Myths of Early Math
Abstract
:1. “Early Math Is Just Counting.”
2. “Children Need to Master Skills and Knowledge Before They Can Solve Problems.”
3. “Young Children Must Sit Down and Learn Math. Sometimes You Just Have to Do Worksheets.”
4. “Time Spent on Math Is Time Taken Away from Play.”
5. “Time Spent on Math is Time Taken Away from Literacy and Social-Emotional Experiences.”
6. “Math Centers Are All You Need.”
7. “The Best Way to Teach Math is through “Teachable Moments.”
8. “Young Children Always Need to Do Mathematics Concretely.”
I find it easier not to do it [simple addition] with my fingers because sometimes I get into a big muddle with them [and] I find it much harder to add up because I am not concentrating on the sum. I am concentrating on getting my fingers right…which takes a while. It can take longer to work out the sum than it does to work out the sum in my head. [By “in my head”, Emily meant that she imagined dot arrays. If that’s what she liked, why didn’t she just use those images? Why did she use fingers? She explains:] If we don’t use our fingers, the teacher is going to think, “Why aren’t they using their fingers…they are just sitting there thinking”…we are meant to be using our fingers because it is easier…which it is not.[54] (p. 35)
9. Final Words
Author Contributions
Conflicts of Interest
Appendix A
|
References
- Sarama, J.; Clements, D.H. Early Childhood Mathematics Education Research: Learning Trajectories for Young Children; Routledge: New York, NY, USA, 2009. [Google Scholar]
- Clements, D.H.; Sarama, J. Learning and Teaching Early Math: The Learning Trajectories Approach, 2nd ed.; Routledge: New York, NY, USA, 2014; p. 380. [Google Scholar]
- Rittle-Johnson, B.; Fyfe, E.R.; Zippert, E. The roles of patterning and spatial skills in early mathematics development. Early Child. Res. Q. 2017. [Google Scholar] [CrossRef]
- Davis, R.B. Learning Mathematics: The Cognitive Science Approach to Mathematics Education; Ablex: Norwood, NJ, USA, 1984. [Google Scholar]
- Halberda, J.; Mazzocco, M.M.M.; Feigenson, L. Individual differences in non-verbal number acuity correlate with maths achievement. Nature 2008, 455, 665–668. [Google Scholar] [CrossRef] [PubMed]
- Wynn, K. Addition and subtraction by human infants. Nature 1992, 358, 749–750. [Google Scholar] [CrossRef] [PubMed]
- Mulligan, J.T.; Mitchelmore, M.C.; Crevesten, N. Reconceptualising early mathematics learning: The fundamental role of pattern and structure. In Reconceptualizing Early Mathematics Learning; English, L.D., Mulligan, J.T., Eds.; Springer: Dordrecht, Germany, 2013; pp. 47–66. [Google Scholar]
- NCTM. Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence; National Council of Teachers of Mathematics: Reston, VA, USA, 2006. [Google Scholar]
- NGA/CCSSO. Common Core State Standards; National Governors Association Center for Best Practices, Council of Chief State School Officers: Washington, DC, USA, 2010. [Google Scholar]
- Carpenter, T.P.; Ansell, E.; Franke, M.L.; Fennema, E.H.; Weisbeck, L. Models of problem solving: A study of kindergarten children’s problem-solving processes. JRME 1993, 24, 428–441. [Google Scholar] [CrossRef]
- Andrews, A.; Trafton, P.R. Little Kids—Powerful Problem Solvers: Math Stories from a Kindergarten Classroom; Heinemann: Portsmouth, NH, USA, 2002. [Google Scholar]
- Stipek, D. Playful math instruction in the context of standards and accountability. Young Child. 2017, 72, 8–12. [Google Scholar]
- Van Oers, B. Emergent mathematical thinking in the context of play. Educ. Stud. Math. 2010, 74, 23–37. [Google Scholar] [CrossRef]
- Clements, D.H.; Sarama, J. Building Blocks, Volumes 1 and 2; McGraw-Hill Education: Columbus, OH, USA, 2007/2013. [Google Scholar]
- Ginsburg, H.P.; Greenes, C.; Balfanz, R. Big Math for Little Kids; Dale Seymour: Parsippany, NJ, USA, 2003. [Google Scholar]
- Griffin, S.; Clements, D.H.; Sarama, J. Number Worlds/Building Block: A Prevention/Intervention Program: Teacher Edition Level B; SRA/McGraw-Hill: Columbus, OH, USA, 2007. [Google Scholar]
- Reikerås, E.; Løge, I.K.; Knivsberg, A.-M. The mathematical competencies of toddlers expressed in their play and daily life activities in norwegian kindergartens. Int. J. Early Child. 2012. [Google Scholar] [CrossRef]
- Seo, K.-H.; Ginsburg, H.P. What is developmentally appropriate in early childhood mathematics education? In Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education; Clements, D.H., Sarama, J., DiBiase, A.-M., Eds.; Erlbaum: Mahwah, NJ, USA, 2004; pp. 91–104. [Google Scholar]
- Van Oers, B. Semiotic activity of young children in play: The construction and use of schematic representations. Eur. Early Child. Educ. Res. J. 1994, 2, 19–33. [Google Scholar] [CrossRef]
- Forman, G.E.; Hill, F. Constructive Play: Applying Piaget in the Preschool; Addison-Wesley Pub. Co.: Menlo Park, CA, USA, 1984. [Google Scholar]
- Aydogan, C.; Plummer, C.; Kang, S.J.; Bilbrey, C.; Farran, D.C.; Lipsey, M.W. An investigation of prekindergarten curricula: Influences on classroom characteristics and child engagement. In Proceedings of the NAEYC, Washington, DC, USA, 5–8 June 2005. [Google Scholar]
- Balfanz, R. Why do we teach young children so little mathematics? Some historical considerations. In Mathematics in the Early Years; Copley, J.V., Ed.; National Council of Teachers of Mathematics: Reston, VA, USA, 1999; pp. 3–10. [Google Scholar]
- Fuligni, A.S.; Howes, C.; Huang, Y.D.; Hong, S.S.; Lara-Cinisomo, S. Activity settings and daily routines in preschool classrooms: Diverse experiences in early learning settings for low-income children. Early Child. Res. Q. 2012, 27, 198–209. [Google Scholar] [CrossRef] [PubMed]
- Stipek, D. Mathematics in early childhood education: Revolution or evolution? Early Educ. Dev. 2013, 24, 431–435. [Google Scholar] [CrossRef]
- Ginsburg, H.P. Mathematical play and playful mathematics: A guide for early education. In Play = Learning: How Play Motivates and Enhances Children's Cognitive and Socialemotional Growth; Singer, D.G., Golinkoff, R.M., Hirsh-Pasek, K., Eds.; Oxford University Press: London, UK, 2006; pp. 145–165. [Google Scholar]
- Razel, M.; Eylon, B.-S. Development of visual cognition: Transfer effects of the agam program. J. Appl. Dev. Psychol. 1990, 11, 459–485. [Google Scholar] [CrossRef]
- Preschool Curriculum Evaluation Research Consortium. Effects of Preschool Curriculum Programs on School Readiness (ncer 2008–2009); Government Printing Office: Washington, DC, USA, 2008.
- Sarama, J.; Lange, A.; Clements, D.H.; Wolfe, C.B. The impacts of an early mathematics curriculum on emerging literacy and language. Early Child. Res. Q. 2012, 27, 489–502. [Google Scholar] [CrossRef]
- National Mathematics Advisory Panel. Foundations for Success: The Final Report of the National Mathematics Advisory Panel; U.S. Department of Education, Office of Planning, Evaluation and Policy Development: Washington, DC, USA, 2008.
- Hamre, B.K.; Pianta, R.C. Early teacher-child relationships and the trajectory of children's school outcomes through eighth grade. Child Dev. 2001, 72, 625–638. [Google Scholar] [CrossRef] [PubMed]
- Howes, C.; Fuligni, A.S.; Hong, S.S.; Huang, Y.D.; Lara-Cinisomo, S. The preschool instructional context and child–teacher relationships. Early Educ. Dev. 2013, 24, 273–291. [Google Scholar] [CrossRef]
- Sabol, T.J.; Soliday Hong, S.L.; Pianta, R.C.; Burchinal, M.R. Can rating pre-k programs predict children’s learning? Science 2013, 341, 845–846. [Google Scholar] [CrossRef] [PubMed]
- Camilli, G.; Vargas, S.; Ryan, S.; Barnett, W.S. Meta-analysis of the effects of early education interventions on cognitive and social development. Teach. Coll. Rec. 2010, 112, 579–620. [Google Scholar]
- Lou, Y.; Abrami, P.C.; Spence, J.C.; Poulsen, C.; Chambers, B.; d’Apollonia, S. Within-class grouping: A meta-analysis. Rev. Educ. Res. 1996, 66, 423–458. [Google Scholar] [CrossRef]
- Piaget, J. How children form mathematical concepts. Sci. Am. 1953, 189, 74–79. [Google Scholar] [CrossRef]
- Van Hiele, P.M. Structure and Insight: A Theory of Mathematics Education; Academic Press: Orlando, FL, USA, 1986. [Google Scholar]
- Wu, H.-H. Understanding Numbers in Elementary School Mathematics; American Mathematical Society: Providence, RI, USA, 2011. [Google Scholar]
- Klein, A.; Starkey, P.; Clements, D.H.; Sarama, J.; Iyer, R. Effects of a pre-kindergarten mathematics intervention: A randomized experiment. J. Res. Educ. Eff. 2008, 1, 155–178. [Google Scholar] [CrossRef]
- Ginsburg, H.P.; Lee, J.S.; Stevenson-Boyd, J. Mathematics education for young children: What it is and how to promote it. Soc. Policy Rep. 2008, 22, 1–24. [Google Scholar]
- Lee, J. Correlations between kindergarten teachers' attitudes toward mathematics and teaching practice. J. Early Child. Teach. Educ. 2004, 25, 173–184. [Google Scholar] [CrossRef]
- Bennett, N.; Desforges, C.; Cockburn, A.; Wilkinson, B. The Quality of Pupil Learning Experiences; Erlbaum: Hillsdale, NJ, USA, 1984. [Google Scholar]
- Moseley, B. Pre-service early childhood educators' perceptions of math-mediated language. Early Educ. Dev. 2005, 16, 385–396. [Google Scholar] [CrossRef]
- Sarama, J.; Clements, D.H. “Concrete” computer manipulatives in mathematics education. Child Dev. Perspect. 2009, 3, 145–150. [Google Scholar] [CrossRef]
- Sowell, E.J. Effects of manipulative materials in mathematics instruction. JRME 1989, 20, 498–505. [Google Scholar] [CrossRef]
- Thompson, A.C. The Effect of Enhanced Visualization Instruction on First Grade Students’ Scores on the North Carolina Standard Course Assessment. Ph.D. Thesis, Liberty University, Lynchburg, VA, USA, 2012. [Google Scholar]
- Steffe, L.P.; Cobb, P. Construction of Arithmetical Meanings and Strategies; Springer-Verlag: New York, NY, USA, 1988. [Google Scholar]
- Ball, D.L. Magical hopes: Manipulatives and the reform of math education. Am. Educ. 1992, 16, 16–18 and 46–47. [Google Scholar]
- Clements, D.H.; McMillen, S. Rethinking “concrete” manipulatives. Teach. Child. Math. 1996, 2, 270–279. [Google Scholar]
- Sarama, J.; Clements, D.H. Physical and virtual manipulatives: What is “concrete”? In International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives; Moyer-Packenham, P.S., Ed.; Springer International Publishing: Switzerland, 2016; Volume 3, pp. 71–93. [Google Scholar]
- Skoumpourdi, C. Kindergarten mathematics with ‘pepe the rabbit’: How kindergartners use auxiliary means to solve problems Eur. Early Child. Educ. Res. J. 2010, 18, 149–157. [Google Scholar] [CrossRef]
- DeLoache, J.S. Rapid change in the symbolic functioning of young children. Science 1987, 238, 1556–1557. [Google Scholar] [CrossRef] [PubMed]
- Outhred, L.N.; Sardelich, S. Problem solving in kindergarten: The development of representations. In People in Mathematics Education. Proceedings of the 20th Annual Conference of the Mathematics Education Research Group of Australasia; Biddulph, F., Carr, K., Eds.; Mathematics Education Research Group of Australasia: Rotorua, New Zealand, 1997; Volume 2, pp. 376–383. [Google Scholar]
- Grupe, L.A.; Bray, N.W. What role do manipulatives play in kindergartners' accuracy and strategy use when solving simple addition problems? In In Proceedings of the 1999 Biennial Meeting of the Society for Research in Child Development, Albuquerque, NM, USA, 15–18, April 1999. [Google Scholar]
- Gray, E.M.; Pitta, D. Number processing: Qualitative differences in thinking and the role of imagery. In Proceedings of the 20th Annual Conference of the Mathematics Education Research Group of Australasia; Puig, L., Gutiérrez, A., Eds.; Mathematics Education Research Group of Australasia: Rotorua, New Zealand, 1997; Volume 3, pp. 35–42. [Google Scholar]
- Foster, M.E.; Anthony, J.L.; Clements, D.H.; Sarama, J. Improving mathematics learning of kindergarten students through computer assisted instruction. JRME 2016, 47, 206–232. [Google Scholar]
- Foster, M.E.; Anthony, J.L.; Clements, D.H.; Sarama, J.; Williams, J.J. Hispanic dual language learning kindergarten students response to a numeracy intervention: A randomized control trial. Early Child. Res. Q. 2018, 43, 83–95. [Google Scholar] [CrossRef]
- Sarama, J.; Clements, D.H. Promoting a good start: Technology in early childhood mathematics. In Promising Models to Improve Primary Mathematics Learning in Latin America and the Caribbean Using Technology; Arias, E., Cristia, J., Cueto, S., Eds.; Inter-American Development Bank: Washington, DC, USA, in press.
- Olson, J.K. Microcomputers make manipulatives meaningful. In Proceedings of the International Congress of Mathematics Education, Budapest, Hungary, 27 July–3 August 1988. [Google Scholar]
- Tymms, P.; Jones, P.; Albone, S.; Henderson, B. The first seven years at school. Educ. Assess. Eval. Account. 2009, 21, 67–80. [Google Scholar] [CrossRef]
- Dewey, J. Experience and Education; Simon & Schuster: New York, NY, USA, 1938/1997. [Google Scholar]
- NCTM. Principles and Standards for School Mathematics; National Council of Teachers of Mathematics: Reston, VA, USA, 2000. [Google Scholar]
- Raudenbush, S.W. The brown legacy and the o'connor challenge: Transforming schools in the images of children's potential. Educ. Res. 2009, 38, 169–180. [Google Scholar] [CrossRef]
- Sun Lee, J.; Ginsburg, H.P. Early childhood teachers' misconceptions about mathematics education for young children in the United States. Australasian J. Early Child. 2009, 34, 37–45. [Google Scholar]
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Clements, D.H.; Sarama, J. Myths of Early Math. Educ. Sci. 2018, 8, 71. https://doi.org/10.3390/educsci8020071
Clements DH, Sarama J. Myths of Early Math. Education Sciences. 2018; 8(2):71. https://doi.org/10.3390/educsci8020071
Chicago/Turabian StyleClements, Douglas H., and Julie Sarama. 2018. "Myths of Early Math" Education Sciences 8, no. 2: 71. https://doi.org/10.3390/educsci8020071