Mathematical Modelling in the Primary School: Exemplifying the Core Components of the Singapore Mathematics Curriculum Framework
- content vs process
- Mathematical problem-solving - mainly the Initiate, Respond, Evaluate (IRE) teaching approach; however what is left out in this teaching approach is the domain of attitudes, processes and metacognition
- Despite students are able to use mathematical model, teachers need a variety of living example of implementation (Black & Williams)
- Students develop models (conceptual representation)
Features
* benefit of using authentic problem
* multifaceted end products
- working towards Mathematical literacy: an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe and explain
Model Eliciting Task - mathematising real-world problems
Implications on Teacher Development
- striking a balance: questioning and listening
- deliberate choice to move away from her routine prescriptive approach so as to encourage more student-directed inquiry, teacher need to apply metacognitive strategies during facilitation
- foster the setting of assumption
- independent modelling experience may be necessary for teachers to apply the framework more rigourously
- modelling tasks require teachers' explicitly offline and online interventions through task design, lesson planning and strategic scaffolding
- PBL (more ill-structured) vs Mathematical Modelling
- independent modelling experience may be necessary for teachers to apply the framework more rigourously
- modelling tasks require teachers' explicitly offline and online interventions through task design, lesson planning and strategic scaffolding
- PBL (more ill-structured) vs Mathematical Modelling
Discussant
- Model as content - the needs for the problem solving
- Model as vehicle - means to an end
- pre-requisite: thorough familiarity with problem context, either existing or through reading (eg. web-based research) or other activity (site visits) and knowledge of relevant mathematics on which to draw: can be different at different levels
- excellent teaching strategies - Resource Kit Challenge is when and how to use them
- students difficulty in articulating thinking processes
- students reluctant/unable to adequately set down their ideas on paper to provide a proper basis for reflection
- tendency to focus too narrowly within potentially
- tendency to jump to conclusions - ahead of modelling
- getting the balance right: problem needs
- meta-metacognitive issues in teacher-student dialogue
Six Roles of Diagram
* scaffolds the complete modelling process - both problem specific and generic
* create structured spaces for student input
* reduces information processing (cognitive) load on working memory
* provides information to teacher - specific student/group
* provides basis for metacognitive activity/prompting
* the box headings are useful for structuring a report
Final thoughts
* Learning new mathemtics is different business from learning to apply existing mathematics (although there can be cross fertislisation)
* teaching and learning modelling
Keynote 5
Teaching for Thinking: How can we Support a Thinking Pedagogy by Linda Darling-Hammond
Strategies to support professional learning
- modelling of well-scaffolded, choice-based, authentic learning opportunities
- collaborative curriculum and assessment development
- lesson study and action research
- case studies of students' learning
- shadowing students through their learning experiences
Webb's Depth of Knowledge Scale
Assessment should support a thinking pedagogy
- as models of good instruction
- as an exemplars of quality work
Accountability should support learning
- intelligent accountability should be design to support learning
"What the best and wisest parent wants for his own child, that must the community want for all of its children. Any other ideal for our schools is narrow and unlovely; acted upon it destroys our democracy."
Keynote 5
Teaching for Thinking: How can we Support a Thinking Pedagogy by Linda Darling-Hammond
Strategies to support professional learning
- modelling of well-scaffolded, choice-based, authentic learning opportunities
- collaborative curriculum and assessment development
- lesson study and action research
- case studies of students' learning
- shadowing students through their learning experiences
Webb's Depth of Knowledge Scale
Assessment should support a thinking pedagogy
- as models of good instruction
- as an exemplars of quality work
Accountability should support learning
- intelligent accountability should be design to support learning
"What the best and wisest parent wants for his own child, that must the community want for all of its children. Any other ideal for our schools is narrow and unlovely; acted upon it destroys our democracy."
-John Dewey
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