Here I am again trying to get into the habit of posting in my blog at least once a month. This time, I want to post about an interesting article about algebra that I read today in the Ocala Business Journal (click link above). Coincidentally, I recently had one of my online algebra students questioning why we need letters (i.e. variables) in mathematics. This student could not comprehend the logic for mixing letters with numbers. Unfortunately, my student has not realized that algebra is about describing patterns or processes instead about arithmetic computations.

Here is the response I sent to my student attempting to clarify the reasons for using variables in algebra:

Dear Student,

When solving real-life problems, we are always missing essential information (the reason is called 'a problem'). Several times finding the missing information involves just doing a simple step: add, subtract, multiply, or divide two amounts.

However, there will be times finding the missing information involves several steps and working backwards. In these instances, the most efficient way to solve a real-life problem is setting the problem as an equation and represent the missing information with variables.

The goal of solving equations is to undo (work backwards or 'reverse engineering') the original steps that created the problem. Working backwards a real-life problem is not an intuitive and easy task to do (examples: solving a crime or auditing a business). Solving equations to the unknown value (the variable -- letter), we are training our brains to think backwards in a logical and structured manner.

Therefore, representing the missing information with a variable (letter) and solving the equation that contains it, we are solving the real-life problem in an efficient manner. This is why we need variables in mathematics.

I hope this helps.

When solving real-life problems, we are always missing essential information (the reason is called 'a problem'). Several times finding the missing information involves just doing a simple step: add, subtract, multiply, or divide two amounts.

However, there will be times finding the missing information involves several steps and working backwards. In these instances, the most efficient way to solve a real-life problem is setting the problem as an equation and represent the missing information with variables.

The goal of solving equations is to undo (work backwards or 'reverse engineering') the original steps that created the problem. Working backwards a real-life problem is not an intuitive and easy task to do (examples: solving a crime or auditing a business). Solving equations to the unknown value (the variable -- letter), we are training our brains to think backwards in a logical and structured manner.

Therefore, representing the missing information with a variable (letter) and solving the equation that contains it, we are solving the real-life problem in an efficient manner. This is why we need variables in mathematics.

I hope this helps.

I will soon be sending to my student the link of the Ocala Business Journal to enhance and support the basic idea I tried to convey above. Articles from the media often tend to add more credibility to what I am trying to do in my classroom: math awareness.