The information shared below is from the Ontario Mathematics Curriculum Grade 1 – 8, 2005.
Our core beliefs for mathematics:
- All students can achieve high standards given sufficient time and support
- All teachers can teach to high standards given the right conditions and assistance
- High expectations and early intervention are essential to success
- Helping students develop a fundamental understanding of mathematical concepts and a positive attitude towards mathematics will give them a foundation for life-long learning
- Families and members of their communities must be encouraged and supported in taking action to promote mathematical understanding with students
The Importance of Mathematics
The study of mathematics equips students with knowledge, skills, and habits of mind that are essential for successful and rewarding participation in society. To learn mathematics in a way that will serve them well throughout their lives, students need classroom experiences that
- help them develop mathematical understanding;
- learn important facts, skills, and procedures;
- develop the ability to apply the processes of mathematics; and
- acquire a positive attitude towards mathematics.
The Ontario Mathematics curriculum provides the framework needed to meet these goals.
Learning mathematics results in more than a mastery of basic skills. It provides students with a concise and powerful means of communicating reasoning, justifying conclusions, and expressing ideas clearly. Through mathematical activities that are practical and relevant to their lives, students develop mathematical understanding, problem-solving skills, and related technological skills that they can apply in their daily lives and, eventually, in the workplace. As students identify relationships between mathematical concepts and everyday situations and make connections between mathematics and other subjects, they develop the ability to use mathematics to extend and apply their knowledge in other curriculum areas, including science, music, and language.
What does Mathematics look like in the classroom?
Students are provided opportunities to learn in a variety of ways – individually, cooperatively, through direction instruction, hands-on experiences, and through examples followed by practice. In addition, mathematics requires students to learn concepts and procedures, acquire skills, and learn and apply mathematical processes. The strategies teachers employ will vary according to both the objective of the learning and the needs of the students.
Research and successful classroom practice have shown that an investigative approach, with an emphasis on learning through problem solving and reasoning, best enables students to develop the conceptual foundation they need. When planning mathematics programs, activities and assignments are provided that encourage students to search for patterns and relationships and engage in logical inquiry.
Manipulatives are necessary tools for supporting the effective learning of mathematics by all students. These concrete and virtual learning tools invite students to explore and represent abstract mathematical ideas in varied, concrete, tactile, and visually rich ways. Moreover, using a variety of manipulatives helps deepen and extend students’ understanding of mathematical concepts.
Fostering students’ communication skills is an important part of the mathematics classroom. Discussions provide students with the opportunity to ask questions, make conjectures, share and clarify ideas, suggest and compare strategies, and explain their reasoning. Students’ understanding is revealed through both oral communication and writing, but it is not necessary for all mathematics learning to involve a written communication component. Young students need opportunities to focus on their oral communication without the additional responsibility of writing.
Promoting Positive Attitudes Towards Mathematics
Students’ attitudes have a significant effect on how they approach problem solving and how well they succeed in mathematics. We can help students develop the confidence they need by demonstrating a positive disposition towards mathematics. Students need to understand that, for some mathematics problems, there may be several ways to arrive at the correct answer. They also need to believe that they are capable of finding solutions. It is common for people to think that if they cannot solve problems quickly and easily, they must be inadequate. However, problem solving of almost any kind often requires a considerable expenditure of time and energy and a good deal of perseverance. Once students have this understanding, we can encourage them to develop the willingness to persist, to investigate, to reason and explore alternative solutions, and to take the risks necessary to become successful problem solvers.