Is it a good approach to heavily depend on visualization to learn math?

Solution 1:

As Lord Farin indicated in the comments, the answer to your title question is heavily subjective, depending on personal preference.

Ultimately this depends more on your learning style. There is no right or wrong way to learn mathematics, so long as you ultimately reach the same truth.

If learning by visuals helps you understand the concepts behind a problem then by all means use it! They are indeed a useful way of putting together letters and numbers in a more physically meaningful way.

On the other hand, while visuals provide helpful guides to understanding what is going on, they do not always constitute mathematical proof. (Though in some geometric cases, such as the Pythagorean theorem they work just as well.) That is to say, do not use images or drawings on your average mathematics examination without proper context or related work.

For instance, if you are taking out a ruler and a pencil to figure out the slope of the tangent to (2,4) on the graph $y=x^2$, you are doing something incorrectly. Drawing the graph may be helpful in contextualizing the algebra, and even help check your answer, but in this case, it is not, strictly speaking, rigorous, an attribute mathematicians pride.

As our friends at Cognitive Sciences StackExchange can tell you, every person has a unique way of learning things: