Concrete Experience: The teacher will provide the children with manipulatives (hands-on materials) that are related to the mathematical concept being taught. Students will be able to model the discovery and understanding of the concept with these materials. An example is using base-ten blocks on a place-value chart in order to model what re-grouping is in subtraction and why it occurs.
Pictorial Representations: The students will be able to represent their conceptual understanding in mathematics with symbols and/or pictorial representations in order to display their understanding of the material. This usually includes drawings or virtual manipulatives to describe what is taking place. For example, after the child displays mastery of the concept of regrouping in subtraction with concrete base-ten blocks, he or she may draw representations of these blocks and cross out the pictures of the blocks to show the place-value being taken away and drawing the lower place value to show the re-distribution of the quantity.
Abstract Representations: The teacher will provide opportunities for children to display their mastery of traditional procedures and fluency in mathematical computation. This may be displayed in a variety of algorithms including the traditional algorithm.