# Variaciones en el desarrollo, influencias socioculturales, y dificultades en el aprendizaje de las matemáticas

### Resumen

Hay evidencias de que la mayoría de los niños entran en la escuela con conocimientos y recursos fundacionales para su aprendizaje matemático. Sin embargo, esta no es la historia completa. Resultados de investigaciones revelan enormes diferencias entre los niveles de competencia matemática de los niños pequeños, y estas diferencias parecen ser más acusadas en los Estados Unidos que en algunos otros países (por ejemplo, China) (Starkey y Klein, 2008). En este artículo se describen los tipos de diferencias que se dan y se ofrece una revisión sobre lo que se sabe acerca de la naturaleza y las fuentes de las variaciones en el desarrollo entre los niños.

### Citas

Arnold, D.H., Fisher, P.H., Doctoroff, G.L., and Dobbs, J. (2002). Accelerating math development in Head Start classrooms. Journal of Educational Psychology, 94(4), 762-770.

Baenninger, M., and Newcombe, N. (1989). The role of experience in spatial test performance: A meta-analysis. Sex Roles, 20, 327-344.

Barbaresi, M.J., Katusic, S.K., Colligan, R.C., Weaver, A.L., and Jacobsen, S.J. (2005). Math learning disorder: Incidence in a population-based birth cohort, 1976-1982, Rochester, Minn. Ambulatory Pediatrics, 5(5), 281-289.

Barbarin, O.A., Early, D., Clifford, R., Bryant, D., Frome, P., Burchinal, M., Howes, C., and Pianta, R. (2008). Parental conceptions of school readiness: Relation to ethnicity, socioeconomic status, and children’s skills. Early Education & Development, 19(5), 671-701.

Barnett, W.S., Yarosz, D.J., Thomas, J., Jung, K., and Blanco, D. (2007). Two-way monolingual English immersion in preschool education: An experimental comparison. Early Childhood Research Quarterly, 22, 277-293.

Baroody, A.J. (1987). Children’s Mathematical Thinking: A Developmental Framework for Preschool, Primary, and Special Education Teachers. New York: Teachers College Press.

Baroody, A.J. (1999). The development of basic counting, number, and arithmetic knowledge among children classified as mentally handicapped. In L.M. Glidden (Ed.), International Review of Research in Mental Retardation (vol. 22, pp. 51-103). San Diego, CA: Academic Press.

Baroody, A.J., and Rosu, L. (2006). Adaptive Expertise with Basic Addition and Subtraction Combinations: The Number Sense View. Paper presented at the American Educational Research Association, San Francisco, CA.

Benigno, J.P., and Ellis, S. (2008). Do parents count? The socialization of children’s numeracy. In O.N. Saracho and B. Spodek (Eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (pp. 291-308). Charlotte, NC: Information Age.

Berch, D.B. (2005). Making sense of number sense: Implications for children with mathematical disabilties. Journal of Learning Disabilities, 38 (4), 333-339.

Blevins-Knabe, B., and Musun-Miller, L. (1996). Number use at home by children and their parents and its relationship to early mathematical room. Early Development and Parenting, 5(1), 35-45.

Bright, G.W., Harvey, J.G., and Wheeler, M.M. (1985). Learning and mathematics games. Journal for Research in Mathematics Education Monograph (whole volume). Reston, VA.

Bronfenbrenner, U. (2000). Ecological system theory. In A.E. Kazdin (Ed.) Encyclopedia of Psychology (vol. 3, pp. 129-133). Washington, DC: American Psychological Association.

Butterworth, B., and Reigosa, V. (2007). Information processing deficits in dyscalculia. In D. Berch and M. Mazzocco (Eds.), Why Is Math So Hard for Some Children? (pp. 65-81). Baltimore, MD: Paul H. Brookes.

Cannon, J., and Ginsburg, H.P. (2008). “Doing the math”: Maternal beliefs about early mathematics versus language learning. Early Education and Development, 19, 238-260.

Cannon, J., Levine, S.C., and Huttenlocher, J. (2007, March). Sex Differences in the Relation of Early Puzzle Play and Mental Transformation Skill. Paper presented at the biennial meeting of the Society for Research on Child Development, Boston, MA.

Carr, M., Shing, Y.L, Janes, P., and Steiner, H. (2007). Early Gender Differences in Strategy Use and Fluency: Implications for the Emergence of Gender Differences in Mathematics. Paper presented at the biennial meeting of the Society for Research in Child Development, March, Boston, MA.

Case, R., and Griffin, S. (1990). Child cognitive development: The role of central conceptual structures in the development of scientific and social thought. In E.A. Hauert (Ed.), Developmental Psychology: Cognitive, Perceptuo-Motor, and Neurological Perspectives (pp. 193-230). North-Holland, Amsterdam: Elsevier Science.

Casey, M.B., Erkut, S., Ceder, I., and Young, J.M. (2008). Use of a storytelling context to improve girls’ and boys’ geometry skills in kindergarten. Journal of Applied Developmental Psychology, 29, 29-48.

Civil, M. (1998). Bridging In-School Mathematics and Out-of-School Mathematics: A Reflection. Paper presented at the annual meeting of the American Education Research Association, April, San Diego, CA.

Clements, D.H., and Sarama, J. (2007). Early childhood mathematics learning. In J.F.K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 461-555). New York: Information Age.

Clements, D.H., and Sarama, J. (2008). Experimental evaluation of the effects of a research based preschool mathematics curriculum. American Educational Research Journal, 45, 443-494.

Clements, D.H., Sarama, J., and Gerber, S. (2005). Mathematics Knowledge of Low-Income Entering Preschoolers. Paper presented at the annual meeting of the American Educational Research Association, Montreal, Quebec, Canada.

Coley, R.J. (2002). An Uneven Start: Indicators of Inequality in School Readiness. Princeton, NJ: Educational Testing Service.

Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. New York: Oxford University Press.

Duncan, G.J., Dowsett, C.J., Classens, A., Magnuson, K., Huston, A.C., Klebanov, P., Pagani, L.S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., and Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43 (6), 1428-1446.

Ebbeck, M. (1984). Equity for boys and girls: Some important issues. Early Child Development and Care, 18, 119-131.

Ehrlich, S.B., and Levine, S.C. (2007, March). What Low-SES Children Do Know About Number: A Comparison of Head Start and Tuition-Based Preschool Children’s Number Knowledge. Paper presented at the biennial meeting of the Society for Research on Child Development, Boston, MA.

Ehrlich, S.B., Levine, S.C., and Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42, 1259-1268. http://babylab.uchicago.edu/research_files/Ehrlich_2006.pdf

Entwisle, D.R., and Alexander, K.L. (1990). Beginning school math competence: Minority and majority comparisons. Child Development, 61, 454-471.

Ernest, P. (1986). Games: A rationale for their use in the teaching of mathematics in school. Mathematics in School, 15(1), 2-5.

Fairweather, H., and Butterworth, G. (1977). The WPPSI at four years: A sex difference in verbal-performance discrepancies. British Journal of Educational Psychology, 47, 85-90.

Feigenson, L., Dehaene, S., and Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314.

Fennema, E., Carpenter, T.P., Jacobs, V.R., Franke, M.L., and Levi, L.W. (1998). A longitudinal study of gender differences in young children’s mathematical thinking. Educational Researcher, 27, 6-11.

Fisch, S.M. (2008). The Role of Educational Media in Preschool Mathematics Education. Teaneck, NJ: Mediakidz Research and Consulting.

Fluck, M., Linnell, M., and Holgate, M. (2005). Does counting count for 3- to 4-year-olds? Parental assumptions about preschool children’s understanding of counting and cardinality. Social Development, 14, 496-513.

Fuchs, L.S., Fuchs, D., Compton, D.L., Bryant, J.D., Hamlett, C.L., and Seethaler, P.M. (2007). Mathematics screening and progress monitoring at first grade: Implications for responsiveness to intervention. Exceptional Children, 73(3), 311-330.

Fuson, K.C., and Kwon, Y. (1992). Korean children’s single-digit addition and subtraction: Numbers structured by ten. Journal for Research in Mathematics Education, 23(2), 148-165.

Fuson, K.C., Richards, J., and Briars, D.J. (1982). The acquisition and elaboration of the number word sequences. In C. Brainerd (Ed.), Progress in Cognitive Development: Volume 1. Children’s Logical and Mathematical Cognition (pp. 33-92). New York: Springer-Verlag.

Fuson, K.C., Fraivillig, J.L., and Burghardt, B.H. (1992). Relationships children construct among English number words, multiunit base-ten blocks, and written multi-digit addition. In J.I.D. Campbell (Ed.), The Nature and Origins of Mathematical Skills (pp. 39-112). New York: North-Holland.

Fuson, K.C., Smith, S.T., and Lo Cicero, A.M. (1997). Supporting Latino first graders’ tenstructured thinking in urban classrooms. Journal for Research in Mathematics Education, 28, 738-766.

Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363-383.

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

Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37 (1), 4-15.

Geary, D.C., and Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175-192.

Geary, D.C., and Hoard, M.K. (2001). Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia. Aphasiology, 15(7), 635-647.

Geary, D.C., Hamson, C.O., and Hoard, M.K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77, 236-263.

Geary, D.C., Hoard, M.K., Byrd-Craven, J., Nugent, L., and Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343-1359.

Genesee, F., Lindholm-Leary, K., Saunders, W., and Christian, D. (2006). Educating English Language Learners. New York: Cambridge University Press.

Gersten, R., Jordan, N.C., and Flojo, J.R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38 (4), 293-304.

Ginsburg, H.P. (1997). Mathematics learning disabilities: A view from developmental psychology. Journal of Learning Disabilities, 30(1), 20-33.

Ginsburg, H.P., and Russell, R.L. (1981). Social class and racial influences on early mathematical thinking. Monographs of the Society for Research in Child Development, 46(6, Serial No. 193), 1-69.

Goldman, S.R., and Pellegrino, J.W. (1987). Information processing and educational microcomputer technology: Where do we go from here? Journal of Learning Disabilities, 20, 144-154.

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496-499.

Griffin, S. (2007). Early intervention for children at risk of developing mathematical learning difficulties. In D.B. Berch and M.M. Mazzocco (Eds.), Why Is Math So Hard for Some Children? The Nature and Origins of Mathematical Learning Difficulties and Disabilities (pp. 373-396). Baltimore, MD: Paul H. Brookes.

Griffin, S., Case, R., and Siegler, R.S. (1994). Classroom lessons: Integrating cognitive theory and classroom practice. In K. McGilly (Ed.), Rightstart: Providing the Central Conceptual Prerequisites for First Formal Learning of Arithmetic to Students at Risk for School Failure (pp. 25-50). Cambridge, MA: MIT Press.

Guiness, D., and Morley, C. (1991). Sex differences in the development of visuo-spatial ability in pre-school children. Journal of Mental Imagery, 15, 143-150.

Hanich, L., Jordan, N.C., Kaplan, D., and Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93 (3), 615-626.

Hasselbring, T.S., Goin, L.I., and Bransford, J.D. (1988). Developing math automaticity in learning handicapped children: The role of computerized drill and practice. Focus on Exceptional Children, 20(6), 1-7.

Ho, C.S., and Fuson, K.C. (1998). Children’s knowledge of teen quantities as tens and ones: Comparisons of Chinese, British, and American kindergartners. Journal of Educational Psychology, 90(3), 536-544.

Holloway, S.D., Rambaud, M.F., Fuller, B., and Eggers-Pierola, C. (1995). What is “appropriate practice” at home and in child care? Low-income mothers’ views on preparing their children for school. Early Childhood Research Quarterly, 10(4), 451-473.

Hyde, J.S., Lindberg, S.M., Linn, M.C., Ellis, A.B., and Williams, C.C. (2008). Gender similarities characterize math performance. Science, 321, 494-495.

Ifrah, G. (1985). From One to Zero: Universal History of Numbers (Lowell Blair, Trans.). New York: Viking Penguin.

Iruka, I., and Barbarin, O. (2008). African American children’s early learning and development: examining parenting, schools, and neighborhoods. In H. Neville, B. Tynes, and S. Utsey (Eds.), Handbook of African American Psychology (Ch. 13, pp. 175-186). Thousand Oaks, CA: Sage.

Jeong, Y., and Levine, S.C. (2005, April). How Do Young Children Represent Numerosity? Paper presented at the biennial meeting of Society for Research on Child Development, Atlanta, GA.

Jordan, N.C., and Montani, T.O. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30(6), 624-634.

Jordan, N.C., Huttenlocher, J., and Levine, S.C. (1992). Differential calculation abilities in young children from middle- and low-income families. Developmental Psychology, 28(4), 644-653.

Jordan, N.C., Levine, S.C., and Huttenlocher, J. (1994). Development of calculation abilities in middle- and low-income children after formal instruction in school. Journal of Applied Developmental Psychology, 15, 223-240.

Jordan, N.C., Kaplan, D., and Hanich, L.B. (2002). Achievement growth in children with learning difficulties in mathematics: Findings of a two-year longitudinal study. Journal of Educational Psychology, 94 (3), 586-597.

Jordan, N.C., Hanich, L.B., and Kaplan, D. (2003a). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74 (3), 834-850.

Jordan, N.C., Hanich, L.B., and Kaplan, D. (2003b). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103-119.

Jordan, N.C., Kaplan, D., Nabors Oláh, L., and Locuniak, M.N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153-175.

Jordan, N.C., Kaplan, D., Locuniak, M.N., and Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research and Practice, 22(1), 36-46.

Jordan, N.C., Glutting, J., and Ramineni, C. (in press). A number sense screening tool for young children at risk for mathematical difficulties. In A. Dowker (Ed.), Mathematical Difficulties: Psychology, Neuroscience and Intervention. New York: Elsevier.

Jordan, N.C., Kaplan, D., Ramineni, C., and Locuniak, M.N. (in press). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology.

Kersh, J., Casey, B., and Young, J.M. (in press). Research on spatial skills and block building in girls and boys: The relationship to later mathematics learning. In B. Spodek and O.N. Saracho (Eds.), Mathematics, Science, and Technology in Early Childhood Education. Charlotte, NC: Information Age.

Klein, A., and Starkey, P. (2004). Fostering preschool children’s mathematical knowledge: Findings from the Berkeley Math Readiness Project. In. D.H. Clements, J. Sarama, and A‑M. DiBiase (Eds.), Engaging Young Children in Mathematics: Findings of the 2000 National Conference on Standards for Preschool and Kindergarten Mathematics Education. Mahwah, NJ: Erlbaum.

Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., and Hedges, L.V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “Math Talk”. Developmental Psychology, 42(1), 59-69.

Knitzer, K., and Lefkowitz, J. (2006). Helping the Most Vulnerable Infants, Toddlers, and Their Families. New York: National Center for Children in Poverty. Available: http://www.nccp.org/publications/pdf/text_669.pdf

Lachance, J.A., and Mazzocco, M.M.M. (2006). A longitudinal analysis of sex differences in math and spatial skills in primary school age children. Learning and Individual Differences, 16, 195-216.

Ladson-Billings, G. (1995). Making mathematics meaningful in a multicultural context. In W.G. Secada, E. Fennema, and L.B. Adajian (Eds.), New Direction for Equity in Mathematics Education (pp. 126-145). Cambridge, England: Cambridge University Press.

Landerl, K., Bevan, A., and Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8-9-year-old students. Cognition, 93, 99-125.

LeCorre, M., Li, P., and Lee, Y. (2004). Numerical bilingualism: Count list acquisition in Korean. (Unpublished raw data.)

Levine, S.C., Jordan, N.C., and Huttenlocher, J. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53, 72-103.

Levine, S.C., Huttenlocher, J., Taylor, A., and Langrock, A. (1999). Early sex differences in spatial ability. Developmental Psychology, 35, 940-949.

Levine, S.C., Vasilyeva, M., Lourenco, S.F., Newcombe, N.S., and Huttenlocher, J. (2005). Socioeconomic status modifies the sex difference in spatial skill. Psychological Science, 16(11), 841-845.

Levine, S.C., Suriyakham, L., Rowe, M. and Huttenlocher, J. (in preparation). What counts in preschoolers’ development of cardinology knowledge? A longitudinal investigation.

Li, P., LeCorre, M., Shui, R., Jia, G., and Carey, S. (2003, October). Effects of Plural Syntax on Number Word Learning: A Cross-Linguistic Study. Paper presented at the 28th Boston University Conference on Language Development, Boston, MA.

Lindholm-Leary, K. and Borasato, G. (2006). Academic achievement. In F. Genesee, K. Lindholm-Leary, W.M. Saunders, and D. Christian (Eds.), Educating English Language Learners: A Synthesis of Research Evidence. New York: Cambridge University Press.

Locuniak, M.N., and Jordan, N.C. (en prensa). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities.

Lubienski, S.T. (2006). Examining instruction, achievement, and equity with NAEP mathematics data. Education Policy Analysis Archives, 14(14). Disponible en: http://dx.doi.org/10.14507/epaa.v14n14.2006

Lubienski, S.T. (2007). What we can do about achievement disparities. Educational Leadership, 65(3), 54-59.

Lutchmaya, S., and Baron-Cohen, S. (2002). Human sex differences in social and nonsocial looking preferences at 12 months of age. Infant Behaviour and Development, 25, 319-325.

Magnuson, K., and Waldfogel, J. (2008). Steady Gains and Stalled Progress: Inequality and the Black-White Test Score Gap. New York: Russell Sage Foundation.

Malofeeva, E., Day, J., Saco, X., Young, L., and Ciancio, D. (2004). Construction and evaluation of a number sense test with Head Start children. Journal of Educational Psychology, 96(4), 648-659.

Mazzocco, M.M.M., and Thompson, R.E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research and Practice, 20(3), 142-155.

McGuinness, D., and Morley, C. (1991). Sex differences in the development of visuo-spatial ability in preschool children. Journal of Mental Imagery, 15, 143-150.

McKeon, D. (2005). Research Talking Points: English Language Learners.

Available: http://www.nea.org/achievement/talkingells.html

McLoyd, V.C. (1990). The impact of economic hardship on Black families and children: Psychological distress, parenting, and socioemotional development. Child Development, 61, 311-346.

Menninger, K. (1958/1969). Number Words and Number Symbols: A Cultural History of Numbers (P. Broneer, Trans.). Cambridge, MA: MIT Press. (Original work published 1958.)

Miller, K.F. (1992). What a number is: Mathematical foundations and developing number concepts. In J.I.D. Campbell (Ed.), The Nature and Origin of Mathematical Skills (pp. 3-38). New York: Elsevier Science.

Miller, K.F., and Stigler, J.W. (1987). Counting in Chinese: Cultural variation in a basic cognitive skill. Cognitive Development, 2, 279-305.

Miller, K.F., Smith, C.M., Zhu, J., and Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6(1), 56-60.

Miura, I.T. (1987). Mathematics achievement as a function of language. Journal of Educational Psychology, 79 (1), 79-82.

Miura, I.T., and Okamoto, Y. (1989). Comparisons of U.S. and Japanese first graders’ cognitive representation of number and understanding of place value. Journal of Educational Psychology, 81(1), 109-114.

Miura, I.T., and Okamoto, Y. (2003). Language supports for mathematics understanding and performance. In A.J. Baroody and A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills—Constructing Adaptive Expertise: Studies in Mathematical Thinking and Learning (pp. 229-242). Hillsdale, NJ: Erlbaum.

Miura, I.T., Kim, C.C., Chang, C., and Okamoto, Y. (1988). Effects of language characteristics on children’s cognitive representation of number: Cross-national comparisons. Child Development, 59, 1445-1450.

Miura, I.T., Okamoto, Y., Kim, C.C., Steere, M., and Fayol, M. (1993). First graders’ cognitive representation of number and understanding of place value: Cross-national comparisons—France, Japan, Korea, Sweden, and the United States. Journal of Educational Psychology, 85(1), 24-30.

National Center for Education Statistics. (2007). The Nation’s Report Card, Mathematics 2007: National Assessment of Educational Progress at Grades 4 and 8. Washington, DC: Institute of Education Sciences, U.S. Department of Education.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Ostad, S.A. (1998). Developmental differences in solving simple arithmetic word problems and simple number-fact problems: A comparison of mathematically normal and mathematically disabled children. Mathematical Cognition, 4(1), 1-19.

Pica, P., Lemer, C., Izard, V., and Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian Indigene group. Science, 499-503.

Ramani, G.B., and Siegler, R.S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79, 375-394. Available: http://www.psy.cmu.edu/~siegler/Ram-Sieg2008.pdf

Rosser, R.A., Ensing, S.S., Glider, P.J., and Lane, S. (1984). An information processing analysis of children’s accuracy in predicting the appearance of rotated stimuli. Child Development, 55, 2204-2211.

Russell, R.L., and Ginsburg, H.P. (1984). Cognitive analysis of children’s mathematic difficulties. Cognition and Instruction, 1(2), 217-244.

Sarama, J., Clements, D.H., Starkey, P., Klein, A., and Wakeley, A. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89-119.

Sarnecka, B.W., Kamenskaya, V.G., Yamana, Y., Ogura, T., and Yudovina, Y.B. (2007). From grammatical number to exact numbers: early meanings of “one”, “two”, and “three” in English, Russian, and Japanese. Cognitive Psychology, 55, 136-168.

Saxe, G.B., Guberman, S.R., and Gearhart, M. (1987). Social processes in early number development. Monographs of the Society for Research in Child Development, 52(2).

Secada, W.G. (1991). Degree of bilingualism and arithmetic problem solving in Hispanic first graders. Elementary School Journal, 92, 213-231.

Séron, X., Pesenti, M., Noël, M.-P., Deloche, G., and Cornet, J.-A. (1992). Images of numbers, or “when 98 is upper left and 6 sky blue.” Cognition, 44 (1-2), 159-196.

Siegler, R.S., and Jenkins, E. (1989). How Children Discover New Strategies. Hillsdale, NJ: Erlbaum.

Siegler, R.S., and Robinson, M. (1982). The development of numerical understandings. In H.W. Reese and L.P. Lipsitt (Eds.), Advances in Child Development and Behavior, Volume 16 (pp. 242-312). New York: Academic Press.

Siegler, R.S., and Shipley, C. (1995). Variation, selection, and cognitive change. In T. Simon and G. Halford (Eds.), Developing Cognitive Competence: New Approaches to Process Modeling (pp. 31-76). Hillsdale, NJ: Erlbaum.

Siegler, R.S., and Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of Cognitive Skills (pp. 229-293). Hillsdale, NJ: Erlbaum.

Starkey, P., and Klein, A. (2008). Sociocultural Influences on Young Children’s Mathematical Knowledge. Contemporary Perspectives on Mathematics in Early Childhood Education. Charlotte, NC: Information Age.

Starkey, P., Klein, A., Chang, I., Qi, D. Lijuan, P., and Yang, Z. (1999). Environmental Supports for Young Children’s Mathematical Development in China and the United States. Paper presented at the Biennial Meeting of the Society for Research in Child Development, Albuquerque, NM.

Starkey, P., Klein, A., and Wakeley, P. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99-120.

Stipek, D.J., and Byler, P. (1997). Early childhood teachers: Do they practice what they preach? Early Childhood Research Quarterly, 12, 305-325.

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

Wechsler, D. (1967). Manual for the Wechsler Preschool and Primary Scale of Intelligence. New York: Psychological Corporation.

Weiss, H., Caspe, M., and Lopez, M.E. (2006). Family Involvement Makes a Difference: Family Involvement in Early Childhood Education (No. 1). Available:

http://www.gse.harvard.edu/hfrp/projects/fine/resources/research/earlychildhood.html

Wilson, R.S. (1975). Twins: Patterns of cognitive development as measured on the Wechsler preschool and primary scale of intelligence. Developmental Psychology, 11, 126-134.

Woods, T.A., and Kurtz-Costes, B. (2007). Race identity and race socialization in African American families: Implications for social workers. Journal of Human Behavior and the Social Environment, 15, 99-116.

Wynroth, L. (1986). Wynroth Math Program—The Natural Numbers Sequence. Ithaca, NY: Wynroth Math Program.

**Edma 0-6: Educación Matemática en la Infancia**, [S.l.], v. 3, n. 2, p. 1-22, oct. 2020. ISSN 2254-8351. Disponible en: <https://edma0-6.es/index.php/edma0-6/article/view/128>. Fecha de acceso: 18 oct. 2022