal.ga.gov/documents/attachments/Questions_Children_Think.pdf

https://www.naeyc.org/math-at-home

https://www.nctm.org/publications/curious/default.aspx

http://www.kidscount1234.com/mathcentersandgames.html

http://youngmathematicians.edc.org

http://talkingisteaching.org/resources/highlights-guide

https://www.education.com/activity/preschool/math/

https://courses.sesamestreetincommunities.org/mathcourse/

https://www.ixl.com/math/pre-k

https://pdg.grads360.org/#program/stem-in-early-childhood

http://thinkmath.edc.org/resource/kindergarten

https://becomingamathfamily.uchicago.edu

NEWS

https://www.childtrends.org/videos/building-your-childs-math-confidence

**Math Resources:**

Achieve. (2013). Closing the expectations gap: 2013 annual report on the alignment of state K-12 policies and practices with the demands of college and careers. Retrieved from https://www.achieve.org/files/2013ClosingtheExpectationsGapReport.pdf.

Bates, A. B., Latham, N. I., & Kim, J. (2013). Do I have to teach math? Early childhood pre-service teachers' fears of teaching mathematics. *Issues in the Undergraduate Mathematics Preparation of School Teachers, 5*.

Bellonio, J. L. (2012). Multi-sensory manipulatives in mathematics: Linking the abstract to the concrete. Retrieved January 31, 2018 from http://www.cis.yale.edu/ynhti/curriculum/units/2001/6/01.06.12.x.html.

Benner, S. M., & Hatch, J. A. (2009). From the editors: Math achievement and early childhood teacher preparation. *Journal of Early Childhood Teacher Education, 30*(4), 307-309.

Benson, H. S. (2003). Glossary of math terms. In D. Koralek (Ed.), *Spotlight on young children and math. *(p. 43). Washington, DC: National Association for the Education of Young Children.

Berkowitz, T., Schaeffer, M. W., Maloney, E. A., Peterson, L., Gregor, C., Levine, S. C., & Beilock, S.L. (2015). Math at home adds up to achievement in school. *Science, 350 *(6257), 196-198.

Broderick, J.T., & Hong, S.B. (2011). Introducing the cycle of inquiry system: A reflective inquiry practice for early childhood teacher development. *Early Childhood Research & Practice*, 13(2).

Butera, G., Friesen, A., Palmer, S.B., Lieber, J., Horn, E.M., Hanson, M.J., & Czaja, C. (2014). Integrating mathematics problem solving and critical thinking into the curriculum. Young Children. 69(1).

Caspe, M. (February 8, 2018). Every child ready for math. Retrieved from https://globalfrp.org/Articles/Every-Child-Ready-for-Math

Chen, J., Hynes-Berry, M., Abel, B., Sims, C., & Ginet, L. (2017). Nurturing mathematical thinkers from birth: The why, what, and how. *Zero to Three, 37*(5), 23-33.

Clements, D.H., & Sarama, J. (2014). *Learning and teaching early math: The learning trajectories approach.*(2nded.). New York: Routlege.

Clements, D.H., & Sarama, J. (2017). Learning trajectories/Teaching strategies gold alignment. Retrieved from https://www.learningtrajectories.org/system/files/inline-files/TSG%20Alignment%20with%20LTs.pdf

Clements, J. Sarama, & A.M. DiBiase (Eds.), *Engaging young children in mathematics: Standards for early mathematics education. *(pp. 401–414). Mahwah, NJ: Lawrence Erlbaum.

Copley, J. (2004). The early childhood mathematics collaborative: A professional development model to communicate and implement the standards. In D. H.

Copley, J. (2010). *The young child and mathematics. *(2nd ed.) Washington, DC: National Association for the Education of Young Children.

Copley, J. (2014). Goals for early childhood mathematics teachers. In H. Ginsburg, M. Hyson and T. Woods (Eds.), *Preparing early childhood educators to teach math: Professional development that works.*(pp. 75-93). Baltimore: Brookes.

Copple, C., & Bredekamp, S. (2009). *Developmentally appropriate practice in early childhood programs serving children from birth through age 8*. (3rd ed.) Washington, DC: National Association for the Education of Young Children.

Department of Education. (2008). *Counting on excellence: How parents can help their children learn mathematics*. Recommendations from the National Mathematics Advisory Panel: US Department of Education.

Development and Research in Early Math Education. (2017). Retrieved from https://dreme.stanford.edu.

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., and Japel, C. (2007). School readiness and later achievement. *Developmental Psychology, 43*(6),1428-1446.

Early, D., Burchinal, M., Barbarin, O., Bryant, D., Chang, F., Clifford, R., et al. (2013). Pre-Kindergarten in eleven states: NCEDL's multi-state study of pre-kindergarten and study of state-wide early education programs (SWEEP): ICPSR.

Eason, S. H., & Levine, S. C. (2017). Math learning begins at home. *Zero to Three, 37*(5), 35-43.

Eason, S.H., & Levine, S.C. (2017). Spatial reasoning: Why math talk is about more than numbers. Retrieved from https://dreme.stanford.edu/news/spatial-reasoning-why-math-talk-about-more-numbers

Eisenhauer, M.J. & Feikes, D. (2009). Dolls, blocks, and puzzles: Playing with mathematical understandings. *YC Young Children, *3(18).

Farran, D., Lipsey, M., & Wilson, S. (2011). Experimental evaluation of the tools of the mind pre-k curriculum. Retrieved from https://my.vanderbilt.edu/toolsofthemindevaluation/files/2011/12/Tools-Report-8-10-11-Appendices-Removed1.pdf.

Fuson, K.C., Clements, D.H., & Beckmann, S. (Eds.). (2010). Focus on prekindergarten: Teaching with curriculum focal points. Reston, VA: NCTM.

Gandini, L. (2008). Introduction to the fundamental values of the education of young children in Reggio Emilia. Retrieved from https://www.reggioalliance.org/resources/free-resources/

Gandini, L. & Goldhaber, J. (2001). Two reflections about documentation. In L. Gandini & C. P. Edwards (Eds). *Bambini: The traditional approach to infant/toddler care.* (pp 124-145). New York: Teachers College Press.

Geary, D. C. (1995). Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. *The American Psychologist, 50*(1), 24-37.

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.

Ginsburg, H., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. *Social Policy Report, *22(1), 1075-7031. Retrieved from http://ezp.slu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=ED521700&site=eds-live

Gordon, A.M., & Browne, K.W. (2014). *Beginnings and beyond: Foundations in early childhood education. *(9thed.). Belmont, CA: Wadsworth.

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.

Heddens, J.W. (1986a). Bridging the Gap between the Concrete and the Abstract. *The Arithmetic Teacher*, 6(14).

Heddens, J. W. (1986b). Improving mathematics teaching by using manipulatives. Kent State University, Retrieved from: http://www.fed.cuhk.edu.hk/~fllee/mathfor/edumath/9706/1hedden.html

Hofer, K.G., Farran, D.C., & Cummings, T.P. (2013). Preschool children’s math related behaviors mediate curriculum effects on math achievement gains*. Early Childhood Research Quarterly.*28, 487-495.

Kagan, S. L., and Gomez, R. (2014). One, two, buckle my shoe: Early childhood mathematics education and teacher professional development. In H. Ginsburg, M. Hyson and T. Woods (Ed.), *Preparing early childhood educators to teach math: Professional development that works.*(pp. 75-93). Baltimore: Brookes.

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.

National Association for the Education of Young Children (NAEYC) and National Council of Teachers of Mathematics (NCTM). (2002). Early childhood mathematics: Promoting good beginnings. Position Statement. Retrieved from http://www.naeyc.org/about/positions/psmath.asp.

National Association for the Education of Young Children. (2015). *Developmentally Appropriate Practice and the Common Core State Standards: Framing the Issues. *Research brief. Washington, DC: NAEYC.

National Association for the Education of Young Children. (2017). *NAEYC Early Learning Standards and Accreditation Criteria & Guidance for Assessment*. Washington,DC: NAEYC. Retrieved from https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/accreditation/earlylearning/Standards%20and%20Accreditation%20Criteria%20%26%20Guidance%20for%20Assessment_April%202017_3.pdf

National Association for the Education of Young Children. (2018). *NAEYC Early Learning Program Accreditation Standards and Assessment Items*. Washington, DC: NAEYC. Retrieved from https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/accreditation/earlylearning/naeyc_early_learning_program_accreditation_standards_and_assessment_items_0.pdf

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 http://www.corestandards.org/Math/Content/K/introduction

National Mathematics Advisory Panel. (2008). The final report of the national mathematics advisory panel. United States Department of Education. Retrieved from https://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

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 https://elem.hcdsb.org/stbenedict/wp-content/uploads/sites/29/2017/11/math_resource_for_parents.pdf

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 http://ezp.slu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=eue&AN=60278873&site=eds-live

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 http://www.healthofchildren.com/E-F/Early-Childhood-Education.html

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.

Tudge, J. R. H., & Doucet, F. (2004). Early mathematical experiences: observing young black and white children’s everyday activities. *Early Childhood Research Quarterly, 19*, 21-39.

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 https://www.mdrc.org/sites/default/files/The_Impact_of_Family_Involvement_FR.pdf

Wager, A. A., & Parks, A. N. (2014). Learning Mathematics through Play. In S. Edwards, M. Blaise, & E. Brooker. (Eds.) *The SAGE Handbook of Play and Learning in Early Childhood*. (p.216-227). London, England : Sage Publications, Ltd.

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.

Weiss, H. B., Lopez, M.E., & Caspe, M. (August, 2017). From the directors. In Global Family Research Project. *Formula for success: Engaging families in early math learning. *Retrieved from https://globalfrp.org/content/download/83/561/file/Early+Math+FINE.pdf

Whitin, D.J., & Whitin, P. (2003). Talk counts: Discussing graphs with young children. *Teaching Children Mathematics, *(3),142.

Witzel, B. S., Ferguson, C. J., & Mink, D. V. (2012). Number sense: Strategies for helping preschool through grade 3 children develop math skills. *YC Young Children, *(3), 89.

Young, J.M., & Reed, K.E. (2018). Encouraging persistence and positive attitudes toward math. *Teaching Young Children*, (11), 5.

**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).

North American Association for Environmental Education. (2010). *Early childhood environmental education programs: Guidelines for excellence*, Washington, DC: NAAEE.

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 :

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