Presenter Information

Phil Daro, University of California

Start Date

16-8-2010 1:00 PM

End Date

16-8-2010 2:15 PM


Standards sequence as well as express priority. On what basis? Learning trajectories sequence through empirical investigation and theory. The sequence, as far as it goes, has empirical validity, but only some sequences have been developed. Standards, in contrast, must choose what students need to learn as a matter of policy. This article will discuss issues of sequence, focus and coherence in mathematics standards from the perspective of the Common Core State Standards (CCSS) for Mathematics in the United States of America. Decisions about sequence in standards must balance the pull of three important dimensions of progression: cognitive development, mathematical coherence, and the pragmatics of instructional systems. Standards are written as though students in the class have learned approximately 100 per cent of preceding standards. This is wild fiction in any real classroom. This difference between the genre convention of ‘immaculate progression’ in standards and the wide distribution of student readiness in real classrooms is a dangerous difference to ignore. Each student arrives at the day’s lesson with his or her own mathematical biography, whatever the student learned on their personal trajectory through mathematics. A spectacular diversity of such personal learning trajectories (PLoTs) faces the teacher at the beginning of each lesson. There are two related manifolds in play during each lesson: the manifold of PLoTs (personal learning trajectories) in the classroom and the manifold of learning trajectories (LTs) that enable the learning of the mathematics being taught. As real as these trajectories may be, neither is in plain sight. What is in plain sight are standards, tests, textbooks and students. LTs are too complex and too conditional to serve directly as standards. Still, LTs point the way to optimal learning sequences and warn against hazards that could lead to sequence errors. Teachers and students need time within the lesson and across the unit to pull students from PLoTs along LTs to the SSTs. This requires standards to be within reach. The types of errors in the way standards might be sequenced are reviewed.

daro.pdf (766 kB)


Import Event to Google Calendar

Aug 16th, 1:00 PM Aug 16th, 2:15 PM

Standards, what's the difference? A view from inside the development of the Common Cord State Standards in the occasionally United States.