Math, the Way it Should Be (Unit 1.6: Summary and a bit of Philosophy)

The last lesson in each unit will go quickly over what was covered in the lessons of the unit and then give some insight into what’s going on in my head with regards to mathematics.  In the Lesson 1.1, we covered addition, subtraction, the signs indicating less than and greater than, and the counting numbers.  In Lesson 1.2 we added zero and the negative numbers to form the integers as well as covering multiplication and some instances of division.  In Lesson 1.3, we learned about the rational numbers, allowing us to carry out division with all integers as well as reviewing addition and multiplication of fractions.  In Lesson 1.4, exponents and roots were introduced, leading to the definition of irrational and complex numbers.  Finally, in Lesson 1.5, the number line and Cartesian plane were introduced as well as some basic vectors and vector operations.  More will come on these topics later.

The first piece of philosophy regarding the education of mathematics that I will share regards the treatment of “word problems”.  In my opinion, word problems are demonized by students everywhere because the way they are taught (or at least, taught to me) requires a step of memorization.  For example, when I was taking my second algebra class in high school, we covered “solution problems” (problems where two or more liquids were combined in a mixture) in great depth (no pun intended).  The teacher I had was a great teacher, but we were taught that every time we encountered a solution problem, we would solve it using the same steps every time.  While this worked for the exact type of problems we faced in class, I feel like this isn’t the best way to solve problems.  Since I learned to approach problems like an engineer, I have started building equations from the problems.  For a new problem, I either create new equations based on what I know about the problem or use a couple, very basic equations (relatively speaking) that I then tailor to the problem.  I use the second approach for complex engineering problems, but the first approach is appropriate for almost all problems faced by high school and underclassmen in college.

I will likely not cover any word problems until later, when I plan on dedicating an entire unit to learning how to do every kind of word problem possible.  Like many things, however, it will require lots of practice to master and experience is something you can’t get on the internet.

-Lane