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How to Maximize Results with Effective Algebra Practice

How much time do teenagers really have for practice? Since they spend hours on the internet and TV, they sleep in on the weekends and they don't appear to get paid big bucks by the hour it may seem that they have all the time in the world just for practicing algebra. Well that might be the case for countries like Japan, Korea or Singapore, but nowhere near it in the US.

The average teenage would spend a few hours a week at best on the entire school duties. The only way to get them to spend more time on homework would be to include watching reality TV shows on the weekly assignments...
The problem with algebra, comparing to other school duties - is that it's not simply memorizing stuff, but performing tasks that are more complex than almost anything else they need to do. Let's look for example at the following math problem:

"Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?"

Solving this kind of a problem can take something like 10-20 stages: understanding the data, assigning variables, using formulas, constructing the equations, combining like terms, finding a common denominator, opening parentheses and so on. Now consider what happens when someone makes a mistake on one of the steps? Obviously that person will end up with the wrong answer. However the biggest problem is that have a slim chance of finding the error.
Most likely the kid will be frustrated and angry about the wasted time, and will move on to the next question. If that one won't work either that will be the end of math practice for that day.

 So what can be done to avoid frustration and wasting time? With new subjects or ones of difficulties, feedback is imperative (see my article on real time feedback). They can get it by asking for help from the teacher, other kids, family, friends or online - but no one should be left alone in this battle. A frustrated teenage will start avoiding the subject and develop an "algebra phobia". It is much better to move on to the next subject and continue only with someone that can help and provide feedback.

So here are the top 10 tips for effective practice:

  1. Do not spend too much time and energy on a single exercise. Make a fair effort to solve the exercises, but if it doesn't work move on and get back to it with some help.

  2. Allocate enough time. Don't start Algebra practice if you have less than 30 minutes. You don't have to use it all, but just the thought of what comes next can kill the practice.
  3. Don't allow interruptions. No emails, IM, Cell phone, parents or anything else. There is no better excuse to stop the practice then welcoming an interruption.
  4. Set clear reachable goals before you begin and meet those goals.
  5. Practice as soon as you can after the class ended. Like paying bills and dentist appointments, practice is usually done at the latest possible time (and for the same reasons). However doing it while the material is still fresh in the mind can save a lot of time.
  6. Always start a new subject with the easy ones. Do not skip them even if they seem too easy they will help getting the principles memorized
  7. Make sure you understand before you start. If the explanations are unclear, ask someone or use the internet to find out. Don't waist too much time trying to solve an exercise while you still didn't figure out what is it that need to be done.
  8. Clear your head. If you have urgent things to do do them first, if they're not urgent write them down and get them out of your consciousness.
  9. Use a calculator (not the one on the computer). It will save you time and "stupid" mistakes, and besides, you need to get use to it since it will be your only friend at the test.
  10. Play background music (if it doesn't disturb you). Not too loud and not to exciting so it won't form an obstruction. Music can serve as a white noise blanket that masks all other interruption (phone rings, opening doors, calling someone, etc).