Weekly Report and Reflection Week #2

Hello friends, today I wanted to talk about relational and instrumental understanding. These are two different ways of perceiving information, and in my opinion they are both equally valuable. To start off our conversation I will go over both teaching methods quickly in case you do not know the difference. Instrumental learning is most commonly seen in high school mathematics. Students are given a rule, an algorithm, or a function which they are to memorize and accept to be true. They then utilize this instrument to solve the math problem which will be provided soon after. Relational instruction works a little differently. Every function, algorithm, and rule that has been taught in the curriculum has a background (whether extensive or short) of mathematical reasoning which makes it legitimate and useful. If one understands how a mathematical concept or equation is derived, they no longer have to memorize it. Within mathematics, relational instruction is often seen in the form of proofs. Relational instruction within math is more commonly seen in a post secondary setting.

http://www.slideshare.net/mrspal/number-sense-8855176

The main question that I wanted to discuss within this blog is: which is better, relational or instrumental instruction? The answer that I as well as many others in education believe to be true is that they are both equally important.  Both forms of instruction have their pros and cons which can be utilized. In a hypothetical scenario where the educator is teaching students of an important equation such as the quadratic equation, relational instruction gives a student a deeper understanding of the mathematical concept. By understanding the derivation, they will be able to apply the the quadratic equation to other problems and areas of mathematics easily. Just as well, students will gain a further understanding of the implications that this equation has in a real world scenario. On the other hand, relational instruction is a much slower process, which is to be expected. Within the classroom, the teacher cannot simply hand their student the equation and tell them to apply it to the problem, but they have to explain why that equation is applicable. Outside of the classroom, students will have to derive the quadratic equation every time they plan to use it because they have not memorized it. Instrumental learning, however, is much more efficient. Students will be able to call upon the quadratic equation immediately and apply it to the problem because they have memorized it. Unfortunately, students will also have a very narrow minded idea of the quadratic equation and its implications. They will be able to solve the problem, but not necessarily understand how that solution affects them. Put simply, the difference between relational and instrumental instruction is a trade off between efficiency and deeper understanding.

Calvin and Hobbes explains the necessity for relational instruction better than I ever could.
http://www.gocomics.com/calvinandhobbes/2011/03/09 

Ideally after an educator is finished teaching a unit students will both have a deep understanding of its concepts as well as be efficient in applying them. Achieving this has to be possible, right? I believe that it is our goal as educators to achieve the perfect balance of relational and instrumental instruction so that we can create a classroom environment where this happens.