Two Uses Of Analogies.

Analogies are those wonderful groups of words that have relationships to each other such as ruler is to line as compass is to circle.  The only time I've ever really seen them used in on the GRE test if you want to get an advanced degree at a college.

The first way analogies are used in math is to help students develop their analytical skills because they often have to compare, contrast, or sequence.  Its understanding relationships between things.  For instance in the ruler is to a line as a compass is to a circle has a relationship of the instrument used to create the object.  A ruler is used to draw a line while the compass is used to create a circle.  If you have students actually verbalize the relationship, it improves both their vocabulary and their understanding of how words relate to each other.

Others such as ray:line::arc: circle shows the relationship of part to a whole because the ray is part of a line while the arc is part of a circle or 5:25::25:625 means that 5^2 = 25 and 25^2 = 625.  The first reads the ray is to the line as the arc is to the circle or five is to 25 as 25 is to 625.  Every analogy shows a relationship.

One way to help student see the relationships is after going over several as a group, before handing out a worksheet which has three of the four provided so they can figure out the last one.  The final step would be to have students create their own analogies from scratch.

It's fairly easy to find free materials for students to practice analogies.  It just takes a little bit of time and voila, you can find them even at Teachers pay Teachers.

The other way analogies can be used is to help students learn the order of things. These I'd neither seen nor heard of so these were a surprise.  These analogies demonstrate things in a visual way.  For instance when discussing the commutative property with students, we usually show them the A + B = B + A and tell them, it doesn't matter what order you add the number in, the answer is the same.  To show it we can discuss putting on  hat and coat vs shoes and socks.   For shoes and socks, we have to put the socks on first and then the shoes.  We can't change the order but when we put on a hat and coat, it doesn't matter whether the hat goes on first or the coat.  The order does not matter for the coat and hat and that is the same for the commutative property.

 As for associative, we show it as A + (B + C) = (A + B) + C.  I usually explain that it means we change who we associate with so in the first part B is associating with C while in the second part A is associating with A.  Another way of looking at it is (Light Blue) bucket = light (blue bucket). In the first part, the bucket is a light blue color while in the second part the blue bucket does not weigh much and this is an example of something that is not associative.  So students can see that not everything in that form is associative.

So there you have it, two ways you can use analogies to help improve mathematical understanding and vocabulary.  Let me know what you think, I'd love to hear.  Have a great day.