Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Defining Communication
 Introduction | Mathematical Communication in Young Children | Additional Strategies | The Teacher's Role | Summary | Your Journal

Developing Mathematical Language

In addition to non-verbal ways to communicate their mathematical ideas, children should use oral language to describe actions, numbers, and shapes in classroom mathematics activities. Students begin this process of developing mathematical language by describing their ideas in their own words -- often invented to fit the situation. Recall the boy in the video clip who first described the pattern block he was holding as "squarish," even though he was not supposed to tell the name of the piece. In his mind, "squarish" did not name the piece; he was describing the piece in his own words. This kind of invented language may occur in all mathematical topics and is an important stage in mathematical development.

The readiness of students to move from invented to standard vocabulary will vary greatly. Recall in the video that some of the students recognized that to be a fractional part, all of the pieces had to be the same size. Others had not made sense of that important concept yet.

Another aspect of oral language that should be considered is listening. By listening to one another and to the teacher, students can become aware of other perspectives and strategies. This is a critical developmental task for young children and will facilitate group work later. Students also begin to learn to ask questions of one another and of the teacher to help clarify and refine their understanding about a concept. In the Finding the Area of Dot-Paper Shapes activity, it was important for children to listen to the description of the pieces so that they could draw them. By listening to the teacher's questions and directions, students began to use the terminology in a natural way.

The Interplay of Written and Oral Language

In the early grades, students begin to learn written language. Drawing pictures and using simple words become significant ways for children to communicate in writing. Most children will use a combination of types of written and oral communication to express their mathematical ideas. As new concepts are introduced, appropriate mathematical vocabulary will also be introduced as part of the concept. Although students may not immediately master this new vocabulary, reinforcement from the teacher and other students, orally and in writing, will help students learn talk mathematically.

It is important for children to have a variety of opportunities to describe their written ideas orally so that they can clarify their understanding and the teacher can assess students' understanding. Working collaboratively also gives students opportunities to share their understanding with their peers through the use of oral language and written notations.

Note that in the Hidden Pattern Blocks activity, many students referred to the shapes by color rather than by name. The teacher's response included the appropriate names of the shapes -- triangle and hexagon. One way to reinforce new vocabulary is to add words to a "word wall" in the classroom. Adding new vocabulary to the word wall gives it a constant presence in the classroom. Children see the written word, use the word orally, and, when they are ready, copy and write the word when they are explaining their ideas in writing.

We need to make many decisions as we provide opportunities for young children to develop vocabulary. Students need a wide variety of experiences in order to have a deep understanding of the mathematical concept that is expressed in mathematical words.

Although we might think that adding color makes the shape more interesting, many young children will associate color as an attribute of the shape. In other words, if a triangle is green, children may develop the misconception that all green shapes are triangles.

Orientation of the shapes is another important decision. The triangles presented earlier do not all "point up." If all of the triangles in a youngster's experience point up, he or she might associate that characteristic with all triangles. It is also important to give students a variety of triangles with which to work so that they can begin to generalize the concept of "triangle" by the attributes of three sides and three angles.

Invented Symbols

Young children are not dependent on standard mathematical symbols to express their thinking in writing. Drawings and other representations can enable children to write their ideas long before they are introduced to the formal symbols of mathematics, as you can see in the example below:

Standard Symbols

When children are ready, we do want them to begin to use the standard symbols of mathematics. Numerals and operational signs (+ - x ÷ =) are all symbols that we would like to have children use by the end of second grade. However, while children are learning these mathematical "codes," it is important for us to understand that skillful use of these codes will come only after many experiences.

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