Making maths meaningful
Day 1 (May 4): Generalisation and Representation
This workshop focused on the following concepts:
Generalisation: Mathematics could provide the best context for developing the skill of making generalisations. Students must get opportunities to investigate numerical and geometric patterns; and express them mathematically in words or symbols. They should analyse the structure of the pattern, and how it grows (or changes); organise this information systematically; and use their analysis to develop generalisations about the mathematical relationships in the pattern.
Representation: This process emphasises the use of symbols, charts, graphs, manipulatives, and diagrams as powerful methods of expressing mathematical ideas and relationships. Students—as ways of communicating mathematical ideas to others—should understand symbolism in Mathematics, along with visual aids (such as charts and graphs). Moving from one representation to another is an important way to add depth of understanding to a newly formed idea.
Learning to record (or represent) thinking in an organised way (both in solving a problem and in sharing a solution) is an acquired skill for many students. As teachers, we must emphasise on the importance of representing mathematical ideas in a variety of ways.
Day 2 (June 29): Reasoning and Problem- Problem-solving
This workshop dealt with reasoning and problem-solving, which are processes that highlight logical thinking that helps us decide if and why our answers make sense.
Students need to develop the habit of providing a rationale as an integral part of every answer. It is also essential for them to learn the value of justifying ideas through logical arguments.
This process describes problem-solving as the vehicle through which students develop mathematical ideas.
Day 3 (August 9th): Connections and Communications
This workshop attempted to acquaint the participants with the importance of connections and communication. Connection: It has two parts: First, it is important to connect within—and among—mathematical ideas. Students need opportunities to see how, in a network of connected ideas, mathematical concepts build on one another. Second, Mathematics should be connected to the real world, and to other disciplines. Students should see that Mathematics plays a significant role in the arts, sciences, languages, etc. Communication: This process points to the importance of being able to talk about, write about, describe, and explain mathematical ideas. Learning to communicate in Mathematics fosters interaction and exploration of ideas in the classroom, as students learn through active discussions of their thinking. As teachers, we need to help our students acquire mathematical language to describe objects and relationships.