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Mental Maths refers to doing calculations ‘in your head’ and involves much more than the recall of basic number facts. The content Descriptors of the Australian Curriculum shows a continuum of strategies, which students need to develop and extend from Foundation to Year 7. An extensive range of strategies enables students to develop a ‘Real Life Skill’, as 75% of the calculations adults carry out is done mentally.With an extensive range of strategies you can use them anywhere, anytime. You don’t need paper & pencil, calculators or your phone!
Confident, Positive & Empowered Learners
An extensive range of mental strategies ensures students are empowered, confident & positive about solving calculations in their head. Teachers need to plan a Mental Math Program that includes exploration, manipulation & explicit teaching of an extensive range of strategies. Teachers need to emphasise how answers are achieved not focus on speed or the correct answer alone. Rote learning, chanting, memorization & ‘Shoot Outs’ do not help students build a repertoire of mental strategies. These are methods to build automatic recall of number facts & consolidate understanding, but if this approach is the only one used in mental programs, students can develop severe maths anxiety, dis-empowerment, negative attitudes & even fear!
Teach, Describe & Share
Mental Maths lessons should involve teaching specific mental strategies. It should also include students describing their versions of events & sharing of ideas about the strategies. Class discussion is very important for sharing mental methods among all students. Consolidation & practise of strategies using quality games and activities help build fluency & automatic recall. Teaching strategies should centre around hands on exploration, discussion, explanation and practise. Be wary of showing students rules to remember & learn by rote (e.g. adding zeros) as they are generally forgotten & misused!
Place Value, Partitioning, & Relationships
Mental strategies are underpinned by Number Sense & Knowledge which directly influences the range of strategies accessible to students. Limited Number Sense & Knowledge results in fewer mental maths strategies & the over reliance on the same strategies for solving computation, e.g. using Counting On to solve everything! The range of key knowledge required is broader than the basic facts for addition, subtraction, multiplication and division. For a solid understanding & application of Mental Maths strategies students need to:
Know that Mental Strategies require use & knowledge of:
- Basic Number Facts
- Counting Sequences
- Place Value Structure
- The meanings of words and symbols
Know how to use Mental Processes to manipulate numbers for easier computation, including:
- Rounding and Compensating
- Splitting Numbers using Place Value, Partitioning and Rearranging the Parts
- Recording Operations on number lines
- Know about relationships between the operations
Mental Maths Strategies – Foundation to Year 6
Mental calculations should be automatic, fast & accurate. But to get to this stage involves countless opportunities to experiment, explore & manipulate multi-step processes. Mental maths is a multi-step, in the head, process, involving many fragments, bits & parts of information to hold, remember & come back to. The best mental strategies help us to hold onto the steps of the calculation in our head as we go along. And the best mental maths program involves explicit teaching, thinking about thinking (metacognition) & discussion of the best strategy for the job. Without this mental maths programs become a memory exercise & and just another procedure to remember. In short POINTLESS!
I have created a 22 page Teaching Resource to help you implement Australian Curriculum Mental Maths into your classroom it includes:
- Australian Curriculum Mental Strategies Content Descriptors & Achievement Standards from Foundation to Year 6
- Research & ‘Best Practice’ notes
- Mental Math Teachers Notes for Foundation – Year 6
- Foundation to Year 6 Mental Math Activities including: – Subitising, Counting on, Partitioning & Compatible Numbers, Rearranging the Parts, Commutative Property, Doubles & Near Doubles, Multiplication & Related Division Facts, Written Strategy & Algorithms