Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Defining Representation
 Introduction | Concrete Models | Written Representations | The Teacher's Role | Summary | Your Journal

Young children enter school with limited ability to express ideas in writing. With formal language instruction in the early grades, students begin to develop the ability to express themselves mathematically by using written words and symbols. However, young children enjoy drawing pictures regardless of their writing skills. They move naturally from the physical representations to written representations by drawing pictures of mathematical ideas. Young children often invent ways to represent mathematical actions. For example, look at the representation of a kindergarten student, who is working on the following problem:

 There were 12 flowers in my yard. I picked four flowers to give to my mother. How many flowers are left?

Can you follow the student's thinking? How is she representing the idea of subtraction? What understanding of subtraction does this representation illustrate?

The student represented the original 12 flowers with a drawing. By circling four flowers and drawing an arrow, she is representing separating these four from the original 12 flowers. Her solution of eight flowers is represented by the numeral 8 and a flower, and it is also represented in the eight remaining flowers of her original drawing.

As students progress through the early grades, they should continue to express their thinking with pictures and (by second grade) with verbal explanations to describe their pictorial representations.

The transition from pictures to more abstract mathematical symbols should be an integral part of students' representations, but it should not be forced on the students. For some students, the connection to numeric and operational symbols comes easily. Others take a longer time to use abstract symbols to represent their ideas. It is important to remember that the goal here is understanding of those symbols and not a rote manipulation of abstract symbols. Inventing strategies, using models and pictorial and symbolic representations, and explaining their ideas should be an essential part of young children's mathematics experience.

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