Page 24 - Math 9-10 (2009)

23
Some Considerations for Program Planning in Mathematics
Teachers who are planning a program in mathematics must take into account considerations in a number of important areas, including those discussed below.
Teaching Approaches
To make new learning more accessible to students, teachers draw 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 mathematical 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 involve students in activities that require higher-order thinking, with an emphasis on problem solving. Students who have completed the elementary program should have a good grounding in the investiga- tive approach to learning new concepts, including the inquiry model of problem solving,4 and this approach is still fundamental in the Grade 9 and 10 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 – individu- ally, cooperatively, independently, with teacher direction, through hands-on experience, through examples followed by practice. In mathematics, students are required to learn con- cepts, procedures, and processes and to acquire skills, and they become competent in these var- ious areas with the aid of the instructional and learning strategies best suited to the particular type of learning. The approaches and strategies used in the classroom to help students meet the expectations of this curriculum will vary according to the object of the learning and the needs of the students.
Even at the secondary level, manipulatives are necessary tools for supporting the effective learning of mathematics. These concrete learning tools invite students to explore and represent abstract mathematical ideas in varied, concrete, tactile, and visually rich ways. Manipulatives are also a valuable aid to teachers. By analysing students’ concrete representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into stu- dents’ thinking and provide supports to help enhance their thinking.5
All learning, especially new learning, should be embedded in well-chosen contexts for learn- ing – that is, contexts that are broad enough to allow students to investigate initial understand- ings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas” of mathematics – that is, the major underlying principles, such as pattern or relationship. This understanding of key principles will enable and encourage students to use mathematical reasoning throughout their lives.
4. See the resource document Targeted Implementation & Planning Supports (TIPS): Grade 7, 8, and 9 Applied Mathematics (Toronto: Queen’s Printer for Ontario, 2003) for helpful information about the inquiry method of problem solving. 5. A list of manipulatives appropriate for use in intermediate and senior mathematics classrooms is provided in Leading Math Success, pages 48–49.