Vectors, matrices, and complex numbers…oh my!
Why learn math?
Students ask this question all the time.
Again … why learn math?
It is a given that there will be standard math concepts that you are required to grasp for success on standardized tests for college admissions. But not everyone attends college.
If we take a step back, it seems that the pinnacle of math knowledge needed is High School math.
What are the minimum math concepts needed?
Some math concepts are essential. I am not debating the necessity of numbers, basic operations, and taxes here.
It is clear some things are required to maintain a certain level of understanding needed to be a productive, socialized member on this pale blue dot.
Here is the spectrum of required math knowledge from toddler to teen:
Pre-School Math – Starting Line
High School Math – Finish Line
Okay—now I have established some sort of bounded spectrum of math knowledge.
Is that enough?
No—but it is a good start.
It is true that the above is the minimum math one needs to get by* in the world today. (*receive the social norms for math intelligence). Just the bare minimum to help you get into that first job out of high school.
Since it is given that there is a spectrum of the required math needed to be a productive member of society, how can we gain a competitive advantage on our peers without going outside of the established math knowledge spectrum?
Most of society does not want to major in math. However, while learning math from Pre-School to High School, you should focus on learning common problem-solving techniques.
Strategies that will give you a competitive edge in life if you actively focus on grasping the problem-solving heuristics outlined below:
Prove mathematical arguments with sound evidence and reasoning.
Make sure to have just enough details for your argument and no more.
Having too little detail can be seen as negative even though you may have sufficient details to prove your case.
Be able to explain your complex reasoning to a 3rd Grader.
Throw out the jargon and filler.
Cut to the essentials of your argument.
Learn common problem-solving models to help when working on a solution.
Proof by Contradiction
Start with negating your hypothesis to lead to a contradiction to help prove your argument.
Use Symmetry to solve problems.
Reduces variables, helps visualize your problem, and provide insight via predictability.
Use Visuals to transform abstract concepts to manageable, concrete structures.
Pattern Recognition
Learn by Discovery
Clarify Relationships
Pigeonhole Principle
Def: If you have more items than containers, at least one container must contain more than one item.
Helps with problem structuring to force yourself to understand all possible scenarios.
Helps to consider a problem's constraints and parameters to help with critical thinking.
Simplify a problem to a more manageable question then transform your solution back.
Understand the basic roots of your problem before moving to more complicated branches.
Study statistics, accounting, and probability.
These concepts are the most transferable math concepts for the real-world.
Show all your steps and work, so someone can follow your arguments, point out flaws, and offer suggestions to a solution.
Be able to distill your logic into manageable chunks that have a clear beginning, middle, and end that ties all your arguments leading to a clear conclusion.
Going back to the original question—why learn math?
We discovered that there is no choice.
You need to learn math to be a productive member of society.
Actively focus on developing problem-solving characteristics that you will use in your life, both professionally and day-to-day.
Since learning math is inevitable in our society, do it for your benefit.
This will lead to more success in your career, which leads to more income.
