# How do professional mathematicians solve problems?

Here is a simple-looking arithmetic puzzle you often come across in puzzle collections. How quickly can you solve it? (Normally I stress that mathematics is not about speed; indeed, most mathematicians I know work slowly, as do I. But this time it’s different. The goal is to see how you do when you work quickly.)

PROBLEM: A bat and a ball cost \$1.10. The bat costs \$1 more than the ball. How much does the ball cost on its own? (There is no special pricing deal.)

How did you do? The most common answer people give instantly to this problem is that the ball costs 10¢. That answer is wrong. But if that’s what you got, you are in good company. If anything, your answer likely shows that you are a good thinker with some well-developed problem-solving strategies. It just that in this case, the problem is worded to trip you up if you follow a strategy that usually works. …

# How can teachers use video games to teach math remotely in the time of COVID?

Faced with students having to learn remotely in their homes due to the pandemic, teachers need to find new ways to keep their students engaged. Educational video games provide an obvious mechanism. If well designed, they are both educational and highly engaging. I don’t say that because I design educational video games; rather I decided to create educational video games because research carried out by me and many others had demonstrated their educational power.

Back when I and some seasoned veterans of the video game world and the educational technology world created BrainQuake, we viewed video games as being ideally suited for use as educational supplements. For children in particular, learning mathematics is best achieved in a class with others students, led by a knowledgeable experienced teacher, we believed. (And some of our team had been teachers.) We still believe that. …

# Game-based math learning can open up new educational possibilities

One question we get asked from time to time from people who have enjoyed playing our launch app Wuzzit Trouble is whether that puzzle is part of our new BrainQuake app. The answer is a “Yes, but …”

Wuzzit Trouble was a standalone mobile game that presented players with 75 puzzles based on a digital gears mechanic. Based on very positive critical reviews and two independent, peer-reviewed, comparison-group university studies that showed the game led to substantial learning gains (see the Research page on our website), we applied for, and were awarded, a 2.5 year, \$1.1M …

# What is an educational video-game?

Like many other companies, BrainQuake often describes our lead products as educational games. But what does that mean, exactly?

It seems like a simple question that will have an equally simple answer: surely, an educational game is one where a player learns something by playing the game.

But that can’t be the answer, because a player learns something by playing any game that involves some kind of problem solving.

I should note that I don’t mean this in the trivial sense that the player learns to play the game. …

# Hard Fun

At BrainQuake we develop “hard fun” math-learning activities.

But what exactly does that term “hard fun” mean? It’s certainly not our term. I first came across it in early in the New Millennium, when I was starting out on my investigation of the potential of video games to provide good mathematics education.

The term was introduced by object-oriented programming pioneer Alan Kay to describe an activity that is both challenging and enjoyable. The educational benefits of hard fun activities include learning how to manage frustration, develop and test new strategies, and gain confidence.

In a video game, hard fun activities provide safe learning environments where students can comfortably experiment, being free of the expectation to be “successful” at the activity the first time they try it. Good strategy-based and role-playing games are developed with this principle in mind. …

# Sir Ken Robinson and the Call for Creativity

Just as I was getting ready to write this week’s blogpost, the news came out that the fabled, British-born, education thought-leader Sir Kenneth Robinson had died, aged 70.

Along with many educators, we at BrainQuake have been greatly influenced by Robinson. His thinking about education, especially in relation to creativity, was made particularly influential by virtue of his ability to give engaging and entertaining — while at the same time highly thought-provoking — public talks. His 2006 TED talk in Monterey, CA, turned him into an Internet star.

I particularly like the animated video of a talk he gave in 2009 at the Royal Society of Arts in London, UK. The RSA edited the hour-long talk down to just over 11 minutes and created an animation. If you are not familiar with Robinson and his work, that provides the quickest way to get an overall sense of his thinking — though almost all the witty ad libs that made his talks (always planned, but unscripted) so entertaining are edited out. …

# What James Paul Gee Taught Us About Video-Game Learning

In 2003, Professor James Paul Gee, a cognitive scientist who at that time was a profes­sor of reading at the University of Wisconsin, published a thought-provoking book titled What Video Games Have to Teach Us About Learning and Literacy. That same year, I and two colleagues at Stanford University organized a three-day research workshop titled Gaming2Learn, aimed at bringing together leading education researchers and successful game developers to examine the prospects for developing good video games that provide good learning. …

# The psychological and social elements of good learning

One of the known benefits of game-based learning is that, providing the game is designed and constructed sufficiently well, it can help students adopt a positive and confident attitude towards the subject the game is intended to develop mastery in— in our case mathematics, with our particular focus being the hugely important general skillset of mathematical thinking and creative problem-solving capacity.

The importance of developing a positive attitude to a subject being learned was highlighted by the cognitive psychologist Carol Dweck in her ground-breaking book Mindset: The New Psychology of Success, first published in 2006, where she contrasted a growth mindset that can lead to good learning, with a fixed mindset that leaves students with a sense they are just not cut out to master whatever it is that is being learned. …

# How do people use math today?

I don’t know the answer to that question. Other than to say they use it in lots of different ways.

I can say that, in many cases, people use math without knowing it, since we have succeeded in creating mathematical tools that where the math is completely hidden.

Google is one example. Search engines are implementations of mathematical algorithms — more complex versions of the familiar procedures we have for adding, multiplying, subtracting, and dividing numbers. Similarly, when we look for items to buy on Amazon or any online store and then place an order, we are instructing mathematical algorithms to meet our needs. …

# Learning math at home during the pandemic

We launched this blog at the same time we released our new BrainQuake mathematics learning and assessment app. (Initially for iOS mobile devices, in due course also for browser access on the Web and for Android devices, both of which currently carry our launch app Wuzzit Trouble.) Not surprisingly, our first sixteen posts have focused on various features of the new app. And future posts will continue to discuss features of our product and ways they can be used, along with announcements of new features as we add them.

But we don’t see ourselves as just another company making and selling a product. All of our team has a background in education (two are former K-12 teachers, one a college math instructor) and we all have experience designing and producing educational technologies. We created BrainQuake because, with years of diverse experience behind us, we felt we had something of value to contribute to mathematics education. As such, we envisage our products being put to good use alongside other resources. Ultimately, this blog is intended to be one of several educational resources we provide. Our goal is to help make the entire system better. To that end, we are constantly examining how we fit in alongside, and both supplement and complement, other educational resources. …