Children's Mathematics Learning: The Struggle to Link Form and Understanding

Abstract

Previous articleNext article No AccessChildren's Mathematics Learning: The Struggle to Link Form and UnderstandingJames HiebertJames Hiebert Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 84, Number 5May, 1984Special Issue: Mathematics Education Article DOIhttps://doi.org/10.1086/461380 Views: 63Total views on this site Citations: 47Citations are reported from Crossref Copyright 1984 The University of ChicagoPDF download Crossref reports the following articles citing this article:Debbie Marie B. Verzosa Pre-service elementary teachers’ reasoning in introducing multidigit subtraction, International Journal of Mathematical Education in Science and Technology 51, no.66 (Jul 2019): 876–892.https://doi.org/10.1080/0020739X.2019.1647573Maulfry Worthington Mathematical Signs and Their Cultural Transmission in Pretend Play, (Feb 2020): 45–65.https://doi.org/10.1007/978-981-15-2821-7_4Charalampos Lemonidis, Nikos Pilianidis The 8th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers, International Electronic Journal of Mathematics Education 15, no.33 (Jan 2020).https://doi.org/10.29333/iejme/7865Maulfry Worthington, Marjolein Dobber, Bert van Oers The development of mathematical abstraction in the nursery, Educational Studies in Mathematics 102, no.11 (Jun 2019): 91–110.https://doi.org/10.1007/s10649-019-09898-3Pamela Moffett Bring calculations to life with meaningful contexts, Early Years Educator 20, no.99 (Jan 2019): 18–20.https://doi.org/10.12968/eyed.2019.20.9.18Der-Ching Yang Performance of Fourth Graders When Judging the Reasonableness of a Computational Result, International Journal of Science and Mathematics Education 17, no.11 (Oct 2017): 197–215.https://doi.org/10.1007/s10763-017-9862-yÖzge DAYI, Mehmet Ali KANDEMİR Farklı Düzeyde Sayı Duyusu Becerisine Sahip İlköğretim Matematik Öğretmen Adaylarına İlişkin Durum Çalışması, Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (Dec 2018): 276–305.https://doi.org/10.17522/balikesirnef.506441Pamela Moffett, Patricia Eaton The impact of the Promoting Early Number Talk project on the development of abstract representation in mathematics, European Early Childhood Education Research Journal 26, no.44 (Jun 2018): 547–561.https://doi.org/10.1080/1350293X.2018.1487166Ilya Sinitsky, Bat-Sheva Ilany Invariant Quantities – What is Invariant and What Changes?, (Jan 2016): 35–97.https://doi.org/10.1007/978-94-6300-699-6_2Rebecca Lynne Patterson, D. Cooper Patterson, Anna-Marie Robertson Seeing Numbers Differently, (Jan 2016): 186–214.https://doi.org/10.4018/978-1-4666-9837-6.ch009Bruce J.L. Brown Identifying Systems of Interaction in Mathematical Engagement, African Journal of Research in Mathematics, Science and Technology Education 18, no.33 (Sep 2014): 231–241.https://doi.org/10.1080/10288457.2014.953293Marjoke Bakker, Marja van den Heuvel-Panhuizen, Alexander Robitzsch First-graders’ knowledge of multiplicative reasoning before formal instruction in this domain, Contemporary Educational Psychology 39, no.11 (Jan 2014): 59–73.https://doi.org/10.1016/j.cedpsych.2013.11.001Helena P. Osana, Nicole Pitsolantis Addressing the struggle to link form and understanding in fractions instruction, British Journal of Educational Psychology 83, no.11 (Nov 2011): 29–56.https://doi.org/10.1111/j.2044-8279.2011.02053.xNancy I. Dyson, Nancy C. Jordan, Joseph Glutting A Number Sense Intervention for Low-Income Kindergartners at Risk for Mathematics Difficulties, Journal of Learning Disabilities 46, no.22 (Jun 2011): 166–181.https://doi.org/10.1177/0022219411410233I. Boticki, Lung Hsiang Wong, Chee-Kit Looi Designing Technology for Content-Independent Collaborative Mobile Learning, IEEE Transactions on Learning Technologies 6, no.11 (Jan 2013): 14–24.https://doi.org/10.1109/TLT.2012.8 Nicole Pitsolantis, Helena P. Osana Fractions Instruction: Linking Concepts and Procedures, Teaching Children Mathematics 20, no.11 (Jan 2013): 18.https://doi.org/10.5951/teacchilmath.20.1.0018M. Gail Jones, Grant E. Gardner, Amy R. Taylor, Jennifer H. Forrester, Thomas Andre Students' Accuracy of Measurement Estimation: Context, Units, and Logical Thinking, School Science and Mathematics 112, no.33 (Mar 2012): 171–178.https://doi.org/10.1111/j.1949-8594.2011.00130.xAmal Hussain Alajmi, Robert Reys EXAMINING EIGHTH GRADE KUWAITI STUDENTS’ RECOGNITION AND INTERPRETATION OF REASONABLE ANSWERS, International Journal of Science and Mathematics Education 8, no.11 (Jun 2009): 117–139.https://doi.org/10.1007/s10763-009-9165-z 김은정, 이정욱 The effects of geometry activities based on problem-solving for geometric development of young children, Korean Journal of Early Childhood Education 29, no.11 (Feb 2009): 31–55.https://doi.org/10.18023/kjece.2009.29.1.002Anna O. Graeber Mathematics Instruction Across the Grades: What Consultants Should Know, Journal of Educational and Psychological Consultation 16, no.44 (Dec 2006): 349–362.https://doi.org/10.1207/s1532768Xjepc1604_9Der‐Ching Yang Number sense strategies used by 6th‐grade students in Taiwan, Educational Studies 31, no.33 (Sep 2005): 317–333.https://doi.org/10.1080/03055690500236845Marta Laupa, Joe Becker Coordinating mathematical concepts with the demands of authority: children’s reasoning about conventional and second-order logical rules, Cognitive Development 19, no.22 (Apr 2004): 147–168.https://doi.org/10.1016/j.cogdev.2003.11.001Effie Maclellan Representing addition and subtraction: Learning the formal conventions, European Early Childhood Education Research Journal 9, no.11 (Jan 2001): 73–86.https://doi.org/10.1080/13502930185208691Marta Laupa Similarities and differences in children's reasoning about morality and mathematics, New Directions for Child and Adolescent Development 2000, no.8989 (Dec 2013): 19–31.https://doi.org/10.1002/cd.23220008903Marta Laupa Children's understanding of logical and conventional rules in arithmetic algorithms, The Journal of Mathematical Behavior 19, no.33 (Jul 2000): 291–305.https://doi.org/10.1016/S0732-3123(00)00048-1Robert Reys, Barbara Reys, Göran Emanuelsson, Bengt Johansson, Alistair McIntosh, Der Ching Yang Assessing Number Sense of Students in Australia, Sweden, Taiwan, and the United States, School Science and Mathematics 99, no.22 (Feb 1999): 61–70.https://doi.org/10.1111/j.1949-8594.1999.tb17449.xJane Perlmutter, Lisa Bloom, Terry Rose, Anita Rogers Who Uses Math? Primary Children's Perceptions of the Uses of Mathematics, Journal of Research in Childhood Education 12, no.11 (Dec 1997): 58–70.https://doi.org/10.1080/02568549709594716Maria Valeras, Joe Becker Children's Developing Understanding of Place Value: Semiotic Aspects, Cognition and Instruction 15, no.22 (Jun 1997): 265–286.https://doi.org/10.1207/s1532690xci1502_4Asha K. Jitendra, Edward J. Kameenui Experts' and Novices' Error Patterns in Solving Part-Whole Mathematical Word Problems, The Journal of Educational Research 90, no.11 (Sep 1996): 42–51.https://doi.org/10.1080/00220671.1996.9944442Ann Dowker Estimation Strategies of Four Groups, Mathematical Cognition 2, no.22 (Sep 1996): 113–135.https://doi.org/10.1080/135467996387499Ian Thompson The role of counting in the idiosyncratic mental calculation algorithms of young children, European Early Childhood Education Research Journal 3, no.11 (Jun 2007): 5–16.https://doi.org/10.1080/13502939585207651Ian Thompson Young children's idiosyncratic written algorithms for addition, Educational Studies in Mathematics 26, no.44 (Jun 1994): 323–345.https://doi.org/10.1007/BF01279519Inger Wistedt Everyday common sense and school mathematics, European Journal of Psychology of Education 9, no.22 (Jun 1994): 139–147.https://doi.org/10.1007/BF03173549Asha K. Jitendra, Edward J. Kameenui An Exploratory Study of Dynamic Assessment Involving Two Instructional Strategies On Experts and Novices' Performance in Solving Part-Whole Mathematical Word Problems, Diagnostique 18, no.44 (Sep 2016): 305–324.https://doi.org/10.1177/073724779301800404Joanne Mulligan Children’s solutions to multiplication and division word problems: A longitudinal study, Mathematics Education Research Journal 4, no.11 (Feb 1992): 24–41.https://doi.org/10.1007/BF03217230Arthur J. Baroody, Janice Hume Meaningful Mathematics Instruction, Remedial and Special Education 12, no.33 (Aug 2016): 54–68.https://doi.org/10.1177/074193259101200307Victoria M. Commins Teaching mathematics for understanding: what is a number?∗, Early Child Development and Care 73, no.11 (Jan 1991): 53–62.https://doi.org/10.1080/0300443910730106Ng Li Fung Lin The effect of superfluous information on children's solution of story arithmetic problems, Educational Studies in Mathematics 21, no.66 (Dec 1990): 509–520.https://doi.org/10.1007/BF00315942Karen C. Fuson Conceptual Structures for Multiunit Numbers: Implications for Learning and Teaching Multidigit Addition, Subtraction, and Place Value, Cognition and Instruction 7, no.44 (Dec 1990): 343–403.https://doi.org/10.1207/s1532690xci0704_4Gilah C. Leder Talking about mathematics, The Australian Educational Researcher 17, no.22 (Sep 1990): 17–27.https://doi.org/10.1007/BF03219470Gerard Giordano Play — Use — Generalize! Three-stage activities for developing math readiness, Day Care & Early Education 17, no.44 (Jun 1990): 13–17.https://doi.org/10.1007/BF01623192Ruth Baranes, Michelle Perry, James W. Stigler Activation of Real-World Knowledge in the Solution of Word Problems, Cognition and Instruction 6, no.44 (Dec 1989): 287–318.https://doi.org/10.1207/s1532690xci0604_1Richard S. Prawat Promoting Access to Knowledge, Strategy, and Disposition in Students: A Research Synthesis, Review of Educational Research 59, no.11 (Jun 2016): 1–41.https://doi.org/10.3102/00346543059001001James Hiebert A theory of developing competence with written mathematical symbols, Educational Studies in Mathematics 19, no.33 (Aug 1988): 333–355.https://doi.org/10.1007/BF00312451Geoffrey B. Saxe Candy Selling and Math Learning, Educational Researcher 17, no.66 (Jul 2016): 14–21.https://doi.org/10.3102/0013189X017006014Nina Kay Buchanan Factors contributing to mathematical problem-solving performance: An exploratory study, Educational Studies in Mathematics 18, no.44 (Nov 1987): 399–415.https://doi.org/10.1007/BF00240987Greta G. Fein Upscaling school: Lessons from the education of young children∗, Peabody Journal of Education 65, no.11 (Sep 1987): 42–54.https://doi.org/10.1080/01619568709538586