Abstract
Formative assessment involves the gathering of information that can guide the teaching of individual or groups of children. This approach requires a sound understanding of children’s thinking and learning, as well as an effective method for gaining the information. We propose that formative assessment should employ a version of clinical interviewing, a flexible method for gaining insight into children’s thinking, and should be based on contemporary research. This paper describes a computer-guided form of Piaget’s clinical interview method which we developed for the formative assessment of young children’s mathematics learning. The research-based interview examines key aspects of mathematical thinking, such as meaningful strategies and concepts. This paper examines the reliability and validity of the method for Kindergarten through Grade 3. Findings indicate that the clinical interview measures the same kinds of overall mathematics constructs as do standardized tests but, unlike standard tests, provides detailed information concerning mathematical thinking. The computer-guided format makes the method easy to administer and, we argue, is invaluable for education.
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References
Baroody, A. J., & Dowker, A. (Eds.). (2003). The development of arithmetic concepts and skills: constructing adaptive expertise. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
Black, P., & Wiliam, D. (2004). The formative purpose: assessment must first promote learning. In W. Wilson (Ed.), Towards Coherence between classroom assessment and accountability. 103rd Yearbook of the National Society for the study of education, Part 2 (pp. 20–50). Chicago: National Society for the Study of Education.
Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: building on the knowledge of students and teachers. International Journal of Educational Research, 17(5), 457–470.
Clement, J. (2000). Analysis of clinical interviews: foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547–589). Mahwah: Lawrence Erlbaum Associates, Publishers.
Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.). (2004). Engaging young children in mathematics: standards for early childhood mathematics education. Mahwah: Lawrence Erlbaum Associates.
diSessa, A. A. (2007). An interactional analysis of clinical interviewing. Cognition and Instruction, 25(4), 523–565.
Dowker, A. (2005). Individual differences in arithmetic: implications for psychology, neuroscience and education. Hove: Psychology Press.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: contributions of working memory and counting knowledge for children with mathematical disability. Experimental Child Psychology, 88, 121–151.
Ginsburg, H. P. (1989). Children’s arithmetic: how they learn it and how you teach it (2nd ed.). Austin: Pro Ed.
Ginsburg, H. P. (1997). Entering the child’s mind: the clinical interview in psychological research and practice. New York: Cambridge University Press.
Ginsburg, H. P. (2009). The challenge of formative assessment in mathematics education: children’s minds, teachers’ minds. Human Development, 52, 109–128.
Ginsburg, H. P., & Baroody, A. J. (2003). The test of early mathematics ability (3rd ed.). Austin: Pro Ed.
Ginsburg, H. P., Pappas, S., Lee, Y. S., & Chiong, C. (2011). How did you get that answer? Computer assessments of young children’s mathematical minds in mCLASS mathematics. In P. E. Noyce & D. T. Hickey (Eds.), New frontiers in formative assessment (pp. 49–67). Cambridge: Harvard Education Press.
Heritage, M. (2010). Formative assessment: making it happen in the classroom. Thousand Oaks, CA: Corwin Press.
Hirsh-Pasek, K., Kochanoff, A., Newcombe, N., & de Villiers, J. (2005). Using scientific knowledge to inform preschool assessment: making the case for “empirical validity”. Social Policy Report, XIX(1), 3–19.
Irwin, K., & Burgham, D. (1992). Big numbers and small children. The New Zealand Mathematics Magazine, 29(1), 9–19.
Kane, M. T. (2001). Current concerns in validity theory. Journal of Educational Measurement, 38(4), 319–342.
Kane, M. T. (2006). Content-related validity evidence in test development. In M. S. Downing & M. T. Haladyna (Eds.), Handbook of test development (pp. 131–153). Mahwah: Lawrence Erlbaum Associates.
Kaufman, A. S., & Kaufman, N. L. (1985). Kaufman test of educational achievement. Circle Pines: American Guidance Service.
Klein, A., & Starkey, P. (1988). Universals in the development of early arithmetic cognition. In G. Saxe & M. Gearhart (Eds.), Children’s mathematics (pp. 5–26). San Francisco: Jossey-Bass.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Charlotte: Information Age Publishing.
Lee, Y. S., Pappas, S., Chiong, C., & Ginsburg, H. P. (2010). mCLASS ® :MATH—technical Manual. Brooklyn: Wireless Generation Inc.
Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 13–103). New York: MacMillan Publishing Co.
Mislevy, R. (2006). Cognitive psychology and educational assessment. In R. L. Brennan (Ed.), Educational measurement (4th ed., pp. 257–306). Washington, DC: American Council on Education.
Nunes, T., & Bryant, P. E. (1996). Children doing mathematics. Oxford: Basil Blackwell.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
PBS. (2011). PBS Child Development Tracker. Retrieved from http://www.pbs.org/parents/childdevelopmenttracker/. Accessed 21 June 2016.
Pellegrino, J. W., Chudowsky, N., & Glaser, R. (Eds.). (2001). Knowing what students know: the science and design of educational assessment. Washington, DC: National Academy Press.
Piaget, J. (1976). The child’s conception of the world (J. Tomlinson & A. Tomlinson, Trans.). Totowa: Littlefield, Adams & Co.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: learning trajectories for young children. New York: Routledge.
Schoenfeld, A. H. (1987). What’s all the fuss about metacognition. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale: Lawrence Erlbaum Associates, Publishers.
Siegler, R. S. (1988). Individual differences in strategy choices: good students, not-so-good students, and perfectionists. Child Development, 59, 833–851.
VanLehn, K. (1990). Mindbugs: the origins of procedural misconceptions. Cambridge: The MIT Press.
Wechsler, D. (2001). WIAT-II: Wechsler individual achievement test–second edition. San Antonio: The Psychological Corporation.
Woodcock, R. W., McGrew, K. F., & Mather, N. (2001). Woodcock-Johnson III tests of achievement. Itasca: Riverside Publishing.
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Ginsburg, H.P., Lee, YS. & Pappas, S. A research-inspired and computer-guided clinical interview for mathematics assessment: introduction, reliability and validity. ZDM Mathematics Education 48, 1003–1018 (2016). https://doi.org/10.1007/s11858-016-0794-8
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DOI: https://doi.org/10.1007/s11858-016-0794-8