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Algebra Tutor: How to Learn Algebra

If you watch local or national news, you may have heard algebra described as the “gatekeeper to higher education” or heard the battle cry of “Algebra for All!” However, what exactly is algebra? Is your child already taking algebra in school and is she on track to complete an Algebra I course in the eighth or ninth grade?

In its September 2008 position statement “Algebra: What, When and for Whom,” the National Council of Teachers of Mathematics (NCTM) described algebra as a systematic way to investigate relationships, describe, organize and understand the world. They proposed that all students, from pre-K through grade 12, should have access to algebra and support for learning it. However, this does not mean that four and five year old children should be solving quadratic equations; it means that all children should be encouraged to build mathematical concepts in a way that will lead to understanding of abstract concepts.

Do you remember the first time you played peek-a-boo with a baby? At first, the baby may have been startled or even cried; his mind could not process the fact that you vanished! When you place something between you and a baby, the baby will not immediately realize that by moving the object he can find you. Now think about early experiences with algebra. An algebraic equation like 4 + x = 7 has a hidden number. A child may know that 4 + 3 = 7 but just like playing peek-a-boo, something is missing from the algebraic equation, and the young child does not know how to get it back and at first does not even connect the equation with the known number sentence.

As children enter school and begin to learn addition and subtraction facts it is not enough for them to memorize those facts. They need to develop a firm understanding of numbers and how to combine and separate them to form new numbers. They need to build fact families like the ones below and understand that there is a variety of ways to express these relationships.

There are many smartphone apps designed to provide practice with number families, operations, and fact fluency and new ones appear almost every day. Find a few that your child enjoys playing, ones that will challenge her to improve her speed and accuracy with basic facts. These games can entertain and educate while you are running errands or waiting in a doctor’s office for an appointment.

During family time, board games involving dice such as Parcheesi, Monopoly, and Backgammon will help children build fluency with these skills. For example, if a child needs to roll a seven to land on an advantageous spot, he should be encouraged to list all the possible combinations of seven using a pair of dice (1 and 6, 2 and 5, 3 and 4). This type of activity helps form lasting mental connections.

Equality is another important algebraic concept that should receive attention beginning in pre-K. Sharing is an important skill for students to learn at this age. They can also learn to share equal quantities by counting and placing items into two or more equal groups. Extend your child’s mathematical learning by asking them to count out an equal share at playtime, snack time, or when doing household chores.

There are many prerequisites to algebra and benchmarks to help you to know if your child is measuring up. The National Mathematics Advisory Panel offers helpful benchmarks for the foundations of algebra by outlining the topics students need to have mastered at each grade level to be on the path to algebra in grade 8. However, these topics alone are not sufficient. Future success in algebra requires building conceptual understanding, computational fluency, and problem-solving skills.

Fads in math education come and go. The winds of change blow in and bring a focus on problem-solving skills with less attention to developing computational fluency with basic facts. This lasts for just as long as it takes to see a lowering of test scores. The next fad may be to drill, drill, drill on basic computational facts to the point that students have no understanding of what they are doing, but they can perform the algorithms quickly. This lasts until those students reach higher-level math courses that require them to solve problems and reason logically. And the cycle continues. Parents need to be the voice of reason and support in their child’s mathematics education. You cannot expect that your child will receive all the math education he needs at school. You too must take an active role in ensuring your children develop understanding, quick recall of basic facts, and skills solving problems. Then when the time comes, they will be ready for an algebra course.

Lastly, remember that science has debunked the myth of a math gene. So why is it that some students are better at math than others? It is most likely their experience or their attitude toward math. Studies have shown that effort does matter. When a child believes he can succeed with math he puts more effort into the task and does succeed. Encourage your child to practice his math skills, challenge him with games and puzzles, and be a good role model by letting your child watch you solve math problems, even if you struggle to find the solution.