Getting better at going mental!
“Beauty in mathematics is seeing the truth without effort.”
George Pólya
When we have young people who are empowered into being able to make decisions about the strategies, skills and understanding they will use in order to solve a given problem, we have young people who demonstrate the command of some crucial components of numeracy. Exploring and applying mental computation strategies supports students in building, and demonstrating, number sense, strategic thinking, and an inherent understanding of the flexibility, properties and patterns that underpin important components of mathematics. In addition, number sense (including part-part-whole knowledge, composition of numbers, ordinality, cardinality, numeral identification and recognition, estimation, generalising, spatial sense, etc.), pattern sense and strategic thinking strongly support the development of skills in mental computation.
Mental computation is important. It is a portable skill that is useful in daily life. Moreover, being able to make strategic decisions and then solve problems without the aid of procedures, calculating or recording devices requires rich learning about how numbers, operations and mathematicians work. Mental computation promotes logical thinking, efficiency, number sense, ownership and creative and critical thinking.
It is important to remember that mental computation is not related to being provided with pages or lists of 'mentals'. Instead, mental computation often requires time to think and the need to combine a range of strategies. 'Fluency is often misinterpreted, with an over-emphasis on speed and memorisation.' (1.) There may not always be one 'most efficient' way to solve a problem and the knowledge, skills, understanding and confidence of students will impact to the choices available to each individual.
For learning in mental computation to be valuable, it needs to support students in developing a broad range of skills, knowledge and understanding, building a rich toolkit students can draw upon in a range of contexts. Teachers make choices about the pedagogies they choose to employ. Swan and Sparrow suggest
'The ten quick questions approach of mental recall produces panic, fear and anxiety in many children and reduces flexibility of thinking. An approach to teaching mental computation whereby children are taught specific strategies which are practiced may not cause as much anxiety but still may reduce flexibility in thinking as children attempt to apply the teacher’s strategy rather than their understood method. Developing mental strategies via discussion should help children gain more flexibility in their approach to solving problems and provide more insight into the properties of the number system. Children will also learn that there is more than one way to arrive at the solution to a problem.' (2).
The Australian Association of Mathematics Teachers (AAMT) argues that 'the importance of mental computation has been identified by a considerable body of research... Research also indicates that an emphasis on mental computation can improve student's development of number, while an early introduction to formal written methods can harm it.' (3).
Mental computation matters. So too do our choices.
'When we emphasise memorisation and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics. We have the research knowledge we need to change this and to enable all children to be powerful mathematics learners. Now is the time to use it.' (1)
Mental computation is important. It is a portable skill that is useful in daily life. Moreover, being able to make strategic decisions and then solve problems without the aid of procedures, calculating or recording devices requires rich learning about how numbers, operations and mathematicians work. Mental computation promotes logical thinking, efficiency, number sense, ownership and creative and critical thinking.
It is important to remember that mental computation is not related to being provided with pages or lists of 'mentals'. Instead, mental computation often requires time to think and the need to combine a range of strategies. 'Fluency is often misinterpreted, with an over-emphasis on speed and memorisation.' (1.) There may not always be one 'most efficient' way to solve a problem and the knowledge, skills, understanding and confidence of students will impact to the choices available to each individual.
For learning in mental computation to be valuable, it needs to support students in developing a broad range of skills, knowledge and understanding, building a rich toolkit students can draw upon in a range of contexts. Teachers make choices about the pedagogies they choose to employ. Swan and Sparrow suggest
'The ten quick questions approach of mental recall produces panic, fear and anxiety in many children and reduces flexibility of thinking. An approach to teaching mental computation whereby children are taught specific strategies which are practiced may not cause as much anxiety but still may reduce flexibility in thinking as children attempt to apply the teacher’s strategy rather than their understood method. Developing mental strategies via discussion should help children gain more flexibility in their approach to solving problems and provide more insight into the properties of the number system. Children will also learn that there is more than one way to arrive at the solution to a problem.' (2).
The Australian Association of Mathematics Teachers (AAMT) argues that 'the importance of mental computation has been identified by a considerable body of research... Research also indicates that an emphasis on mental computation can improve student's development of number, while an early introduction to formal written methods can harm it.' (3).
Mental computation matters. So too do our choices.
'When we emphasise memorisation and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics. We have the research knowledge we need to change this and to enable all children to be powerful mathematics learners. Now is the time to use it.' (1)
References:
1. https://news.stanford.edu/2015/01/29/math-learning-boaler-012915/
2. http://www.aamt.edu.au/content/download/21441/285094/file/tdt_MC_swan1.pdf
3. http://www.aamt.edu.au/Topdrawer/Mental-computation
1. https://news.stanford.edu/2015/01/29/math-learning-boaler-012915/
2. http://www.aamt.edu.au/content/download/21441/285094/file/tdt_MC_swan1.pdf
3. http://www.aamt.edu.au/Topdrawer/Mental-computation