Page 17 - Math 9-10 (2009)

16 THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS
In addition, making connections between the mathematics they study and its applications in their everyday lives helps students see the usefulness and relevance of mathematics beyond the classroom.
Representing
In secondary school mathematics, representing mathematical ideas and modelling situations generally takes the form of numeric, geometric, graphical, algebraic, pictorial, and concrete representation, as well as representation using dynamic software. Students should be able to go from one representation to another, recognize the connections between representations, and use the different representations appropriately and as needed to solve problems. Learning the various forms of representation helps students to understand mathematical concepts and rela- tionships; communicate their thinking, arguments, and understandings; recognize connections among related mathematical concepts; and use mathematics to model and interpret mathemat- ical, physical, and social phenomena. When students are able to represent concepts in various ways, they develop flexibility in their thinking about those concepts. They are not inclined to perceive any single representation as “the math”; rather, they understand that it is just one of many representations that help them understand a concept.
Communicating
Communication is the process of expressing mathematical ideas and understandings orally, visually, and in writing, using numbers, symbols, pictures, graphs, diagrams, and words. Students communicate for various purposes and for different audiences, such as the teacher, a peer, a group of students, or the whole class. Communication is an essential process in learning mathematics. Through communication, students are able to reflect upon and to clarify ideas, relationships, and mathematical arguments.
The development of mathematical language and symbolism fosters students’ communication skills. Teachers need to be aware of the various opportunities that exist in the classroom for helping students to communicate. For example, teachers can:
• modelproperuseofsymbols,vocabulary,andnotationsinoralandwrittenform;
• expect correct use of mathematical symbols and conventions in student work;
• ensure that students are exposed to and use new mathematical vocabulary as it is introduced (e.g., by means of a word wall; by providing opportunities to read, question, and discuss);
• provide feedback to students on their use of terminology and conventions;
• ask clarifying and extending questions and encourage students to ask themselves similar kinds of questions;
• ask students open-ended questions relating to specific topics or information;
• model ways in which various kinds of questions can be answered.
Effective classroom communication requires a supportive and respectful environment that makes all members of the class comfortable when they speak and when they question, react to, and elaborate on the statements of their classmates and the teacher.
The ability to provide effective explanations, and the understanding and application of correct mathematical notation in the development and presentation of mathematical ideas and solu- tions, are key aspects of effective communication in mathematics.