Planning for effective teaching

'Planning for effective teaching and learning involves designing a flexible sequence of learning activities, and being clear about the concepts students will be developing in each activity to reach the desired goal of relational understanding.'

(Skemp, 1976)

Planning should involve:

• starting with familiar contexts, concrete materials and prior knowledge, and moving to generalisations and abstract ideas (and back and forth between these as needed)
• using rich mathematical and statistical tasks
• responding to student diversity and prior knowledge
• using a variety of effective teaching strategies
• making transitions between increasingly abstract representations
• giving students opportunities to confront their misconceptions
• selecting activities that prompt students to link verbal thinking and visual imaging to the concepts being learned
• scaffolding students’ reasoning
• using learning materials to focus student attention on key concepts.

Specific activities

• Informal inference – Planning a statistical sequence of activities for students to understand concepts such as population, sample and sampling variability in order to make an inference when comparing two groups. The sequence starts with a population of data cards. Students take and compare samples and are scaffolded to develop their own decision rules for making inferences about populations from samples.
• Kiwi Kapers – Starting with a population of kiwis, students develop concepts of sample, sampling variability and population.
• Engaging in proofs, for example, the square of an odd number is odd – investigate patterns, progressing from counters/ arrays through to more abstract diagrams and hence to algebraic generalisation.
• Activity: Skid marks
• Activity: Linking integration and differentiation
• Activity: I am just not fast enough

Further information

• Skemp, R. (1976) Instrumental Understanding and Relational Understanding Mathematics Teaching, 77, 20–26. Retrieved from http://www.skemp.org.uk/ [click on papers].
• CensusAtSchool – Informal inference
• Pedagogy and personalisation – UK
• Example of UK secondary lesson plans

Last updated September 26, 2012

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