What are suggestions for patterns in daily lives that deal with mathematics?

My answer to a question on Quora: What are suggestions for patterns in daily lives that deal with mathematics?

The first thing that comes to mind is the most mundane: numbering, first of all, house numbers on streets in towns and cities. They make quite an impression on a 4 years old child when first explained to her:

  • house numbers are odd on one side and even on another;
  • they grow in one direction;
  • if look in the direction of increase of numbers, then odd numbers are on the left hand side of the street, even are on the right hand side.

It is useful to bring child’s attention to street signs with street names on them, as well as shops’, cafe’s, barbers’, hairdressers’ signs: in some cities there is a custom to include the name of the street in the name of establishment, so Coronation Butchers are likely to be on the Coronation Street. In short: at the very first opportunity, when child just starts to read and count, explain to her the structure of the street.

Please notice that I am talking about structures, not about patterns.

Mathematics is not a science of patterns, as some people claim,

Mathematics is about structures hidden behind patterns (and many other things).

Structures are much richer and more interesting than patterns.

Let us look at another episode with the same child: he and the adult observe an ant on a trunk of a tree in a city park. Adult invites the child to observe that the trunk for the ant looks like a street, and patches of algae and moss are like lawns and bushes. Child: “And branches are side streets”.

A year later, the child is already able to use a standard city map and confidently guide the adult and a little sister through an unknown to them part of the city. Adult: “And where is our next turn?” Child, glancing at the map: “at this T-junction ahead  of us, to the right”. Adult: “And the name of another street?” Child, after quickly checking the map: “Station Road”.

Map is a mathematical object, and is in a mathematical relation with real streets. etc. in the city; this relation is called scaling (or, in more geometric terms, similarity or homothety). But the exactly the same concept of scaling can be introduced to a child using an ant on a tree trunk as an example. Scalings are close relatives of symmetries; the both concepts are facets of really deep, important, and abstract mathematical structures: groups of transformations. Of course, there is absolutely no need to mention all that stuff to a child; at ages of 4, 5, 6, years, just to help kids to see some glimpses of mathematics in the world around them is more than sufficient.

Summary:

if you want to see mathematical structures in the world around you, try to see the world through the eyes of a child.