When students move into algebra, they begin using mathematics to have conversations.
Prior to algebra, everything we do is really definition. It’s teaching children what numbers, addition and subtraction are and how to think about them from different perspectives via the number line, groupings, quantities, fractions, and decimals. Then they transition into algebra, where formal mathematical language is starting to be used. They begin writing things in the language of math, the language they’ve been learning this entire time.
Sadly, this entire process often happens without children even knowing it. The algebra teacher doesn’t explain that everything they need to understand has been a prerequisite to understanding the conversations they will have. This can cause a lot of stress for your child both at school and at home.
Luckily, you can work with your child to help them develop their language, just like we did for early elementary and late elementary concepts.
Here are two key places students are confused when faced with algebra for the first time and how you can help them overcome these issues. This is by no means exhaustive but is a great starting point for ensuring your student is ready for Algebra and beyond.
One place where children have a lot of issues with algebra is the equal sign. The equal sign basically means that the quantity on both sides of the equation are the same. We notice this when students do not understand, for example, “Why we are subtracting 5 from both sides?”
A gamification of the idea of equals typically uses a balance and changing quantities on either side to show the relationship between more, equal, and less. However, at this age, you can just work with students on the definition so they can understand it. Playing with ideas involves testing them to see if they can identify when the symbols (>, =, < ) are used in statements that are true or false. For example: 5=5 (true), 4=5 (false), 4 < 5 (true).
Once the student is able to communicate around the above ideas, a parent or teacher can begin to build more complicated language around it. For example, an equation is two expressions that are related by an equal sign. An expression is any statement that you can make in mathematics such as 5x+5 or 5+4 or etc…
Because math jargon quickly builds upon itself, it is very important that there is understanding at every step of the way, because otherwise it is very easy to lose students when statements are made about more complicated objects.
Another issue is that many children at this stage are still relying on memorization skills that they may have picked up when learning their multiplication tables. They just want to memorize the steps on how to solve an equation so they can pass a test.
Unfortunately, if you’re showing a child how to solve a problem and they attempt to memorize the steps instead of understanding why the strategies work, it will be difficult for them to achieve the goal of passing the test. Algebra is an exercise in problem solving and it uses all of the language that came prior in elementary school. 5x+4 = 9 has multiplication, addition, and needs the student to understand the quantity on the left is the same as the quantity on the right in order for them to be able to even start to approach solving the problem.
Algebra as a practice and division of mathematics deals with abstraction. The conversations and ideas talked about are more vague (but no less precise) than earlier mathematics. Rules of thumb that previously could be used to help students achieve no longer apply. Not everything written on paper, just with regular language, need even be true. In fact, an algebra problem may even be a hypothesis instead of solely existing as an equation.
Helping your child to succeed in algebra starts with helping them to understand some definitions. For example, look at all the basic symbols you’ll be using such as exponents, the equal sign, or the greater than sign. The Elephant Learning app does a very thorough and rigorous job of defining these concepts to eliminate any of your child’s common misconceptions.
After showing a child the definitions, we then test their knowledge of the definitions by presenting them with true or false statements. As they begin to develop an idea of what true and false means in terms of algebra, they begin to build their logic skills. The more students develop their logic, the more intuition they’ll have when it comes to problem solving skills, taking their math ability to an entirely new level.
At the end of the day, algebra comes down to these three steps: define, recognize and produce. No matter if your child is in middle school or a PhD math program, it’s all about defining (can you understand it?), recognizing (can you identify it?), and producing (can you use it to produce results or new research?). If you can help your child with these three aspects of algebra at home, they’ll be better set up for success in the classroom and the future.
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