Get Better Results When Practicing Solving Algebra Equations

Solving equations in algebra, like any other skill, gets better with practice.

However, there are ways to boost your efficiency so that you learn more with less work. This means spending less time solving equations and memorizing algebra formulas, and more time doing other things you really want to get to.
Here we're going to talk about some ways you can get better at the process of learning algebra by looking at the context of the math involved.
Think back to when you first learned the distributive property, which may have been before Algebra 1. You started off writing equations like 3(2+4) = 3(2) + 3(4) and then solving them from there to make sure that you got the same thing on both sides of the equation. After the first equation or two you wrote, you started to get a better idea of what the property did and what it meant.

You kept on writing a number of similar equations like 5(1+3) = 5(1) + 5(3) and working them out, and you quickly got a very good handle on the distributive property in the context of small, whole numbers. If at that point we immediately changed the context and asked you to do something with the equation 274(32x - 15) = 37, chances are you would get stuck without realizing what to do.
This is because the shift in context was huge and you couldn't make the jump without getting confused or anxious. The number one cause for learning problems in all of mathematics, including Algebra 1, is anxiety and a lack of confidence in the ability to learn. Most of the anxiety in math comes from changing context too quickly compared to what the student is ready for. To get around this, there are two approaches.

The first approach is to slow down and change context more slowly.
In the jump from the regular equation 5(1+3) = 5(1) + 5(3) to the algebraic equation 274(32x - 15) = 37, this would mean putting in a few intermediate problems to look at, like 3(x+1) = 21.
This approach helps the student in the moment, but doesn't do anything to address the long term problems that the student has.

This is a bit of a band aid approach, and we're looking for a cure.
The second approach is to make the student more comfortable with changing contexts quickly.
This involves building up pattern recognition skills and can be done by teaching concepts in slightly more abstract ways, and then allowing the students to create specific examples, encouraging the students to be as off the wall and crazy with what they come up with as possible. When teaching the distributive property, this could mean starting it off as something like triangle times the sum of circle plus square, and then saying that equals triangle times circle plus triangle times square.

At this point, you could ask the students to put in any thing they like for triangle, circle and square. This approach would establish the relationships needed for seeing distributive property patterns more quickly than the traditional approach.