Understanding the Reasoning Behind Basic Algebra

[installshu]

TL;DR

I’ve been thinking about how beginners learn algebra and wanted to get some opinions.

Hi everyone,

I’ve been thinking about how beginners learn algebra and wanted to get some opinions.

When solving a basic equation like:

2x + 6 = 14

it’s easy to learn the steps and arrive at x = 4. But is it more important for a beginner to understand why we can subtract 6 from both sides and then divide by 2?

Or is it better to first become comfortable with the standard methods and develop the deeper understanding over time?

I’d be interested to hear how others approached algebra when they were learning it.

 

[PeroK]

Why not? It gives you an equation you can solve, $2x =$ some number.

In this case, you could also divide by 2 first.

Apart from that, what else do you propose?

 

[Herman Trivilino]

But is it more important for a beginner to understand why we can subtract 6 from both sides and then divide by 2?

Depends on the learner's goal. Some learners just want to know how to make answers, others want to make sense. Regardless, there's nothing difficult about learning that if two expressions are equal and you subtract $6$ from both sides they're still equal.

There's a deeper understanding that you didn't mention. The real reason that $x=4$ is the solution to $2x+6=14$ is that $4$ is the number you multiply by $2$ and then add $6$ to get $14$.

 

[erobz]

Regardless, there's nothing difficult about learning that if two expressions are equal and you subtract $6$ from both sides they're still equal.

It's not difficult, but I do recall "getting it"(I learned algebra mostly as an adult though).

I teach my kids by balance scale type problems. There is an intuitive understanding about physical balance at a pretty young age. You might balance shapes with them, and you can use other balance scales "like two triangles balance a square" to give them an intuitive understanding about substitution. I think getting this abstract idea cemented in before they really even know numbers all that well is beneficial.