Making connections is a very human activity. Setting aside our own personal connections of family, friends, and communities, we see that we also make connections outside of our personal relationships. We observe patterns and similarities in nature and connect the ones that make sense to us. This God-given desire to order and sort like objects is a reminder of our creation mandate from the garden, and never goes away. Even high school students want to connect things. We know in our head that algebra and geometry are both high school math classes, but we feel that they are different. How are they connected? Why are they connected?
This doubt in our minds find rest when we dive into the world of mathematics and discover the discoverers. When we see that algebra can be explained with geometry, we are excited to see the connection, but then wonder why we study algebra first. If geometry was discovered first, then why do we moderns start with algebra?
These questions are good and they show that our students are thinking more about their math learning than most. I want to answer them, but I want them to find the beauty and glory in the progression of how mathematics is learned now. So I ask them to make a connection. How can you express the truth of the pythagorean theorem without using the variables? Would you use words, pictures, or both? How could you make it clearer? As most algebra students know, a graph is a picture of what's happening behind the algebra, but it's not exact. Once a student sees how hard it is to express geometry truths in english, he begins to understand his need to learn the language of Algebra. This gap fuels our creative minds to explore a world that we may have ignored before. Thus we come full circle as connectors and image bearers of the one true Connector.