Assessing 10- to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test

References

• Batanero, C., and E. Sanchez. 2005. “What is the Nature of High School Students’ Conceptions and Misconceptions about Probability?” In Exploring Probability in School, edited by G. Jones, 40 vols, 241–266. New York: Springer US.
   Google Scholar
• Berch, D. B. 2005. “Making Sense of Number Sense: Implications for Children with Mathematical Disabilities.” Journal of Learning Disabilities 38 (4): 333–339.10.1177/00222194050380040901
   PubMed Web of Science ®Google Scholar
• Cai, J. 1995. “A Cognitive Analysis of U.S. and Chinese Students’ Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex Problem Solving.” Journal for Research in Mathematics Education Monograph Series 7: i–151.
   Google Scholar
• Cai, J., and F. K. Lester. 2005. “Solution Representations and Pedagogical Representations in Chinese and U.S. Classrooms.” The Journal of Mathematical Behavior 24 (3–4): 221–237.10.1016/j.jmathb.2005.09.003
   Google Scholar
• Caleon, I. S., and R. Subramaniam. 2010. “Do Students Know What They Know and What They Don’t Know? Using a Four-Tier Diagnostic Test to Assess the Nature of Students’ Alternative Conceptions.” Research in Science Education 40 (3): 313–337. doi:10.1007/s11165-009-9122-4.
   Web of Science ®Google Scholar
• Cetin-Dindar, A., and O. Geban. 2011. “Development of a Three-Tier Test to Assess High School Students’ Understanding of Acids and Bases.” Procedia-Social and Behavioral Sciences 15: 600–604.10.1016/j.sbspro.2011.03.147
   Google Scholar
• Chinn, C. A., and W. F. Brewer. 1993. “The Role of Anomalous Data in Knowledge Acquisition: A Theoretical Framework and Implications for Science Instruction.” Review of Educational Research 63 (1): 1–49.
   Web of Science ®Google Scholar
• Clement, J. 1982. “Algebra Word Problem Solutions: Thought Processes Underlying a Common Misconception.” Journal for Research in Mathematics Education 13: 16–30.10.2307/748434
   Google Scholar
• Dehaene, S. 2001. “Precis of the Number Sense.” Mind and Language 16: 16–36.10.1111/mila.2001.16.issue-1
   Web of Science ®Google Scholar
• Dunphy, E. 2007. “The Primary Mathematics Curriculum: Enhancing Its Potential for Developing Young Children’s Number Sense in the Early Years at School.” Irish Educational Studies 26 (1): 5–25.10.1080/03323310601125088
   Web of Science ®Google Scholar
• Dyson, N. I., N. C. Jordan, and J. Glutting. 2013. “A Number Sense Intervention for Low-Income Kindergartners at Risk for Mathematics Difficulties.” Journal of Learning Disabilities 46 (2): 166–181.10.1177/0022219411410233
   PubMed Web of Science ®Google Scholar
• Glenberg, A. M., T. Sanocki, W. Epstein, and C. Morris. 1987. “Enhancing Calibration of Comprehension.” Journal of Experimental Psychology: General 116 (2): 119.10.1037/0096-3445.116.2.119
   Web of Science ®Google Scholar
• Hirsch, L. S., and A. M. O’Donnell. 2001. “Representativeness in Statistical Reasoning: Identifying and Assessing Misconceptions.” Journal of Statistics Education 9 (2): 1–22.
   Google Scholar
• Huang, R., and J. Cai. 2011. “Pedagogical Representations to Teach Linear Relations in Chinese and U.S. Classrooms: Parallel or Hierarchical?” The Journal of Mathematical Behavior 30 (2): 149–165.10.1016/j.jmathb.2011.01.003
   Google Scholar
• Jiang, C., S. Hwang, and J. Cai. 2014. “Chinese and Singaporean Sixth-Grade Students’ Strategies for Solving Problems about Speed.” Educational Studies in Mathematics 87 (1): 1–24.
   Web of Science ®Google Scholar
• Jordan, N. C., J. Glutting, and C. Ramineni. 2010. “The Importance of Number Sense to Mathematics Achievement in First and Third Grades.” Learning and Individual Differences 20 (2): 82–88.10.1016/j.lindif.2009.07.004
   PubMed Web of Science ®Google Scholar
• Jordan, N. C., C. Raminent, and M. W. Watkin. 2010. “Validating a Number Sense Screening Tool for Use in Kindergarten and First Grade: Prediction of Mathematics Proficiency in Third Grade.” School Psychology Review 39 (2): 181–195.
   Web of Science ®Google Scholar
• Li, M. N., and D. C. Yang. 2010. “Development and Validation of a Computer-Administered Number Sense Scale for Fifth-Grade Children in Taiwan.” School Science and Mathematics 110 (4): 220–230.10.1111/ssm.2010.110.issue-4
   Google Scholar
• Lin, Y-C., M. N. Li, and D. C. Yang. (forthcoming). “Diagnosing Students’ Misconceptions in Number Sense via a Web-Based Two-Tier Test.” Eurasia Journal of Mathematics, Science & Technology Education.
   Web of Science ®Google Scholar
• Markovits, Z., and J. T. Sowder. 1994. “Developing Number Sense: An Intervention Study in Grade 7.” Journal for Research in Mathematics Education 25 (1): 4–29.10.2307/749290
   Web of Science ®Google Scholar
• McIntosh, A., B. J. Reys, and R. E. Reys. 1992. “A Proposed Framework for Examining Basic Number Sense.” For the Learning of Mathematics 12 (3): 2–8.
   Google Scholar
• Menon, R. 2004. “Elementary School Children’s Number Sense.” International Journal for Mathematics Teaching and Learning. http://www.cimt.plymouth.ac.uk/journal/default.htm.
   Google Scholar
• Metsisto, D. 2005. “Reading in the Mathematics Classroom.” In Literacy Strategies for Improving Mathematics Instruction, edited by J. M. Kenney, E. Hancewicz, L. Heuer, D. Metsisto, and C. L. Tuttle, 9–23. Alexandria, VA: Association for Supervision and Curriculum Development.
   Google Scholar
• National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
   Google Scholar
• Reys, B. J. 1994. “Promoting number sense in middle grades.” Teaching Mathematics in the Middle School 1: 114–120.
   Google Scholar
• Reys, R. E., and D. C. Yang. 1998. “Relationship between Computational Performance and Number Sense among Sixth- and Eighth-Grade Students in Taiwan.” Journal for Research in Mathematics Education 29 (2): 225–237.10.2307/749900
   Web of Science ®Google Scholar
• Sood, S., and A. K. Jitendra. 2007. “A Comparative Analysis of Number Sense Instruction in Reform-Based and Traditional Mathematics Textbooks.” The Journal of Special Education 41 (3): 145–157.10.1177/00224669070410030101
   Web of Science ®Google Scholar
• Sowder, J. T. 1992. “Estimation and number sense.” In Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, edited by G. A. Douglas, 371–389. New York: Macmillan Publishing.
   Google Scholar
• Sreenivasulu, B., and R. Subramaniam. 2013. “University Students’ Understanding of Chemical Thermodynamics.” International Journal of Science Education 35 (4): 601–635.10.1080/09500693.2012.683460
   Web of Science ®Google Scholar
• Stankov, L., and J. Crawford. 1997. “Self-Confidence and Performance on Tests of Cognitive Abilities.” Intelligence 25 (2): 93–109.10.1016/S0160-2896(97)90047-7
   Web of Science ®Google Scholar
• Stankov, L., and B. Dolph. 2000. “Metacognitive Aspects of Test-Taking and Intelligence.” Psychologische Beitrage 42 (2): 213–227.
   Google Scholar
• Tan, K. C. D., N. K. Goh, L. S. Chia, and D. F. Treagust. 2002. “Development and Application of a Two-Tier Multiple Choice Diagnostic Instrument to Assess High School Students’ Understanding of Inorganic Chemistry Qualitative Analysis.” Journal of Research in Science Teaching 39 (4): 283–301.10.1002/(ISSN)1098-2736
   Web of Science ®Google Scholar
• Tobin, K. G., and W. Capie. 1981. “The Development and Validation of a Group Test of Logical Thinking.” Educational and Psychological Measurement 41 (2): 413–423.10.1177/001316448104100220
   Web of Science ®Google Scholar
• Treagust, D. F. 1988. “Development and Use of Diagnostic Tests to Evaluate Students’ Misconceptions in Science.” International Journal of Science Education 10 (2): 159–169.10.1080/0950069880100204
   Web of Science ®Google Scholar
• Tsai, C. C., and C. Chou. 2002. “Diagnosing Students’ Alternative Conceptions in Science.” Journal of Computer Assisted Learning 18 (2): 157–165.10.1046/j.0266-4909.2002.00223.x
   Web of Science ®Google Scholar
• Verschaffel, L., B. Greer, and De Corte, E. 2007. “Whole Number Concepts and Operations.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by F. Lester Jr., 557–628. Charlotte, NC: Information Age.
   Google Scholar
• Yang, D. C. 2005. “Number Sense Strategies Used by 6th‐Grade Students in Taiwan.” Educational Studies 31 (3): 317–333.10.1080/03055690500236845
   Web of Science ®Google Scholar
• Yang, D. C., and M. N. Li. 2013. “Assessment of Animated Self-Directed Learning Activities Modules for Children’s Number Sense Development.” Journal of Educational Technology and Society 16 (3): 44–58.
   Web of Science ®Google Scholar
• Yang, D. C., M. N. Li, and C. I. Lin. 2008. “A Study of the Performance of 5th Graders in Number Sense and Its Relationship to Achievement in Mathematics.” International Journal of Science and Mathematics Education 6 (4): 789–807.10.1007/s10763-007-9100-0
   Google Scholar
• Zakay, D., and J. Glicksohn. 1992. “Overconfidence in a Multiple-Choice Test and Its Relationship to Achievement.” Psychological Record 42 (4): 519–525.
   Web of Science ®Google Scholar