Response to arbitrary and necessary knowledge

Hewitt’s article highlights crucial distinctions between arbitrary and necessary knowledge and explores their subtle differences in how students acquire these concepts.

This reminds me of Building Thinking Classrooms, a book I’ve been reading. The first chapter serves as a guide for integrating non-curricular activities before starting a new lesson. These activities typically involve complex, thought-provoking, and highly engaging questions. Students draw on their prior knowledge, experiment with it, adapt it in new ways, and engage creatively with their existing mathematical skills. I find this process highly constructive for developing necessary knowledge, as students become active participants in their own learning, fostering a proactive and exploratory mindset.

After such activities, teachers can introduce a new lesson where arbitrary knowledge is taught. Because students are already in an intellectually active state, they are more receptive to learning and retaining arbitrary knowledge. They can better establish connections, create mental maps, and apply personalized methods to internalize the material more effectively. This sequence of active engagement followed by direct instruction supports a balanced learning experience, combining discovery and structured teaching to deepen understanding and retention.