Arbitrary and Necessary

  

Arbitrary and Necessary

 

 

In Dave Hewitt's piece "Arbitrary and Necessary," he distinguishes between two aspects of the mathematics curriculum: those that are "arbitrary" and those that are "necessary." The "arbitrary" refers to conventions and labels, such as naming shapes or defining the order of coordinates, which have been socially agreed upon but could have been different. These are facts that students need to memorize, as they cannot be derived through experience. On the other hand, "necessary" knowledge refers to concepts that can be deduced through reasoning, such as the relationships between angles in geometric figures, which students can discover independently with the right tasks or guidance.

As a mathematics teacher, this perspective encourages me to differentiate between content that students must simply memorize versus content that they can actively explore and discover for themselves. For "arbitrary" elements, I need to ensure that my students understand the importance of these conventions for communication and problem-solving within the mathematical community, but also help them see these conventions as choices that could have been different. For "necessary" content, my focus should be on guiding students to build awareness and understanding through exploration, rather than simply providing them with facts to memorize. This means creating learning experiences that help students connect with the underlying principles and relationships in mathematics, fostering their ability to reason and understand rather than rely solely on rote learning.