Faculty of Education - Research Publications
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ItemBeyond Accuracy: A Process for Analysis of Constructed Responses in Large(The Korean Society of Educational Studies in Mathematics, 2022-08-31)This article reports a detailed analysis of errors made by early algebra students who are learning equation solving. Whilst we aim to deepen the knowledge base that can be used by teachers and curriculum writers to plan instruction, the main goal of this article is to demonstrate a 5-step process that we have developed to analyse, summarize, visualize and grasp meaning from large numbers of short constructed responses to mathematics questions. This data-driven process is illustrated using responses from 3,010 students to an online test, which is intended to be highly diagnostic and used for formative purposes. The test consisted of 14 very carefully selected linear equations to solve. Students entered only the numerical answers. Although nearly all the errors identified have been previously reported in the literature, the study provides insights into their prevalence in this target population and demonstrates how they correspond to other characteristics of the students’ algebra, including the strategies that they use to solve these linear equations. It also provides a practical example of using short constructed responses as a window into students’ thinking.
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ItemSpecific Mathematics Assessments that Reveal Thinking: An Online Tool to Build Teachers’ Diagnostic Competence and Support Teaching(Springer, 2018)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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ItemSMART Assessment for Learning(International Society for Design and Development in Education, 2009)“Specific Mathematics Assessments that Reveal Thinking,” which we abbreviate to “smart tests,” provide teachers with a quick and easy way to conduct assessment for learning. Using the internet, students in Years 7, 8, and 9 undertake a short test that is focused strongly on a topic selected by their teacher. Students’ stages of development are diagnosed, and sent to the teacher immediately. Where available, on-line teaching resources are linked to each diagnosis, to guide teachers in moving students to the next stage. Many smart tests are now being trialled in schools and their impact on students’ and teachers’ learning is being evaluated. Design issues are discussed.
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ItemGetting SMART about assessment for learning(The Mathematical Association of Victoria, 2009)“Specific Mathematics Assessments that Reveal Thinking”—or smart tests—provide teachers with a quick and easy way to conduct assessment for learning. Using the internet, students in years 7, 8, and 9 undertake a short test that is focussed strongly on a topic selected by their teacher. Students’ stages of development are diagnosed, and sent to the teacher within minutes. Many tests have been produced and are now being trialled in 7 Victorian schools. Where available, on-line teaching resources are linked to each diagnosis, to guide teachers in moving students to the next stage. This project is sponsored by the Australian Research Council and Victoria’s Department of Education and Early Childhood Development.
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ItemInvestigating Students' Numerical Misconceptions in Algebra(Mathematics Education Research Group of Australasia, 2009)