Getting formative information for the classroom from large international and national math assessments

iStock_000016940545XSmallLarge-scale international and national assessments monitor the health of an education system, but they can also provide valuable formative information, argues this study from Assessment in Education.

Study: “”Large-scale mathematics assessment: looking globally to act locally,” by Brian Doig, Assessment in Education, November 2006, Volume173, Number 3, pp. 265-288.

Large-scale international and national mathematic assessments can provide formative information for teachers if the data is reworked and re-presented in formats more appropriate for educators, according to a recent article in
Assessment in Education. 
Information about student achievement can be used to make inferences about teaching practices that can be used at the classroom level, writes researcher Brian Doig, who presents examples of some re-analyses of national and international data.

Main research question: How can data from large-scale international and national mathematics assessment reports be used to inform teachers about the effects of their classroom practices?

Method: The author provides examples of how researchers and research organizations, using Item Response Theory, have reanalyzed mathematics data from the Third International mathematics and Science Study (TIMSS) and other large-scale assessments to provide data that could be used by educators for formative purposes.

Main research question: How can schools that have reformed the way they teach mathematics align assessments with the new math curriculum and with the latest research on math education?


• Large-scale math assessments contain valuable formative data but it is
hidden unless results are re-analyzed and presented in ways more suitable for

•To be useful, this data must include implications for the classroom and the
basis for inferences about educators’ teaching practices.

•Data from national and international assessments can help increase
understanding of student needs and achievement and contribute to reforms of
educational systems.

Findings: Below are some examples of how researchers have reanalyzed data to provide formative information to educators:

  • Scale anchoring of TIMSS data by one research organization helped provide a greater understanding of what 9-year-old and 14-year-old students have learned in mathematics. Researchers identified items that students at different levels had a high probability of answering correctly. Those items were provided to mathematics education experts, who described what understandings and skills students needed to answer the items correctly.
  • In New South Wales, Australia, researchers reanalyzed results for a half-million students from its Basic Skills Testing Program for Year 3 and Year 6. Students’ possible responses to questions were examined in terms of the percentage of students that selected each possible response. Selection of responses was also broken down by the percentage of students that selected each response by gender and subgroup. To emphasize the classroom relevance of the expert analysis, each section concluded with a teacher’s observations on classroom implications.
  • Exploring errors by students can also provide useful information, according to researchers from the University of Manchester in the UK who did an error analysis of national mathematics tests taken by English and Welsh students. Error analysis can provide important diagnostic information for teachers. Ability estimates were used to compute the mean ability of students who made each error. A student’s total score and the errors likely to have been made provide information about student achievement. This type of test review can help support and educate teachers and lay the foundation for better practice, according to the UK researchers.


From Assessment for Learning: 12 recent studies on formative assessment and aligning assessments with learning goals, published by Educational Research Newsletter August 2007

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