Teaching Mathematics in Primary Schools 2nd Edition

Operational Sense

Developing a sense of operations is a key component of number study. Students learn the four operations and their relationships with the other operations in order to develop this sense. The focus of the book is on developing understandings (as opposed to doing mathematics), in this case operational sense.

MAB Addition | MAB Subtraction | Empty Number Line

 

MAB Addition

MABs or Dienes blocks are commonly used for teaching number and operations. They are perhaps the most common tool used by teachers for these concepts. The blocks are used to represent place value and the recursive nature of the base 10 number system – you get ten of a particular unit and then trade it for one of the subsequent unit (ie 10 ones are traded for 1 ten; 10 tens are traded for 1 hundred). The important aspect of teaching using this resource is that the meaning is not implicit in the blocks but rather the teaching needs to make this explicit. In some cases students do not understand the link between the blocks, the actions and the words – the merely move the blocks as directed by the teaching without making the connections with the trading and the addition process. The language used when using the blocks is also important as teaching needs to make the links between the concrete representations of the blocks, the symbolic form as recorded with the use of numbers and the language being used.

Addition without trading or regrouping:

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Addition with trading or regrouping:

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MAB Subtraction

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Empty Number Line

The empty number is an innovation arising from the reforms in The Netherlands and challenges most of the thinking about place value and operations that dominate most Western curriculum. The empty number encourages the development of students' intuitive understandings of number and operational sense. Students are able to work at a level that suits their current understandings with the teacher assuming a role of bringing their thinking forward until it resembles more powerful forms of mathematical thinking. The empty number line is a flexible tool that is used in ways that resemble student's own thinking processes. Using the empty number line allows an intuitive understanding of number and place value to be developed before formal study has been introduced.

Subtraction is not taught in the same way as most Western curriculum document but the commutative principle is a dominant feature – which supports the development of number and operational sense. Rather than see addition and subtraction as relatively discrete operations, the Dutch program sees them as mutualistic concepts so that subtraction is seen more in terms of missing addends – e.g. "34-27" is more likely to be read as "What do I need to add to 27 to make 34?"

An understanding of basic number facts is extended to the 100s through this model.

Empty Number Line: Addition

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Empty Number Line: Subtraction

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Teaching Mathematics in primary Schools 2nd edition