Classifying quadrilaterals is one of those skills that adults love to make fun of with those, ‘I didn’t learn anything useful, but I learned the difference between a rhombus and a trapezoid.’ jokes that teachers hate. The thing is, when students learn to categorize and classify quadrilaterals, that’s not all they are learning. They are learning an entire way of thinking that is fundamental to making sense of the world and understanding its nature. It’s not just about trapezoids. It’s about:
-identifying on which attributes to focus and which to ignore. Anyone who’s heard a recent political argument where the opposing side focuses on minor details can see why we need this.
-finding the defining common attributes.
We use this to simplify our overwhelming world. Think of all the variations of drinks that could be called ‘coffee.’ If we stop to define each of them every morning, we’d never get to work.
-comparing and contrasting attributes.We use this all the time in decision making. Why is one choice better than the other? What properties do they have in common? Which are different?
-looking at overlapping groups.It’s through classifying quadrilaterals that we learn the ‘all squares are rectangles, but not all rectangles are squares’ concept. Very young children will overgeneralize and call anything fluffy a ‘dog.’ As they become more and more refined at classifying things, they start to realize that this one is a Labrador, but it’s still a dog, and this one is a bear, which is not a dog at all. They learn that dogs and bears are both part of a larger group called ‘mammals.’ This is a big step for developing minds. Seeing how categories fit together an overlap helps students make sense of what is otherwise chaos. It helps them see where the commonalities lie and what separates them.
-understanding the idea of ‘mutually exclusive’ groups.This concept that, if something is in one group, it cannot possibly be in another group is crucial for making sense of the world. Students learn that by classifying quadrilaterals. They learn that trapezoids and squares are mutually exclusive groups, and that a shape cannot possibly be in both categories. It’s the opposing concept to the ‘all squares are rectangles’ concept.
Teachers know the importance of these skills, even if meme-makers and drunk uncles don’t. That’s why preschool teachers let students sort objects. They sort them by size, color, shape, etc. It’s the concrete beginning of being able to classify things (and later ideas) by specific property. As students grow, they begin to sort letters and numbers, capitals and lowercase, and eventually different fonts and scripts. But sorting and classifying is the basis for being able to do this fluently and become literate. It’s also one reason why I teach geometry at the beginning of the school year.
We adults use these classifying skills all the time without even realizing it. When you walk into a grocery store, you know where to find spinach, because it’s a vegetable and falls under ‘produce.’ Yes, it’s also green, but that’s not the defining attribute because grocery stores are not organized by color. On a more complex level, we use the same set of skills to organize the natural world. Scientists categorize plants and animals based on common characteristics. We need these classification skills to navigate the everyday world. And we can develop them through sorting and classifying quadrilaterals.
Happy Teaching (& Classifying Quadrilaterals)!!