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12/30/2014 8 Comments

Teaching Your High School Students About Applied Versus Theoretical Math

Why Make the Distinction?

Teaching High School - Applied and Theoretical Math
Have some of your students already mentally "ruled out" a major in mathematics?

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.

Worksheet Included to Guide Your Class Research and Discussion

Applied and Theoretical Math in High School
Teaching High School - Worksheet for Applied and Pure Mathematics
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8 Comments
Ronny
2/21/2016 09:05:35 am

Interesting page.:) Where are the answers to the questions you have listed in bullets? I'm currently a math major, junior (pure math) and wonder where all this abstract algebra is used. I want to go into math education as well! But I ask myself many why I'm a math major when I see all this abstract proof business with group theory and such, please help me understand! Thanks :)

Reply
Math Giraffe link
2/23/2016 08:31:16 pm

Hi Ronny,
I know the feeling! I felt the same way in some of those abstract algebra classes (and even computer science!)
Some of the group theory can come in handy in computer programming, cryptography (working for government agencies, etc.) The interesting thing is that now as we implement some of the pure math into technology, does it blur the lines between pure and applied math? That's what I like students to start to discover in their research (bullet question #2). Usually, each student is more drawn to / interested in one or the other, so it's fun for them to see that math has two distinct branches and see the differences and the possible overlap.
Thanks so much for commenting! I hope you enjoy your last year and love teaching! :)
-Brigid

Reply
Kristina
6/6/2021 06:49:22 pm

What was the name of that math class you took? My son does not like math ("When will I ever use unit circle, mom?"), and we are considering whether he should take pre-calc, probability/stats or "mathematical modeling" for his last two years of high school.

Reply
Math Giraffe link
6/8/2021 12:43:37 pm

Hi Kristina,
The one that was the first math class I liked was a double course (double block period) of AP Calculus blended with Physics. So it introduced so many really interesting crossovers between math and science. Everything was applied to Physics alongside learning each part of the Math, which was really cool. What makes a huge difference (in math, especially) is the teacher. So it may be worth checking to see if you can find out who teaches each class. Otherwise, I'd recommend the pre-calc if he plans to go on to any college math (or science), but if he won't really need that, the other two could be nice options. Prob/stats can get boring, depending on the teacher, in my opinion. Does he have any ideas yet what he may want for his future adventures? :) Have a great day!
-Brigid

Reply
Kristina
7/14/2021 07:17:36 am

Thank you for your response. I agree that a good teacher can make the class. He has a few ideas as to what he wants to do in the future: physical therapist (so he can work for a sports team), history teacher (so he can coach) or archaeologist. He is signed up for pre-calc; I am hoping for one of the more creative teachers!
K

gas strands link
7/13/2021 11:17:10 pm

Thank you!
More Details From:
https://www.edukasyon.ph/courses/senior-high-tracks/academic/gas-general-academic-strand

Reply
angeles university foundation courses link
8/2/2021 12:58:23 am

Such nice ideas.. you have written it so well. Love this post!

Reply
philsca link
8/8/2021 10:25:24 pm

Extremely interesting. Thank you for giving such an informative blog.

Reply



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