Archive of ‘Maths’ category

Maths Misconceptions

Maths PD

Needs to focus on efficient planning and programming strategies
Clear indicators of learning progression
Identifiable evidence of learning – depth of understanding
Meet needs of learners and teachers

4 key principles of Maths PD
1. Identify what is the mathematics that needs to be improved
– the number skills
– strategies
– relationship between concepts – How can I use strategies?

2. Broad range of teaching strategies and learning activities – social constructivist framework to ensure positive disposition toward mathematics
3. Assessment informs practice
4. Teacher Reflection – what worked, what does student learning highlight, misconceptions evident, successful strategies, what needs to be changed

Baseline data determined by prior knowledge activities. Be clear about what you want to find out. Clear purpose for the learner too. For example to find out a student’s understanding of fractions, proportional reasoning use different number lines. “Put 5 numbers along the following number lines, without using decimals.”


Decide what it is we want to improve.
– fluency – Quicksmart, intervention program,
Skoolbo, practice for all
Multiplication facts
‘Secret Code’ strategies for efficient mental computation
– more students in higher bands
Develop problem solving skills
Depth of understanding
Recognises patterns and makes generalisations
To develop Proficiencies (refer to verbs) as well as conceptual understanding choose a chunk of mathematics eg. Fractions

Collection model
Partition model
Comparative model

Relationship to decimals

Steps forward
1. Identify needs through analysis of PAT maths and NAPLAN data. Aspects of mathematics.
2. Prior knowledge activities to establish where understandings are, and identify misconceptions. (Place value, fractions, decimals in years 3-7. Number skills and strategies Secret Code in R-2, as well as practical problem solving in areas of measurement, data collection, and student initiated investigations.)
3. Explore concept, identify how conceptual understanding develops.
4. Provide a range of teaching strategies and learning opportunities for teachers to implement at different levels.
5. Analyse work samples, processes used, observations and reflect on successes and aspects that need to be changed. “How do these inform future teaching/ learning?”

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Reflection on an article – Ann Baker Workshop Preparation

Learning to Think: An American Third Grader Discovers Mathematics in Holland

By Eve Torrence
This article emphasises the importance of allowing students to discover for themselves efficient computation methods and problem solving strategies.
Teaching points:

  • provide realistic problems to solve that students can relate to
  • provide opportunities for students to share their strategies ( so they can learn from each other and adopt strategies)- over time accumulate a collection of flexible problem solving strategies
  • “guided reinvention” – a constructivist approach
  • ¬†informal methods encourage personal approaches which make more sense to the student – rather than an algorithmic approach which may result in inflexibility
  • memorisation of multiplication facts doesn’t encourage flexible thinking
  • encourage students to use easier multiplication facts as landmarks from which to derive more difficult facts
  • learning through understanding is an approach that students must be encouraged to use very early
  • focus on developing mathematical fluency and flexibility and this can reignite their interest in and enjoyment of mathematics as a creative and pleasurable activity
  • understanding is what matters the most…“because learning mathematics is all about learning to think.”

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