Tom Peters has written quite a bit about the huge market opportunities in providing goods and services designed for two populations – women and old geezers.

I thought of this today as, for the thousandth time, I went through the pre-check line only to have my titanium knee set off the security alarm and get patted down. X-ray scanners are in limited supply while people who have had joint replacements are an increasing number. Why isn’t anyone addressing this opportunity?

Another uncool, overlooked market is rural communities. I just spent two weeks in North Dakota and one of the first things I did when I got home was have someone order 100 USB drives with our logo so that we could put the game on it and mail it to schools. In many places where I travel, it can take an hour to download 1 GB. If the connection drops in the middle, you may need to start over. While I can download both of our games in under 2 minutes in our office in Santa Monica, in some of the places I visit, that can take all morning.

I have yet to show our game to teachers who were not enthusiastic about it. Even when we have technical difficulties – and we do, because we are just getting out of beta May 1st – they are willing to work with us to get them fixed.

When Maria was at a tech event in New York City, a venture capitalist in one of the panels told her point blank ,

No one is interested in Indians.

You know where people are interested in Indians? On the reservations, in school districts with large Native American populations.

Angie at powwow


Often, people tell me,

“The education space is overcrowded”

This makes me laugh. The education space is overcrowded with multiple-guess games and shooting games – you know, shooting and spelling, shooting and multiplication, click on the rocket ship with the number that equals 3 x 5 . Have you ever watched children play these games? Often they just randomly click as fast as they can on as many ships or bananas or whatever it is.

So far, we have spent over $350,000 and a year and a half developing 7 Generation Games.  Not all of that has been everyone working full time on just the game. I would estimate we’ve had the equivalent of 2.5 full-time people for a year. We have almost 18 months remaining on our Phase II grant during which there will be at least 3 people working full time.

Today, I’m analyzing the quiz data that comes in daily to see where students are failing in the game. This pretty much validates what we have seen in four weeks of observations at our beta sites this spring semester.

When I read a year or so ago about a 13-year-old who put together in a weekend some app that was selling really well on the app store, I laughed. If you are selling something that a 13-year-old can knock together in three days with an SDK his mom bought him and a book from the public library, then your market is going to be pretty damn crowded.

If it requires actual data to document that it really is educational, you apply that data to track problems both with users and your program, you create dialogue, story line, artwork –  then I don’t think your market is going to be so crowded.

If you want to see what we are up to, you can download Spirit Lake: The Game here for 9.99

If you don’t want to shell out ten bucks (cheapskate!) you can check out the pretest we are working on for our second game, Fish Lake, here, just to see some of the type of data we collect to decide if the game is working. Note, this is a work in progress that will be ready for schools in the fall semester.



So, this is day 13 of the 20 day blogging challenge, and I skipped over day 12 (although I may go back to it). The prompt was

“Tell about a favorite book to share or teach. Provide at least one example of an extension or cross-curricular lesson.”

My favorite resource is not actually a book, it is a magazine, Mathematics Teaching in the Middle School, published by the National Council of Teachers of Mathematics. One of my favorite parts of the magazine is the Palette of Problems section, which is a bit odd because often I find myself thinking … this problem has no point, for example,

“How many birth dates in a century have the property that the sum of the month and the day equal the value of the last two digits of the birth year?”

I do realize that some students will be interested just in the challenge of solving a problem. However, for many students, the apparent lack of application can be very de-motivating. Most of the problems, though, can be adopted to our games with really simple modifications or may just give me ideas for a problem that would fit right in. For example, this is an extension of a problem in this month’s issue



Zoongey Gniw is looking for a wife.  He is from the Catfish clan and people from the same clan are not allowed to marry. His uncles are going to trade with two different bands. In the first band, 12% are from the Marten clan, 20% from the Crane clan, 64% from the Bear and Loon clans and the rest from the Catfish clan. His other uncle is going to trade with a band where 11% are from the Catfish clan. It is going to be a hard decision which uncle to accompany, says his father.

Not at all, says Zoongey Gniw, and he steps over to the first uncle. How did he decide?

This fits perfectly in our game. There is a video clip on clans, narrated by the inimitable Debbie Gourneau from Turtle Mountain. The prohibition on marrying within clans is historically accurate. As far as the interest of our students today, not only are many of them from tribes that have  the clan system described, but they are also, like most middle school students, interested in the opposite sex, having a boyfriend or girlfriend, so the topic is inherently interesting.

I like this magazine, and I call it that deliberately, rather than an academic journal. All of the journals I read and nearly all of the academic texts talk in theory about what needs to be done and why but not nearly enough on how to effectively do it, whether the topic is teaching mathematics or running a company. Mathematics Teaching in the Middle School is all about how to do things.

When I was in graduate school, it was common for professors to mock teachers who “aren’t interested in anything longer-range or deeper than what am I going to do on Monday.”

That’s the attitude you have the luxury of having if you don’t have to actually show up and teach on Monday.

The Invisible Developer had commented that I write an awful lot about SAS and maybe I should write about some other language. For Christmas last year, someone gave me an impact.js license so I made a little game where players drop snares to catch rabbits and collect berries. This doesn’t have much educational value,  I was just playing around. I thought it would be amusing to have the food items they collect in the game be equal in value to the number of calories in that item.

If you have impact and wanted to do this yourself, here is what you would do.

1. Basic stuff - include game.entities.berry, game.entities.rabbit and any other food item in your main.js script. It goes right at the beginning with any other entities you require



– more stuff –


2. Create the score in your game info function that stores information

GameInfo = new function(){ = 0;
— other stuff you want to initialize


3. When you extend the game to add your own cool stuff include an addFood function

MyGame = ig.Game.extend({

– init and other functions

addFood: function(amt){
//pickup item += amt; //add caloric value to the food score

– draw and other functions


4. To each entity script, add a function that defines how the player gets the food. Here are two examples.

Collecting berries

In the case of the berries, the player will just walk by the bushes and collect the berries. Think Pac Man!

In your berry.js file add a check function like this

EntityBerry = ig.Entity.extend({

— other stuff

check: function(other){
if ( == “player”){;

So …. it is about 5 calories per berry. When the player walks by a bush and comes into contact with a berry (picks the berry), the berry disappears and the player’s food count goes up by 5.

Snaring rabbits

Here is a second example. In this one, they drop snares around the virtual woods and when they snare a rabbit they get 1,000 points which is the approximate calorie content of a dressed rabbit, according to the USDA Nutrient database . I assumed this yielded an average of 2 pounds of meat.

For my rabbit I have extended the rabbit.js script as follows

EntityRabbit = ig.Entity.extend({

— other stuff

kill: function(other){;

But what is going to kill my rabbits? The snares, of course, so I added this into my snare.js script

EntitySnare = ig.Entity.extend({

— other stuff

check: function(other){
if ( == “rabbit”){
other.receiveDamage(100,this) ;;


Since the rabbit only has 100 health points, that kills it off so your rabbit disappears and your food value goes up by 1,000.

As you can see, you could easily add shooting deer, buffalo and other food in the same way.


After I had played around with this for a bit, I thought it was a waste to just trash it so I put it into our upcoming game, Fish Lake, in between levels. When they finish Level 3, they play this game and then go on to Level 4. Our main game is 3-d, this is just a little interlude. I like to throw surprises into the game so kids like it and keep playing.


Someone in Los Angeles was very upset by our Spirit Lake game where players shoot wolves and buffalo. She said she just could not kill animals. (The Invisible Developer asked me if she was aware that they were virtual animals and not real.) I told her that our games are based on Native American history and history is what happened, not what you think should have happened or wanted to happen. In fact, there is a very touching story in Fish Lake narrated by Debbie Gourneau of the Turtle Mountain reservation on how many people died of starvation and how many more would have died were it not for the jackrabbits.


buffalo in the snowClick here to get Spirit Lake: The Game for $9.99


P. S. The amount of information produced by USDA is nothing short of amazing, and I don’t say that just because they funded are grant. They really are incredible.



Yesterday, I did the Happy Dance in my office when we finished version 2.2 of Spirit Lake.

I said that despite taking me away from virtually every other interest in my life, being obsessed with a start-up is worth it.


In thinking it over today, I realized that 7 Generation Games meets every possible desire I could have

Julia16Mental – making a game truly challenges me both intellectually and creatively every day. It began with creating, with my partners, a vision of a virtual world – what would the people look like, the scenery, what would they do? How would this dovetail with math? How can we make it interesting enough that children keep playing it? On top of all of these questions is how to write the code to get it to run, record data and for all of the parts – database, 2D program, web input forms, 3D programs – to work together. There really isn’t anything more satisfying in life than seeing something that started out existing only in my brain becoming real. It’s exactly like being a parent except that 16 years from now the games won’t tell me I’m ruining their life by refusing to sign them up for a club soccer team.

Emotional – there is the good part of the emotion of working on 7 Generation Games. We are sincerely striving to make it easier for more kids to learn math. When our games succeed, students improve their chances of passing grades, graduating from high school and going on to college because math is a hierarchical subject. If you don’t understand division, you aren’t going to get fractions. If you don’t understand ratios you’ll fail geometry and statistics. They also learn Native American history, pick up some words in native languages and even increase their vocabulary in English. There is also the elimination of the negative part of working many other places. I can make my own hours and since I am allergic to mornings, I can get up at 10 a.m. Because I telecommute, I almost never have to drive in LA traffic. I seldom have to wear a suit. I work only with really smart, motivated, interesting people. The teachers who use our games and provide us feedback are a delight because they are the ones who are on the forefront trying new things, and not shy about giving their ideas for improvement.

Physical – if we’re going on Maslow’s hierarchy of needs, this is the basic ones, food, shelter, heat, etc. While our Chief Marketing Officer joined up because she expects us to make a lot of money, and I’m not averse to that, we do make enough to cover the bills. We’re not yet making what we would be if we had taken corporate job offers, but it covers private school for The Spoiled One, trips to see Darling Daughter Number Three continue to dominate the world in mixed martial arts, wedding expenses for The Perfect Jennifer and visits to The Even More Perfect Grandchildren. My goal is to be like Bill Gates, both in making software a billion people use and in giving away a billion dollars.

Today I worked on making a game more fun for kids. Tomorrow, I will work on putting in new ideas, new challenges for helping kids learn more. Yes, I actually get to do this for a living as a grown-up. How awesome is that?

Buy our game. It’s awesome. Best $9.99 you’ll spend today.

7 Generation Games Logo

Really useful advice for start-ups on How Not to Die from Paul Graham emphasized

 The number one thing not to do is other things. If you find yourself saying a sentence that ends with “but we’re going to keep working on the startup,” you are in big trouble…. We’re taking on some consulting projects, but we’re going to keep working on the startup. You may as well just translate these to “we’re giving up on the startup, but we’re not willing to admit that to ourselves,” because that’s what it means most of the time. A startup is so hard that working on it can’t be preceded by “but.”

In particular, don’t go to graduate school, and don’t start other projects.

As my co-founder, Maria and I discussed today, that is absolutely true but it’s also true that it may take some time to get to the “Nothing but the startup” point. In our case, we had existing contracts we needed to fulfill, mine with consulting clients and hers with ESPN and Fox News Latino. You also have to be in the financial position that you can afford to not only work at a reduced salary for years but at the same time pay for expenses – artwork for the game, animation, travel expenses to demonstrate the game. As you grow, there are other expenses for tech support, promotional items like the posters the teachers put up in the classrooms, the $25o I just paid to have a table at Women 2.0 Founder Friday in Los Angeles.

artwork from the gamePaul Graham’s article was the second-best advice I have read on starting a business. The best was a book by Paul Hawken I bought over 20 years ago called Growing a Business. He advised a couple of things. One is that you learn how to do as much for yourself as possible instead of paying for expensive “experts”. Justin Flores does our artwork,  with occasional contributions from Gene Wilson, because I totally suck at art. Other things, whether it is CSS or sound editing with Garageband, I just learned. I took a class at MacWorld one year, bought some books. Yes, I took several books out of the library, too, instead of buying them. Hawken’s other advice was to keep your operating costs as low as possible, thus making it possible to follow the advice of Graham 20 years later which is to just do your start-up.

We have an office upstairs where The Invisible Developer works, shielded from all human eyes, and an office downstairs where I work and so does Marisol, Maria when she is in town and the occasional intern. Because we have been in this location in Santa Monica for over 30 years and the city has rent control, the rent for our space comes up to under $500 a month. The down side of that is that it is not at all feasible for us to move. The Spoiled One would like us to move to Ojai. I’d really like to live somewhere we could have a dog, but it is not in the cards.

Doing “nothing but a startup” means saying “No” a lot, and saying “Yes” to the right things.

If you are  doing “nothing but a startup”, it is not just that almost all of your time and attention is going to be focused on that, but almost all of your decisions, too, are based on “how will this affect our company?” This can be something like can we move or more amorphous like the topics you learn more about. I did a lot of SAS programming for over 30 years and now I’m doing much less of that and more javascript. I’m skipping the SAS Global Forum for the first time in several years and will probably go to an HTML5 conference in San Francisco instead.

It’s good to be learning new stuff  in a new area, but there is also new stuff in the old area – like the SAS model selection procedures, that I really wish I had time to learn. I’ve been writing on my blog less. I quit teaching at Pepperdine University as an adjunct because I just could not commit the time to showing up once a week for four months straight.

It’s absolutely beautiful weather most of the time in Santa Monica and I rarely make it outside because I am working. I’ve quit volunteering nearly as often. I teach judo once a week at Gompers Middle School and several times a year, I have to get a friend of mine to substitute for me. I’ve resigned from all non-profit boards I used to be on except for one, and when the board chair term expires this year, I’m stepping down from that.

As consulting contracts have expired, I haven’t renewed them. I’ve turned down several offers to teach classes, present at conferences and take on new consulting clients.

I wrote a book on matwork for judo and mixed martial arts last year, but I’m not working on another book.

All of this has now enabled me to spend 8, 10 or 12 hours a day most days doing nothing but working on 7 Generation Games (while only getting paid for less than half of those hours!) and the result is that we are progressing far faster than we were a year earlier.

Is it all worth it? Yes.



When I add up all of the ad revenue from this blog on top of the business it garners, in a good month it might average out to $30 an hour and in a not-so-good month maybe $10. Since my consulting rate is a heck of a lot more than $30 an hour you might wonder why I bother. If you read this blog regularly you can guess that it is the same reason I do most things, for the hell of it.

However, occasionally there are some perks that are priceless. One of those was the opportunity to be on the call this morning on the White House call with Sam Kass, Executive Director of Let’s Move. Thanks a million to Blogher for setting this up. I am SO-O not a morning person and the call was at 8 a.m. Pacific time. I almost tried to get Maria to fill in for me but she tactfully pointed out that it would be hard for her to pass off for me because she did not sound sufficiently old.

So, barely awake on my first cup of coffee, I still learned a lot on this call. There were many bloggers, with diverse interests, and the question and answer session at the end revealed that. A nutritionist asked about the likelihood of stopping junk food and soft drink sales in schools. A food blogger asked about the quality of school lunches. When Sam Kass mentioned documented higher math scores among students with free breakfast programs, of course I perked up and asked for more details.


me with daughters

(Maria is on the left. I’m the wrinkled one on the right. Darling Daughter # 3 is in the middle, apparently exhausted from 66 seconds of effort. Thanks to Hans Gutknecht for the photo.)

Now, I’m good at math and I thought if three hours after school are important – often the time between when kids get out of school and their parents get home – and you have at most one hour of physical activity, what are kids doing in after-school programs in the other two hours. Surely, they can’t spend two hours just eating fruits and vegetables, right?The most interesting part to me was the lengthy discussion of the three hours after school as being vitally important. This is a personal interest of mine, since for the last three years, I have volunteered at an after school program teaching judo. (The daughter in the middle started that judo program five years ago and taught it for the first two years.) It was also interesting, though, because he mentioned the importance of 60 minutes of physical activity a day, at least 30 minutes of it occurring in school seems to be a goal.

Our games are used in a couple of after school programs, and that’s great. However, the games we have available now are aimed at mathematics in grades 3 through 6. What about older kids?

I visit a lot of disadvantaged communities and one of the disadvantages students have is that they don’t really have much idea of the type of opportunities out there for future careers, what people do or how they get those jobs. So … I thought one thing I could offer immediately is an inside look at making computer games. Not one to let grass grow under my feet, I sent an email this evening to 30 teachers I know and linked to a few parts of the game we are working on now. These are in pretty rough form. However, if the students check in every day after school they can see what we have done in the past 24 hours. It should be fun for them to see how the game takes shape. Some of the pages don’t have sound yet. They don’t have the bells and whistles and “yoo-hoo” that comes up when a student passes a quiz or goes up a level.

That whole “Take your child to work day” isn’t available to a lot of students, and if they live in a small rural community, the kind of jobs they can be taken to is limited. So … I decided to reach out to students after school and take a whole lot of them to work with me for the next six weeks. Too often, whether it is software or scientific research, students are presented with the final product and think it is made by people who are far smarter and more talented than them. If they only saw how rough it is at the beginning and the amount of hacking into shape it takes — and now they will.

There’s been quite a bit of discussion on twitter lately regarding generalists versus specialists. This article on KD Nuggets reported an even split in their poll numbers regarding whether companies try to hire a generalist who has knowledge of all areas required by a data scientist, as opposed to those who said that they hired a team of individuals, each one with some of the skills.  In case you are wondering, the required skills were:

  • statistics/ machine learning
  • hacking
  • databases
  • industry/ domain knowledge

There was even some discussion as to whether the Data Scientist possessing all of those skills is indeed a mythical creature like the unicorn. (This irked me somewhat because it is not the first time I have been mistaken for a unicorn. Not only do I possess all of those skills, but I am also a Hispanic grandmother running a start-up. )team with no unicorn shirts

This is NOT, however, a post about my awesomeness but rather about the value of both generalists and specialists even in a small business.

I highly recommend reading this Wired article by Samuel Arbesman, Let’s Bring the Polymaths – and the Dabblers – Back . I do agree with many of Arbesman’s points. Universities are NOT the bastions of innovation that they like to believe. Although some innovators may start at universities, they almost invariably leave. There are multiple reasons. One is, as Arbesman notes, is that universities demand specialization. You are a professor in a specific department and specialize in middle school mathematics education. You publish articles in journals on middle school mathematics. If you have an idea for a computer game, well, that is the computer science department. If you think it would be cool to have an adventure game that is set in a historically accurate pre-European contact North America, well, the History department or Native American Studies are where you do that.

I completely agree with Arbesman that both video games  and start-ups are stitching together diverse areas of specialization, and he describes our start-up , 7 Generation Games, pretty well.

The part where I disagree is with some people who seem to think that we would be better off to replace specialists with generalist. True, if I had to pick one or the other, it would be the generalists, and, as I wrote on the 7 Generation Games blog, I am about half of our development team currently, as well as CEO, and, despite the doubters, it suits me.

However, even as a small company, I think our strength is in having both generalists and specialists. I am pretty good at statistics and programming, know enough about databases and quite a bit about mathematics education and teaching in disadvantaged communities. I’m a good writer and I can give presentations at conferences and pitch at start-up events.

However, again, we have The Invisible Developer who is an amazing programmer and even more amazing still, quite modest about it. He has been referred to by friends and family alternately as Code Warrior, Computer God and The Rocket Scientist (now retired). Almost all Dennis does is software development, with the occasional pitching in on tech support.

Ernie does technical support. He may pitch in to do some video editing or game testing in a pinch, but mostly he does tech support from one end to the other, testing compatibility with different operating systems, answering user questions, maintaining the tech support site, writing documents for tech support.

Maria does marketing. Both Erich and I have presented at conferences, Dennis or I might blog about what we are doing, but overall whether it is making slide decks for investor pitches, a one-sheet to distribute at conferences or selecting which incubator application to submit and when to pass, it’s Maria’s call and her work. Again, she can review contracts, do voice over for video or pinch-hit in other ways, but mostly, she’s writing, blogging, tweeting, meeting and organizing all of the aspects thereof.

Marisol is probably the only real generalist in the company – she does everything for powerpoints for presentations to mailing packages to making Easter egg movies that pop up in the game.

While Erich is mostly providing cultural expertise on Native American history, meeting with the schools to coordinate testing and advising on how to improve the game for the school sites, he also does some editing and presenting at conferences.

Then there are those who are strictly specialists – Justin and Gene do artwork, Danny does animation. The rest of us may crop an image now and again or animate a character across a page as a sound plays, but we are no artists and we know it.

We need generalists – Maria and I meet weekly and try to scope out where we are, where we’re going and keep all the pieces together. On the other hand, without the specialists – people like Dennis who will spend two weeks on trying to get the water in the game flow like real water, or Erich who will drive to Belcourt to get someone to record a story so that the grandmother talking sounds like a real grandmother from Turtle Mountain – our game wouldn’t be nearly as good as it is and I don’t believe our company would be nearly as successful.

And we don’t even want to mention what my artwork would look like …


man in canoe

Artwork not by me, thank God

Today was my most recent experience in the clash of commercial and academic cultures. For seven years, I was an assistant and then associate professor, teaching statistics and research methods, writing articles for academic journals. For five years before that, I was a graduate student at the University of California. I even did a post-doc on an NIH fellowship. All the research things. So, I am well aware, as my colleague at lunch today was telling me, that the National Science Foundation prefers studies where subjects are randomly assigned to experimental and control groups. Randomized controlled trials are the gold standard of research, as the textbook I’m using to teach biostatistics says about every third page.

“Yeah, we’re not doing that.”

In response to her shocked look, I explained,

“Last year, when we did the pilot study for 7 Generation Games, we were able to get a control group but that was before we had our data in that showed the children at the two schools that played our game did significantly better in math. Now, the superintendent of schools is telling me that they want to be in the experimental group, too, because he is not going to face down parents and tell them that their children did not get to use a program that he believes would have helped their children do better in math because — well, what reason could he give them that would be satisfactory? Because it would help us provide more credible evidence to the Institute for Education Sciences? Seriously, why the hell would that parent on an American Indian reservation chance that their child would perform worse in math so that we could get better data for our study? Does that make sense to you? As for randomly assigning them to be in the group to play the game – how can we do that? We can offer it to low-income schools at no cost but if they are over-worked with a hundred competing responsibilities (as many, many teachers are), already have their curriculum planned for the year, are part of some reform that doesn’t allow them to do anything but a specific lesson plan or unwilling/uninterested for any other reason, we cannot MAKE them use the game.”

She nodded that she saw my point but then suggested hopefully that we could do a random assignment by classroom, within school.  I told her that we had that idea, too, but the teachers who used the game and found their students doing better and enjoying math class more shared the link to download the game, and the teacher resource site with other teachers at their school. My colleague exclaimed,

“That’s terrible! You have contamination of implementation!”

I corrected her,

“Or, as the teachers called it, not being an asshole. Look, say you’re a teacher in a school without a lot of resources where children are generally performing below grade level. You get this new game that your kids love to play and they are doing better on their math tests. The teacher next door asks can she get a copy and you say, “No”, because a bunch of researchers want to see how much worse the kids in the class next door will be doing by the end of the year. Of course you don’t do that. You share it with the other teacher because you care about students in your school and you also don’t want her throwing an eraser at you.”


7 Generation Games LogoYou can buy a copy of Spirit Lake: The Game for $9.99 and we’ll even give a free copy to a Title I school to boot


What are we doing to solve our research dilemma? Well, since it is a computer game backed up with a  database of student performance data, we can track how long and how many times each student plays our game. In the pilot study, we found that not only did the intervention classrooms perform better than the controls, but that students who played the game more out-performed those who played less.

An additional possibility is to do a pre-test at our same intervention schools next fall, then a post-test after eight weeks. Start the game in the ninth week of school and then test again after another eight weeks. We do have some schools we could use as control groups but they are so different to not really be helpful – our intervention schools are primarily on or near American Indian reservations, so using control groups in downtown Los Angeles would not be that informative, I don’t think.

A cross-over design has been suggested, but there are those teachers again, who I have to meet with and say,

“Look, I know that we asked you to use this game because we thought it would help your students do better in math and they would enjoy it. Now that it seems to be working, we want you to stop and see if your students do worse for the next couple of months. What do you say, because, you know, science.”


Several years ago, I was reassured once again that I had married the right person when The (much smaller then but equally) Spoiled One asked him,

“What does the name of your book mean, God created the integers?”

He explained that while one can have 1 rabbit

rabbitor 2 rabbits


You can have zero rabbits.

All of those are concrete things that exist in nature. You cannot, however, have one-half of a rabbit or one-seventeenth of a rabbit.

Well, theoretically, you could, if you killed it and chopped it into four pieces, as The Spoiled One gruesomely pointed out. Her father, who watches too much Monty Python countered that then it would not be the rabbit as God made it but, in fact, an ex-rabbit.

All of which brings me to Fish Lake, the game we are working on currently, which involves fractions. It really has not been that difficult to come up with believable examples of how early Native Americans might have used fractions -

“Leave for camp when the lack is three-quarters in the shadow.”

“We used two rabbits to make enough stew for two people. If you are out hunting alone and just making stew for yourself, you would make half as much, so you’d only need one rabbit.”

As our Dakota cultural consultant, Dr. Erich Longie pointed out, of course the Dakota people used math. The traveled over a very wide area and would meet up in the same locations, it was hardly by accident – well, you’ll have to see the next two games.

The part I am having a hard time with, though, is coming up with realistic uses of percentages and decimals. I can see where a chief might have 100 warriors and need to put them into four groups, say, to attack from four different directions. So, 25/100 = 1/4  and maybe then each group would get 1/4 of the food, 1/4 of the war ponies and so on.hunter on horseback


I really can’t think of any situations, though, where the chief would sit down and say,

“Okay, 75% of the warriors have a horse, that is the equivalent of 3/4.  Thinking of it another way, if I had ten warriors, 7.5 of them would have a horse.”

We have four cultural components – two are Dakota (Sioux) and two are Ojibwe (Chippewa) and they have given us a lot of great examples using math for travel, measurement, building tipis and wigwams, calculating odds when deciding to try to steal a buffalo pony and more. However, I’m still puzzling over how to include realistic problems to meet common core standards on decimals and percentage equivalence with fractions.

God may not have only created the integers, but I am pretty dead certain that it is accountants and engineers who created the decimals.

Any creative suggestions would be much appreciated.

If you have not listened to the TED talk by Conrad Wolfram, I highly recommend you do. If you have any interest in math education, the odds are great that his talk is far more important than anything else you could possibly doing in the next 20 minutes.

If you think the name sounds familiar, it’s because he is one of the masterminds behind Mathematica.

What is so fascinating about his ideas? In a nutshell, he says that we teach calculation – addition, multiplication, exponentiation, logarithms – as math. That takes up 80% or more of our curriculum because it is not easy for most people to learn, it requires memorization and they don’t want to learn it (so it probably requires more badgering).

We spend a few years in childhood learning “math facts” – subtraction, division, multiplication, addition. We spend a few more in adolescence, if we are “good at math” – learning how to compute sines, tangents, logarithms, derivatives. Then, for the rest of our lives, we almost never do that by hand again.

This change occurred during my lifetime and it was one occasion where it actually benefited me to be poor. I could not afford a calculator in high school, so while all the more affluent kids whipped through their homework using calculators, I had to work it all out. When we took the SATs, unlike now, you were not allowed to use a calculator, so I did much better then they did.

Back then, it made sense. Calculators cost hundreds of dollars and you could not just assume you would always have one handy. As I sit here, there is calculator and several types of statistical and mathematical software on my desktop, laptop and iPad. There are even a couple mathematical apps, and, of course, the ubiquitous calculator, on my cell phone. When there are four devices capable of computation I can reach from where I am sitting it really doesn’t make sense to spend years of teacher and student time insuring that every child knows that 13 x 13 = 169.


One use Wolfram sees for computation is estimation. I wholeheartedly agree with him there. In writing our math education games, the next major update is going to have better analysis of student errors.

You are being attacked by rabid wolves. You’re just a kid, you can only hit a wolf about once every 5 times and 7 wolves are coming at you. How many arrows do you need?

There is an important difference between the student who answers this question with 33 and with 5 or 187. If they repeatedly make that type of error, it is clear that in the first case, they are good at estimation but not so good at computation. That is one reason we give two tries for most answers, and we almost never have multiple choice. We want to distinguish among the student who knows the answer but was in a hurry and didn’t read the problem completely, the student who understood the problem and did not get the calculation exactly right and the student who is completely confused.

I just watched this video for the first time a few days ago, and Spirit Lake: The Game was already out to our testers and ready to be uploaded. However, you’ll see some changes based on these ideas in the update in October, and even more in the new game we are making now.

Seriously, what is the point of learning new ways of thinking about math if you don’t do anything about them?

Your turn.


artwork from game7 GENERATION GAMES






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