Publication Cover
Educational Psychology
An International Journal of Experimental Educational Psychology
Volume 37, 2017 - Issue 2
1,041
Views
12
CrossRef citations to date
0
Altmetric
Articles

Developing a learning progression for number sense based on the rule space model in China

, &
Pages 128-144 | Received 01 Mar 2016, Accepted 19 Sep 2016, Published online: 30 Sep 2016

References

  • Adams, R. (Ed.). (2002). PISA 2000 technical report. Paris: OECD.
  • Alonzo, A. Z., & Gotwals, A. W. (2012). Learning progressions in science: Current challenges and future directions. Rotterdam: Sense.10.1007/978-94-6091-824-7
  • Alonzo, A., & Steedle, J. T. (2008). Developing and assessing a force and motion learning progression. Science Education, 93, 389–421.
  • American Educational Research Association, American Psychological Association, & National Council on Measurement in Education (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
  • Baroody, A. J., Cibulskis, M., Lai, M., & Li, X. (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6, 227–260.10.1207/s15327833mtl0602_8
  • Beglar, D. (2009). A Rasch-based validation of the vocabulary size test. Language Testing, 26, 1–22.
  • Birenbaum, M., Kelly, A. E., & Tatsuoka, K. K. (1993). Diagnosing knowledge states in algebra using the rule-space model. Journal for Research in Mathematics Education, 24, 442–459.10.2307/749153
  • Briggs, D. C., Alonzo, A. C., Schwab, C., & Wilson, M. (2006). Diagnostic assessment with ordered multiple-choice items. Educational Assessment, 11, 33–63.10.1207/s15326977ea1101_2
  • Catley, K., Lehrer, R., & Reiser, B. (2005). Tracing a prospective learning progression for developing understanding of evolution. Washington, DC: National Academy of Sciences.
  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3–29.10.2307/749551
  • Dogan, E., & Tatsuoka, K. (2008). An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS-R. Educational Studies in Mathematics, 68, 263–272.10.1007/s10649-007-9099-8
  • Duncan, R. G., & Hmelo-Silver, C. E. (2009). Learning progressions: Aligning curriculum, instruction, and assessment. Journal of Research in Science Teaching, 46, 606–609.10.1002/tea.v46:6
  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). London: Sage.
  • Griffin, S. (2004). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173–180.10.1016/j.ecresq.2004.01.012
  • Jones, G. A., Thornton, C. A., Putt, I. J., Hill, K. M., Mogill, A. T., Rich, B. S., & Van Zoest, L. R. (1996). Multidigit number sense: A framework for instruction and assessment. Journal for Research in Mathematics Education, 27, 310–336.10.2307/749367
  • Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20, 82–88.10.1016/j.lindif.2009.07.004
  • Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, N. M. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175.10.1111/cdev.2006.77.issue-1
  • Kaplan, H. A. (2012). Prospective preschool teachers’ ideas for developing the number sense of children. Procedia-Social and Behavioral Sciences, 46, 3870–3874.10.1016/j.sbspro.2012.06.163
  • Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The attribute hierarchy method for cognitive assessment: A variation on Tatsuoka’s rule-space approach. Journal of Educational Measurement, 41, 205–237.10.1111/jedm.2004.41.issue-3
  • Li, M. N., & Yang, D. C. (2010). Development and validation of a computer-administered number sense scale for fifth-grade children in Taiwan. School Science and Mathematics, 110, 220–230.10.1111/ssm.2010.110.issue-4
  • Li, F., Yu, N., & Xin, T. (2009). Development of diagnostic math test for grader 4 and grader 5 based on the rule space model. Psychology Development and Education, 3, 113–118.
  • Liu, X. F. (2005). Using Rasch model to validate stages of understanding the energy concept. Journal of Applied Measurement, 6, 1–18.
  • Liu, X. F., & McKeough, A. (2005). Developmental growth in students’ concept of energy: Analysis of selected items from the TIMSS database. Journal of Research in Science Teaching, 42, 493–517.10.1002/(ISSN)1098-2736
  • Markovits, Z., & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25, 4–29.10.2307/749290
  • McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2–44.
  • Mohan, L., Chen, J., & Anderson, C. W. (2009). Developing a multi-year learning progression for carbon cycling in socio-ecological systems. Journal of Research in Science Teaching, 46, 675–698.10.1002/tea.v46:6
  • National Research Council. (2007). Taking science to school: Learning and teaching science in grades K-8. Washington, DC: The National Academies Press.
  • Neumann, K., Viering, T., Boone, W. J., & Fischer, H. E. (2013). Towards a learning progression of energy. Journal of Research in Science Teaching, 50, 162–188.10.1002/tea.v50.2
  • Plummer, J. D., & Maynard, L. (2014). Building a learning progression for celestial motion: An exploration of students’ reasoning about the seasons. Journal of Research in Science Teaching, 51, 902–929.10.1002/tea.21151
  • Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research), expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago, IL: The University of Chicago Press.
  • Reys, R., Reys, B., Emanuelsson, G., Johansson, B., McIntosh, A., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99, 61–70.10.1111/ssm.1999.99.issue-2
  • Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29, 225–237.10.2307/749900
  • Sengul, S., & Gulbagci, H. (2012). An investigation of 5th grade Turkish students’ performance in number sense on the topic of decimal numbers. Social and Behavioral Sciences, 46, 2289–2293.
  • Shuard, H., Walsh, A., Goodwin, J., & Worcester, V. (1991). Primary initiatives in mathematics education: Calculators, children, and mathematics. London: Simon & Schuster.
  • Tatsuoka, K. K. (1983). Rule space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345–354.10.1111/jedm.1983.20.issue-4
  • Tatsuoka, K. K. (1984). Caution indices based on item response theory. Psychometrika, 49, 95–110.10.1007/BF02294208
  • Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79, 317–339.10.1007/s11336-013-9362-0
  • Tsao, Y. L. (2005). The number sense of preservice elementary school teachers. College Student Journal, 39, 647–679.
  • Tsao, Y. L., & Lin, Y. C. (2011). The study of number sense and teaching practice. Journal of Case Studies in Education, 2, 1–14.
  • Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Yang, D. C. (2003). Teaching and learning number sense – An intervention study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, 1, 115–134.10.1023/A:1026164808929
  • Yang, D. C., Reys, E. R., & Reys, J. B. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7, 383–403.10.1007/s10763-007-9124-5
  • Yang, D. C., & Wu, W. R. (2010). The study of number sense: Realistic activities integrated into third-grade math classes in Taiwan. The Journal of Educational Research, 103, 379–392.10.1080/00220670903383010

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.