Skip to main content
SpringerLink
Log in

Leveraging Relational Learning Mechanisms to Improve Place Value Instruction

  • Chapter
  • First Online:
Constructing Number

Part of the book series: Research in Mathematics Education ((RME))

Abstract

In this chapter, we focus on the difficulties children face when learning place value and how current psychological theories of relational learning may be leveraged by teachers. We discuss two major psychological mechanisms known to support relational learning—statistical learning and structure mapping—and review the evidence showing how these mechanisms are implicated in place value learning. We further identify a set of four specific instructional elements teachers could use to engage and support these learning mechanisms. We also review three major curricula for teaching place value, including Developmentally Appropriate Mathematics, Number Talks, and the Montessori Method, in light of this conceptual framework. Our review highlights both strengths of these current curricula and ways they might be modified to more fully leverage relational learning mechanisms and increase student learning.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alibali, M., Young, A. G., Crooks, N. M., Yeo, A., Wolfgram, M. S., Ledesma, I. M., … Knuth, E. J. (2013). Students learn more when their teacher has learned to gesture effectively. Gesture, 13(2), 210–233.

    Article  Google Scholar 

  • Alibali, M. W., & Nathan, M. J. (2007). Teachers’ gestures as a means of scaffolding students’ understanding: Evidence from an early algebra lesson. In R. Goldman, R. Pea, B. Barron, & S. J. Derry (Eds.), Video research in the learning sciences (pp. 349–365). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Anderson, A. (2013). A practical guide to early numeracy instruction for general and special educators. Journal of Education and Training, 1(1), 11–18. https://doi.org/10.11114/jets.v1i1.18

    Article  Google Scholar 

  • Aslin, R. N., Saffran, J. R., & Newport, E. L. (1998). Computation of conditional probability statistics by 8-month-old infants. Psychological Science, 9(4), 321–324.

    Article  Google Scholar 

  • Barrouillet, P., Camos, V., Perruchet, P., & Seron, X. (2004). ADAPT: A developmental, asemantic, and procedural model for transcoding from verbal to Arabic numerals. Psychological Review, 111(2), 368.

    Article  Google Scholar 

  • Bassok, M., & Medin, D. L. (1997). Birds of a feather flock together: Similarity judgments with semantically rich stimuli. Journal of Memory and Language, 36(3), 311–336.

    Article  Google Scholar 

  • Berko, J. (1958). The child’s learning of English morphology. Word, 14(2-3), 150–177.

    Article  Google Scholar 

  • Boaler, J. (2015). Fluency without fear: Research evidence on the best ways to learn math facts. Reflections, 40(2), 7–12.

    Google Scholar 

  • Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031.

    Article  Google Scholar 

  • Bowdle, B. F., & Gentner, D. (2005). The career of metaphor. Psychological Review, 112(1), 193–216.

    Article  Google Scholar 

  • Bransford, J. D., & Schwartz, D. L. (1999). Chapter 3: Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24(1), 61–100.

    Article  Google Scholar 

  • Byrge, L., Smith, L. B., & Mix, K. S. (2014). Beginnings of place value: How preschoolers write three-digit numbers. Child Development, 85(2), 437–443.

    Article  Google Scholar 

  • Carey, S. (2004). Bootstrapping & the origin of concepts. Daedalus, 133(1), 59–68.

    Article  Google Scholar 

  • Chan, W. W. L., Au, T. K., & Tang, J. (2014). Strategic counting: A novel assessment of place-value understanding. Learning and Instruction, 29, 78–94.

    Article  Google Scholar 

  • Childers, J. (2011). Attention to multiple events helps two-and-a-half-year-olds extend new verbs. First Language, 31(1), 3–22.

    Article  Google Scholar 

  • Christie, S., & Gentner, D. (2010). Where hypotheses come from: Learning new relations by structural alignment. Journal of Cognition and Development, 11(3), 356–373.

    Article  Google Scholar 

  • Clerkin, E. M., Hart, E., Rehg, J. M., Yu, C., & Smith, L. B. (2017). Real-world visual statistics and infants’ first-learned object names. Philosophical Transactions of the Royal Society B, 372(1711), 20160055.

    Article  Google Scholar 

  • Colunga, E., & Smith, L. B. (2003). The emergence of abstract ideas: Evidence from networks and babies. In L. Saitta (Ed.), Philosophical Transactions by the Royal Society B. Theme Issue: The abstraction paths: from experience to concept (Vol. 358, pp. 1205–1214).

    Google Scholar 

  • Colunga, E., & Smith, L. B. (2005). From the lexicon to expectations about kinds: A role for associative learning. Psychological Review, 112(2), 347–382.

    Article  Google Scholar 

  • Ettlinger, M., & Zapf, J. (2011). The role of phonology in children’s acquisition of the plural. Language Acquisition, 18(4), 294–313.

    Article  Google Scholar 

  • Fuson, K. C. (1990). Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value. Cognition and Instruction, 7(4), 343–403.

    Article  Google Scholar 

  • Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26(1), 9–25.

    Article  Google Scholar 

  • Geary, D. C., Bow-Thomas, C. C., Liu, F., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development, 67(5), 2022–2044.

    Article  Google Scholar 

  • Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74(3), 213–239.

    Article  Google Scholar 

  • Gentner, D. (1988). Metaphor as structure mapping: The relational shift. Child Development, 59, 47.

    Article  Google Scholar 

  • Gentner, D. (2010). Bootstrapping the mind: Analogical processes and symbol systems. Cognitive Science, 34(5), 752–775.

    Article  Google Scholar 

  • Gentner, D., Anggoro, F. K., & Klibanoff, R. S. (2011). Structure mapping and relational language support children’s learning of relational categories. Child Development, 82(4), 1173–1188.

    Article  Google Scholar 

  • Gentner, D., & Christie, S. (2010). Mutual bootstrapping between language and analogical processing. Language and Cognition, 2(2), 261–283.

    Article  Google Scholar 

  • Gentner, D., & Markman, A. B. (1994). Structural alignment in comparison: No difference without similarity. Psychological Science, 5(3), 152–158.

    Article  Google Scholar 

  • Gentner, D., Ă–zyĂĽrek, A., GĂĽrcanli, Ă–., & Goldin-Meadow, S. (2013). Spatial language facilitates spatial cognition: Evidence from children who lack language input. Cognition, 127(3), 318–330.

    Article  Google Scholar 

  • Gervasoni, A., Hadden, T., & Turkenburg, K. (2007). Exploring the number knowledge of children to inform the development of a professional learning plan for teachers in the Ballarat diocese as a means of building community capacity. Mathematics: Essential Research, Essential Practice (pp. 305–314).

    Google Scholar 

  • Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15(1), 1–38.

    Article  Google Scholar 

  • Goldstone, R. L., & Byrge, L. A. (2014). Perceptual learning. In M. Matthen (Ed.), The Oxford handbook of philosophy of perception (pp. 1–16). New York: Oxford University Press.

    Google Scholar 

  • Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. Journal of the Learning Sciences, 14(1), 69–110.

    Article  Google Scholar 

  • Goldstone, R. L., & Wilensky, U. (2008). Promoting transfer by grounding complex systems principles. Journal of the Learning Sciences, 17(4), 465–516.

    Article  Google Scholar 

  • Golinkoff, R. M., Hirsh-Pasek, K., Cauley, K. M., & Gordon, L. (1987). The eyes have it: Lexical and syntactic comprehension in a new paradigm. Journal of Child Language, 14, 23–45.

    Article  Google Scholar 

  • Hainstock, E. (1978/1997). The essential Montessori. New York: Penguin Books.

    Google Scholar 

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

    Article  Google Scholar 

  • Hieber, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14(3), 251–283.

    Article  Google Scholar 

  • Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., & Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111–132.

    Article  Google Scholar 

  • Ho, C. S. H., & 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.

    Article  Google Scholar 

  • Hockema, S. A. (2006). Finding words in speech: An investigation of American English. Language Learning and Development, 2(2), 119–146.

    Article  Google Scholar 

  • Howden, H. (1989). Teaching number sense. The Arithmetic Teacher, 36(6), 6–11.

    Article  Google Scholar 

  • Humphreys, C., & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10. New York: Stenhouse.

    Google Scholar 

  • Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1(2), 75–86.

    Article  Google Scholar 

  • Keil, F. C., & Batterman, N. (1984). A characteristic-to-defining shift in the development of word meaning. Journal of Verbal Learning and Verbal Behavior, 23(2), 221–236.

    Article  Google Scholar 

  • Kosslyn, S. M. (2006). Graph design for the eye and mind. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67(6), 2797–2822.

    Article  Google Scholar 

  • Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning. Psychological Review, 99(1), 22.

    Article  Google Scholar 

  • Laski, E. V., Ermakova, A., & Vasilyeva, M. (2014). Early use of decomposition for addition and its relation to base-10 knowledge. Journal of Applied Developmental Psychology, 35(5), 444–454. https://doi.org/10.1016/j.appdev.2014.07.002

    Article  Google Scholar 

  • Laski, E. V., & Yu, Q. (2014). Number line estimation and mental addition: Examining the potential roles of language and education. Journal of Experimental Child Psychology, 117, 29–44.

    Article  Google Scholar 

  • Lillard, A., & Else-Quest, N. (2006). The early years: Evaluating Montessori. Science, 313(5795), 1893–1894.

    Article  Google Scholar 

  • Lillard, A. S. (2005). Montessori: The science behind the genius. New York: Oxford University Press.

    Google Scholar 

  • Lillard, P. P. (1980/1997). Montessori in the classroom. New York: Random House.

    Google Scholar 

  • Liu, J., Golinkoff, R. M., & Sak, K. (2001). One cow does not an animal make: Young children can extend novel words at the superordinate level. Child Development, 72(6), 1674–1694.

    Article  Google Scholar 

  • Loewenstein, J., & Gentner, D. (2005). Relational language and the development of relational mapping. Cognitive Psychology, 50(4), 315–353.

    Article  Google Scholar 

  • Markman, A. B., & Gentner, D. (1996). Commonalities and differences in similarity comparisons. Memory & Cognition, 24(2), 235–249.

    Article  Google Scholar 

  • Matlen, B., Gentner, D., & Franconeri, S. (2014). Structure mapping in visual comparison: Embodied correspondence lines? Proceedings of the Cognitive Science Society (p. 36).

    Google Scholar 

  • McClelland, J. L., & Rogers, T. T. (2003). The parallel distributed processing approach to semantic cognition. Nature Reviews Neuroscience, 4(4), 310–322.

    Article  Google Scholar 

  • McNeil, N. M., & Fyfe, E. R. (2012). “Concreteness fading” promotes transfer of mathematical knowledge. Learning and Instruction, 22(6), 440–448.

    Article  Google Scholar 

  • Miura, I. T., Okamoto, Y., Kim, C. C., Chang, C., Steere, M., & Fayol, M. (1994). Comparisons of children’s cognitive representation of number: China, France, Japan, Korea, Sweden, and the United States. International Journal of Behavioral Development, 17(3), 401–411. https://doi.org/10.1177/016502549401700301

    Article  Google Scholar 

  • Mix, K. S. (2010). Spatial tools for mathematical thought. In K. S. Mix, L. B. Smith, & M. Gasser (Eds.), The Spatial Foundations of language and cognition (pp. 41–66). New York: Oxford University Press.

    Google Scholar 

  • Mix, K. S., Prather, R. W., Smith, L. B., & Stockton, J. D. (2014). Young children’s interpretation of multi-digit number names: From emerging competence to mastery. Child Development, 85(3), 1306–1319.

    Article  Google Scholar 

  • Mix, K. S., Smith, L. B., Stockton, J. D., Cheng, Y. L., & Barterian, J. A. (2017). Grounding the symbols for place value: Evidence from training and long-term exposure to base-10 models. Journal of Cognition and Development, 18(1), 129–151.

    Article  Google Scholar 

  • Moeller, K., Klein, E., Fischer, M. H., Nuerk, H. C., & Willmes, K. (2011). Representation of multiplication facts-evidence for partial verbal coding. Behavioral and Brain Functions, 7(25), 1–9.

    Google Scholar 

  • Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. C. (2011). Early place-value understanding as a precursor for later arithmetic performance—A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851.

    Article  Google Scholar 

  • Montessori, M. (1917). The advanced Montessori method (Vol. 1). New York: Frederick A. Stokes.

    Google Scholar 

  • Montessori, M. (1934). Psychoarithmetic. Laren: Montessori-Pearson.

    Google Scholar 

  • Morgan, P. L., Farkas, G., & Maczuga, S. (2015). Which instructional practices most help first-grade students with and without mathematics difficulties? Educational Evaluation and Policy Analysis, 37(2), 184–205.

    Article  Google Scholar 

  • Moura, R., Wood, G., Pinheiro-Chagas, P., Lonnemann, J., Krinzinger, H., Willmes, K., & Haase, V. G. (2013). Transcoding abilities in typical and atypical mathematics achievers: The role of working memory and procedural and lexical competencies. Journal of Experimental Child Psychology, 116(3), 707–727.

    Article  Google Scholar 

  • Namy, L. L., & Gentner, D. (2002). Making a silk purse out of two sow’s ears: Young children’s use of comparison in category learning. Journal of Experimental Psychology: General, 131(1), 5–15.

    Article  Google Scholar 

  • Nosofsky, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10(1), 104–114.

    Google Scholar 

  • Novick, L. R., & Bassok, M. (2005.) Problem solving). In K. J. Holyoak & R. G. Morrison (Eds.), Cambridge handbook of thinking and reasoning (pp. 321–349). New York: Cambridge University Press.

    Google Scholar 

  • Paik, J. H., & Mix, K. S. (2003). US and Korean children’s comprehension of fraction names: A reexamination of cross–national differences. Child Development, 74(1), 144–154.

    Article  Google Scholar 

  • Paik, J. H., & Mix, K. S. (2006). Preschoolers’ use of surface similarity in object comparisons: Taking context into account. Journal of Experimental Child Psychology, 95(3), 194–214.

    Article  Google Scholar 

  • Parrish, S. (2014). Number talks: Helping children build mental math and computation strategies, Grades K-5. Sausalito, CA: Math Solutions.

    Google Scholar 

  • Parrish, S. D. (2011). Number talks build numerical reasoning. Teaching Children’s Mathematics, 18(3), 198–206.

    Article  Google Scholar 

  • Piantadosi, S., Tenenbaum, J., & Goodman, N. (2012). Bootstrapping in a language of thought: A formal model of numerical concept learning. Cognition, 123(2), 199–217. https://doi.org/10.1016/j.cognition.2011.11.005

    Article  Google Scholar 

  • Post, T. R. (1988). Some notes on the nature of mathematics learning. Teaching mathematics in grades k-8: Research based methods (pp. 1–19).

    Google Scholar 

  • Pruden, S. M., Hirsh-Pasek, K., Maguire, M., & Meyer, M. (2004). Foundations of verb learning: Infants categorize path and manner in motion events. In Proceedings of the 28th Annual Boston University Conference on Language Development (pp. 461–472).

    Google Scholar 

  • Recchia, G., & Jones, M. N. (2009). More data trumps smarter algorithms: Comparing pointwise mutual information with latent semantic analysis. Behavior Research and Methods, 41(3), 647–656.

    Article  Google Scholar 

  • Richland, L. E. (2015). Linking gestures: Cross-cultural variation during instructional analogies. Cognition and Instruction, 33(4), 295–321.

    Article  Google Scholar 

  • Richland, L. E., & McDonough, I. M. (2010). Learning by analogy: Discriminating between potential analogs. Contemporary Educational Psychology, 35, 28–43.

    Article  Google Scholar 

  • Richland, L. E., Zur, O., & Holyoak, K. J. (2007). Cognitive supports for analogies in the mathematics classroom. Science, 316(5828), 1128–1129.

    Article  Google Scholar 

  • Ross, S., & Sunflower, E. (1995). Place-value: problem-solving and written assessment using digit-correspondence tasks. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.

    Google Scholar 

  • Siskind, J. M. (1996). A computational study of cross-situational techniques for learning word-to-meaning mappings. Cognition, 61(1), 39–91.

    Article  Google Scholar 

  • Smith, L. B., Colunga, E., & Yoshida, H. (2010). Knowledge as process: Contextually cued attention and early word learning. Cognitive Science, 34(7), 1287–1314.

    Article  Google Scholar 

  • Smith, L. B., Jones, S. S., Landau, B., Gershkoff-Stowe, L., & Samuelson, L. (2002). Object name learning provides on-the-job training for attention. Psychological Science, 13(1), 13–19.

    Article  Google Scholar 

  • Smith, L., & Yu, C. (2008). Infants rapidly learn word-referent mappings via cross-situational statistics. Cognition, 106(3), 1558–1568.

    Article  Google Scholar 

  • Son, J. Y., Smith, L. B., & Goldstone, R. L. (2008). Simplicity and generalization: Short-cutting abstraction in children’s object categorizations. Cognition, 108(3), 626–638.

    Article  Google Scholar 

  • Son, J. Y., Smith, L. B., & Goldstone, R. L. (2011). Connecting instances to promote children’s relational reasoning. Journal of Experimental Child Psychology, 108(2), 260–277.

    Article  Google Scholar 

  • Stevenson, H., & Stigler, J. W. (1994). Learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York: Simon and Schuster.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Simon and Schuster.

    Google Scholar 

  • Thompson, C. A., & Opfer, J. E. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development, 81(6), 1768–1786.

    Article  Google Scholar 

  • TIMSS HF. (2007). Mathematics and science achievement of US fourth-and eighth-grade students in an international context (NCES 2009001 Revised). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, US Department of Education.

    Google Scholar 

  • Treiman, R., & Kessler, B. (2006). Spelling as statistical learning: Using consonantal context to spell vowels. Journal of Educational Psychology, 98(3), 642–665.

    Article  Google Scholar 

  • Uttal, D. H., O’Doherty, K., Newland, R., Hand, L. L., & DeLoache, J. (2009). Dual representation and the linking of concrete and symbolic representations. Child Development Perspectives, 3(3), 156–159.

    Article  Google Scholar 

  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston, MA: Allyn & Bacon.

    Google Scholar 

  • Van de Walle, J. A., Karp, K. S., Lovin, L. H., & Bay-Williams, J. M. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)(Teaching Student-Centered Mathematics Series) Saddle River, NJ: Pearson Education.

    Google Scholar 

  • Vendetti, M. S., Matlen, B. J., Richland, L. E., & Bunge, S. A. (2015). Analogical reasoning in the classroom: Insights from cognitive science. Mind, Brain, and Education, 9(2), 100–106.

    Article  Google Scholar 

  • Waxman, S. R., & Gelman, R. (1986). Preschoolers use of superordinate relations in classification and language. Cognitive Development, 1, 139–156.

    Article  Google Scholar 

  • Werker, J. F., & Yeung, H. H. (2005). Infant speech perception bootstraps word learning. Trends in Cognitive Sciences, 9(11), 519–527.

    Article  Google Scholar 

  • Xu, F., & Tenenbaum, J. B. (2007). Word learning as Bayesian inference. Psychological Review, 114(2), 245–272. https://doi.org/10.1037/0033-295X.114.2.245

    Article  Google Scholar 

  • Yu, C., & Smith, L. (2007). Rapid word learning under uncertainty via cross-situational statistics. Psychological Science, 18(5), 414–420. https://doi.org/10.1111/j.1467-9280.2007.01915.x

    Article  Google Scholar 

  • Yuan, L., & Smith, L. B. (under review). Learning the generative principles of a symbol system from limited examples. Cognition.

    Google Scholar 

  • Yurovsky, D., Fricker, D. C., Yu, C., & Smith, L. B. (2014). The role of partial knowledge in statistical word learning. Psychonomic Bulletin & Review, 21(1), 1–22. https://doi.org/10.3758/s13423-013-0443-y

    Article  Google Scholar 

  • Zuber, J., Pixner, S., Moeller, K., & Nuerk, H. C. (2009). On the language specificity of basic number processing: Transcoding in a language with inversion and its relation to working memory capacity. Journal of Experimental Child Psychology, 102(1), 60–77.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by NSF grant #1664781 to the first author and NSF grant #1621093 to the second author. Special thanks to Naomi Swenson for her able assistance with manuscript preparation and permissions.

Author information

Authors and Affiliations

  1. Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, USA

    Kelly S. Mix

  2. Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA

    Linda B. Smith

  3. Department of Teacher Education, Michigan State University, East Lansing, MI, USA

    Sandra Crespo

Authors
  1. Kelly S. Mix
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linda B. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sandra Crespo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kelly S. Mix .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Anderson Norton

  2. Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA

    Martha W. Alibali

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mix, K.S., Smith, L.B., Crespo, S. (2019). Leveraging Relational Learning Mechanisms to Improve Place Value Instruction. In: Norton, A., Alibali, M.W. (eds) Constructing Number. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-00491-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00491-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00490-3

  • Online ISBN: 978-3-030-00491-0

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation