Why Make the Distinction?
It is pretty common for high school students to make judgements about mathematics in general based on their experience in math classrooms throughout their education (which makes sense - can't blame them!). Obviously, the math they have been exposed to is limited to the topics in K-12 curriculum and is limited to the teaching styles that are common in early, middle, and secondary education.
However, a student can become completely turned off to mathematics without ever even getting a peek at certain fields within math. Don't let your students give up on a future in a mathematical area they have never even heard of yet!
I experienced this myself, and was so lucky to have one last math class during senior year of high school to knock some sense into me. I had disliked math all along. Because of scheduling changes, I ended up taking one last class even though my math credit requirements were already satisfied. The last minute peek into higher level math got me so interested that I chose a major and career in Math! I ended up going into math education.
Without that class, I would never have discovered my LOVE for math. I have also experienced this as a teacher. Sometimes, when students get a glimpse into theoretical or applied math, they realize that they truly do not hate all math.
Before your students leave high school, give them a peek at the options that lie ahead. Be sure that they are aware that there are fields within mathematics that may interest them far more than the math they have studied so far. It may just make the difference for someone who truly is meant for a career in math and does not yet realize it.
Some topics for discussion:
- What is the difference between Applied Mathematics and Pure/Theoretical Mathematics? What types of college courses and careers fit into each area?
- How fluid are the distinctions between Applied and Theoretical Math? Research number theory, which used to be a topic in Theoretical Math. How is it used now as an Applied topic in computer encryption systems? What about graph theory - its past as a theoretical topic and its present applications?
- Research vector geometry and linear algebra. How does a video game developer use these "Applied Math" topics? Research abstract algebra and proof theory. What is the value in the work of mathematicians in these fields?
After they do a little research, have your students make a quick chart with examples of Theoretical and Applied Math topics. Have each student determine which area they might prefer to study. Here is a worksheet to guide your students in this short project. Another option is to work as a whole class and collaborate to make one huge chart on the board. Enjoy!
Click on the images to download.