As a student, do you prepare for a test by staring at the examples in your textbook? Have you been known to reread a chapter several times over and over before an important exam? New research indicates a surprisingly effective study method that beats these old-fashioned techniques: Stop studying and give yourself a test!

Teachers and students often employ elaborate studying techniques including repetition (also known by some as “cramming”) and mind mapping, which involves creating detailed word and picture diagrams showing the connections between facts, to help students synthesize the material. These strategies are popular among educators because they require students to recite terminology and make connections by elaborately displaying the material.

However, a recent report by two Purdue University researchers, as published in Science Magazine, indicates that these methods are far less helpful than simply taking a test on the subject matter.  Researchers Jeffrey D. Karpicke and Janell R. Blunt arranged a series of experiments with 200 college students to test their academic success using various study methods. They determined that retrieval — the brain’s function of accessing data from memory — was the most useful tactic of all, because it enhances learning by forcing the brain to make inferences and admit gaps in knowledge.

In fact, students who read a passage and were tested on the contents afterward retained about 50% more of the details one week later than students who used these other studying methods. It’s simple: While most other techniques identify what students THINK they know, testing demonstrates what they actually know — and what they still need to learn.

What does this mean for students? Abandon studying altogether, of course! (Just kidding.) The most effective studying method is individual to each student, and often it involves a combination of different learning techniques. Perhaps the most important thing for a student to learn is how they learn best.

But if you’re struggling with a subject, you might want to try the researchers’ advice:  Rather than reading a chapter six times, read it once and then make yourself complete a little quiz. Without cheating, try to identify the main concepts, create and solve sample problems, and define key terms. You’ll be testing your brain to find the gaps in your understanding, and you’ll be able to modify your studying strategy based on your results.

No longer do tests have to be the stressful finish line, or the bane of a student’s existence. Rather they can be the means to a successful study session that can improve your test scores. Since studying is a process that continues far beyond your school years, carefully developing your best personal study model is a good idea for now, and the rest of your life.

If you’re a struggling math or science student, check out Virtual Nerd’s math and science tutorials, presented in our patent-pending Dynamic Whiteboard, which lets you drill down to ask personalized questions — See if you can predict what our video tutors will say before they say it — just like you would on any self-assessed quiz. It’s like having a virtual tutor, and at the fraction of a cost!

p.s. Stay tuned for an exciting announcement… It involves Virtual Nerd and taking quizzes, but that’s all I can say (for now)

Last time we talked about why it was so important to be able to do basic arithmetic before you tackle Algebra. Hopefully since then you’ve been inspired, perhaps even by the Olympic spirit, to practice your times tables and other key skills. Keep up that practice and keep those skills strong, even as we go forward and consider the second key to Algebra success.

Key to Algebra Success #2

Embrace the Unknown(s): Variables

Algebra I is when you first meet variables, and by way of introduction you’re told variables are symbols used to represent known or unknown numbers.

Does that sound like it came out of nowhere?

Feel like variables are totally unconnected to what you’ve seen before? Then this might interest you: You’ve always used symbols to represent numbers.

Don’t believe me? Well, let’s just count some numbers up, shall we? We can start with 1, then 2, 3, 4, 5 and so on. Now think back to when you learned to count. Isn’t it true that someone had to tell you what the symbol “1” meant? It probably wasn’t too hard to understand that “1” stands for the idea of a single thing, like one lunchbox, one nap time mat, one juice packet, and only one cookie allowed. And “2” was also easy to learn, like the 2 cookies stolen while no one was looking, or 2 minutes sitting alone in the corner “thinking about what you did”…

Variables, just like the more familiar “1” and “2”, are symbols that represent something numerical. So from the very beginning of your math education, you were exposed to one of the underlying concepts behind variables, without even knowing it! I think that’s pretty cool, because it shows us something very familiar and natural about variables.

But there’s also something new about variables, right?

Absolutely. There is something about variables that is quite different from symbols like “1”, “2”, or “3”, and this difference is where the real power of variables comes from.

Here’s the deal: variables, like “x” or “y”, can stand for ANY number, whereas constant symbols like “1”, “2”, and “3” always stand for a single specific number.

When you’re dealing with the symbol “3”, you can visualize three things swimming around in your head. But when you’re working with a variable like “x”, you may not know what number “x” represents, and visualizing the unknown is tricky business! How can you know if what you’re visualizing is accurate?

It’s the fact that variables stand for an unknown quantity that makes them so different and often so dreaded. But fear of the unknown is no good reason to turn away from Algebra, especially given the power that working with variables can bring.

So what is this power you speak of?! What good are variables?

Well, variables are useful because we’re often faced with problems where something is unknown, and figuring out the unknown is easiest if we use some Algebra rules to help ourselves.

For example, imagine we have a Hard Drive with 700 GB of available storage space. It’s brand new, totally empty, and on the drive we want to store a whole bunch of 3 GB high definition video clips. How might we figure out how many video clips will fit?

We could take the long road, and start counting, but if we introduce a variable, we’ll be able to solve the problem much faster. We’ll talk through that process, but first check out the diagram below to see it in action.

We know that 1 video takes up 3 GB, 2 videos take up 2•3 GB, and 3 videos take up 3•3 GB. So to find the total space taken up by the videos, we multiply the number of videos by 3 GB.

That means that the natural thing to do, is to create a new variable called ‘v’, to represent the total number of videos that fits on the disk.

We don’t know what value ‘v’ has, but we do know that the same rule we used to figure out how much space 1, 2, or 3 videos takes up will work for ‘v’ videos. So we can say that ‘v’ videos will take up v•3 GB of space. We want that total space to fill up the drive, so we set it equal to 700 GB. That gives us the equation, v•3 = 700.

Now we can use rules of algebra to solve this problem by division, and we discover that v= 233 and 1/3 videos. So we can fit 233 videos completely, and have a bit of space left over on the 700 GB hard drive. If you want to see in detail how to solve equations like this, we’ve got a great Virtual Nerd tutorial that shows you how to do it!

What just happened here?

Had we solved this problem by counting or guessing, it could have taken a while. Instead, the variable ‘v’ helped us get the answer very quickly and helped us see the general method for solving this kind of problem. That example only scratches the surface of the power of variables, and the more you work with variables, the more you’ll appreciate what they can do.

Variables are also useful in Physics and Chemistry because they can be used to create equations summarizing laws of Nature. Sometimes doing math with those equations leads scientists to predict new things that people later observe to be true. That’s what happened with antimatter particles and even the Celestial Object Formerly Known as Planet Pluto!

We’ll cover those topics in the future, but for now, sit back, relax, and let your newfound appreciation for variables sink in!

Algebra throws many students for a loop. It doesn’t have to.

In this series of posts, I’ll share with you some insights I’ve gained during my years as a tutor.

I’ve worked with hundreds of students. I’ve noticed many similar issues that contribute to their Algebra struggles, and I’ve seen the success that comes from addressing those issues. In the coming weeks, we’ll examine 5 keys to success in Algebra that really stand out.

Let’s get started!

Key to Algebra Success #1:
Strong funda-MATH-tals!

Before you take Algebra you spend years working on basic arithmetic skills. And when you work on Algebra problems, you’ll see those problems assume your arithmetic skills are strong. If you can’t quickly add and subtract 1- and 2-digit numbers, or recall your times tables, or work with fractions, you’ll have trouble keeping up. Math fundamentals, or funda-MATH-tals, are incredibly important.

Sometimes trouble with arithmetic is a sign of too little practice.

Maybe you just didn’t have the patience or interest to do all the homework assigned to you, or maybe you learned to rely on the calculator too early. In that case you have to go cold turkey on the calculator. Go old school. Take out a pad of paper(!) and a pencil, and start practicing.Or take advantage of technology and find programs to help you drill things like times tables, long division, addition, and multiplication (see comments for suggestions).

Sometimes, trouble with arithmetic stems from a general difficulty with memorization.

After all, the times tables and the methods for adding and subtracting or multiplying big numbers are just rules that you kind of have to know, and memorizing stuff like that can be hard. In fact there are lots of students out there who love math and have an intuitive feel for working with numbers but just can’t seem to memorize things. These students often struggle in math class not because they don’t understand the ideas, but because they have trouble executing some of the rules efficiently.

When memorization becomes the struggle, you have to try to play games with the numbers and discover patterns that help make sense of what you’re trying to learn.

Let’s take a quick look at the times table and pick out a couple of rows and columns to see what patterns we can see.

Notice that along the 5 row, each number ends either in a 5 or a zero. Can you see which answers end in zero?

Well, it’s the ones that you get when you multiply 5 by an even number!

5 • 2 = 2 • 5 = 10
5 • 4 = 4 • 5 = 20
5 • 6 = 6 • 5 = 30
5 • 8 = 8 • 5 = 40

If you look closer, you might notice something absolutely stunning! The 10’s digit of the answer is just half of the even number that is multiplying 5!

So to multiply an even number in the 9×9 times table by 5, all you do is take half the even number and put a zero after it!

That’s a simple rule you can use for 8 boxes in the 9×9 times table. Remembering one rule, one pattern, gives you 8 pieces of knowledge!And with a couple more rules based on other patterns, we can easily fill in the entire 9×9 table.

That’s the power of patterns, and it’s one of the best ways to overcome any struggles you have with memorization!

Overwhelmed?

Worried about all of the work you have to do to master these fundamental skills?
Just think about the power these skills grant you!

With a firm foundation in arithmetic, you’ll be in a great position to conquer Algebra, and with Algebra other doors open up for you. Algebra will expand your mind, teach you to think in new ways, and give you tools for seeing the world differently.

With Algebra you’ll be able to study Physics, Biology, Chemistry, Calculus, Differential Equations, and maybe more.

The world around us has so much mathematical structure, and it would be such a shame to let an initial struggle with arithmetic get in the way of appreciating all that wonder and beauty.

Even though there’s a lot of work involved, I promise you it’ll be more than worthwhile!

So, get to work! Start building your funda-MATH-tals today!

And don’t forget to come back for the remaining 4 parts in our series!