References

Introduction

Ginsberg, H. P., Lee, J. Su, & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social Policy Report. Giving Child and Youth Development Knowledge Away. Retrieved from https://files.eric.ed.gov/fulltext/ED521700.pdf

Sherman-LeVos, J. L. (2010). Mathematics instruction for preschoolers. Encyclopedia of Early Childhood Development. University of California, Berkeley.

 

Chapter 1

Clements, D., Sarama, J., & Dibiase, A. (2004). Engaging young children in mathematics. Standards for childhood mathematics education.  Mahway, NJ: Lawrence Erlbaum Associates.

Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.

National Association for the Education of Young Children. (2010). Early Childhood Mathematics: Promoting Good Beginnings. Retrieve at https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/psmath.pdf

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

 

Chapter 2

Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA : Jossey-Bass; a Wiley Brand.

Dweck, C. S. (2007). Mindset: The new psychology of success. New York: Random House.

Kansas State Department of Education. (2017). 2017 Kansas mathematics standards. Retrieve from https://community.ksde.org/Default.aspx?tabid=5255

 

Chapter 3

Clements, D. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(5), 270-275.

Geist, E. (2009). Children are born mathematicians: Supporting mathematical development, birth to age eight. Pearson Education, Inc.

Greenberg, J. (2012). More, all gone, empty, full: Math talk every day in every way. Young Children, 67(3), 62-64.

McLane, J. B. (2003). “Does not.” “Does too.” Thinking about play in the early childhood classroom. Erikson Institute Occasional Paper Number 4.

Morin, A. (2014). Math skills: What to expect at different ages. Retrieve from https://www.understood.org/en/learning-thinking-differences/signs-symptoms/age-by-age-learning-skills/math-skills-what-to-expect-at-different-ageshttps://www.understood.org/en/learning-thinking-differences/signs-symptoms/age-by-age-learning-skills/math-skills-what-to-expect-at-different-ages

Sarama, J., & Clements, D. (2009, March). Teaching math in the primary grades: The learning trajectories approach. Young Children, 64(2), 63-65.

Thelen, E., & Smith, L. B. (1996). A dynamic systems approach to the development of cognition and action. Cambridge, MA; MIT Press.

 

Chapter 4

Beneke, S., Ostrosky, M. M., & Katz, L. (2008, May). Calendar time for young children: Good intentions gone awry. Young Children. 63(3), 12-16.

Clements, D. (2001). Mathematics in the preschool. Teaching children mathematics, 7(5), 270-275.

Copple, C. (2004). Mathematics curriculum in the early childhood context. In D. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Mahway, NJ: Lawrence Erlbaum Associates.

Geist, E. (2009). Children are born mathematicians: Supporting mathematical development, birth to age eight. Pearson Education, Inc.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197.

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

Resilient Educator. (2021). Important math skills in early childhood. Retrieve from https://resilienteducator.com/classroom-resources/important-math-skills-early-childhood-educators-should-teach/

Seo, K. H., & Ginsburg, H. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. Clements & J. Sarama (Eds.), Engaging young children in mathematics. Mahway, NJ: Lawrence Erlbaum Associates.

 

Chapter 5

GreatSchools Staff. (2012, November). Why are standards important? Retrieved from  https://www.greatschools.org/gk/articles/why-are-standards-important/

Kansas State Department of Education (2014). Kansas Early Learning Standards. Retrieve from https://www.ksde.org/Portals/0/Early%20Childhood/KsEarlyLearningStandards.pdf

National Association for the Education of Young Children. (2010). Early Childhood Mathematics: Promoting Good Beginnings. Retrieve at https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/psmath.pdf

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.

 

Chapter 6

Hiebert, J., Thomas, P. Carpenter, E., Fennema, K. C. Fuson, D. W., Human, P. Murray, H., & Oliver, A. (1997). “Making sense: Teaching and learning mathematics with understanding.” Potsmouth, NH: Heinemann.

Lappan, G., & Phillips, E. (1998). Teaching and learning in the Connected Mathematics Project. In L. Leutzinger (Ed.), Mathematics in the middle (pp. 83-92). Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.

National Council of Teachers of Mathematics. (2010). Research Brief: Why is teaching with problem solving important to student learning? Retrieved from https://education.wsu.edu/documents/2018/12/center-public-education-rural-schools-report.pdf/

Pólya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Princeton University Press.

 

Chapter 7

Burns, M. (2007). About teaching mathematics: A K-8 resource. 3rd ed. Sausalito, CA: Math Solutions.

Gersten, R. & Chard, D. (1999). “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities.” The Journal of Special Education (33)1, 18-28.

Howden, H. (1989). Teaching number sense. Arithmetic Teacher. 36(6), 6-11.

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

Tondevold, C. (2019). Subitizing: A mathematical foundation. Retrieved at https://www.therecoveringtraditionalist.com/subitizing-foundation-math/?inf_contact_ky=70acd20e359cdbf4c75a4aa5c95ee8aecc0558ed5d4c28cbfab114022b1ec50d

Van de Walle, J. A., Karp, K. A., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally. Pearson. New York, New York.

 

Chapter 8

Brickwedde, J. (2012). Developing base ten understanding: Working with tens, the difference between numbers, doubling, tripling…, splitting, sharing & scaling up. Retrieved from http://www.uwosh.edu/coehs/cmagproject/concepts/documents/Developing_Base_Ten_Understanding.pdf

Dougherty, B. J., Flores, A., Louis, E., & Sophian, C. (2010). Developing essential understanding of number and numeration for teaching mathematics in pre-k-2. Reston, VA: National Council of Teachers of Mathematics.

Kansas State Department of Education. (2017a). 2017 Kansas mathematics standards. Retrieve from https://community.ksde.org/Default.aspx?tabid=5255

Kansas State Department of Education. (2017b). 2017 Kansas mathematics standards flip book Kindergarten. Retrieve from https://community.ksde.org/LinkClick.aspx?fileticket=-tRaP9RRIvU%3d&tabid=5646&mid=15542

Kansas State Department of Education. (2017c). 2017 Kansas mathematics standards flip book 2nd grade. Retrieve from https://community.ksde.org/LinkClick.aspx?fileticket=mlBPiVeqbhY%3d&tabid=5646&mid=15542

National Council of Teachers of Mathematics. (2015). Calculator use in elementary grades [Policy Statement]. Retrieved from https://www.nctm.org/Standards-and-Positions/Position-Statements/Calculator-Use-in-Elementary-Grades/

National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, D.C.: National Academy Press.

Wright, R. J., Stanger, G., Stafford, A. K., & Martland, J. (2006). Teaching number in the classroom with 4-8 year olds. London, UK: Paul Chapman Publications/Sage.

 

Chapter 9

Kansas State Department of Education. (2017). 2017 Kansas mathematics standards flip book 2nd grade. Retrieve from https://community.ksde.org/LinkClick.aspx?fileticket=mlBPiVeqbhY%3d&tabid=5646&mid=15542

National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, D.C.: National Academy Press.

Nichol, M. (n.d.). Estimate vs. Guess. Retrieved July 18, 2020, from https://www.dailywritingtips.com/estimate-vs-guess/

 

Chapter 10

Kansas State Department of Education. (2017). 2017 Kansas mathematics standards. Retrieve at https://community.ksde.org/Default.aspx?tabid=5255

Siebert, D. (2007). Fractions. Section 1: Iterating and partitioning. Retrieve from https://mathed.byu.edu/~peterson/Fractions%20Unit%20Sec%201.pdf

Stramel, J. (2021). A standards-based approach to teaching elementary mathematics. Great River Learning. Dubuque, IA.

Van de Walle, J. A., Karp, K. A., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally. Pearson. New York, New York.

 

Chapter 11

Common Core Standards Writing Team. (2013, September 19). Progressions for the Common Core State Standards in Mathematics (draft). Grades K–5, Geometry. Tucson, AZ: Institute for Mathematics and Education, University of Arizona.

Egsgard, J. C. (1969). Geometry all around us – K-12. The Arithmetic Teacher, 16(6). 437-445.

Kansas State Department of Education. (2017). 2017 Kansas mathematics standards flip book 1st grade. Retrieved from https://community.ksde.org/LinkClick.aspx?fileticket=-tRaP9RRIvU%3d&tabid=5646&mid=15542

Lappan, G. (1999, December). Geometry, the forgotten strand. National Council of Teachers of Mathematics. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Glenda-Lappan/Geometry_-The-Forgotten-Strand/

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

Schroeter, E. (2017). Part 1: The importance of spatial reasoning and geometry in kindergarten. Retrieve from http://thelearningexchange.ca/importance-spatial-reasoning-geometry-kindergarten/

Shaughnessy, J. M. (2011, October). Let’s not forget geometry. National Council of Teachers of Mathematics. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/J_-Michael-Shaughnessy/Let_s-Not-Forget-Geometry!/

Van de Walle, J. A., Karp, K. A., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally. Pearson. New York, New York.

 

Chapter 12

Bahr, D. (2008). Elementary mathematics is anything but elementary. Boston: Cengage Learning.

Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers’ “algebra eyes and ears.” Teaching Children Mathematics, 10(2). 70-77.

Common Core Standards Writing Team. (2011, May 29). Progressions for the Common Core State Standards in Mathematics (draft). K, Counting and Cardinality; K–5, Operations and Algebraic Thinking. Tucson, AZ: Institute for Mathematics and Education, University of Arizona.

de Garcia, L. A. (2008, November 24). Algebraic thinking. Strategies for teaching elementary mathematics. https://mathteachingstrategies.wordpress.com/2008/11/24/algebraic-thinking/

Earnest, D., & Balti, A. A. (2008). Instructional strategies for teaching algebra in elementary school: Findings from a research-practice collaboration. Teaching Children Mathematics. 14(9), 518-522.

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

Seeley, C. L. (2004). A journey in algebraic thinking. [President’s Message]. Retrieved from https://www.nctm.org/uploadedFiles/News_and_Calendar/Messages_from_the_President/Archive/Cathy_Seeley/2004_09_journey.pdf

Stramel, J. (2021). A standards-based approach to teaching elementary mathematics. Great River Learning. Dubuque, IA.

 

Chapter 13

Levine, J. H. (1997). Introduction: What is data analysis? Retrieved https://www.dartmouth.edu/~jlevine/stuff/intro%20copy/IntroStuff/006%20Introb.html

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Mathematics Methods for Early Childhood by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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