Teachers and students experienced some difficulty unpacking these terms as they are not typically used in math classrooms.Making clear to students what the process of critical thinking involves is difficult if it is not clearly understood.In order to provide a consistent and full analysis of the equations, students had to discuss all aspects of each one.
It also invites students to collaborate with each other, to share ideas, and make mathematical decisions.
This focus on mathematical decision making naturally requires students to consider many different options—ways of doing math, using tools, and solution methods—allowing students at varying levels of understanding an opportunity to immediately participate and feel safe and confident in sharing their ideas.
More recently, however, I have attended TC² professional development opportunities that have been focused on math including sessions sponsored by the Ontario Teachers’ Federation, online webinars and a summer institute all delivered by Laura Gini-Newman on Sustaining Inquiry.
These have helped me delve deeper into how to implement a critical inquiry approach to learning in math in a sustained way that nurtured a growth mindset in students.
For example, qualifiers (or key words used to determine criteria) such as are often used to explicitly invite students to make mathematical judgments or decisions.
Qualifiers encourage students to think about the quality of their responses and to justify them, not to think only about whether they have arrived at the correct response.
This led to more thorough analyses requiring students to think about what they already knew and understood to be mathematically true (accurate math knowledge) about each equation, and all the mathematical details (evidence) given in each equation—two basic considerations that underpin all sound mathematical reasoning.
Implementing critical inquiry in the classroom initially generated a sense of discomfort for teachers in my department, myself included.
In many cases students who are typically hesitant to contribute to class discussions are now able to have a voice amongst their peers as they work through thinking tasks.
This includes students with weaker background knowledge as well as students who are proficient but lack the confidence to participate in regular open class discussions.