In 1997, the Ontario government, undertook an ambitious reform of its elementary school (K-8) mathematics program. The reform emphasized math instruction using challenging problems, student construction of multiple solution methods, and mathematical communication and defense of ideas. In a recent issue of Assessment in Education, two researchers examine Ontario’s efforts to align a large-scale assessment with a reformed math curriculum.
Study: “The challenges and possibilities of aligning largescale testing with mathematical reform: The case of Ontario.” Assessment in Education: Principles, Policy & Practice”, by Alex Lawson and Christine Suurtamm, Volume 13, Number 3, November 2006, pp. 305-325.
Conclusion: Math reforms emphasize skills such as problem solving, student construction of multiple solution methods, and mathematical communication and defense of ideas. When aligning math assessments with a reformed curriculum, educators face the challenge of how to assess these distinct skills that students rarely use in isolation. Testing should attempt a more global assessment students interrelated uses of these skills. When revising assessments, educators should incorporate the latest research in math learning and education. A more in-depth and up-to-date understanding of the mathematical development of children would also benefit teachers in the classroom as they attempt to make shifts in instruction and gauge students’ understanding and progress.
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?
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Participants: Teachers, administrators and other staff in the McKinney, Texas school district. The participants included 37 teachers for grades 2-12, 11 principals and assistant principals and librarians in 8 schools. The district had used a curriculum-based rapid assessment system from StandardsMaster since 1999.
Method: Participants were interviewed individually for 50 minutes using a semi-structured interview protocol. Researchers conducted observations in 10 randomly selected classrooms and interviewed three to five randomly selected students from each classroom to assess quality of instruction.
Numeration and number
Data management and probability
Algebra and patterning
Teachers and consultants helped create and test field items for each cell in the matrix, resulting in 20
performance items. The rest of the test was made up of multiple-choice items to
Findings: While the matrix seemed to offer a simple solution, the problem was test items developed by educators had isolated these processes into discrete categories. For example, while communication was one of the cognitive areas the province wanted to measure in the assessment, it is difficult to measure communication apart from mathematical ideas.
A monograph from the Third International Mathematics and Science Study (TIMSS, 1996), warns that use of a process category-by-content-strand matrix, while it has a long history, generates such serious difficulties. Use of such a matrix states the TIMSS monograph, “failed to take into account the interrelatedness of content or of cognitive behaviors, and that this forces the description of information into unrealistically isolated segments.”
Many problems require all four processes at once: problem solving, calculating, understanding and communication. So rather than assessing one cognitive process at a time, each item should evaluate all processes, the researchers note. This would support the vision of mathematics as “problem-solving in action” as opposed to the view that it is that is “mechanistic and atomized”. The researchers stress the importance of incorporating the latest research on children’s mathematical learning in revising assessments, i.e., what do mathematical understanding and proficiency look like in Grade 3? Research could provide a more accurate description of what a child is capable of doing and help educators better assess progress.
From Assessment for Learning: 12 recent studies on formative assessment and aligning assessments with learning goals, published by Educational Research Newsletter August 2007