The Math of Khan

About a month and half ago, I signed up for Khan Academy, an educational website that features lectures and exercises on everything from basic math to computer science. The website, which seeks to provide “a free world-class education for anyone anywhere,” is certainly a step up from Lumosity. Instead of having users play “fun” games that are meant to improve their memory and problem solving, Khan Academy gives users real math problems to solve. And people seem to like this model: Khan Academy’s YouTube channel now has over 1.5 million subscribers, and the highest-viewed video, a TED Talk by founder Salman Khan from two years ago, has over three million views.

Calculators, like this one, are your friend! (Image courtesy of Stock Exchange.)

My goal in registering for Khan Academy was to improve my math skills, and it seems like a pretty non-threatening place to practice. The learning model allows users to learn at their own pace: I had the option of starting at square one (basic addition) or jumping right into more complicated concepts like calculus and algebra. And Khan Academy tracks each user’s progress, which means I can go back and look at how I was doing when I started compared to how I’m doing now (as opposed to Lumosity’s “You can’t see how you’ve progressed unless you pay us” model). Khan Academy also rewards users with badges; earning one always gives me a strange sense of pride and accomplishment.

Admittedly, I haven’t logged onto Khan Academy very often since I signed up for it. It’s hard to get motivated to do something that strikes such fear into my heart (i.e. math). However, every time I log in and try my hand at some math problems, I feel good about what I’m accomplishing; I feel like I’m making progress each time I label a graph correctly or identify which fraction in a pair is greater than the other.

Founder Sal Khan has been the subject of acclaim as well as criticism in the media, though. For every article praising Khan for the possibility of revolutionizing the American school system, there’s another one questioning his abilities as a teacher or pointing out his video tutorials' flaws.

The debate rages on, but for now, I'll just keep doing exercises about square roots.

Janet Goertzen

Janet graduated from Bishop’s University with a Bachelor of Arts in English in 2010. She hopes to someday make a living from her words while continuing to avoid the terror of numbers. In her spare time, Janet can be found reading, playing trivia games, watching cat videos, or correcting people’s grammar on the internet.

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Training My Brain Online

Lumosity is “the web’s most popular brain training program,” and claims to help users improve skills such as memory and problem solving through games that are based on neuroscience. If users train regularly (Lumosity recommends at least three sessions a week), they should see improvements in their daily lives.

I signed up for Lumosity in mid-September and have been completing training sessions at least three times a week since then. Each training session consists of three games (or five games for paid users), a different selection every time. Lumosity chooses games for each user based on a set of training priorities, which the user chooses. My top five were memory, problem solving, attention, flexibility, and speed. Each user can also select a type of training to receive – Standard, Advanced, or Student – to determine the difficulty of each game.

So, have I noticed a difference in my everyday life since I’ve started my training with Lumosity? The short answer is no. An overview of my Brain Performance Index (BPI) suggests that I’ve been steadily improving since I began, and that my best “Brain Areas,” based on my performance in certain games, are attention and flexibility. Certainly, I’ve found that most of the games I play get easier as time goes on. But I don’t think it’s because I’m getting smarter, or thinking more logically, or becoming more observant. I think it’s because I’m just becoming more familiar with the games, especially since I play all of them at least once a week, and some of them twice a week or more.

However, Lumosity is steadfast in their claims that their games can improve people’s brain abilities. An entire section on the website is dedicated to the science behind Lumosity, and it features a number of peer-reviewed studies. But of course Lumosity is going to share success stories on their website, so I searched other sources for studies on the subject. Both DailyTech and The Guardian ran articles this year that acknowledge the murky science behind Lumosity’s model and also touch upon the idea that maybe users improve in certain games simply because they grow more familiar with them.

Whether these “brain training” games are actually doing what they claim to do or not, I admit I enjoy playing some of them. And since a game’s primary function is to be fun, that’s not the worst thing in the world.

Janet Goertzen

Janet graduated from Bishop’s University with a Bachelor of Arts in English in 2010. She hopes to someday make a living from her words while continuing to avoid the terror of numbers. In her spare time, Janet can be found reading, playing trivia games, watching cat videos, or correcting people’s grammar on the internet.

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Overcoming Math Anxiety

A chewed-up pencil is representative of my past math-related experiences. (Image courtesy of Stock Exchange.)

Something that makes me feel better about my phobia of math is the knowledge that I am not alone. (Something else that makes me feel better is the fact that my skills with numbers are no longer being tested, and that I am allowed to use a calculator in my everyday life – but that’s another story.)

A quick Google search of “math anxiety” yields over nine million results. Most of these results link to pieces about how common math anxiety really is, as well as strategies to help people overcome this concern. Most of these tips are for high school students. They don’t exactly apply to me – I’m not writing math tests every few weeks anymore – but they are still worth thinking about, and they can actually be applied to a lot of other anxieties as well. For example, it’s important to recognize that math anxiety is an emotional response to something intimidating – it has nothing to do with intelligence and everything to do with confidence. Chances are, if you don’t believe you can do something, you won’t do it. On the flipside, if you believe in yourself, you’re a lot more likely to succeed.

A widespread belief is that girls are more prone to math anxiety than boys, and that boys are better at math. However, this article from Science Daily refutes both of those beliefs. In one study, elementary and high school students were asked to measure their level of anxiety. It concluded that girls more often report general anxiety about math. But when it comes to math tests, reported levels of anxiety are about the same. Another study suggests that some girls underperform in math class because they believe the stereotype that girls are inherently bad at math, creating a self-fulfilling prophecy.

In my quest to conquer my fear of math and logic puzzles, I’m keeping these articles and studies in mind – particularly the lesson that confidence is key and I shouldn’t get discouraged if I make mistakes. Like all things in life, success in math means not being afraid of being wrong; it's an important part of figuring out how to be right.

Janet Goertzen

Janet graduated from Bishop’s University with a Bachelor of Arts in English in 2010. She hopes to someday make a living from her words while continuing to avoid the terror of numbers. In her spare time, Janet can be found reading, playing trivia games, watching cat videos, or correcting people’s grammar on the internet.

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Are You Out of Your Vulcan Mind?

The website Sporcle is one of the best time-wasters ever invented. It is home to literally thousands of quizzes, on everything from Pokemon to world homicide rates to Agatha Christie novels to the most common Pope names. Seriously – search just about any topic on Sporcle and you’ll find a quiz about it. I’ve been playing games on Sporcle regularly for about the past five years, but I typically stick to topics that I know I will excel in: Game of Thrones trivia, lyrics to Beatles songs, spelling challenges. Those are all firmly in my wheelhouse. I’ve stayed as far away from logic quizzes as possible – until now.

I wish I could get some guidance from this guy. (Image courtesy of Wikimedia.)

I’m going to attempt a quiz called Nimble Number Logic Puzzle. The title already has me worried, and the ending of the url – “hardest-logic-puzzle-ever” – has me terrified. But this blog is all about facing my fears, so I’ll channel my inner Spock and think logical thoughts.

About five tries in, I am officially frustrated. So far, my fourth try has been the most successful, and I spent most of my fifth try attempting to quickly recreate my previous try, using my memory instead of my skills of deduction. Perhaps on my next attempt, I’ll use logic instead of my memory.

By my eighth try, I am getting very close to solving it, but still making mistakes. I can do this.

At a certain point, I get excited about getting the puzzle done correctly and I start to make typos – which end the game. Of course, this just gets me more frustrated, and I make more mistakes.

Finally, on about my 12th official try, I solve it! I’m flooded with a sense of relief and satisfaction – I don’t even care that it took me so many tries and I made so many mistakes. I finished it, and I did it all by myself, and I didn’t even look at the user comments for help. I did it!

Of course, I read the user comments after finishing the quiz, and most people were saying that it was the “easiest logic puzzle ever,” which makes me feel a little disheartened, but hey. I struggled with it and I conquered it. I'll work my way up to the harder puzzles, but for now, the important thing is that I'm making strides.

For more logic puzzles, as well as puzzles on any topic imaginable, visit Sporcle. 

Janet Goertzen

Janet graduated from Bishop’s University with a Bachelor of Arts in English in 2010. She hopes to someday make a living from her words while continuing to avoid the terror of numbers. In her spare time, Janet can be found reading, playing trivia games, watching cat videos, or correcting people’s grammar on the internet.

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My Hellish Challenge Begins

I have never been a fan of math.

Actually, let me rewind a little. In elementary school and middle school, I was fine with math. I never enjoyed it, but I also did perfectly well in all of my math classes. It was high school where my problems began. When I was in grades nine through twelve, my math homework regularly had me in tears. Combine a basic aversion to numbers with a lack of willingness to ask for help and you’ve got my math class experience. 

Image courtesy of freedigitalphotos.net

If you’ve ever heard of the theory of left brain vs. right brain dominance, you can probably come to the conclusion that I’m more of a right-brained thinker. According to the theory, different sides of the brain control different types of thinking, and furthermore, most people are dominated by one side of the brain. The right-brained thinker is creative and expressive, while the left-brained thinker is more logical and analytical. Although this theory has recently been debunked, I still think there’s validity to the concept that some people are creative-minded, while others are more logic-based – regardless of which part of their brain they use more.

I’ve decided it’s time to challenge myself and face my phobia of numbers and logic. I’m going to try things I thought I never would: Sudoku, logic puzzles, and more. I’ll also record my progress at Lumosity, the brain training website where I’ve created a free account. The exercises at Lumosity will theoretically help me improve my memory and logic skills.

First up, I tried my hand at a Sudoku puzzle at websudoku.com. I attempted a puzzle on Easy and managed to solve it, after a couple errors, in 10 minutes and three seconds. Not bad, right? And – this is important – I didn’t totally hate doing it. This seems like a promising start.

Lumosity, on the other hand, seems like it will be more of a challenge. Some of the training exercises are easy and straightforward enough, but others – like solving math problems inside raindrops before they flood the screen – are harder, especially with all that added pressure. If I keep up with my training, I should see improvements in my memory, attention, and problem solving.

Click here for more information about left brain vs. right brain theory, and here for more information about the debunking of left brain vs. right brain theory.

Janet Goertzen

Janet graduated from Bishop’s University with a Bachelor of Arts in English in 2010. She hopes to someday make a living from her words while continuing to avoid the terror of numbers. In her spare time, Janet can be found reading, playing trivia games, watching cat videos, or correcting people’s grammar on the internet.

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