The Learning Assessment Framework for Multiplicative Thinking
http://www.education.vic.gov.au/Documents/school/teachers/teachingresources/discipline/maths/assessment/lafcomparativ.pdf
Scaffolding Numeracy in the Middle Years
http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/learnassess.aspx
Common Misunderstandings – Multiplicative Thinking
http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/learnassess.aspx
Newman’s Error Analysis – You will need to log in to PAT Teaching Resources (email as user name)
https://oars.acer.edu.au/norwood-primary-school Then go to Teacher Resources
Multiplication and Division – Maths Assessment Project
http://map.mathshell.org/download.php?fileid=1592
Multiplicative Thinking Tasks
https://aare.edu.au/data/publications/2006/sie06375.pdf
Our learning progression brainstorm (using Multiplicative Thinking article):
Content:
- counting and splitting
- skip counting
- large collections
- repeated addition (2s, 5s, etc.)
- repeated subtraction
- hold both numbers in head – number of objects within each group and number of groups
- hold both numbers and the total
- visualise 3×4, 4×3 move from additive to multiplicative strategies
- factors, product – arrays
- multiplication and division – commutative, inverse relations
- language develops – for each, times, as many
- symbolic representation, diagrams
Implications for teaching/ learning
Pedagogy:
- Developing opportunities for students to use effective strategies – arrays
- Challenge to show different ways
- Communicate – in different ways
- Explicit role modelling
- Language used by students – allow opportunities for talk, and for listening in to hear their language (gaining insight into their thinking)
- Variety of representations – words, pictures, symbols
- Moving from familiar to unfamiliar contexts
- Questioning and enabling prompts
- Allow opportunities for collaboration
- Think boards
- Visualisation – drawing how they see the problem
