The purpose of this critical analysis was to investigate the young children’s sense of numerical magnitudes and the important attributes of classrooms where children in kindergarten and first grade are exposed to mathematics. This study aimed to offer guidelines that will assist teachers as they teach mathematics to children between the ages of five and seven.
Similar content being viewed by others
References
Ansalone G., Biafora F., (2004). Elementary school teachers’ perceptions and attitudes to the educational structure of tracking Education 125(2): 249–259
Antell S., Keating D., (1983). Perception of numerical invariance in neonates Child Development 54: 695–701
Ball D. L., (1991). What’s all this talk about “discourse”? The Arithmetic Teacher 39(3): 44–47
Ball D. K., (1992). Magical hopes: Manipulatives and the reform of math education American Educator 16: 14–18
Baker E. L., Mayer R. E., (1999). Computer-based assessment of problem solving Computers in Human Behavior 15(3/4): 269–282
Beevers C., Goldfinch J., Pitcher N., (2002) Aspects of computer-based assessment in mathematics Active Learning in Higher Education 3(2): 159–176
Bennett P., Elliot M., Peters D., (2005). Classroom and family effects on children’s social and behavioral problems The Elementary School Journal 105(5): 461–499
Bruner J. S., (1966). Toward a theory of instruction Belknap Press Cambridge, MA
Bruner J. S., (1996). The culture of education Harvard University Press Cambridge, MA
Chapin S. H., Eastman K. E., (1996). External and internal characteristics of learning environments The Mathematics Teacher 89(2): 112–115
Clements D. H., Sarama J., (2005). Think math! Scholastic Parent and Child 13(2): 25
Cobb P., Yackel E., Wood T., Wheatley G., (1988). Creating a problem solving atmosphere Arithmetic Teacher 36(1): 46–47
Emenaker C., (1996). A problem-solving based mathematics course and elementary teachers’ beliefs School Science and Mathematics 96(2): 75–85
Fuson K. S., Briars D. J., (1990). Using a base-ten blocks learning/teaching approach for first and second grade place-value and multidigit addition and subtraction Journal for Research in Mathematics Education 21: 180–206
Gallistel C. R., Gelman R., (2000). Non-verbal numerical cognition: From reals to integers Trends in Cognitive Sciences 4: 59–65
Gardner H., (1991). Assessment in context: The alternative to standardized testing. In Gifford B., (eds) Changing assessments: Alternative views of aptitude, achievement and instruction Kluwer Academic Press Boston (pp. 239–252)
Goddard R. D., Hoy W. K., Woolfolk-Hoy A. W., (2000). Collective teacher efficacy: Its meaning, measure, and impact on student achievement American Educational Research Journal 37(2): 479–507
Hargreaves M., Shorrocks-Taylor D., Threlfall J., (1998). Children’s strategies with number patterns Educational Studies 24(3): 315–331
Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Oliver, A., & Human, P. (1997). The nature of classroom tasks. In (author) Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann
Hiebert J., Carpenter T. P., (1992). Learning and teaching with understanding In Grouws D. A., (ed.), Handbook of research on mathematics teaching and learning Macmillan New York (pp. 65–97)
Hunting R. P., (2003). Part-whole number knowledge in preschool children Journal of Mathematical Behavior 22: 217–235
Huntley-Fenner G., (2001). Children’s understanding of number is similar to adults’ and rats’: Numerical estimation by 5- to 7-year-olds Cognition 78: B27–B40
Lappan G., Schram P.W., (1989). Communication and reasoning: Critical dimensions of sense making in mathematics In Trafton P., Shulte A., (Ed.), New directions for elementary school mathematics NCTM Reston, VA. (pp. 14–30)
Lipton J. S., Spelke E. S., (2003). Origins of number sense: Large number discrimination in human infants Psychological Science 14: 396–401
Marsh L. G., Cooke N. L., (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities Learning Disabilities Research and Practice 11(1): 58–65
Marzano R. J., Pickering D. J., Pollock J. E., (2001). Classroom instructions that works: Research-based strategies for increasing student achievement Association for Supervision and Curriculum Development Alexandria, VA
Maxim G. W., (1989). Developing preschool mathematical concepts The Arithmetic Teacher 37(4): 36–42
Moore D., Benenson J., Reznick J. S., Peterson M., Kagan J., (1987). Effect of auditory numerical information on infants’ looking behavior: Contradictory evidence Developmental Psychology 23: 665–670
National Association for the Education of Young Children and National Council of Teachers of Mathematics. (2002, April). Early childhood mathematics: Promoting good beginnings. Joint position statement. Washington, DC: NAEYC
National Association of School Psychologists. (2005). Position Statement on Ability Grouping and Tracking. Retrieved on 12/03/2005 from http://www.nasponline.org/information/pospaper_ag.html
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics National Council of Teachers of Mathematics Reston, VA
National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics National Council of Teachers of Mathematics Reston, VA
National Council of Teachers of Mathematics (1995). Assessment standards for school mathematics National Council of Teachers of Mathematics Reston, VA
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics National Council of Teachers of Mathematics Reston, VA
Neuman S. B., Copple C., Bredekamp S., (2000). Learning to read and write: Developmentally appropriate practices for young children National Association for the Education of Young Children Washington, DC[ED463904]
Nicol C., Crespo S., (2005). Exploring mathematics in imaginary places: Rethinking what counts as meaningful contexts for learning mathematics School Science and Mathematics 105(5): 240–251
Padrón Y. N., (1992). Comparing bilingual and monolingual students’ perceptions of their classroom learning environment In Waxman H. C., Ellett C. D., (Eds.), The study of learning environments University of Houston Houston, TX pp. 108–113
Pierce C., (1994). Importance of classroom climate for at-risk learners Journal of Educational Research 88: 37–42
Resnick L. B., Omanson S. F., (1987). Learning to understand arithmetic In Glaser R., (Ed.), Advances in instructional psychology Erlbaum Hillsdale, NJ (pp. 41–96)
Rimm-Kaufman S. E., Sawyer B. E., (2004). Primary-grade teachers self-efficacy beliefs, attitudes toward teaching, and teaching practice priorities in relation to the responsive classroom approach The Elementary School Journal 104(4): 321–341
Russell S. J., (2000). Developing computational fluency with whole numbers Teaching Children Mathematics 7(3): 154–158
Sherin M. G., (2002). A balancing act: Developing a discourse community in a mathematics community Journal of Mathematics Teachers Education 5: 205–233
Sophian C., Adams N., (1987). Infants’ understanding of numerical transformations British Journal of Developmental Psychology 5: 257–264
Starkey P., Cooper R., (1980). Perception of numbers by human infants Science 210: 1033–1035
Starkey P., Spelke E., Gelman R., (1983). Detection of intermodal numerical correspondences by human infants Science 222: 179–181
Starkey P., Spelke E., Gelman R., (1990). Numerical abstraction by human infants Cognition 36: 97–128
Strauss M. S., Curtis L. E., (1981). Infant perception of numerosity Child Development 52: 1146–1152
Thompson P. W., (1992). Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics Journal for Research in Mathematics Education 23: 123–147
Uttal D. H., Scudder K. V., Deloache J. S., (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics Journal of Applied Developmental Psychology 18: 37–54
Vacc N. N., (1993). Implementing the professional standards for teaching mathematics: teaching and learning mathematics through classroom discussion The Arithmetic Teacher 41(4): 225–227
Wang M. C., Haertel G. D., Walberg H. J., (1993). Toward a knowledge base for school learning Review of Educational Research 63: 249–294
Waxman H. C., Huang S. L., (1997). Classroom instruction and learning environment differences between effective and ineffective urban elementary schools for African American students Urban Education 32(1): 7–44
Whitenack J. W., Knipping N., Novinger S., Underwood G., (2001). Second graders circumvent addition and subtraction difficulties Teaching Children Mathematics 8(4): 228
Wolfe J., (2002).Learning from the past: Historical voices in early childhood education2 Mayerthorpe, Piney Branch Press Alberta, CA
Wolfgang C. H., Stannard L. L., Jones I., (2001). Block play performance among preschoolers as a predictor of later school achievement in mathematics Journal of Research in Childhood Education 15(2): 173–180
Wynn K., (1992). Addition and subtraction by human infants Nature 358: 749–750
Xu F., Spelke E. S., (2000). Large number discrimination in 6-month-old infants Cognition 74: B1–B11
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Varol, F., Farran, D. Early Mathematical Growth: How to Support Young Children’s Mathematical Development. Early Childhood Educ J 33, 381–387 (2006). https://doi.org/10.1007/s10643-006-0060-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10643-006-0060-8