how to build learning progressions: formative assessment’s basic blueprints presentation 3
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How to Build Learning Progressions: Formative Assessment’s Basic Blueprints Presentation 3. Siobhán Leahy Dylan Wiliam. Learning hierarchies. Universal Addition before multiplication Natural (apparently) Multiplication before division Differentiation before integration Arbitrary - PowerPoint PPT PresentationTRANSCRIPT
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How to Build Learning Progressions:Formative Assessment’s Basic Blueprints
Presentation 3Siobhán LeahyDylan Wiliam
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Learning hierarchies
• Universal– Addition before multiplication
• Natural (apparently)– Multiplication before division– Differentiation before integration
• Arbitrary– Areas of triangles before areas of parallelograms
• Optional– The Romans before the Vikings
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Progression in early number skills• Denvir & Brown (1986a,b)• Learning hierarchies– Empirical basis: almost all
students demonstrating a skill must also demonstrate sub-ordinate skills
– Logical basis: there must be a clear theoretical rationale for why the sub-ordinate skills are required
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SMILE network
• 2000 individual tasks• Written as engaging
activities, and then ordered by levels
• Levels determined logically and empirically
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“A millionaire”
• Task on exchange rates and their inverses
• Originally placed at level 3 (average 11 year olds)
• Found to be too hard at that level, and moved up, and up, eventually ending up at level 6 (average 15 year olds)
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Why develop progressions locally?
• Learning progressions only make sense with respect to particular sequences of instructional materials
• Learning progressions are therefore inherently local• Learning progressions developed by state or national
experts are likely to be difficult to useand often just plain wrong
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Proposed process
• A group of teachers teaching the same grade– identifies one substantive skill or concept in the standards
for the grade they teach– identifies a pre-requisite skill or concept in the standards for
each of two preceding grades– identifies a skill or concept in the two following grades for
which the focal skill or concept is a pre-requisite.– generates, for each of the five elements, six test items, with
each item at one grade intended to be more difficult than each of the items for earlier grades
– administers the test to their own students
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Raw student data
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Sort students by raw score…
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…highlight items by grade…
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… sort items by difficulty…
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…add student and problem curves…
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…and highlight non-scaling items…
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…and non-scaling students
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Focus for teachers’ discussion
• Two kinds of misfit– Items too hard or easy for the concept– Items do not scale (e.g., high-scorers fail to get easy items)
• Possible reasons– Unrelated to the progression– The progression is wrong– The item is ambiguous– Confusing or incomplete instruction
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What next?
• If everything’s OK– improved feedback to students
• More likely, improve:– Items– allocation of items to grades– curricular sequencing– Instruction– feedback to students