District Frameworks - Mathematics
Mathematics as Communication
Mathematics can be thought of as a language "because of its power to represent and communicate ideas concisely." (NCTM. 1989, p. 78) It is a language that is important for students to learn so they are able to make sense of mathematical situations and to communicate about these situations with others. Learning how to look at a real situation from a mathematical perspective, talk about the mathematics of the situation, translate the everyday language into mathematical symbols and notation in order to find a mathematical solution, and then interpret the solution in the context of the original situation is an important part of learning mathematics. Learning the language of mathematics develops gradually, and has to be continually connected to what students understand to make it meaningful.
Communication also is important in mathematics since it is a tool for learning. Students learn mathematics as they talk and write about what they are doing. Students become actively engaged in doing mathematics when they are asked to think about their ideas and talk with and listen to other students, sharing ideas, strategies, and solutions. Writing about mathematics helps students reflect on their work and clarify ideas for themselves. Writing also is a way for teachers to identify students' understandings and misconceptions.
Students also benefit from opportunities to learn to read mathematics-to read things written about content they already understand, and later to read in order to learn new content.
In grades K-4 the study of mathematics shall include numerous opportunities for communication so that students will:
- Relate physical materials, pictures, and diagrams to mathematical ideas;
- Reflect on and clarify their thinking about mathematical ideas and situations;
- Relate their everyday language to mathematical language and symbols;
- Realize that representing, discussion, reading, writing, and listening to mathematics are a vital part of learning and using mathematics.
In grades 5-8 the study of mathematics shall include opportunities to communicate so that students will:
- Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods;
- Reflect on and clarify their own thinking about mathematical ideas and situations;
- Develop common understandings of mathematical ideas, including the role of definitions;
- Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas;
- Discuss mathematical ideas and make conjectures and convincing arguments;
- Appreciate the value of mathematical notation and its role in the development of mathematical ideas.
In grades 9-12 the mathematics curriculum shall include the continued development of language and symbolism to communicate mathematical ideas so that all students will:
- Reflect upon and clarify their thinking about mathematical ideas and relationships;
- Formulate mathematical definitions and express generalizations discovered through investigations;
- Express mathematical ideas orally and in writing;
- Read written presentations of mathematics with understanding;
- Ask clarifying and extending questions related to mathematics they have read or heard about;
- Appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas.
ADULT BASIC EDUCATION
In the adult basic education classroom, curriculum design shall include approaches to teaching mathematics as communications which allow the learner to:
- Develop appropriate reading, writing, listening and speaking skills necessary for communicating mathematically in a variety of situations.
- Discuss with others, reflect and clarify their own thinking about mathematical outcomes, and make convincing arguments and decisions based on these experiences.
- Define everyday, work-related or test-related mathematical situations using concrete, pictorial, graphical or algebraic methods;
- Appreciate the value of mathematical language and notation in relation to mathematical ideas.