Very few children like mathematics, especially as they move forward into learning algebra. They will hit a wall, get frustrated and ask “Why do I have to learn this? Will I ever use this in real life?” Unfortunately, adults tend not to have a response to these questions. It is common sense that you should know mathematics, but I know I haven’t run across a single person who has been able to make an argument that responds with these inquisitive and disgruntled children. To be completely honest, the reason why most adults don’t have an answer to this is because they asked these same questions when they were children and still haven’t found a satisfactory answer to it.
These questions have now existed for generations; it seems like quite a daunting task at this point, but it’s easier that you’d think.
Algebra is a tool. You aren’t learning algebra to learn algebra. You are learning algebra to learn how to simplify problems, how to group a set of problems and, most basically, how to think. It teaches you how to think quantitatively and how to rationalize relationships between two or more things.
Main Aspects of Algebra People have Trouble with:
- Using letters to replace numbers. This is an important concept, especially if you want to learn calculus, geometry, probability, statistics or how to write proofs.
- Using and understanding inequalities. This should be a basic concept; everyone understands 1<2, etc. The problem comes in the combination of inequalities and either algebra or absolute values or both. This is important if you want to learn calculus or write proofs. (geometry?)
- Using equations with multiple variables. This is also important, and as basic as using letters to replace numbers as far as foundations go; it’ll be built upon in calculus, geometry, probability, writing proofs, sciences such as physics or chemistry or biology and computer programming.
- Using piece-wise functions. Piece-wise functions will be used most often with inequalities and graphing, and later in probability functions; it is a way of thinking about functions that you should try to master just because it will be useful. It will follow you to probability, calculus and writing proofs.
- Using matrices. I’ve always hated and struggled with matrices and I made the mistake of marginalizing them, only to hate myself later. They are vital if you ever need to learn linear algebra, cryptography, computer programming or computational physics.
- The ability to draw and read graphs of equations. If you are a visual learner, this should be easier for you to understand than just staring blankly at equations. If you aren’t, it is still a useful skill that will be vital if you want to continue on to calculus, probability,statistics, or sciences such as physics and chemistry. (Graphical computer programming comes to mind, too!)
- Understanding complex numbers. This is a tricky one, and most people think that there isn’t any real-world use for them; but there is. Theoretical physics (studying the workings of atoms and their parts) has found that sometimes the universe can only be explained mathematically by using complex numbers. Not that you will use them for this, in particular, but they will continue to come up in calculus, linear algebra, writing proofs and, again, theoretical physics.
- Understanding powers. This is an extension of multiplication; basically a way of simplifying multiplication. Like most simplifications in mathematics, though, they come with their own special rules. I would suggest that for each new rule for using powers, think back to what that means in terms of what you already understand. This will come back to haunt you in calculus, probability, statistics and sciences such as chemistry or physics.
- Understanding how to factor a polynomial. This truly becomes easier with practice and the diversity of approaches you become comfortable with. It is increasingly more important in calculus. Useful in writing proofs and sciences such as chemistry and physics.
- Understanding exponents and logarithms. exponents and logarithms come in handy in analyzing graphs of data later in life. They also give you a kind introduction to the concept of inverse functions. -all forms of statistics (from the social sciences to the physical sciences), investments and sciences like chemistry and physics
- Understanding how to re-write an equation into different forms. This is perhaps the most important concept you can get from algebra: knowing what you have and how to re-organize what you already know. Applications extend to geometry, calculus, probability, statistics, linear algebra, computer programming and sciences such as chemistry and physics.
Algebra is a tool. It isn’t a goal, it is the means toward a goal. It isn’t meant to be confusing. It is a way to simplify even harder concepts. Everything that is taught in an algebra class is building the students up to the next set of concepts.
So, what is the answer to the original questions?
“Why do I have to learn this?” You have to learn this so that you can learn the next concept.
“Will I ever use this in real life?” No, but if you don’t learn this – if you give up now – you won’t be able to understand more complex concepts taught in this class. For the more here-and-now and grade-oriented: because if you don’t learn this by the time the next concept is introduced, your grades will only drop.
It’s hard to swallow, but it is absolutely key for students to understand this basic fact: they are in this for the long haul and should buckle down and just keep at it.
The worst thing you can do is give up or believe that you can’t do it because you can and you will, if you just keep at it.
Related articles
- Algebra on Demand is HERE – The Khan Academy (aodandmore.wordpress.com)
- Probability is not the best the goal for undergraduate math education (superconductor.voltage.com)
- Why Kids Hate Math (vuotkho.wordpress.com)
- Free Algebra Webinar (nchomeschoolinfo.wordpress.com)
