Our board is working on five specific student outcomes: Collaboration, Communication, Critical Thinking, Creativity, and Problem Solving.
These are considered skills that students will need to be successful, both in our system and upon graduating. These skills are not only specific ends in themselves, but ways to explore the math content.
Below is a starting point on what these skills might look like in mathematics. This references the three part math lesson extensively; some you may want to check out that page first.
Collaboration: sharing responsibility in pursuit of a common objective
Students collaborate throughout the various stages of a three-part lesson. During group analysis of the problem or task, they share knowledge and methods to solve the problem.
Later on, during the Consolidation phase, students assume collective responsibility for sharing and analyzing different approaches.
Communication: expressing and interpreting meaning through a variety of forms
We often default to written communication as the main (and sometimes the only) method for our students to demonstrate understanding of a concept, or mastery of a skill. Oral communication is critical to student learning, and should be used as a key tool for advancing mathematical knowledge in the classroom.
Teachers need to nurture a math talk learning community, and students should be expected to use oral communication at several critical points in a three part math lesson: during initial sharing of the Minds On activity, during group work, throughout the whole-class sharing of approaches and solutions, and to co-construct the learning goal at the end of the lesson.
Problem Solving: exploring a challenge for which a resolution is not obvious
This is a key component of a three part lesson. Students are asked to tackle problems or thinking tasks for which they have not previously explored clear solution methods, or had established procedures for solutions modelled.
Critical Thinking: using purposeful, analytical, reflective processes in various contexts
Students are thinking critically in mathematics when they analyze other solutions and methods, and defend their own answers in response to the questions of others. This ties heavily into the reasoning and proving math process in the Ontario curriculum.
Creativity: Developing a product, process or idea by integrating original thinking with existing knowledge
The key part of this outcome is integrating original thinking with existing knowledge. This should be required of students in any math class where the focus is not just on memorizing supplied procedures. It’s also an in tegral part of true problem solving – students take the knowledge and skills they have and apply it to new situations.
This parallels the role of creativity in the work of ‘professional’ mathematicians. They take their large knowledge base of mathematics and apply it to new issues in original ways. Eminent mathematicians have said that the only difference between the work of a creative mathematician and that of a student is that of degree.