Math: All You Need Is Games

Image By Rebecca Angel

I was the kid that had to stay in at recess in second grade. Was I bad? No, I needed extra help in subtraction. Sister Brendan, a very nice old lady (who gave me snacks too) sat patiently with me each day to get my wee brain to learn the tools of taking away in an equation. I was a smart kid, and I could memorize how to do it, but I didn’t understand why and that made me second guess myself and screw up on tests. Eventually I got the concept, but I also learned another lesson: Math isn’t fun.

But it can be! My teen son loves to play board and card games with his young cousin. They both homeschool, so I suggested he come up with a math curriculum for her that incorporated games we already owned to teach the concepts she was supposed to learn in second grade (according to Common Core for a reference). Her parents thought that was great, and when she took a simple test at the end of the year, she aced it. No boring textbooks and worksheets!

Unlike most math curricula that teach one concept at a time, games utilize several skills at once in a fun atmosphere that keeps the challenges from getting overwhelming. Basically, instead of learning to do math on its own, the student is using math to play the game.

Granny Apples is a good example of multiple math skills at once. It is a simple game of tossing wooden apples on the ground and counting the different types to find a total score. However, it involves fractions, addition, subtraction, sets, and is all mental math in a visual setting. There is no writing involved, which is perfect for learning concepts without tripping over the writing/reading challenges. It is a fast game with tactile satisfaction with smooth wooden objects.

Bakugan is perfect for those writing/reading challenges, and so fun that kids will not care. Each sphere is tossed into a ring and pops open to reveal a monster. Each monster has a number printed on it for its “battle score.” But these scores are up to triple digits. The student must keep track of all the digits, keep their columns neat, and continually add and subtract to figure out if they win the battles.

Polyhedron Origami is not a game, but the best way to teach geometry of three dimensional shapes—by building them with paper. It is not difficult, but requires attention to detail, with a satisfying ending of something beautiful with math. Using this method, even the youngest students can make truncated octohedrons, and know what that means!

Phase 10 Card Game is all about sets, patterns, and reasoning.

Could there be a more entertaining way to learn graphing skills than Battleship?

The top half of the Yahtzee sheet is a fun introduction to multiplication. Rolling dice, counting, and writing. Over time, students will count the dice faster and faster based on the visual sets of dots on each die. This is learning sets and geometric reasoning for multiplication skills. Sounds complicated, but in this game, it’s just fun.

Games like Cathedral Chess, TangoesMancala, and Connect 4 are ways to teach spatial reasoning, patterns, shapes, strategy, structure, reasoning, and mental acuity. They range in complexity, but are able to be played by children as young as five in simple formats.

Check out some other posts about math games here and here and here and here.

What games does your family play that teach math concepts?

Kids Won’t Shy Away From Geometry in ‘Land of Venn’ App

Image: Land of Venn Geometric Defense, used with permission.

I fall short in the math area of STEM. I hated geometry in school. I can’t repeat on this site the words that come to mind when the term trigonometry is used. When my daughter comes home with requests to work on her math facts, I go to the computer and look for an app that will help her. At this point, it isn’t because I’m afraid of the math, it is because I am afraid that my dislike of the 4-letter word will rub off on her, or worse, I will teach her something incorrectly and ingrain a bad example that will serve as the seed for so many math lessons to come.

This said, the newest app in my anti-math mom arsenal is called Land of Venn Geometric Defense. The characters have such interesting and unique names, I would not do it justice in explaining the purpose of the game, but their video pretty much tells you everything:

There is a lot visually happening in this app. Some of the platform bits move, but are not interactive which makes it challenging to tap and drag the correct thing at times. Sometimes there are so many things to tap and drag that a tablet is a preferred surface to make geometric shapes on. Especially if you are an adult playing this game, it’ a good idea to drag out the tablet unless you want the added challenge of a small screen and adult fingers. On a phone, another obstacle is potions (when you get them) that take up room in the bottom of the screen and cover up bad guys, taking precious time away from making your geometric shapes of villain destruction. In later levels, quadrilaterals are requested for ultimate destructive power against the juice-stealing varmints. Again, adult fingers on a phone screen aren’t the best combination for achieving a 3-star rating on a level.

straight line
They call it a straight line, I call it a line segment. What do you call it? Image: Land of Venn, used with permission.

My only observation about the geometric facts the game presents is a technicality, the shortest distance between two points is a line segment—but for kids, this is not a necessary point (pun intended).

The video above features most of the intro video to the app. It took me several times through the video on a tablet and phone to understand the thick accent in the opening scene. Once I heard it on the computer, I understood. Thankfully, I didn’t need to understand the video to play the game. It is mainly for flavor.

Minor complaints aside, this app is much easier for kids to handle with their tiny fingers, and they hear things better on average than us deaf old fogies. My kids couldn’t wait for me to finish my testing of the app so that they could give it a try.

The Adventure Time-like art is amazing. The game features crisp lines which aids in making the game playable. The areas shown in the game are beautiful. It, like other cartoons of the same style, is a little gory. Some of the attacks used on the invaders send knives out of the ground into the offending parties. It is a little graphic, but I don’t have a problem with my 5- and 9-year-old kids playing the app.

1st world levels
After the ten areas are completed, the arch at the top becomes a mini game to test the players retention of the shapes they made in the game. Image: Land of Venn, used with permission

The game has three areas to complete with ten levels in each. Each area ends with a gate that unlocks after each type of geometric shape is correctly identified. I really like this part of the game. It adds a different way of learning and adds repetition into the game without the player really noticing. The test was a nice break from the mad tapping. After unlocking all three gates, I was looking for more.

Originally, the game was only available in the App store for $4.99. It has expanded to the Amazon store and is available for $0.99. An Android version will be available after a few bugs are worked out in Beta testing (I ran through beta testing on my Samsung. After an initial download issue, the game played beautifully on the device, so I am hopeful the game will be available to the public soon). The development team is very involved with fixing any issues and has listened to feedback to produce a superior app for kids learning.

GeekMom received this item for review purposes.

Odd Squad: Warehouse 13 For Kids

© 2014 The Fred Rogers Company

Pete Lattimer and Myka Bering best move over; they have been replaced by a younger crew.

Agent Olive and Agent Otto are the stars of Odd Squad, a Canadian/American show that debuted in Canada and on PBS Kids on November 26, 2014. My sons discovered it about a month ago. I have to say, kids, grandparents, and parents alike are all enjoying the escapades of this quasi-governmental agency.

© 2014 The Fred Rogers Company

Odd Squad is an agency run by children, who seemingly stop aging at age 10. They investigate strange or odd phenomenon, as the local branch in their town. It is unclear whether this is a localized oddity, such as Sunnydale’s hell mouth, or if such oddities are nationwide.

If you open your mouth and start barking instead of talking, Odd Squad can help. If a swirling vortex appears in the park, Odd Squad can help. If pizzas across town are being delivered with two pieces missing, Odd Squad can help.

Sometimes the storylines are well suited to a kids show, but most of the time they could be easily adapted to Warehouse 13, The X-Files, or Once Upon a Time without skipping a beat. There is some excellent writing at work here, and some very innovative, creative minds. Each episode starts with a quick fix case before moving into the main storyline.

The show frequently nods its head at mainstream shows that have come before it. The transport operator is always O’Malley, O’Hare, O’Brien, O’Donohue, or something of the like, in seeming reference to Chief O’Brien from Star Trek: The Next Generation. There is an episode featuring animals called Centigurps, who populate headquarters like Tribbles. The storage facility, in which they store artifacts, animals, or other oddities that need to be contained and collected, is remarkably reminiscent of Warehouse 13. It’s a lot of fun watching for allusions and references in these episodes. Things that my children will never pick up on, but that tickle me to no end.

Ms. O © 2014 The Fred Rogers Company

The show has great writing and a great atmosphere, but also a great lineup of main characters. This really sets Odd Squad apart from other kids’ shows. The two main characters are Agent Olive and Agent Otto. Olive is the veteran, while Otto is her rookie partner. They play off each other nicely, and bring out the best in each other. Olive is the more straight-face agent, while Otto serves well as a foil. Their strengths play off each other, and the cases are solved best when the pair are working together.

The head of the organization is Ms. O. Ms. O has been around since the 80s, and rules Odd Squad with a big stick and an even bigger voice, but always with a juice box in her hand. Ms. O is obviously a homage to the Judi Dench years of the James Bond franchise, and it is wonderfully played. Ms. O has the answers to the most obscure problems, and is always several steps ahead of her agents. She trusts them implicitly, but will not tolerate running in headquarters.

Agent Oscar is the squad’s resident scientist and inventor. He has a gadget for everything—and I do mean everything. Olive and Otto go to Oscar whenever they need technical help, and he is usually sent to the field by Ms. O to assess a situation that the other agents can’t handle, such as the Hydraclops or the vortex.

Dr. O © 2014 The Fred Rogers Company

The cast has a great gender and racial balance, and so far stays far away from playing up to stereotypes. In one scene, Olive, Otto, Oscar, and Dr. O are fighting off robots in the princess room. Olive and Dr. O send Otto and Oscar out of the room, and retreat to the door backwards while firing at the robots. Olive proclaims “I never liked princesses” and Dr. O concurs. It’s a really well played scene. Just when you think they are going to kowtow to some form of stereotype, the producers subvert it, make fun of it, or make it irrelevant.

Dr. O is Odd Squad‘s resident doctor. She is a very eccentric character with great problem solving skills. She frequently reminds the other agents, “I’m a Doctor,” and while usually I might chaff against a girl character reminding us of that, in no way does it come across as negating her value. It is a personality quirk and simply amplifies her eccentricity. Nothing in this show belongs to the boy characters and nothing to the girls, and it is a wonderful to see and to have modeled to my two sons.

Odd Squad uses math to investigate strange occurrences and to come up with solutions. This is the only part of the show that feels laborious to the adults watching. However, both of my kids count and add along with Olive and Otto, and it has really made a dent in my five-year-old’s indifference to math.

The show also teaches perseverance and teamwork. It frequently goes over the idea that it’s okay to go through several wrong solutions on your way to finding the right one, a big believer in trial and error. The episodes always start with a voice-over by Agent Olive: “My name is Agent Olive. This is my partner Agent Otto. This is ____.” The third thing shown on the screen is always something random, that never has anything to do with the storyline that follows. The best one so far has been “This is Emmy Noether.” It is wonderful to think of how many kids (and adults, ahem) then looked up Emmy Noether, whom Einstein described as the most important woman in mathematics. This show uses math, but it shows how everyone can use math and how important it is.

So far my favorite episode has been episode 21: “6:00 to 6:05.” In this episode, we learn the dangers of confusing 6:05 with 1:30. It features the dinosaur storage facility at Odd Squad headquarters, a time machine, and a girl’s passion for toy dinosaurs. Absolutely brilliant.

My son’s favorite episodes are anything involving a character called Delivery Doug, who delivers egg salad sandwiches in his egg mobile. It’s what’s for lunch in our house these days.

You can watch Odd Squad online at or PBS Kids during the week. Each episode is made up of two 11-minute adventures and the show is aimed at ages 5-8. We stream through our Roku channel.

Kalk: A Card Game That Makes Math Fun!

Image: Kalk (Used with permission)

I was cruising Kickstarter the other day, as one does, and I came across something unexpected among the plethora of games and comics that I usually love to back. It was a math game.

Now, math is on my mind a lot these days. Both my son and I learn math almost organically. Workbooks are like tedious torture to us, because we need to see the math in action. So I have been looking for ways that I can help him learn in a way that makes sense to us. We’ve had a lot of fun with Math Dice and other games like that.

Kalk might just be the next math game in our library.

After watching their Kickstarter video (which does an awesome job at explaining how the game works) and talking with designers Tommy and Jonathan a bit via email, I could tell these guys were both enthusiastic about their game and passionate about sharing a love of math with everyone, even those who have a hard time with it. I took the opportunity to ask them a few questions about their game, so hopefully others could share in their enthusiasm.

GeekMom Mel: What inspired you to make Kalk?

Jonathan: When I was young, my mom and I used to go on the street and she used to ask me to sum up car’s license plates, after a while it became easy and she challenged me to get to specific numbers by using + – x ÷, just like our goal number in Kalk.

GMM: Why math? Do you have a special relationship with the subject?

Tommy: Jonathan is more into math actually, but we both created this game in order to bring math to kids and parents in a cool and fun way, so everybody will like it, like we do!

GMM: What do you think makes Kalk different?

Tommy: Kalk is a very simple game. It takes less than 10 seconds to learn how to play. This was one of our challenges in creating something simple, yet challenging and inspiring. You can actually choose the difficulty by adding more cards, playing with our magic cards, or choosing your competitors.

GMM: What do you think is the funnest part about math, maybe something that even people who hate math can appreciate?

Jonathan: The funnest part in math, in our opinion, is the ability to solve things in different ways. It always amazes us how creative our minds can be! For example, we are posting several challenges during the week on our Facebook page, and it’s always fun to see people solving our riddles in different ways.

Image: Kalk (Used with permission)

GMM: Were you good at math growing up?

Tommy: Jonathan was really good! He’s like a little professor even though he doesn’t admit it. He used to help me in school, but it didn’t help that much. However, since Kalk was created, my math skills got better. Jonathan still wins ⅘ of the times! :)

GMM: Tell us a little about the process of designing your game. What was the funnest part? Which part was the hardest?

Jonathan: The design process of Kalk was very cool! Me and Tommy used to play Kalk long before we launched the project. Back then, I started to imagine how it will look. The hardest thing I did was to design the right numbers that will look clear, fun, and appealing to both kids and parents. The funnest part was to print the first pack of Kalk and playing it for the first time!

GMM: Do you have any advice for parents who might have kids who struggle with math?

Tommy: We would suggest to go really slow with it, for some kids (like me!) it doesn’t come naturally. Try to make math more like a fun riddle, or a challenge and less like just an assignment.

Image: Kalk (Used with permission)

GMM: Anything you’d like to add?

Tommy and Jonathan: We would like to add that we are really excited about this project and hope we will fund it within 20 days. It will be much appreciated if people could help us spread Kalk to the right people because unlike other “cool” projects on Kickstarter, those educational projects are a bit behind.

We really care about kids’ education these days, and believe that Kalk is a part of the solution with all the crazy technology games that you can find today. We miss sitting in the living room and play cards with friends.

We have created Kalk because we think it’s time to exercise our brain and reinforce our math skills (… and hopefully yours too!).

Best of luck with your Kickstarter campaign, Tommy and Jonathan. This looks like an awesome game, and I know I’ll be backing it!

For more details, or to back the Kickstarter, please check out Kalk‘s campaign!

Geek-twisting Holiday Songs

Image By Rebecca Angel

Oh, who wants the same old boring lyrics to our holiday favorites?  Altering words to existing songs is a playful, challenging, and creative endeavor. It’s the fan-fiction of music. Winter and Christmas tunes are so well-known, it’s a great place to start. Here are some people who have already done so with a geeky twist:

The Twelve Days of Future Christmas created by Bridge 8, goes through a list of current science topics that are on the verge of becoming reality! “12 drones delivering…”

(TUNE: “Oh Christmas Tree”)
Oh, number Pi. Oh, number Pi. Your digits are nonending,
Oh, number Pi. Oh, number Pi. No pattern are you sending.
Want more math Christmas songs? Go here!

Hee-hee. This is some crazy editing. Star Trek TNG in “Make it So!”

You better watch out; you better not sneeze.
You better not cough, ’cause you’ll spread a disease….Viruses are comin’ to town.
“Catch” all the lyrics here.

This one doesn’t change the lyrics so much as it is performed in a geeky way. All electronic devices band in “Feliz Navidad.”

Pirate Christmas Carols! This is from me. I’ve written a lot of these. Here is one you can listen to with lyrics. No Ale!No Ale! No Ale! No Ale! Six months at sea with no dark, stout or pale.

So what’s does your family geek out about? Make it a family game to rewrite lyrics to a familiar holiday tune. You’ll be singing it every year afterwards!

Here’s one I wrote about my favorite Avenger…

Loki Was A Gentlemen
(To the tune of God Rest Ye Merry Gentlemen)
Loki was a gentleman when he took all the power.
His smile was quite debonair as he told us to cower.
“Sweet lady, kneel before me now, no need to look so sour.
Many thanks, this encounter’s been a joy, been a joy.
Many thanks, this encounter’s been a joy.”

Primo: A Mathematical Board Game

Primo Board, showing the color-coded numbers along the line to 101. © Primo

I am always on the lookout for ways to help children to practice their mental mathematics skills. Children need lots of opportunities to use these skills to ensure that they have a really good grasp of mental calculation, which is vital as they take mathematics tests and also as a life skill. However, drilling these skills with worksheets can be dry and boring, so other tactics are required.

Over the years that I’ve been teaching, I’ve developed a few games of my own, but when I heard of Primo, I thought I’d check it out and see if it would be a useful addition to my teaching arsenal.

Primo is a board game designed to help children practice their mental calculation skills while playing a game of both skill and chance, based around the power of prime numbers. The board is the main draw here. It is cleverly designed to show the divisors of a number by color coding, acting as a support for those who might need a little extra help and also showing the patterns of the numbers.

Players have two pieces on the board, and race to see who can make it to 101 first by rolling two dice and using their scores to move the pieces. If a piece lands on an opponent, they are sent back to the start. Players can use all four operations to move their pieces forward and backward along the number line, meaning that their mathematical skills get a good workout.

Extra excitement is added in the form of both positive and negative cards, which are drawn when the player lands on a prime number. Some have to be played immediately, while others can be kept and played when they will produce the most reward, or the most havoc.

I must admit that it took me a while to get my head around the rules, but once I’d got it, it wasn’t as complicated as I’d feared at first glance. I did find that the difficulty of the game dropped off too early for the group that I played Primo with, as we found that as our counters got closer to 101 we couldn’t use multiplication or division arithmetic to move our pieces. However, we played with the basic rules, and there will be sets of rules available that will adjust the length and difficulty of the game. It could also be a good learning opportunity for children to come up with their own rules that extend the game or adjust its difficulty. You could use one piece per player and just add and subtract with younger children, for example.

I think that Primo is a really great idea, and is well executed too. I particularly like the color-coded board, which as an educator I can think of lots of other uses for, too! The tactics of advancing your pieces while also trying to knock others off the board can inspire some great mathematical thinking and will really help to keep those mental mathematics cogs turning. I can see a group of adults spending quite a while agonizing about which move to make to stop their opponents and also to race for the prime spot of 101. Personally, I can see myself using this in the classroom to keep mental mathematics practice fun and engaging.

The Primo Kickstarter has already met its funding goal, but it does have a few days left if you’d like to order your own game.

GeekMom received this item for review purposes.

Geektastic Cookie Cutters You Can Print

R2-D2 cookie cutter design file and printed work by bluedynno

A few weeks ago, a friend asked me if you could 3D print cookie cutters, and indeed you can. Much easier than bending your own copper! Then this week when looking for a design to test the setup of a new printer, that seemed like as good a choice as any. And Thingiverse, the repository of shared 3D printer design files, has a bevy of geektastic cookie cutters ready to print—here are just a few:

User theo has a whole set of geeky cookie cutters: The Apple, Arch Linux, and Open Hardware logos; a floppy disk; and a Pac-Man ghost.

Open hardware geeks can also print a cookie cutter of the Arduino logo or the Raspberry Pi logo.

Star Wars


Video Games

Doctor Who


  • Pi
  • A mole for celebrating Mole Day
  • Cookiequations—a set to make impressions for cookies with equations on them
  • More cookie equations pieces to use with number cookies: e, i, pi, phi, Sigma (big and little), i, sqrt(-1), and integral sign

Other Geekery


Bach’s Mobius Strip

Composite image By Rebecca Angel
Composite image By Rebecca Angel

Sometimes when artists visualize music, it detracts from the piece (scenes from Fantasia come to mind…), but this little animation by Jos Leys shows just how brilliant Bach can be.

Check it out with your kids, make a mobius strip, and then listen to the music again on the instrument Bach used to compose it.

The Fun on Peg + Cat Adds Up This Fall on PBS Kids

This fall, PBS Kids is premiering a brand-new show aimed at encouraging preschoolers to explore problem-solving skills and basic math concepts. Peg + Cat is the creation of Billy Aronson and Jennifer Oxley, who was also the creative director for Wonder Pets and 3rd and Bird.

The Chicken Problem © Random House

Oxley’s involvement alone was enough to get me interested in the new series, but it wasn’t until my daughter and I picked up The Chicken Problem at the library that we really began to be excited. Written by the show creators, The Chicken Problem is a fantastic introduction to Peg’s world. Peg is a girl who loves solving problems with her friend, Cat, and she has a personality that immediately leaps off the page and promises to translate well to the small screen.

The most striking part of Peg + Cat’s world, though, is the mathematical concepts that make up their world—literally. Flowers are created out of division signs, the clouds drifting in the sky are infinity symbols, and each page hides formulas and numbers. A commenter on the Peg + Cat opening song on YouTube identifies a formula in the background as a partial differential equation of a wave function.

If The Chicken Problem is any indication, Peg + Cat will be a fantastic way to get preschoolers like my daughter excited about solving problems. Three games are already up on the PBS Kids web site, and the pattern recognition activity Chicken Dance really got her wheels turning. According the PBS Kids press release, Peg and Cat’s adventures will take them across the whole wide world and beyond.

Each episode features a story in which Peg and Cat encounter an unexpected challenge that requires them to use math and problem-solving skills in order to save the day. Their adventures take viewers from a farm to a distant planet, from a pirate island to a prehistoric valley, from Romeo and Juliet’s Verona to Cleopatra’s Egypt to New York’s Radio City Music Hall. While teaching specific math lessons, the series displays the value of resilience and perseverance in problem-solving.

Peg + Cat premieres October 7, 2013 on PBS Kids.

Just HOW Badly Do You Need that A in Math?


Are you struggling in math? Have you ever considered what extremes you might go through to get those taxes done accurately? Or to balance your checkbook? Perhaps you need to finish up that statistical comparison of two backyard weather stations for your next GeekMom review.

Have you considered electrical stimulation to improve those skills? Roi Cohen Kadosh’s team at Oxford University has proven that it’s possible. Continue reading Just HOW Badly Do You Need that A in Math?

Happy Birthday, Sophie Germain!

Sophie Germain's grave, photo by Miek Messerschmidt on Wikipedia, cc.
Sophie Germain’s grave, photo by Miek Messerschmidt on Wikipedia, cc.

Today marks the 237th birthday of the French mathematician Sophie Germain (1776-1831). Germain was barely a teenager when the turmoil of the French revolution forced her to spend much of her time locked safely indoors. With not much else to do, Germain read her way through her father’s library and found herself deeply interested in the works on Archimedes, Sir Isaac Newton, and Leonhard Euler.

As you can imagine, Mathematics was not a proper subject for a young woman to learn, so she spent most of her life working by correspondence under the male pen name “Antoine-August Le Blanc.” Due to her interest in number theory inspired by Archimedes, she corresponded with many famous mathematicians specializing in number theory, such as Joseph Louis Lagrange, Adrien-Marie Legendre, and Carl Friedrich Gauss. She sent them her work and enticed so much interest from them that she eventually had to admit her true identity. Lagrange continued to be her mentor, while Gauss replied with the following remarkable quote:

“The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person of that sex, that, because of our mores and our prejudices, has to encounter infinitely more obstacles and difficulties than men in familiarizing herself with these thorny research problems, nevertheless succeeds in surmounting these obstacles and penetrating their most obscure parts, she must without doubt have the noblest courage, quite extraordinary talents and superior genius.”

Germain later became interested in a contest by the Paris Academy of Sciences “to give the mathematical theory of the vibration of an elastic surface and to compare the theory to experimental evidence.” This was essentially a brand new field of mathematics and the amount of work and innovation involved scared away potential candidates. Germain was in fact the only participant in the competition. Despite her immense talent, her submission to the contest was riddled with errors due to her lack of formal education. The Academy extended the contest multiple times and Germain persisted. She continued to work on the problem and presented an improved solution at every iteration. Her persistence paid off, her third submission was accepted and she became the first woman to win a prize from the Academy in all of its long history beginning in 1666. However monumental the win, Germain still not allowed, as a woman, to attend sessions at the Academy until many years later due to a friendship with mathematician Joseph Fourier (Fourier Series, discovered greenhouse effects).

After the years spent working in the contest in elasticity theory, Germain returned her first love, number theory. More specifically, she focused on Fermat’s Last Theorem.

You may recall Fermat’s famous theorem which proposed, in 1637, that for any three integers a, b, and c, an + bn = cn cannot be true for any integer value for n greater than 2. Perhaps even more famous is Fermat’s note about his theorem: “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” The puzzle of discovering Fermat’s “marvelous proof” has been the world’s most difficult mathematics problem ever since.

Germain did the first major advancement on proving Fermat’s Last Theorem in 200 years since its inception. Prior to Germain, Fermat’s Last Theorem had only been proven by other mathematicians for n values 3, 5, and 7. Germain worked a subset of the original theorem, known as Sophie Germain’s Theorem:

“Let p be an odd prime. If there exists an auxiliary prime P = 2Np + 1 such that if xp + yp + zp = 0 (mod P) then P divides xyz, and p is not a pth power residue (mod P). Then the first case of Fermat’s Last Theorem holds true for p.”

Germain’s work proved the theorem for all primes smaller than 100. It wasn’t a full proof, but it was a big step forward.

While her work in elasticity was fundamental to the field, she remains most famous for her work on Fermat’s Last Theorem–in my book at least, but I have a soft spot for Fermat’s Last Theorem. Please join me today in celebrating Germain’s life and the advancement for women in mathematics. Happy birthday, Germain! May we all be as self-starting, persistent, and courageous as she was.

No Starch Press Manga Guides Make Science Fun

Image courtesy No Starch Press

Have you ever read a textbook cover to cover? I’m in grad school. I’ve had to do it more than once. It usually requires massive amounts of caffeine and re-reading a lot of pages. Well, there’s some good news. No Starch Press has The Manga Guide series on textbook topics, such as statistics, electricity, and molecular biology. The manga books are written by Japanese subject matter experts. They  have been translated to English and (thankfully) rearranged to read from left to right.  Update: I’m told the Japanese originals were left to right, so no rearranging was necessary.

I have three sample use cases in my house, so No StarchPress provided me with three sample books. First is my 11-year-old daughter. She volunteered to read The Manga Guide to Electricity. Next up is my husband, who is studying for his GRE and has discovered that he’s forgotten everything he ever learned in high school math. He read The Manga Guide to Linear Algebra. I’m taking a graduate class in quantitative analysis this semester, so my book was The Manga Guide to Statistics.

All three of these books turn out to be very similar in plot. Character A is struggling with a topic and put into a situation that requires them to learn the subject matter from Character B. It doesn’t matter if they were sent from an alternative dimension with advanced electrical capabilities or trying to get closer to a school crush, the subject matter takes center stage in all of these books. Each goes through a series of illustrated examples that teach the concepts, and the struggling learner interrupts with lots of questions.

I thought that the idea would end up being so hokey that it would disguise the learning material, but I was drawn in to what turned out to be fairly cute stories within a couple of pages. My husband had several GRE prep books, Khan Academy, and a course through Udacity, but it ended up being manga that taught him the most, probably because of the struggling-learner-with-lots-of-questions approach.

I found The Manga Guide to Statistics to be surprisingly good as well. There was the manga story line, of course, but the book also had lots of problems you could work out yourself. The instructions showed you how to do the computation in Excel. Thank goodness. I’m sure a lot of students appreciate learning about statistical concepts and research methods without learning any of the math, but I’m not one of them. Working out frequency distributions or standard deviations really helps me see what those vocabulary words mean in action. The silly and very Japanese examples (the mean price of ramen in an imaginary building with only ramen restaurants) were actually pretty fun.

Speaking of Japanese, that may be the one caveat for this series. The books are translated to English, but there are still illustrations with Japanese text (which may or may not have been mirrored to make the comic books read left to right – I can’t tell). There are lots of cultural references to Japan. That makes sense and is completely part of the charm if you’re a manga fan. However, my daughter struggled with some of these cultural differences as she read. Little things like knowing what “Yen” meant. She’s a Miyazaki fan and no stranger to manga, but she’s also an 11-year-old American. An older child is more likely to see the cultural differences as interesting instead of a barrier to comprehension.

Even with that caveat, this was a cute and smart series. I’d  recommend The Manga Guide to home-schoolers, summer break supplemental learning, college students trying to brush up on a topic, and anyone with a love of anime or manga that wants to learn more about a math or science topic. I’d say the age range starts around middle school, but pay attention to the subject matter.  The books are overall solidly written and make hard science topics entertaining



Muse of Nerds: College Physics, Innovative Robotics, Homeschooling — Dr. McColgan Can Do It All!

For my Muse of Nerds this month, I’ll formally introduce you to someone I have talked about in the past: Dr. Michele McColgan of Siena College. I met her through our homeschooling group (she has two elementary-aged children) and she has introduced my kids to science, math, robots, computer programming, alternative energy, a Lego Robotics Team…and more than I remember. I first mentioned Michele in this post about soccerbots. And then again about a year-long project our four children worked on with RPGs and robotics.

At the moment, she teaches the general physics sequence to science and math majors, and electronics and optics for physics majors at Siena College, homeschools her two children, runs the Saturday Scholars program for inner-city youth, organizes summer camps in Physics, Alternative Energy, and Robotics, uploads regular YouTube tutorials, mentors Siena’s physics teams to participate in Siena’s Center for Innovation and Entrepreneurship, supervises summer research projects for physics undergraduate students, and prepares pre-service physics teachers.

She’s also really nice.

Michele agreed to answer a few questions for GeekMom.

You use robotics to teach physics concepts. How did you come up with this idea?

Before he passed away, I often met with Les Rubenfeld, the founder of RPI’s CIPCE program (Center for Initiatives in Pre-College Education.) He was a math professor and was passionate about teaching math with robotics. We would meet at Bruegger’s near Siena and discuss potential ways to collaborate to bring robotics to more students. He suggested that there was more to robotics than just programming the robots to take sensor input and program the robot to respond. He suggested that there was more science to teach. That inspired me to find the physics in robotics. So far, I’ve created robotics activities to teach physics topics including: kinematics (displacement, velocity, and acceleration); measurements to calculate gravity; force of friction; gear ratios for speed and power; impulse; angular velocity and linear velocity; and identification with light sensor data.

What aspect of your work inspires you? (and what are you currently fired up about?)

– Learning new things. I hate being bored. I’m always finding new problems to solve.
– I really enjoy the variety of things that I do. Change is really important for creativity. Revisiting past projects is important, too. Being a physics professor offers opportunities for both.
– Creating fun activities that naturally include science (like duct tape circuits.)
– Creating online resources to allow kids to complete projects at their own pace and allows me to grow my resources.
– Finding ways to show kids that science and math are interesting and fun when you’re solving real problems — not fake problems that someone makes up because you ” should” learn certain things.

Obviously you are a creative person in designing your programs. How can you pass along this creativity to your science and technology students?

I believe in modeling! I like to lead by example. I like to meet students wherever they are. I hate the phrase “you should know that”. I think it’s so important to meet students where they are. Shaming students shuts them down. Encouraging them, whatever their background, allows them to move forward and embrace learning about physics and math.

I think it’s so important for students to take control of their learning. I arrange my classroom and choose activities that require active engagement, not passive learning.

When students show an interest in any of my projects, I do everything I can to support their interests. I give out supplies and let students borrow equipment. I’m interested in their questions and problems and I believe they can do it. I also suggest that learning physics is a journey that takes time and effort. Even if you don’t completely master the material in my classes, that’s okay. Mastery takes time and effort and offers wonderful rewards. I believe that anyone can learn physics – it’s not a field reserved only for rocket scientists. Physics is so rich and covers such a broad range of topics, everyone can find something that’s relevant to them.

Thanks, Michele! And if you want to see even more of what she does, here’s some cool links:

STEM to STEAM: The Importance of Arts in Science

For this month’s Muse of Nerds, I quickly grabbed onto the STEM to STEAM movement (adding ‘arts’ to the technical.) Creativity is the foundation for advancement in all fields. The arts — writing, music, art, theater and dance — paired with science, technology, engineering and math, foster a relationship between both sides of the brain for maximum human innovation potential. Trying to place STEM at the top of the educational plant stifles growth.

In 1858, Friedrich Kekule published a paper that showed, visually, how atoms bond chemically. He continued to play with the design until in 1865, he put carbon as a six-sided ring (hexagon) with chains and links, which gave rise to organic chemistry. Kekule started out as an architect before switching to the new science of chemistry. The visualization of chemical bonding didn’t come out of experiments in the lab, but a daydream while riding the bus. His brain looked at chemistry with an architect’s eye.

Daniel Tammet holds the European world record for reciting pi from memory. Daniel can “sense” if a number is prime. I think it’s important to mention that Daniel has high-functioning autism because many educators tend to steer children on the Autism spectrum towards STEM fields. However, Daniel uses the arts to “see” numbers. He is a lucid writer with his book, Born on a Blue Day. The way he was able to memorize pi was by creating a visual landscape in his mind. Clearly, art and math are tied for him.

Science News had a special issue on August 14, 2010  devoted to our minds on music. It was a fascinating look at how music influences our growth emotionally and mentally. In it there was a quote from Istvan Molnar-Szakacs, a neuroscientist at the University of California, Los Angeles, “In terms of brain imaging, studies have shown listening to music lights up, or activates, more of the brain than any other stimulus we know.” That’s just listening! As Daniel Levitin, director of the music perception, cognition and expertise laboratory at McGill University in Montreal explained, “Music processing is distributed throughout the brain…and playing an instrument, in particular, is an ensemble activity. It involves paying attention, thinking ahead, remembering, coordinating movement and interpreting constant feedback to the ears, fingers and, in some cases, lips. It is one of the most complicated tasks that we have.”

How could that kind of thinking be considered extracurricula? That’s the saddest part. STEM in education is not just getting the funding for special programming, but amazing mental tasks like music aren’t even in the BASIC CURRICULUM!

This very morning I was teaching a creative writing class to some junior high students. The stories will be used to later design and program robots (based on challenges the writing students come up with). The writing students have to be creative to make their challenges cohesive with their story lines. The robotic students have to be creative in designing and programming robots. Tying the two endeavors together gives the project more weight.

Have you ever been to a science museum? Did you attend any of the fantastic theater shows? Watching a story unfold is basic human communication. Lecturing is not.

My children were taking a botany course and convinced their teacher to demonstrate their plant family identification ability using interpretive dance. Seriously. Their teacher was cool about it and let them try. They took all the information they knew about these plant families (memorizing), decided on what was the most important and distinguishable traits (critical thinking) and then came up with movements to convey the information in a clear way (innovation.) By using their full body to translate the concepts, more parts of their brain were used. Do you think they will remember the information better than if they wrote it out on a test? Can your fingers remember a song on the piano from when you were a child? Muscle memory is a powerful tool.

My husband teaches genetics and is frustrated at the lack of “creative and independent thought” the students portray. Students walk in the classroom lacking good reading, writing, and critical thinking skills. The scientists getting prizes don’t spit out what they were taught. They dream, they doodle, they hum, they dance their way to success.

Celebrate Pi Day by Learning the Secret of the Circle

circle-300x257Hands-on projects are great learning tools for kids, especially when they involve the word ‘secret’. I can’t think of a better way to celebrate Pi Day (March 14 or “3.14”) with kids than to help them unlock the circle’s secret and discover Pi!  This fun activity uses common office supplies and household materials and is easy even for younger kids.

Materials needed

  • A compass or two different sized round containers from which to trace around the bottom
  • A sharpened pencil
  • A ruler
  • A calculator
  • Long lengths of heavy string or yarn
  • Scissors to cut the string


Follow these steps to discover the secret of the circle.

Tip: Use a compass to draw two different sized circles. It’s best to draw them of drastically different sizes.

  1. Lay out the length of string around the outside edge of the first circle, cutting it to fit precisely once around the outer edge.
  2. Now measure the length of string using the ruler and record this measurement as the circumference of the large circle.
  3. Draw a line through the center of the large circle and extend it to the edges of the circle. This is the diameter.
  4. Measure the diameter of the large circle using your ruler and record this number as the diameter of the large circle.
  5. Now, calculate the ratio of C/d (circumference divided by the diameter). A calculator is best for younger students so that they understand the concept of Pi even if they haven’t yet learned division.
  6. Repeat these steps for the smaller circle.

The secret of the circle is that no matter what size circle you start with, dividing the circle’s circumference by its diameter (C/d) always yields Pi!  Note that this activity will likely not  yield precisely Pi because of the somewhat crude measuring techniques.  However, repeating this exercise for many different sized circles reveals the pattern that holds the circle’s deepest secret.

Further reading

Here is a bit more information on Pi.

Wikipedia’s Pi information.

I found this lesson in one of my favorite math teaching aids, ‘Math Wizardry for Kids‘.


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What Do Smart Zombies Want? Apps For Better Brains!

Image by Tim

I’m not sure what kind of geeky conversations go on in your households, but a common lament in my house is the lack of quality zombie apps on the market. Rather than listening to this diatribe yet again, I suggested that my son write it all down. Here’s his take on the state of the zombie app market, along with his idea of the perfect zombie app.

Do you have a strange obsession with the undead? I certainly do, but when I look for apps that are zombie related, they’re always either violent or boring. A solution? An app that is

  • Educational. If you’re going to be on an app, may as well get more brains.
  • Entertaining. I despise boring apps, especially educational ones.
  • Non-Gory. Zombies don’t have to splatter blood even if they need a little brain hors d’oeuvre every once in a while.

So how could this be combined, while making it attractive to geeky kids?  Maybe something like this.

The app could ask this question: You’re trapped in a pet store. You have locked the zombies in the back room, but need that space. In order to get in without getting attacked, you need to do some quick thinking.

Each zombie used to have a pet. The number of pets each zombie had are: 3, 2, 0, 5, 10, 6, 4, 1, 9, and 10.

What is the mean number of pets formerly owned by the zombies? What is the modal number of pets owned by the zombies, and what is the median number of pets?

A: Mean: 5, Median: 4.5, Mode: 10

B: Mean: 8, Median: 6, Mode: 0

C: Mean: 0, Median: 6, Mode: 8

Say you answered A.

A: is correct. The average number of pets owned by zombies is 5. The middle number of pets owned by zombies is 4.5, and the most common number of pets is 10.

Then a game screen would come up. It would look like a whack-a-mole stand, except at the top it said Whack-un-dead.

Hands would start to rise from the ground, like the moles in whack-a-mole, and you could tap to hit them.

Say you answered B or C:

Hands would start to come from the corners of the screen and make the screen look like it was cracking. Then a scream. The question would come up again with the wrong answer you just guessed marked by an X that looks like it was made by finger nails.

Sounds pretty cool right? I’ve looked for apps in the past. One was called Math Zombie. I thought this would be perfect. I opened the app, and it turned out just to be a math game that had nothing at all to do with zombies. I then tried an app called Zombie Farm. It turned out to be fun, non-gory, but not educational. Then Zombie Pizza. I thought this would be good with fractions and things. It was, again, fun, non-gory, but taught absolutely nothing. I’ve searched just zombie in general in the app store, and the ones that come up are often violent. Some of these other games do have valuable skills to offer though, like hand eye coordination, faster reaction times, and strategy. But they don’t have just plain skills out in the open. Maybe someday this is will be a reality, but for now, good look finding an app  that’s not soaked in red, entertaining enough to raise the dead, and helps build your BBRRAAAIIIIINNNSSS!!!!!!!

—Missing-Limb Tim

So, GeekMom readers, can you help a Geekling out?  Does anyone have a worthwhile zombie app to recommend for a discriminating tween?

How Stephen King Taught Me Percentile Rank and the Normal Curve

Adapted from Wikimedia Commons

I was driving my ’58 Plymouth Fury on a long trip out of Boulder, Colorado to a strange town in Maine, when I stopped at a hotel along the way for a needed caffeine boost. A man in glasses and a way with words came over and asked, “So, what do you know about percentile rank and the normal curve?”  It was strange for a pick-up line, but…

Ok, ok, that’s not what happened. Frankly, I doubt that Stephen King could have taught me these fundamental concepts in a conversation as well as he taught them to me in one of his novels. Here’s what really happened.

I was taking a research methods class, going through a phase in which I transformed from Geek Type E (English Lit Major) to Geek Type S (Social Scientist). The statistics gave me trouble, given my earlier career as a math-avoidant bibliophile. I understood, on a basic level, the concept of the normal curve. I was willing to accept that many kinds of data follow a distribution pattern where there are a few data points at one end, a lot in the middle, and a few at the other end. We’ve all heard of the bell curve.

Percentiles and percentile ranks (definitions differ slightly) also made intuitive sense to me as an overachieving nerd who understood that my SAT score could also be expressed as what percentage of test-takers scored at or below my score.

What I couldn’t get was how these two concepts relate to one another, and the biggest stumbling block was that percentile rank is not an equal-interval score. That means that the difference between the 25th and 30th percentiles is not the same as the difference between the 55th and 60th percentiles, or the 90th and the 95th percentiles. 30-25 = 5. 60-55 = 5. 95-90 = 5. So why is it that when it comes to percentiles, 5 does not mean the same thing as 5?  The technical explanation is that percentile ranks are tied to the normal curve, so some are closer than others.

I still didn’t get it.

Enter the Master of Horror. In a serendipitous moment, I picked up a copy of King’s The Long Walk. In the novel, 100 boys living in a contemporary dystopia participate in an event called the Walk. They have to maintain a speed of 4 miles an hour, there are no stops or resting breaks, and failure to keep moving or abide by any of the strict rules of the contest results in immediate death. Soldiers stay with the walkers, ready to shoot at any moment. The contest ends when there is only one walker alive.

As the novel opens, a few boys are shot right away. They have mental or physical problems that immediately take them out of the contest. Most of the others keep on going, until there are big losses around the midpoint. When it gets down to the last five walkers… well, what they go through is unbearable. The tension of wondering who will make it, who can keep lifting his feet and putting them down, who can suppress the psychological terror of it all long enough to keep on going, is vintage King.

It’s also a near-perfect representation of percentile rank and why differences are not equal. I realized that if you plotted how long each boy walked before being shot, you would end up with a normal curve. Since there were 100 boys, each boy’s placement could be equated to percentile rank. Now I could see that 5 does not always equal 5. The difference between walkers who came in at, say, 55th and 60th places was inconsequential. It is easy to imagine them switching ranks because there was very little to distinguish them from one another. But the difference between coming in as the winner and coming in fifth was profound. The boys in the middle were all about the same, the boys who died at the beginning and end were both very different from the group as a whole and from one another. Aha!

Normal curve in The Long Walk

If it still doesn’t make sense to you Primary Geek Type Es, read the book and then come back to this post. You’ll see what I mean. Students take note, however. Reading horror novels as a method of studying for your statistics classes is generally not recommended. On the other hand, we could explore probability calculations for encountering scary creatures in dark, wooded areas, or incidence and prevalence rates for vampire infections in the general population…