Breaking the Al-Jabr Code
Effective tips for teaching Algebra
by Christine Gapuz
Algebra can seem so much like a foreign language to your students that it would make more sense to call it Al-Jabr, its original Arabic name. With language, getting the fundamentals down is a manageable job—conjugation, basic sentence structure, pronunciation of special characters and so on. The difficulty is becoming eloquent enough to make conversation, to express coherent ideas.
The same goes with Algebra. Even if your students have already learned the basics—addition, subtraction, multiplication—the hard part is being fluent enough to solve complex equations that are supposed to make sense of real world problems.
If learning a new language is always a tough task (especially if the language sometimes resembles hieroglyphics), then studying Algebra can indeed pose a similar kind of challenge to your students. As the teacher, you can help them bridge that gap by first emphasizing why it is important to learn this particular branch of Mathematics. You also need to create a class environment that fosters inquiry, collaboration and creativity—and of course, enjoyment in learning. Indeed, there are actually many ways to help your students decipher the Algebra code.
Here are a few tips to get you started—
PRACTICAL MATH. Who said Algebra applies to the clouds? (Okay, it was Victor Hugo.) So what if Fran Lebowitz, an American writer, once said, “In real life, I assure you, there is no such thing as Algebra.”? You can disprove these errors by making sure the class remains connected with real world situations and applications. As much as possible, introduce examples of the uses of Algebra in “the real world.” Engineering, geometry and even art are just some fields that employ and apply algebraic concepts. Emphasize the fact that Algebra doesn’t limit itself to equations and identities. Algebra can also teach them how to analyze and strategize when it comes to solving problems.
MANIPULATION OF EXPRESSIONS. Manipulatives are interactive objects that students freely use in class to help them have a concrete grasp of abstract mathematical concepts. They’re excellent tools for teaching Algebra, especially for beginner classes. To get an idea of different Algebra manipulatives you can check out www.picciotto.org/math-ed and www.nlvm.usu.edu. Manipulatives may not be readily available in local stores but a bit of resourcefulness is all you need. In the Philippines, teachers Rosalia Vicente and Cristina David presented a study on using Algebra tiles in teaching the factoring of 2nd degree polynomials during the 2011 LEAP Educators’ Conference. Though the sample group was just one class, the results were promising. In the same way that kids suddenly enjoy lessons on fractions when taught using cakes or pizza (or other types of food), you can also use food to get your students excited for your classes.
2X=TWICE THE FUN. Young learners can only take so much alphanumeric madness in an hour. Algebra is highly prone to becoming routine and repetitive. Mix up your strategies and techniques by doing away with pen-and-paper exercises or drills and playing games every once in a while. Give the blackboard or whiteboard a day off for some manipulatives or slideshows. Don’t shy away from using funny word problem examples. While this may seem to run counter to making word problems that are real world tasks, they add a breath of fresh air to assessment and discussion. For example: If a dinosaur is chasing you…
ALGEBRA ART. Not all students are gifted with artistic skills. But all students are sure to enjoy some experimentation with art, whether they are adept at it or not. Amaze them once more by using art as a form of assessment or final project. There are so many art projects you can teach your class. One of these is modulo art, a pattern art based on modular arithmetic. This art form is based on a grid of multiplication or addition tables for integers. You can give it a twist by using algebraic expressions instead of integers. There are various types of patterns, and even the simplest design will look mind-blowing once finished. You can also ask your students to play around with lines or curves on graphing paper. Ask them to create drawings on the Cartesian plane and then derive the equations of each line or curve. You can also explore string art (Girls will especially enjoy this!) or pin and thread art.
ONE STEP AT A TIME. Let’s admit it: Algebra requires discipline and determination in finding that elusive x or y. Every step must be meticulously followed, from the transposition of variables and constants to the distribution and factoring of algebraic expressions. Students need to start on this level so that they can be well-acquainted with the concepts and steps in analyzing and solving an algebraic problem. The best way to do this is, of course, to make sure that you present the process in an organized, orderly and neat manner. Most Math teachers have perfected this one-step-per-line way of presenting on the board. This serves as a great means of modeling for your students. When solving, it will also be easy to identify at what point they made an error.
EMPHASIS ON SIGNS. In Algebra, if you miss one step or overlook one detail, the whole process is busted. From changing signs when transposing, to distributing when multiplying expressions, there always seems to be steps that students tend to miss or forget. To help them out, make sure to always emphasize these steps (Changing signs is a blockbuster!) every time you show examples. You should never take them for granted, as if they were given and obvious. Mark them using circles, arrows or different-colored chalks or markers. It might seem tedious and repetitive, but trust us, your students will thank you in time.
NON-LINEAR ANALYSIS. While Algebra requires rigorous obedience to rules and procedures, it doesn’t mean that’s the only way you can ensure and assess student understanding. Knowing the ins-and-outs of a process will enable your students to work on variations of a problem. Once your students have mastered the basics, up the ante by reversing the problem and see if they can work it out on their own. A simple exercise involves asking your students to create algebraic expressions from a given value of a variable. They’re used to solving for x, so this time around, why not get them to craft the problem? This is a simple and short test of whether your students really grasped the ideas behind the concepts discussed in class.
COLLABORATION FOR A SOLUTION. Why allow your students to agonize over a problem in isolation when they can also work together towards a solution? Working together with other learners can boost a student’s interest as well as confidence. Peer tutoring or tandem learning has been proven helpful to students who are lagging behind. In fact, activities like Algebra tiles and other manipulatives can be done in groups, too. If you don’t have those, a simple quiz bee can do wonders. The competition can heighten the excitement in your class. You can also try relay-style games to see if your students can work on every step of a particular type of problem.
AUTHENTIC ASSESSMENT. The best way to counter the “There is no Algebra in real life” myth is to use authentic forms of assessment in class. It’s true that knowledge of Algebra is relevant in various professions, but your students have many years to go before they have that “Aha!” moment about their future job. That doesn’t mean, however, that they can’t start applying Algebra in their own lives right now. Authentic assessment means putting your students in practical, real world situations that will involve their use of skills to accomplish certain tasks. Algebra, despite its strange etymology, was always meant to be relevant in real life. A true understanding of it means that one is able to use it in day-to-day activities like cooking or baking or even shopping. So encourage your students to drop their pen and paper, go out of the classroom, and do some Algebra!