Mathematics & Mental Architecture
In his 2017 book Robot-Proof: Higher Education in the Age of Artificial Intelligence, the President of Northeastern University in Boston, Joseph E. Aoun outlined how higher education is changing to reflect the demands of our increasingly automated economy. He wrote that students need the cognitive capacities to tackle problems that may not have even emerged yet. Students need to develop mindsets over bodies of knowledge - what Aoun called mental architecture instead of mental furniture for this capacity building to occur. For Aoun, mental architecture is beyond rote learning and is exemplified by intellectual flexibility and creativity so that students learn to think differently than machines.
The need for conceptual learning is, perhaps, most needed in mathematics. To differentiate themselves from machines, students need to understand underlying mathematical principles so that they can be critical of machine output, make a wide array of applications, and understand why math problems are approached in certain ways to provide a deep appreciation of the discipline on a level not yet achieved by artificial intelligence. At Holy Name of Mary College School, we take this approach to mathematics education seriously, exemplified by incorporating parts of Peter Liljedahl's work out of Simon Fraser University in Vancouver. Liljedahl argues for “thinking classrooms” in mathematics education and in the November 2023 edition of HNMCS' Stargazer we introduced the “thinking classroom” to our community. Much of Liljedahl’s math-specific work echoes what Aoun champions more generally to prepare students for the world they live in today. To maximize the necessary effects of “thinking classrooms” students need to transform how they feel about mathematics and their ability to be successful at it. In other words, students need a strong sense of self-efficacy if they are to learn mathematics the way today’s world demands.
Our math teachers bring intentionality to changing the way our students perceive mathematics. For example, in both Grade 11 Functions and Grade 12 Calculus and Vectors, teachers regularly have students practice their skills on vertical non-permanent surfaces (whiteboards). This reduces the students’ fear of making mistakes and increases their desire to contribute to class discussions. Moreover, it mitigates their sense of anonymity in class and has them feeling engaged and part of their own learning. The students also work in small groups or in pairs when practicing their math skills so that they can learn from each other, which fosters a sense of inclusion. All of this builds a student’s confidence in mathematics.
In Grade 10 mathematics and in Grade 12 Advanced Functions, students are encouraged to build their independence and self-sufficiency as learners - much needed in a post-secondary environment. All lessons are posted on the learning management system and students can get caught up on any content they missed, which develops mindsets to succeed at independent tasks and time management. By incorporating the latest technology in lesson delivery, students learn using interfaces with which they’re already familiar, bringing a sense of comfort and safety to the learning environment. The most important concepts are prioritized, which provides them with the foundational knowledge to confidently use mathematics in creative and advanced ways.
In Grade 9, students are provided with open-ended problems that require them to think critically and approach solutions using multiple strategies. One example had students employ generative artificial intelligence to outline different ways to understand proportions in the real world. Students engage in collaborative problem solving, learn from and with peers through peer presentations and group work assignments, and apply their learning to real world applications. All of this gives students a sense that they are interacting with mathematics instead of having it imposed on them, which reassures them of their mathematical abilities.
By incorporating many of the principles inculcated by Peter Liljedahl to get students thinking differently about mathematics so they can better embrace it, the faculty at HNMCS purposefully help students build the mental architecture necessary to succeed in today’s post-secondary world and beyond.
- Mr. Ryan Baker, Interim School Leader & Director of Academics
