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Language is the Core for Mathematical Concepts
Rosemary Reuille Irons Early Childhood Mathematics Consultant Brisbane, Australia [email protected]
Wisconsin Mathematics Council 2013
R. Irons 2013
It is generally recommended that to improve mathematics education in the United States, more emphasis needs to be placed on conceptual understanding.
Desimore et al, 2005; Thompson 2008
Payne and Rathmell original model
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The Model enhanced by Irons and Irons
R. Irons 2013
Child's language
The everyday language that involves measurement mathematical ideas
Materials language The language that comes from using concrete and pictorial materials
Mathematical language
Symbol language
The language specific to mathematics concept
The symbol for the concept or abbreviated word
R. Irons 2013
R. Irons 2013
What is subtraction?
When we present situations involving subtraction, what language do we use?
Subtraction has a broad range of language.
What language do we need?
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Rosie needs 12 apples. She has picked 7 apples. How many more apples does she need?
Rosie had 12 apples in a bag. She took out 7 apples. How many apples are in the bag now?
Rosie has 12 red apples and 7 green apples. How many fewer green apples does she have?
R. Irons 2013
Take Away
Child’s language
Materials language
Mathematical language
Symbolic language
Unknown addend
Child’s language Materials language Mathematical language Symbolic language
Compare
Child’s language Materials language Mathematical language Symbolic language
R. Irons 2013
Common Core State Standard 1.AO.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Deep Conceptual Understanding – Language Ranging From Words to Symbols
Common Core State Standard 1.AO.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Common Core State Standard 1.AO.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Common Core State Standard 1.AO.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Common Core State Standard 1.AO.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
R. Irons 2013
Child’s language
8
Take Away
Child’s language
Unknown addend
Child’s language
Compare
Child’s language
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Materials language
Concrete – take away
8
What do students see? What becomes the focus?
take away 2
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R.Irons 2012
Materials language
Concrete/pictorial materials – take away
8 take away 2
R. Irons 2013
Materials language
Concrete/pictorial materials – take away
8 take away 2 cover up 2
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Materials language
Concrete/pictorial materials – take away
8
take out 2 8 cover up 2
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R.Irons 2012
Four cars in the carpark. How many more will drive in to make ten cars in the carpark?
R.Irons 2012
8
There are 8 altogether. How many are covered?
Materials language
Concrete/pictorial materials – unknown addend
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8 cover up 2 How much more is 8 than 2?
Materials language
Concrete/pictorial materials – compare
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