Mathematical Encounters

The Unschooled Mind

In his book, the Unschooled Mind, psychologist Howard Gardner talks about how students bring misconceptions to the study of mathematics, how they apply algorithms in rigid, non-connected ways, while at the same time adhering to a blind obedience to authority which leads to fragile knowledge. As a remedy, Gardner recommends “Christopherian encounters” (named after the explorer) which force students to reflect on the viability of the misconceptions that they hold. 

“In every student there is a five year olds unschooled mind struggling to get out and express itself.” – Howard Gardner

In this book, the author creates situations (“mathematical encounters”) where students reflect on the viability of the misconceptions that they hold through their interactions in the encounter. 

ChatGPT: Gardner suggests that children enter school with strong yet imperfect mathematical theories. However, rather than embracing and expanding upon these existing theories, schools according to Gursky (1991) often disregard them and introduce new ones. This approach fails to acknowledge that these theories can coexist within a child’s mind, even if they appear contradictory. While students may be able to regurgitate information taught in the classroom upon request, the flawed ideas they hold onto are not abandoned. Consequently, Gardner argues that when faced with new situations outside the school environment, students tend to revert back to the simplistic theories they held at the age of five. 

Case-in point-Stewart. We will start off by learning about Stewart, a student in one of the classes that the author  interacts with in an impromptu “math encounter.” The reader will clearly see the conundrum Stewart’s teacher will face in helping the Stewarts in her class.

ChatGPT: Let’s examine the case of Stewart as an illustrative example. Stewart is a student whom the author encounters during an impromptu “math encounter” in one of the classes. This encounter highlights the predicament that Stewart’s teacher will inevitably confront when attempting to assist students like Stewart in her class.

What follows is series of encounters that will help students to comprehend and then hopefully overcome the misconceptions or misunderstandings that they hold.