Relational and Instrumental Understanding

Thinking and learning processes occur in two main different ways known as relational and instrumental understanding. Where one is easier to learn and to teach than the other, the other proves to be the most important thing that needs to be the focus of every teacher, especially in mathematics.

Instrumental thinking, in short, is knowing how to get from point A to point B. It gives a step by step process that can be followed. This is the easier one to teach because it doesn't explain why, just how. Students also typically prefer this method because it's easier for them to remember and it's not as difficult to understand but this is what limits them because they don't learn how to see how things are connected and how they can be transposed into different situations.

Relational thinking is knowing how to do something and why it is done. It's knowing how to take different routes to find answers and connecting not only A and B but also the rest of the alphabet. This is harder to learn simply because it's not just an easy answer. It requires reasoning and it also requires more time.

Instrumental understanding is not related to relational understanding, but relational is related to instrumental because instrumental doesn't include any relational understanding. It's just knowing a process. Relational understanding, on the other hand, includes instrumental understanding plus more.

Mathematics is how numbers apply to every day life whether that's in the grocery store or in a NASA laboratory. It proves why certain things are the way that they are.

I learn math best if I understand why and if I can see all the different reasons why. Math has never been an easy thing for me and I usually have to see different ways to approach a problem before it really starts to make sense. I think that my students will learn best this way as well. By asking why, reasoning skills are developed that will help them to make connections for themselves. If students are just told how to do something, they'll choke when something out of the ordinary shows up because it didn't follow the pattern that they were shown how to do. It's also important for them to see all the different possibilities and angles that can be taken to find a solution. Each student will think different and one way might be great for one student while another doesn't understand. I think they'll learn best if they understand why and if they can see many possibilities to a solution.

Math assignments are great. You can't just learn math by listening to a teacher lecture, there has to be hands on experience that is varies within a topic so that they can see the application. I also have always thought that it was good that I had to memorize my times tables back in second grade.

I think that teachers that don't know how to teach are detrimental to students learning math. Teachers that don't care, aren't excited, don't show the application in every day life, and only show one way how to do something and can't explain why.