Abstract
In this chapter, we describe the design of an online system for the formative assessment of students’ understanding of mathematics and discuss how it develops diagnostic competence and influences teaching. The smart-test system covers many mathematics topics studied by students between about 10 and 16 years of age. It is programmed to provide teachers with an automated diagnosis of their own students’ stages of development in specific topics and to report on an individual’s errors and misconceptions, in order to inform teaching. Our claim is that teachers’ diagnostic competence increases when they have easy access to information about their own students’ thinking. In turn, this can further improve teaching, and hence learning. By drawing together evaluative data from four sources, we highlight aspects of teachers’ initial responses to formative assessment and the effect of using this system on their knowledge for teaching and the subsequent changes to teaching practice. Overall, teachers report that using the smart-tests has improved their knowledge of the thinking of individual students as well as of students in general (i.e., their pedagogical content knowledge), and that they can use this information in several ways to adjust their teaching. Paradoxically, using smart-tests reduces the demand for teachers to have specific knowledge for diagnosis and at the same time increases this knowledge and so improves their diagnostic competence.
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Acknowledgements
An early version of this paper (Steinle & Stacey, 2012) was presented at the 12th International Congress on Mathematical Education. The smart-test system was developed at the University of Melbourne by Kaye Stacey, Vicki Steinle, Beth Price and Eugene Gvozdenko, with initial funding from the Australian Research Council Linkage Projects Program LP0882176 in partnership with the Department of Education and Early Childhood Development, Victoria, then further contracts with DEECD and the Catholic Education Office (Melbourne). We thank Ms Valerie Everist, Ms Sara McKee and Mr Terence Griffin for assisting teachers with using this system and for participating in interviews, and all the teachers and students who have contributed to this project to date and continue to do so.
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Stacey, K., Steinle, V., Price, B., Gvozdenko, E. (2018). Specific Mathematics Assessments that Reveal Thinking: An Online Tool to Build Teachers’ Diagnostic Competence and Support Teaching. In: Leuders, T., Philipp, K., Leuders, J. (eds) Diagnostic Competence of Mathematics Teachers. Mathematics Teacher Education, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-66327-2_13
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