In the book and movie The Martian, astronaut Mark Watney is stranded on Mars when the rest of his crew barely escapes a sandstorm in which Watney is injured, and left for dead. Surviving in a hostile alien environment takes every ounce of courage, ingenuity and humor he can muster, invoking biology, chemistry, physics, and duct tape. The author Andy Weir, the scriptwriter Drew Goddard, and director Ridley Scott do a magnificent of avoiding (in Andy's words) “sounding like a Wikipedia article”, and instead create a rousing (in Drew's words) “love letter to science”.

After seeing the film, it dawned on me that the entire film is a glorious example of how to teach mathematical problem solving through story telling — something I believe is much needed in mathematics education. And indeed I found several articles online discussing the Math of The Martian, and The Martian is full of Word Problems. Here are five lessons all math teachers can learn from The Martian. (Warning: Spoilers ahead.)

**Make the viewer care about the problem****. **Word problems in math class are lousy stories — mere equations with names attached — so students race through them without bothering to think carefully. In the Martian, you care about the problems Watney faces because you want him to survive, and because you are intrigued by the unfamiliar other-worldly setting. The classic educational game Oregon Trail uses a similar plot device — you are a pioneer leading a team of settlers out to the American West — to draw students into a singularly memorable educational experience.

A good way to make students care about word problems is to put student names and interests into the problem. It's a simple trick, but it helps. The app and web site Bedtime Math captures student interest by leading with a popular image or intriguing news story, then asking questions about the story. You can do something similar by basing word problems on current events, or topics you are studying in class. You can also have students make up problems for others to solve — students are more motivated to solve problems that came from other students.

**Let the problems lead**. Problem solving is naturally dramatic. You encounter a problem you don’t know how to solve. You try something. It doesn’t work. You try something else. Eventually you have an insight and triumph. That’s the dramatic arc of story telling, and also of problem solving.

Author Andy Weir constructed The Martian by solving the unfolding sequence of problems that he put in front of his protagonist. Watney solves his food problem by farming potatoes. But where will he get water on Mars? Andy had to call on his rusty knowledge of chemistry to solve that one, and early readers corrected his mistakes. He let the actual science guide the plot, which led to a delightfully plausible story.

Just as Andy did not in advance where his plot was going, you as a teacher do not need to know in advance all the answers to the problems you pose. Instead, show your students that it is okay to struggle, to not know, and follow the problem wherever it leads.

**Make thoughts visible**. Every problem Watney solves has visible consequences. Plants grow. Warmed vehicle interiors allow him to wear less clothes. Rocket fuel explodes when the chemical mixture isn’t quite right. In contrast, solving a math problem on a worksheet has no visible consequence, so it is hard to care about the result. In Dan Meyer's TED talk Math Class Needs a Makeover, he shows how to turn a drab word problem into an arresting visual experience.

**Show the emotion**. The Martian includes plenty of technical detail without ever losing narrative momentum. How? First, there is plenty of drama in the numbers. To survive Watney needs 1,500 calories a day. Growing potatoes will provide him with 115,500 calories. That will extend his food supply 76 days, which alas is far short of the thousand or so days he needs to last.

But more importantly, Watney is an astronaut, a human with a preternatural ability to focus on solving problems as they come up, even in the face of death. Especially in the face of death. So his palpable enthusiasm for numbers is an expression of his character. And of course what we're really seeing here is author Andy Weir's infectious zest for problem solving. By showing us the full range of Watney's emotions, from joy to despair, the author keeps us engaged in the story.

Many teachers are self-conscious about showing the full emotion of problem solving, because that means admitting that you don't always know what to do, can be bored or intimidated by problems, and sometimes make mistakes. But if we want students to be able to feel comfortable with uncertainty we need to start by modeling it ourselves. If we always act like we know exactly what we are doing, then students will do the same, covering up their confusion by pretending they understand, and never correcting their own misunderstandings.

A good way to make everyone feel safe with expressing emotion is to present puzzles that you have not tried yourself, and that require original thinking. That puts you and the class in the same position. Your role as teacher is to coach students to ask good questions. And you can do this confidently even if you don't know the answers yourself.

**Show the messiness**. This is where The Martian really shines. Drama is about things going wrong. And in The Martian just about every type of thing that can go wrong does: from faulty weather prediction, freak accidents and mistaken assumptions (calculating the oxygen in the habitat without accounting for his own breathing), to political maneuvering (cooperating with China), logistical tradeoffs (shaving days off a production schedule), and ethical decisions (save Watney or save the other five crew members?).

And this is where schools get it all wrong. Traditional math classes prepare students to answer highly manicured, abstract problems like “find solutions to the equation x^2 – 5x + 6 = 0”. To this end, worksheets remove all messiness: no story, no context, no multiple solutions, only problems that fit a specific format. The result is students who memorize formulas without understanding what they mean, and cannot apply their learning to situations that differ even slightly from the forms they see in textbooks. By protecting students from the messiness of problem solving, we cripple them, and give them the false impression that problem solving is neat and efficient.

For students to master mathematics, they need to be experience math in the wild — full-bodied situations with real consequences and no neatly prepared roadmaps. Only by encountering meaningful problems, failing, and recovering, can students learn what it means to survive in the world mathematically. In the future I hope to see more stories like The Martian woven into mathematics education.