# 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