A leading American expert in mathematics education told delegates to the ACER annual conference that curriculum standards set for students are written as an  ‘immaculate progression’ but in reality students arrive each day with a spectacular variety of mathematical biographies.

Philip Daro, one of three leading the writing of Common Core State Standards (CCSS) in Mathematics in the United States argued that more consideration must be given to the diversity among students.

Mr Daro was visiting Australia to deliver a keynote address to the ACER annual conference. He said that each state in the U.S. has had its own standards until now. The CCSS have been adopted by over 30 states.

Mr Daro argued that the process of developing curriculum content standards for school mathematics is complicated by the fact that they need simultaneously to take account of:

• research evidence about the nature of mathematics learning, and in particular, the sequence in which students typically develop mathematical understandings;
• policy decisions about the mathematics that all students should be learning as a matter of priority; and
• the ‘spectacular diversity’ of students’ levels of mathematics achievement in any given year of school.

“If curriculum content standards do not take all three of these factors into account, then they can be seriously at odds with what happens in classrooms,” Mr Daro said.

“For example, some standards fail to recognise the great diversity in students’ levels of mathematics achievement in any given year of school.  They are written as though students have learned everything (100%) in the standards for the preceding grades.

“This assumption of an ‘immaculate progression,’ is a wild fiction in any real classroom.”

According to Mr Daro, teachers need tools that illuminate rather than obscure the varying individual learning trajectories that students are on.

Rather than portraying where students ‘can’ or ‘should’ be at a given point in time, standards should ‘map’ stations through which students are led in their mathematics learning, from wherever they start.

Philip Daro was a member of the lead writing team for the Common Core State Standards in Mathematics. He has directed, advised and consulted to a range of mathematics education projects.

Mr Daro’s conference paper, Standards, what's the difference? A view from indisde the development of the Common Cord State Standards in the occasionally United States, and presentation slides are available from the ACER research repository.

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