Page 32 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

SOME CONSIDERATIONS FOR PROGRAM PLANNING IN MATHEMATICS
Teachers who are planning a program in mathematics must take into account considera- tions in a number of important areas, including those discussed below.
INSTRUCTIONAL APPROACHES
To make new learning more accessible to students, teachers build new learning upon the knowledge and skills students have acquired in previous years – in other words, they help activate prior knowledge. It is important to assess where students are in their mathe- matical growth and to bring them forward in their learning.
In order to apply their knowledge effectively and to continue to learn, students must have a solid conceptual foundation in mathematics. Successful classroom practices engage students in activities that require higher-order thinking, with an emphasis on problem solving.6 Learning experienced in the primary, junior, and intermediate divisions should have provided students with a good grounding in the investigative approach to learning new mathematical concepts, including inquiry models of problem solving, and this approach continues to be important in the senior mathematics program.
Students in a mathematics class typically demonstrate diversity in the ways they learn best. It is important, therefore, that students have opportunities to learn in a variety of ways – individually, cooperatively, independently, with teacher direction, through invest- igation involving hands-on experience, and through examples followed by practice. In mathematics, students are required to learn concepts, acquire procedures and skills, and apply processes with the aid of the instructional and learning strategies best suited to the particular type of learning.
6. See the resource document Targeted Implementation & Planning Supports for Revised Mathematics (TIPS4RM): Grade 7, 8, 9 Applied and 10 Applied (Toronto: Queen’s Printer for Ontario, 2005) for helpful information about problem solving.