# EMF Math vs. The Traditional Approach to Learning Mathematics

Cole Travers completed the EMF Math program during grades 6-8 through his public school district. He wrote the following guest blog post in which he compares EMF with a traditional high school math class and explains why EMF was excellent preparation for college.

Throughout my three years in EMF, I got to learn mathematics in the way that a mathematician understands it. Now that I am in 9th grade and in a traditional math class, I can compare this experience to my EMF experience.

The main difference is that EMF focused on the why of math, while traditional classes focus on the how of math.

In EMF, I was not just given statements of mathematical laws and properties and told to use them. EMF always made those formulas available, even during the major tests at the end of sections.

Instead, I actually had to prove why they are true using logic. Proofs challenged my perspective on math and while they made math many times more difficult, they also made it many times more enjoyable and satisfying.

My EMF experience made me want to keep learning the “why” behind the formulas and graphs that I see now in my traditional class, but, unfortunately, I don’t get to do that.

To do well, I simply memorize a few formulas or graphs and apply them on homework, periodic quizzes, and unit tests. I can forget them as soon as we’re done with the unit, because they never come up again.

At first, the more challenging part of a traditional class was doing a lot of calculations quickly.

In EMF, quizzes and tests were untimed due to their difficulty and the unimportance of speed in true mathematics. Now I have one class period, or around 45 minutes, to finish a quiz or a test.

At the beginning of the semester, using formulas two dozen times in 45 minutes was not something I was used to. But after a short time and a little practice, it got easier.

I also now see that going the other direction — understanding concepts deeply when you’ve been taught to be fast — is much harder.

Because I only have to memorize and apply formulas in my traditional class, the advanced skills that I learned in EMF — digging deep into a concept, solving problems creatively, and writing proofs — are not directly applicable right now.

EMF certainly will help in college math courses because they are more about actually understanding math. Plus the advanced material in EMF just made it really interesting.

I probably would have been completely bored in math all through middle school if I had not been in EMF.

Another difference is that in EMF, the ideas were interconnected and made sense as part of a bigger picture. As I learned new concepts in EMF, I also learned how they linked back to previous concepts. In order to solve EMF’s most complex problems, I usually had to bring old and new ideas together and come up with a new way to apply them.

On a related point, how I learned to think in EMF actually helps me in classes other than math. The way EMF taught me to delve deeper and to layer new knowledge onto prior knowledge enabled me to do better than many of my peers in Biology Honors, for example.

As with EMF, this is quite a challenging class and the material builds on itself. EMF helped me in ways bigger than mathematics by teaching me how to learn difficult subjects. I think I will be much better prepared to succeed in college because of EMF.

Current EMF students should feel confident that they will do well in traditional high school math classes, even though these classes are very different from EMF.

Understanding the material in high school math classes isn’t hard at all. Students just have to use a different approach, mainly memorization and application.

I would encourage middle school students to enjoy EMF as much as they can because it is definitely the most interesting way to learn math that I have ever experienced.