2: Knowing and Learning

Thinking mathematically/scientifically involves understanding the topic at hand but also understanding what is at work within the problem or the concept. To truly understand something you have to not only know what you are trying to work on but you must have an understanding of what is going on that makes the math work or that explains why something does it does.

In relation to Fish is Fish, human learning is quite similar. The young fish had been told that “fish is fish”, but just because he was told that it did not mean that he truly understood why it was or why it had to be that way. Once the fish tried to become something else and explored that part of the world and his abilities, he realized that when he was told that “fish is fish”, he understood the meaning because he had experience with it and had explored why it was that way. Much like human learning, we do not necessarily understand something just because we are told about it. We require an understanding of why and we want to understand so that we can gain the ability to think about the subject we are trying to grasp.

The seasons are caused by the rotation and tilt of the earth in relation to the sun. Because the earth is tilted on its axis, during certain parts of its rotation around the sun, the northern hemisphere may be closer or further from the sun and vise-verse for the southern hemisphere. The hemisphere that is closer to the sun receives more direct sunlight, causing summer. The hemisphere that if further from the sun receives indirect sunlight, causing winter. For the times in the earth’s rotation that both the northern and southern hemispheres receive the same amount of direct sunlight, those two periods are spring and fall.

The phases of the moon are caused by the positions of the moon, and the sun at given points in time. Because the moon rotates the earth, and in turn, the earth rotates the sun, there is always one half of the moon that will be illuminated by the sun. The phases are caused by how the moon moves around the earth and how the light from the sun hits the moon and reflects.

It was interesting to see how often these misconceptions occur but also how long they stick with each individual. From high schoolers to professors, they all maintained the same misconception. Their ideas do make some sense because they rationalize what they know to come up with this explanation that they feel makes the most sense. In theory, the closer you are to something that is hot, the hotter you become, and the further away from it you are, the less hot you are. The ideas about the clouds and the moon may have come from cloudy days they witnessed or that sometimes on cloudy nights you cannot see the moon from earth.

Knowing and learning go hand in hand. To learn something you must know what you learning about, and you must know what the background information is on that topic. To know is to have a strong understanding of something, while to learn is to attempt to gain an understanding. These go hand in hand when trying to become a competent math or science student. Math and science are subjects that require constant use of previously learned topic and an understanding of those same topics. To become a competent student you must understand the differences between knowing something and having something memorized or having just learned something. Learning something is not the same as understanding it. You might learn that the moon goes through phases, but this not mean you understand why the moon has phases or why we see it the way we do. Learning is the surface, understanding is going in deep into the material to be able to explain it to yourself or to others. To be able to understand how someone else is thinking is difficult. But you can start by asking them to explain something to you, or to put what they learned to the test. Assessing what was learned and what was understood is useful to both students and teachers. It is here when you address any misconceptions, through an activity or an exploration of the topic, teachers can see how the students put what they learned to the test and see if they understand and now know the topic.