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Margaret E. Kosal is an assistant professor in the Sam Nunn School of International Affairs at Georgia Tech. She earned her Ph.D. in chemistry at the University of Illinois-Urbana-Champaign and her B.S. in chemistry at the University of Southern California. During graduate school, Prof. Kosal co-founded a high-tech start-up company that developed sensors to detect explosives, chemical weapons, and biological weapons. She was a Science Fellow in the Center for International Security and Cooperation at Stanford University and served as Science and Technology Advisor in the Defense Department. Prof. Kosal’s research explores two interrelated areas: weapons of mass destruction (WMD) and emerging technologies.

I was asked to write a perspective on girls and women in science – what I’ve seen change in the years since I was a girl interested in science, what I see now as a professor and role model for up-and-coming students (both male and female), and what still needs to change. The observations and stories below reflect my experience as a small-town girl from the rural Midwest who went to a big city on the West Coast for college, who served in the Pentagon, and who currently teaches at a major research university in the South.

This year was the twentieth anniversary of my graduation from high school, so reflection seems apt. When I graduated high school, I knew that I wanted to study the physical sciences. I loved chemistry, physics, and astronomy. I loved the idea of understanding and being able someday to push the boundaries of knowledge myself. For me, pursuing science was about discovery, exploration, and understanding how the Universe worked. Math and science were ‘hard.’ I liked the challenge; I wanted to be challenged.

The Importance of Good Teachers

It didn’t take 20 years ago for me to realize the importance of teachers to students’ success, especially fostering and supporting girls’ interest in science and math. As much now as they were then, high school teachers are essential to sustaining US capacity in science and technology and even more crucial for encouraging girls in the sciences and mathematics. I suspect that all the girls in my high school felt the subtle social cues (or explicit comments) dissuading us from actively pursuing and excelling in science. Every scientist we learned about, every constant, every equation – if it had a name, it was that of a man. We noticed as young girls in science that there didn’t seem to be a place for women in science. I was fortunate to have very good teachers overall, but my chemistry teacher specifically deserves recognition. Girls, just as much as the boys, were called on and encouraged to contribute to discussions, to actively engage in hands-on lab experiments, and to lead in the demonstrations that we organized at local elementary schools. He spoke plainly and openly about issues of equity with respect to representation and participation in the classroom. What we may not have been able to articulate as teenagers, he validated. He made it a normal rather than an exceptional part of the conversation: girls were good in science and were expected to participate actively. It just was; it wasn’t special. The standards were the same regardless of gender, and we each had a fair shot to succeed or to fail.

In today’s era of backlash and hyper-criticism of teachers, I’m not sure that a teacher, especially a young one, could do that. At the same time teachers like my high school chemistry teacher are needed more than ever now. I am concerned greatly about the increasing disincentives and hostility toward schoolteachers that has punctuated US domestic politics this year. That is a significant change from just ten years ago. Because much of what affects schools happens at the local level, parents can truly have an impact in their own districts. I encourage all parents to write letters to their local newspapers and blogs and to attend school board meetings. Be a voice in support of the teachers who will have an impact on your children’s future.

The Blame Game

As an undergraduate student, something my research advisor told me still rings true to this day. At the time, he had been supervising graduate students and post docs for more than 20 years. He noticed that when experiments fail, female students blamed themselves. On the other hand, he observed that the male students almost always attributed failure or negative results to the experiment, to the equipment, to the reagents, etc. While my own students aren’t doing experimental chemistry, I still see the same patterns in some of them almost 20 years later. Some of the best and most conscientious female students in my research group do this. I make a point to alert them to this behavior, and sometimes that’s enough to be effective. I also gently remind them to stop apologizing for successes or failures, and when things don’t work out, to see those situations as learning opportunities.

This likely isn’t a phenomenon that starts in college. Girls (and boys) need opportunities to risk intellectually, to fail, and to acquire the skills to deal with the consequences. As one of my favorite posters from the Materials Research Society starts “Science: If you’re not making mistakes, you’re doing it wrong;” failure is part of basic research in the sciences and engineering. A recent study written up in the New York Times, “Can A Playground Be Too Safe?“, discusses how increasing efforts aimed at eliminating physical risk on playgrounds were seen to impact emotional development negatively in a broader context, as well as making playgrounds boring for kids. For much longer, girls have been insulated from or socially prompted to avoid outright that kind of physical behavior and risk. My recommendation: more rock climbing, camping, soccer, and skateboarding for girls (and boys)!

Mentoring Can Make a Difference

As an undergraduate and as a young graduate student, I did not receive informal guidance or mentoring in the process of navigating grad school, including the admissions process, nor in understanding what being a professional scientist entailed. I didn’t realize this omission then, but I obviously found my way on my own to some extent. While very few would describe me as passive or timid, I’m not sure that I would have known how to ask for such guidance. For me, those experiences and lessons learned likely contributed to my independent initiative. At the same time, I wonder how much further I might be in my career had I had the informal or formal mentoring that many of male peers received. I don’t see this lack of mentoring as having changed all that much either. If universities would more publicly and formally support mentorships and if more professors reached out proactively to offer guidance, all students and the science and engineering disciplines as a whole would benefit.

US Moving in the Right Direction

On a wider level, I’ve observed greater recognition of the increasing need for American students to pursue studies in science, technology, engineering, and math (STEM) fields (e.g., the National Academy of Sciences 2005 report “Rising Above the Gathering Storm“). Over the last 30-plus years, efforts to encourage women and minorities to pursue science and mathematics have been supported and established by federal agencies like the National Science Foundation, by national-level private organizations like the American Association of University Women, and by others such as the organization MentorNet. Those models for getting girls and minorities to pursue STEM fields should be explored for general application to the US population.

The skills that I learned, whether I knew it or not, while being a female chemistry student and as a young female PhD scientist, have helped me in all of my pursuits, whether while serving as Science and Technology Advisor in the Pentagon or while organizing skydiving jumps. That definitely hasn’t changed. They’ve all required robust analytical problem-solving and independent initiative, and each time, the majority of my colleagues have been male. Some may think of this as having some special skill set that allows me to be a successful woman in a “man’s world,” but that mistakenly focuses on my gender instead of my abilities. I really look at myself as having developed the skills to succeed now and in the future where science and math abilities, combined with good old-fashioned drive and ingenuity, are critical to any person’s success.

I’m an innate optimist, and what I think has changed most definitely for the positive is the attitude and assumptions of girls today. While there is certainly no shortage of vacuous pop culture in these first decades of 21st Century, the options for girls and women continue to expand. There are more women leaders serving as public role models, and this is a very good thing for girls today and for the nation overall.

For more information on ways to keep girls interested in STEM subjects, read the prior blog post from IMACS.

Have you heard a story like this before: My daughter used to enjoy math and science when she was in elementary school. She’s always been strong in those subjects. But now that she’s going into 7th grade, it’s no longer “cool.” She’s actually afraid that her classmates won’t like her anymore if they find out how talented she is. Her computer science teacher called to tell me that she doesn’t want to take the honors programming class next year, even though she was the top student in his class last year. How do I make her understand that she should pursue her natural talents regardless of what her so-called friends think?

There is no easy or single answer to this difficult parenting problem. The factors that motivate a child are often as unique as that child. But in our experience at IMACS, one factor seems to be pretty consistent across the board: In this age range, parental influence starts to wane, sometimes rapidly, and outside parties such as friends and teachers gain in influential power. If you don’t have buy-in from a tween or teenager on a particular idea that involves her, then you’re probably not going to get anywhere. In fact, there’s a good chance that the reaction you get is the exact opposite of the one you want. Such is the process of growing up. It just seems more painful to now find yourself on the parental side of this equation.

There are two broad pieces of advice that we can offer based on the anecdotal evidence we see and hear with our female students. One is to get your daughter involved in one of the growing number of programs that promote science, technology, engineering and math (STEM). The earlier you get girls excited about STEM, the better. Studies have shown that if girls are not interested by middle school, it’s almost impossible to get them to pursue any of these fields in college or as a career. Getting your daughter involved in math and science enrichment during elementary school is a great first step. Whatever the age, look for a program with a healthy proportion of female participants, or even a girls-only program if available in your area. When a girl is surrounded by other girls who are also interested in these subjects, then being a “math and science girl” doesn’t seem so “out there,” and the stereotype that STEM is for boys is less likely to be reinforced. Your daughter might also feel more confident and willing to take more risks in learning if she’s not surrounded by boys.

The other piece of advice is to find a trusted adult female who works in a STEM field to mentor your daughter. It’s important for girls to have STEM-minded peers, but they also need successful female role models to look to and learn from. We mean no disrespect to the many excellent male mentors out there, but there is no doubting the power of “seeing is believing” when it comes to convincing girls that they can have a successful future in STEM. And while it’s inspiring to read interviews with Google’s Marissa Mayer or actress Danica McKellar, building a positive one-to-one mentoring relationship with an accessible adult has much more impact. Your daughter can receive regular guidance that address the specifics of her situation (e.g., career options, scholarship applications, college admissions). Plus, it will be coming from an adult other than Mom or Dad who, at this stage of adolescence, have zero credibility.

Below, we’ve compiled a non-exhaustive list of organizations, programs and resources for encouraging and motivating talented young girls to get and stay engaged with STEM. Many have organized mentor matching services. If your daughter is approaching high school, we’ve also included two organizations that focus exclusively on high school girls. We encourage you to explore these links and to inquire further in your local communities for similar opportunities. Your daughters are counting on you, whether they know it or not.

Organizations that Encourage and Support Young Girls in STEM

National Girls Collaborative Project (NGCP) – The NGCP brings together US organizations that focus on motivating girls to pursue careers in STEM fields. The program directory currently lists over 2,000 organizations and programs by geographic location. Select “Mentoring” in the “Resources Needed” list to find programs that offer mentoring services. The NGCP Web site also has an extensive list of resources, including the NGCP newsletter and links to dozens of girl-serving organizations and Web sites.

Girls’ Electronic Mentoring in Science, Engineering and Technology (GEM-SET) – GEM-SET is part of the Women in Science & Engineering program at the University of Illinois at Chicago. The goal of GEM-SET is to connect young girls in middle school and high school with professional women mentors in the STEM fields. Girls must be affiliated with a partner organization.

Inspiring Girls Now In Technology Evolution (IGNITE) – IGNITE originated in the Seattle school district and has grown to include chapters around the country. The organization connects middle and high school girls with professional in STEM careers who act as role models and mentors. Programs also include job shadowing, field trips, career fairs, guidance for internship, scholarship and college admission applications.

Girls, Math & Science Partnership (GMSP) – The Carnegie Science Center in Pittsburgh sponsors this program for 11-17 year old girls. The main BrainCake Web site is designed to be totally cool, fun and interactive – so very now. Girls can also fill out a simple survey to be matched with a mentor.

Association for Women in Mathematics (AWM) – The AWM Mentor Network matches mentors with girls and women who are interested in mathematics or are pursuing careers in mathematics. Grade school and high school girls can apply. Mentors may be women or men, but students have the option of indicating a strong preference for a female mentor on the application.

Aspire – Aspire is the K-12 outreach program sponsored by Society of Women Engineers (SWE). The organization’s signature event is WOW! That’s Engineering where local SWE chapters bring girls and women engineers together to learn about and do engineering. You can contact your regional SWE section to find out if they will be hosting a WOW! That’s Engineering fair in your area.

Sally Ride Science – This organization was established by America’s first woman in space to support girls’ and boys’ interest in math and science, and to make a difference in society’s perceptions of girls’ roles in technical fields. Sally Ride Science sponsors one-day science festivals for 5th – 8th grade girls. Girls entering 4th – 9th grades may participate in hands-on science camps that provide an opportunity to explore science, technology, and engineering on the campus of some of the most prestigious universities. Locations for the summer 2011 included Stanford, Berkeley, UCSD, MIT and Caltech. The parent handbook includes very helpful information and advice on raising talented girls.

My Gifted Girl – My Gifted Girl is a community for gifted girls and women in all subjects, including STEM fields. They serve as a resource for parents, educators, mentors and other organizations that support talented girls and women. Free membership gives you access to My Gifted Girl message boards where mentors can answer posted questions and contribute in specific subject matter areas.

Looking Ahead to High School

National Center for Women & Information Technology (NCWIT) – The NCWIT Award for Aspirations in Computing recognizes high school girls for their computing-related achievements and interests. Winners are chosen for their computing and IT aptitude, leadership ability, academic history, and plans for post-secondary education. Just reading the profiles of past winners is an inspiring experience. They demonstrate that you will find talented girls from a variety of backgrounds and experiences no matter where you look across the country.

Digigirlz – Digigirlz is Microsoft’s program to give high school girls the opportunity to learn about careers in technology. The company hosts Digigirlz Days where students get to interact with Microsoft employees and see what it’s like to work there. They also sponsor multi-day High Tech Camp for girls at no cost.

This week, IMACS catches up with an old friend, Mark Engelberg. Mark was part of the inaugural class of Project MEGSSS students in Broward County, Florida, when that program began in 1983. MEGSSS (Mathematics Education for Gifted Secondary School Students) was an ambitious public school course of study with a curriculum designed specifically for the brightest math students. The Broward program became IMACS in 1993. Like many of his fellow MEGSSS/IMACS alumni, Mark went on to an accomplished career in a STEM-related field. He is known for having designed the bestselling logic game, Chocolate Fix, as well as adding thousands of new challenges to the popular Rush Hour game.

How did Chocolate Fix evolve from an idea to a bestselling game to the basis for a new logic curriculum?

Chocolate Fix started out as a product called Gridworks. Gridworks was my first collaboration with ThinkFun, and its creation was very much a team effort. Bill Ritchie, the CEO of ThinkFun, had the initial inspiration to build a visual logic puzzle system. I proposed the pattern-matching framework for the clues and made the case that such a system would be simple, elegant, and expressive. Two very brilliant and prolific puzzle designers, Serhiy Grabarchuk Jr. and Scott Kim, ran with the idea and came up with the initial book of 60 puzzles. And of course, ThinkFun’s excellent artists and graphic designers came up with the product’s look and feel. It was a real thrill to work with so many talented individuals.

The funny thing, looking back, is that at the time, we weren’t entirely certain whether such a clue system would be rich enough to create challenging and interesting puzzles. Yet nearly a decade later, we haven’t even come close to exhausting Chocolate Fix’s potential; we’re constantly discovering clever new types of puzzles that can be expressed within the system.

Meanwhile, Chocolate Fix received the Parents’ Choice Gold Award in 2008, and in 2010, the Bunge Lab at UC Berkeley published a study that named Chocolate Fix as one of a handful of puzzle games that were shown to increase IQ. We know of at least one geometry teacher who has successfully used Chocolate Fix to teach his students the skill of constructing mathematical proofs. This is all exciting stuff, and it looks like Chocolate Fix has a bright future. Right now, we’re looking at ways to combine all the things we’ve learned about Chocolate Fix and turn it into an actual curriculum for teaching logic, problem solving, and mathematical proof skills.

You were also instrumental in using technology to develop thousands of new challenges for the Rush Hour app when the initial thought was that all the “good” challenges were gone. What are your thoughts on how technology continues to affect how we play games?

Technology touches every facet of our lives, and games are no exception. Computer games, for example, now form one of the largest segments of the entertainment industry. Even when it comes to non-electronic games and puzzles, computers play an important role behind the scenes. Nearly every crossword puzzle and sudoku are created these days with the assistance of computers. Artificial intelligence programs continue to shed new light on strategies for the world’s deepest games, including Chess, Go, and Poker. So to me, it seemed perfectly natural to apply my programming skills to the task of creating fresh new Rush Hour challenges.

You are the inventor of two other games – Animalogic and Snorkels. Tell us about them.

Animalogic received the Parents’ Choice Gold Award in 2009. Like Chocolate Fix, it is a solitaire puzzle system that comes with a book of challenges. The premise is that you have to successfully get 16 colored animals across a river, but the animals will only line up behind other animals that match in type or color. It’s a nice spatial, attribute-matching puzzle system with simple rules that even the youngest of kids can understand, but the puzzle book has a full range of difficulty levels, including expert challenges that will give adults a mental workout.

Snorkels is a two-player strategy game where each player controls a team of cute, colorful aliens with the goal of being the first to capture one of your opponent’s aliens. The capturing mechanism in Snorkels comes directly from the ancient Asian strategy game Go, which is widely regarded as the deepest strategy game ever devised (even deeper than Chess!). In fact, I created Snorkels primarily to be a “gateway game” to Go, which happens to be my favorite game. Snorkels is satisfying in its own right, but once you master Snorkels, you’ll find it a snap to learn and enjoy Go.

You recently said that the MEGSSS program, which is now part of the IMACS curriculum, gave you the logical thinking skills that enabled you to develop Chocolate Fix. Can you elaborate on that?

When creating the clue system for Chocolate Fix, I was heavily inspired by my experience with Book 1 of the Elements of Mathematics series, “Introductory Logic.” [Editor’s note: This material now forms the Logic for Mathematics I (LM1) curriculum at IMACS.] In a strong sense, each proof challenge in EM Book 1 is a kind of puzzle, and I wanted to capture that kind of thinking in Chocolate Fix. The partial grid clues are a form of disjunction, and the ability to put multiple constraints within one pattern are a kind of conjunction. (Gridworks also featured negative clues. We removed them from Chocolate Fix to simplify the system, but we hope to bring them back as part of the curriculum we’re developing.) When solving a challenging Chocolate Fix puzzle, you can expect to use Inference by Cases, Indirect Inference, and other techniques now taught in the LM1 course at IMACS.

Describe your career path from when you graduated from MEGSSS to your current work in puzzles and games and curriculum development. Who or what experiences influenced you along the way?

After MEGSSS, I went to Rice University, where I double-majored in Computer Science and Cognitive Sciences. From there, I programmed virtual reality simulations at NASA, and then got into the computer game industry, working at Sierra On-line and Rad Game Tools. These days, I’m primarily a stay-at-home dad, but I continue to dabble in puzzles and games when I have spare time.

With respect to puzzles and games, my biggest influence is my own childhood. I logged a lot of hours playing computer adventure games, solving puzzles in GAMES Magazine, and playing boardgames with friends. I was fortunate in college to find a group of friends with similar interests, and I ended up learning a lot about puzzle construction through our many conversations and brainstorming sessions about what worked and what didn’t. I try to create the kinds of things I would have enjoyed when I was in middle school.

If someone reading this thinks he or she has the next brilliant idea for a game or puzzle, what should he or she do next?

The beauty of the Internet age is that it is so easy to get your idea out there. Learn how to program so you can put together a mobile or Web app to showcase your idea.

Build your future on a solid IMACS foundation. Take our free aptitude test today.

Former IMACS instructor, Brandi Parsell, offers advice on how to address the ultimate question in a way that stimulates logical reasoning and critical thinking skills.

It can be endearing, or at times downright frustrating – that eternal question, “why?”. When bright children discover that single word, they seem to grab onto it and won’t let go. Sometimes the answers are simple, and sometimes we find ourselves at a complete loss for words.

This innocent question, however, is a signal to parents that a child is ready to be challenged to think logically. The creativity is there – we can see it in their everyday play. It is how we encourage that creativity and shape it into critical thought that will form a solid basis for a child’s learning ability.

Critical thinking is one of the hardest subjects to teach older students; any schoolteacher will tell you so. But if you begin to give your children the necessary tools when they are as young as three or four years old, they can develop these skills more easily. When the question of “why” is put once again on the table, the best policy is to ask, don’t tell. Challenge your children; ask what they think the reason might be. Chances are you will be pleasantly surprised.

Often parents believe that when their child reaches school age, he or she will at last find satisfaction for that curiosity. Talented students, though, may become bored with traditional school curriculum. When such a student is not challenged to exceed our expectations, this frustration often takes the form of careless errors and lack of effort. If children begin to develop these kinds of bad habits, too often they give up quickly when faced with a truly challenging problem. It is important that bright students are encouraged to go beyond what is merely “expected” of them.

“Talented students owe it to themselves to stretch their minds as far as they can,” said Burt Kaufman, co-founder of IMACS. Burt spoke from experience. For over 40 years he worked closely with bright pre-college students and developed challenging mathematics curriculum materials to stimulate them to become true students – disciplined logical thinkers with an insatiable thirst for knowledge and understanding.

Parents are a child’s first teachers, and the best teachers don’t give away the answers. Turn your child into a detective, and yourself into their greatest source for clues.

An IMACS foundation in logical thinking sets students on a path to successful learning. Take our free aptitude test to begin your IMACS journey.

IMACS chats with Thomas Rutkowski, Assistant Professor in the Department of Anatomy and Cell Biology at the University of Iowa Carver College of Medicine. Prof. Rutkowski received his Ph.D. in cell biology from UC San Francisco and his B.S. in biotechnology with a minor in chemistry from the University of Delaware. He completed his post-doctoral fellowship at the Howard Hughes Medical Institute/University of Michigan. Prof. Rutkowski is also an alumnus of Project MEGSSS of St. Louis, Missouri, the sister program to Project MEGSSS of Broward County, Florida. The latter became IMACS in 1993. All three programs share a common curriculum that teaches students how to think critically using logic and reasoning.

Tell us what you’re currently working on in the lab.

My lab studies how cells respond to perturbation (“stress”) in the endoplasmic reticulum (ER). Sensing ER stress and responding appropriately is essential for the development and normal function of many different cell types, and dysregulation of the response contributes to a number of human diseases. We have two main interests. The first is understanding how ER stress contributes to fatty liver disease (FLD), which is the most common liver disease in the western world. FLD is latent and reversible in most people, but can progress to hepatitis, cirrhosis, or liver cancer, which are all irreversible. We have evidence that the ER stress response fundamentally alters how fat is metabolized in the liver, and that these alterations might contribute to FLD.

Our other interest is in understanding how the ER stress response senses the nature, strength, and persistence of the stresses that activate it, and then alters cell physiology to generate the appropriate response. For example, the ER stress response is activated both in immune cells when they are stimulated to produce antibodies, and in the liver after a meal—two very obviously different stimuli. What makes the ER stress response in the liver cell different from the response in the immune cell? This project actually has a significant mathematical component, and we are collaborating with a professor in the department of mathematics to build a mathematical model of the ER stress response. We will use the model to predict how the cell will respond to stresses of different types, thereby (hopefully) understanding how the signaling networks of the response are wired.

What are some of the potential applications of your research?

The simple answer to this question is that if we understand how cellular stress responses alter fat metabolism in the liver, then we will better understand how conditions like obesity, alcoholism, and hepatitis C infection lead to liver dysfunction and liver cancer, and ideally be able to prevent these problems. With the number of obese adults in the U.S. rapidly approaching one in three (not to mention the comparatively smaller but still significant numbers of alcoholics and hepatitis C patients), understanding and treating fatty liver disease and its downstream consequences is a huge challenge.

Of course, the larger reality is that basic research often comes with substantial but unforeseen rewards. By understanding basic cell biology we ultimately gain insight into many diseases, as well as normal human biology. A classic example I like to give is the MutS gene—which was first identified by a group studying DNA repair in bacteria, which would seem to most to be a highly esoteric topic with little practical value. However, the human equivalent of this gene later turned out to be involved in hereditary colon cancer. The rewards that come from simply asking how cells work, while perhaps harder to pin down, are probably far greater in the long run than anyone can imagine.

How did your experience in Project MEGSSS studying what is also the IMACS curriculum influence your path from high school to your present career?

I think in two ways, one somewhat abstract and the other fairly concrete. I think the abstract influence was in helping me to realize that my intellectual potential was far greater than I'd appreciated. In fact, I think most people never have a moment where they realize how limitless their own potential is, and that is a shame. When you go from being bored to death by long division in a traditional elementary school curriculum to learning college-level logic—and realizing that you are in fact learning it—it suddenly seems more reasonable to think big: big ideas and big aspirations. In this kind of curriculum, you are also exposed to other students who have already hit upon this realization. Then, as now, I think it stimulates my own thinking to be exposed to those who think about things on a wholly different plane, with incredible depth and creativity. Being a scientist, it is clear that big ideas are what move progress forward. MEGSSS was really my first exposure to the world of big ideas and creative thinkers that has (hopefully) shaped my initial inclinations toward science and how I've approached it since I've become a practicing scientist.

The other more concrete influence is in how we are using mathematics to inform our understanding of biology. In our quest to understand how cellular stress pathways work, one of the approaches we are taking is to develop a mathematical model of the stress pathway. By that I mean that each of the steps in the process is replaced by a differential equation that (ideally) accurately describes it. The point of this process is to develop a dynamic mathematical representation of the response that allows us to do computational experiments that we cannot do in real life, and so learn more about how the stress response works as a complex unit. Many biologists shy away from this kind of investigation, because they don't intuitively appreciate how broadly applicable math is to problems in other areas and they aren't comfortable with the language. Admittedly, we are collaborating with a mathematician to help us with our modeling, but I think that programs like MEGSSS and IMACS makes students much more aware of how diverse a field mathematics is, and also makes them so much more comfortable with the language, and willing to apply it elsewhere.

You’re a parent with a mathematically precocious child. What are some of the activities you engage in as a family to help foster that talent?

We ultimately try to expose our children to new ideas (mathematical and otherwise) and challenge them to reason through problems they don't understand without pushing so hard as to turn them off. As my mother used to say, ”Use what you know to figure out what you don't know.&rdquoMath has to be fun; learning has to be fun. Opportunities present themselves if you just look around. For example, we used the weather changes to illustrate the concept of rate of change. Here in Iowa we are blessed, or perhaps cursed, with four very distinct seasons. In the summer and winter months, the temperature doesn't change much over time, but it changes quite rapidly from early fall to late fall, or early spring to late spring. Notice how the temperature might be warmest in the summer and coldest in the winter, but it changes the most in the spring and fall? Differential calculus at work, and hopefully introduced in a low-key way. Our primary goal as parents is to do whatever we can to keep them interested in math (and learning in general); if we can successfully do that, I hope they'll naturally take to whatever curricula they are exposed to. Of course now that our oldest is entering third grade, and getting to the point where boredom with his regular math curriculum is starting to be a problem, we have had to look more actively for ways to foster his interest. I vividly remembered my exposure to logic and number theory in my first summer with MEGSSS (after fifth grade) and have since ordered those beginning books for him.

There is a lot of talk about the challenges the US faces in math and science education. From your point of view as a professor and a parent, what actions need to be taken to help US students become competitive again in the new global environment?

The U.S. is far and away the world leader in scientific research, which makes the mathematical and scientific illiteracy of the general population all the more discordant and alarming. We absolutely cannot sustain our technological edge in this environment—partly because we will no longer continue to produce talented scientists and mathematicians; and partly because a population that does not understand math and science will not support them intellectually or financially. A majority of Americans do not accept the idea of evolution—that all life arose by descent with modification from a common ancestor—despite the fact that it is the central organizing principle in biology, paleontology, and, importantly, medicine, and is one of the best supported scientific theories ever devised. A large minority of Americans do not accept that human activity is warming the planet, despite this too being an extremely well-supported theory and having reflected the consensus scientific view for nearly 20 years.

Where does this illiteracy come from? I think it ultimately arises from the fact that science (and math) represent fundamentally unique ways of thinking about the world that are simply not well-taught in schools. Science is not knowing the difference between igneous rock, sedimentary rock, and metamorphic rock. It is not repeating some ”experiment&rdquothat's been done thousands of times over by millions of students with a prescribed result. Science is inquiry. It is observing the world, asking a question, forming a hypothesis, testing the hypothesis, and discarding the hypothesis if the test falsifies it, or moving forward with it if the test supports it. Every student learns this as ”the scientific method,&rdquobut how many get to put it into practice, to address a question to which the answer is unknown? How many science teachers make this kind of investigation the centerpiece of their curriculum, versus simply presenting a series of facts that must be memorized and ”labs&rdquothat must be suffered? Knowing that, as a scientist I am learning the answers to questions that have never been answered before, however big or small, is one of the true excitements of my vocation.

The same applies to math as well; math is not a worksheet full of arithmetic problems. It is a language that can be applied to real world problems, and requires its own way of thinking. There are teachers who approach science and math in this way, but I am convinced they are few and far between, and many others who want to probably feel they cannot, lest their students perform poorly on standardized tests. That people are not generally trained to think this way is evident from our national discourses. Debates are driven by ideology, with every viewpoint given equal weight. Arguments are made by assertion and evidence is cherry picked to support a preformed viewpoint. This is totally antithetical to scientific thinking, where the evidence drives the viewpoint and the viewpoint is subject to change based on the weight of that evidence. If science and math education in this country were geared toward teaching those ways of thinking, rather than toward the accumulation of information needed to pass a standardized test, I think not only would the population be more scientifically literate, and not only would we maintain our scientific edge, but we would also have much better informed and more productive dialogues on the issues facing society.

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IMACS introduced Boosted Learning for Achievement on Standardized Tests (BLAST) in 2007 to help second graders who are struggling in math. After receiving a growing number of inquiries from parents searching for an effective remedial math program, we saw that it was time to make the benefits of our curriculum more widely available. IMACS is all about helping students reach their potential in math, and we firmly believe in this philosophy for all children regardless of natural ability.

BLAST, which is funded primarily through corporate sponsorship, is open to students who score below the 70th percentile in problem solving in first grade on the Stanford Achievement Test. Here are some highlights from our inaugural BLAST class:

• The average increase in math score across all students was 15 percentage points.
• Two-thirds of the students improved their math scores. The average increase among this group was 27 percentage points.
• Of the students who improved their math scores, more than half also improved their reading scores by an average of 19 percentage points.
• Every student in the bottom third of the class according to the first year’s math scores increased his or her math score. The average increase among this third was 29 percentage points.
• All but one of the students in the bottom third of the class according to the first year’s reading score increased their reading scores. The average increase among this third was 23 percentage points.

While our BLAST kids gained a lot from their IMACS experience, we were also able to take away some valuable lessons on how to help students who are having difficulty with math.

Learn to Think, THEN Think to Learn

Most children who come to us struggling with math have not sufficiently developed the ability to think logically and critically. And this is true whether they are below average or gifted and talented. Most have never been exposed to any kind of training in this area because the traditional approach to teaching is based on the assumption that logical reasoning and critical thinking skills will develop almost as a side benefit of studying the core subjects. It’s not quite putting the cart before the horse. Rather it’s more like having a stand-alone cart and hoping that a horse will trot on over to be attached. What we’ve found in both our BLAST program and in our advanced math program is that if you start children off by teaching them how to think logically, it makes a world of difference in their ability to learn whatever material comes after. And mathematical logic, like other subjects, can be taught and learned. It’s the intellectual equivalent of pumping iron in the gym when you’re training for competitive sports. Students first build up their critical thinking skills so that they are ready and, just as importantly, feel ready to be take on a challenging subject.

Individual Attention Encourages Risk-Taking

So how do we help students feel ready? It’s really just about rekindling and harnessing the natural curiosity they were born with. When a child is struggling with math, he or she may not feel comfortable speaking up in large group settings to answer questions or ask for help. Children with above average math abilities may feel the pressure of expectations. They may believe that they have to understand right away and cannot make mistakes. Those who are not naturally strong in math may fear being labeled as “dumb” if they give incorrect answers or admit that they don’t understand. They may also worry that others will think they are trying to “act smart” if they participate in class. At IMACS, we are able to break through this barrier of self-consciousness by working with children in small groups. When our students realize that they are in a place where it’s okay to take risks and make mistakes, they let down their guard and allow their natural curiosity take over. Simply put, they rediscover the joy of learning and leave the program feeling empowered to take on challenging work. A parent of one of our students summed it up beautifully: “BLAST went beyond my expectations. In a matter of 10 weeks, I have seen my child work with numbers on her free time and love math. Her self-esteem is soaring unbelievably.” That’s exactly the kind of feedback that makes us want to rise and shine each and every morning.

While we have our own in-house logic exercises that we use with our students, we’re also a big fan of logic games by ThinkFun. We like that ThinkFun games are affordable and constructed well to last a long time. And they usually have multiple levels of difficulty, which makes them accessible to a wider range of ages and abilities. Another great source are the weekly logic puzzles posted every Friday on our Facebook page. If you have a suggestion for other logic games or ways to help struggling students, please leave a comment.

If you are interested in being a corporate sponsor of BLAST, please send us an email at info @ eimacs.com.

IMACS online classes are designed to fit into your schedule. Take our free aptitude test to see if our program is right for you.

(Este blog tambien esta disponible en Español.)

This week, IMACS asks Dr. Arturo Cifuentes to share his colorful opinions on a variety of topics. Dr. Cifuentes received his Ph.D. in applied mechanics and M.S. in civil engineering from Caltech. He spent five years at the prestigious IBM Thomas J. Watson Research Center. Dr. Cifuentes then moved to Wall Street, where he spent 15 years working in the fixed income market. During the recent financial meltdown, he was invited to testify before Congress as an expert witness on the subprime crisis. Dr. Cifuentes is currently an Adjunct Professor in the Department of Industrial Engineering at the University of Chile and writes a monthly column for El Mercurio.

As you were growing up, what made you realize that you had a talent for math and science? How did you become interested in pursuing degrees and a career in engineering?

My father was an engineer who did a lot of consulting work. He enjoyed very much what he did and talked quite often about the “problems” he was trying to solve. I found that fascinating. I think, in a way, that enthusiasm motivated me to investigate in more detail what he did. And I liked it.

Also, having early access to all the books by Yakov Perelman was a turning point in my life. Those books were fun to read, intriguing, and very powerful and persuasive. My father did not believe in libraries; he felt that any book worth reading should be at home. The fact that I had access to many books since I was a child was fantastic. And the Perelman books convinced me (I am still convinced) that any career in science or a closely related field could be rewarding and interesting.

In your opinion, what needs to happen with math and science education in the United States in order for US students to remain competitive globally?

Parents should turn off their TVs, buy more books, and tell their children the truth: Sure, learning something like math or physics can be a lot of fun and can be rewarding, but it involves a lot of hard work and effort. And if those who believe in Intelligent Design could be persuaded otherwise, that would be quite helpful.

Two tendencies, or perhaps ideas, which in my opinion are pretty bad and should be eliminated, are the following (and I acknowledge that most people will disagree with me here):

[i] The growing emphasis on group work and team effort. Learning something like math is pretty much a lonely effort, a solo journey. People have to accept that. There is nothing wrong with team effort (soccer, for instance, is about that). But certain things (playing the piano, for example) require a lot of NON-group work. Math is one of those things.

[ii] Computers in the classroom. There is nothing wrong with using computers. But introducing them at an early age (with the idea of making learning fun) is a disaster. Children must learn to think conceptually first. And when introduced to computers, they should learn how to program them instead of learning how to react via a mouse to some external stimulus.

Now that the space age seems to be coming to a close, what is going to be the stimulus for intellectual and scientific pursuits going forward?

Well, in science and technology, whenever a door closes, several windows open. The advances in genetics, bio-engineering and neuroscience are very exciting; the same with computer science and communications. In physics, whoever manages to reconcile relativity and quantum mechanics will be the new Einstein (or Newton). Not to mention many more practical problems that still remain unsolved: earthquake prediction, for example.

You are a voracious reader. What book or books would you recommend to today’s students and why?

I was fascinated by Tom Sawyer and Huck Finn when I was a teenager. I read them in Spanish, and they were as good as in English. I also read Kafka, Cortazar, Hesse and Poe. Unfortunately, Etica para Amador by Fernando Savater is not available in English. I think every teenager should read that book. Finally, Richard Feynman’s Surely You’re Joking, Mr. Feynman is a must. If anyone thinks science is boring, this is the book to read.

How did you go from doing structural engineering research on thermal stress and circuit boards to analyzing complex financial securities?

I had been working at IBM Research in New York for five years, doing a lot of interesting stuff, and never thought about going anywhere else. Unfortunately, IBM was having a difficult period and they decided to cut costs. That meant that instead of using 100% of our time and effort to do research, we were supposed to go out and find funding (i.e., write grant proposals, etc.). The minute I saw the first few forms and all the paperwork involved in getting a government grant, I was done. I decided that I was not going to spend the rest of my life begging for money. That took the fun away from the research.

I loved (and still love) New York, and my wife had a good job there, so I decided to stay there and look for work. I quickly became aware that there were not many options for scientists in the New York area. Fortunately, a friend who worked on Wall Street asked me if I would consider interviewing with his firm.

“I don’t know anything about finance,” I said.

“As long as you can do Monte Carlos,” he explained, “you will be fine.”

I knew Monte Carlos. And in a few weeks I moved to the financial field.

But at the end of the day (as bankers like to say), it is all the same: thinking analytically and logically about problems. If you have a good background in math, it is easier to jump from one field to another. You learn to quickly identify the essentials and then the math helps. The key is to acquire good quantitative skills when you are young; you can easily learn the rest later. But if you don’t get your math tools under control by the time you are twenty, it is probably too late.

You currently write a column on business and economics, and you previously wrote an opinion column reflecting your varied interests in topics such as soccer and travel. Technical people are often stereotyped as having narrow focus and weak communication skills, so to what do you attribute your broad range of interests and abilities?

When I grew up I never had that impression. (I mean, that technical people had a narrow focus.) My father, who was a civil engineer, spoke several languages, and he often quoted Shakespeare in English and Goethe in German. He had a great library at home and read a lot. And his interests were very wide. I remember one Saturday (many years ago, I was ten or twelve probably) we went to his favorite bookstore and came back with three books: one dealing with humidity in high rise buildings and how to control it; a second book was about the evolution of financial markets in Chile; and the third book was about Freud. I still remember what the salesperson said: “I have seen many people buying these books before, but I have never seen the same person buying all three!” Well, that was my father. He was a very important influence and example when I grew up. He was a guy with many interests and skills. I owe him a great deal.

Any parting words of advice to the students and parents who are reading this?

When you are older than fifty, you tend to give more advice than you should. So I will be brief: Do what you like and follow your instinct. And remember, life is not about career choices or promotions. It is about love and friendship. Nothing else matters. Although having good math skills is always a plus.

Students worldwide take IMACS classes online. If you’d like to find out more, sign up for our free aptitude test or contact IMACS at info @ eimacs.com.

In the third and final part of our summer series on thinking games, we look at three strategy games that are deceptively simple. We use these games at IMACS to sharpen the critical thinking skills of our students. While chess is rightfully considered by many as the ultimate strategy game, we like the three games below because the simple rules are very easy to learn, even for someone as young as five or six, and each game does not take an eternity to play. Best of all, each is kid-tested and IMACS-approved!

Quoridor by Gigamic

Game Essentials: Quoridor is a fantastic game of strategy, especially for those who like mazes. In the typical two-player setup, the pawns are placed on the middle squares of opposite sides of a 9×9 board. The winner is the first to maneuver her pawn from its starting position to any of the nine squares on her opponent’s side. Generally speaking, you can move one square at a time, forward or backward or left or right but usually not diagonally. You can also jump over your opponent’s pawn when the two pawns are face to face. Seems trivial so far, right? That’s because we haven’t yet discussed the fences! You see, at each turn, a player can choose to either move her pawn or to impede her opponent by putting up a fence that blocks or lengthens the opponent’s path. Twenty fences are divided evenly at the start of the game, and the main rule governing them is that you can’t use them to block all possible paths – there must be at least one way to get from one side of the board to the other. The video below from Gigamic illustrates these rules:

For brevity’s sake, the video showed a short and simple game. But, in fact, games are typically much more complex. With each fence placed on the board, an increasingly complicated maze of paths from one side to the other is built. And the results can be downright maddening! One minute, you think you’re making good progress only to have your pathway dead-ended by your opponent, in which case you have to backtrack, costing precious moves. Another time, you may turn the tables on your opponent by blocking him only to be obstructed by your own fence placement later in the game.

As with most abstract strategy games, winning depends on your ability to think ahead about the possible outcomes of available moves and select the optimal path. In other words, to take your strategy beyond simply “move forward – block opponent,” you must build and analyze a decision tree in your mind. You also need to think offensively and defensively at all times. For example, if you are progressing alongside a series of fences, your opponent will almost certainly use a new fence to block you just as you get to an opening. However, if you use one of your fences to block the path behind your pawn, then your opponent may not be allowed to block your way forward if it would close off all paths. Still, you must be careful to use your fences judiciously so that you don’t run out of them too soon.

Quoridor may also be played with three or four players. Each player selects one of the four sides of the board as the side for his pawn’s starting position and works toward being the first to reach the opposite side. Divide the fences up so that each player has an equal number with as few left over as possible. Then just follow the rules of movement and fence placement from the two-player game.

Recommended Age: The manufacturer suggests ages 6 and up, and we tend to agree. The rules of play are simple, but it does take a certain level of maturity to keep from getting frustrated when your opponent repeatedly blocks off your path.

Brain Play-To-Price Ratio: Quoridor lists for $29.99 but can be found for around $23. The rules and objective are easy for the youngest or most inexperienced players to learn, but mastering the game is a fun challenge that will engage children and adults alike for many years. As with most Gigamic board games, Quoridor is made of sturdy wood. And under Gigamic’s 10-year warranty, all you have to do to get free (love it!) replacement game pieces is send a letter to Gigamic.

Easier Adaptation: Gigamic makes a version called Quoridor Kid for ages 5 and up that costs about $5 less. The board is 7×7 instead of 9×9, and there are 16 fences instead of 20. The neutral-color game pieces and board are replaced by cute little mice, colorful fences and a cheerful board. Each mouse has a different colored nose which matches one of four colored cheese wedges on each side of the board. This nose-to-cheese match helps keep little ones focused on exactly which side of the game board they are aiming to reach. The smaller board typically means that a game of Quoridor Kid lasts a shorter amount of time. But the game rules are the same as Quoridor, and thus encourage the same kind of strategic thinking, albeit with a smaller number of paths to consider. The choice between starting with Quoridor Kid or going straight to Quoridor depends on whether you think your child would be more willing to stay engaged with the game due to the cute mouse-and-cheese theme. After all, you could just use the inner 7×7 section of “grown-up” board by ignoring the edge squares, as well as four of the fences.

Noteworthy: You can sample Quoridor online before deciding on a purchase. Just know that manipulating the fences online is not nearly as natural as when you’re holding the real thing in your hand.

Quarto by Gigamic

Game Essentials: Quarto is a two-player game that comes with 16 solid wood pieces and a sturdy 4×4 wooden board. All pieces not yet placed on the board are available to each player. The object of the game is simple: Be the first player to get four pieces that share a common feature in a line and call out “Quarto!” The line can be horizontal, vertical or diagonal, and you do not have to have placed all four pieces on the board yourself. So what are the possible common features? There are eight: a game piece can be light or dark, circular or square, short or tall, and hollow or solid. (A little elementary combinatorics confirms that we should, indeed, have 16 unique game pieces.) Here’s the kicker that makes Quarto stand out from other N-in-a-row games – you don’t pick the pieces that you place on the board; your opponent does! The following video illustrates these rules:

Quarto hones the mind’s ability to recognize patterns. This simple twist of picking out your opponent’s pieces comes with great responsibility for you must take care not to literally hand him the win. If you see that there is already a line with three circular pieces, then choose a square piece for him. If you’ve set yourself up to win with a short piece, then you might try to force your opponent to hand you one by giving him all the remaining tall pieces to play, assuming that such a move doesn’t give him the win.

As with games like tic-tac-toe or Connect Four, a primary strategy with Quarto is to set up more than one possible way to win so that if your opponent blocks one, you can still try to win with another. The ultimate two-pronged approach is to build two lines around two opposing features, e.g., one line of light pieces and another line of dark pieces. Then no matter what piece your opponent hands you next, you’re guaranteed a win because the piece you get, in this example, has to be either light or dark.

Recommended Age: The manufacturer suggests ages 6 and up, but a bright kindergartener should be able to enjoy this game. The rules are very simple. The only thing that takes getting used to is having your opponent choose the pieces that you place on the board instead of selecting them yourself.

Brain Play-To-Price Ratio: Like Quoridor, Quarto lists for $29.99 but can be found for around $23. If you want to experience either game for less, look for the travel editions. The craftsmanship is still excellent, but the smaller size will save you at least another $5. Quarto is fun for all ages, and Gigamic’s 10-year warranty and generous replacement policy applies to it as well.

Multipurpose: For small children, the wood pieces make for obvious fun as building and balancing blocks to hone fine motor skills. But you can also use them to introduce Venn diagrams. Just draw two large overlapping circles on a piece of paper and decide what characteristic each circle represents. For example, one circle can be tall pieces and the other circle can be hollow pieces. Ask your child to place each of the 16 pieces in the appropriate area of the paper. Change up what the circles represent and do it again. Add a new characteristic and expand to three overlapping circles. Not enough room on a sheet of paper? Get some yarn or raid the belts in Dad’s closet and make overlapping loops instead.

Easier Adaptation: With younger or less experienced players, you can simplify the objective by using just one, two or three of the four characteristics to make a winning line. For example, the first person to get four of the same color or four of the same shape in a line wins. Forget about height and hollowness until players feel ready to add on another level of difficulty.

Noteworthy: The Quarto rules also suggest a variation for advanced players that allows for nine more winning configurations. Specifically, in addition to getting four pieces in a line, you can win by getting four in a square. Just try keeping your eyes on all those possibilities!

Othello by Mattel

Othello, also known as reversi, is a widely-played classic game of strategy that has been around in some form since the late 1800’s. Its trademarked slogan sums it up beautifully: “A minute to learn, a lifetime to master!”™ With its simple rules, Othello can be played by children as young as five, even though the recommended age is eight to adult. If you’ve never had the pleasure of playing this game, watch the video explanation below:

Othello is an ideal game for teaching one of the key elements of strategy games, which is to think longer-term even if it means not choosing a move that seems optimal in the short-term. If you approach each turn with the goal of maximizing the number of disks of your color at the end of that one turn, then you will surely lose. Experienced players focus, instead, on setting up “helper” positions that will lead to the capture of certain prized locations on the board. These coveted spots (e.g., corners and edges) give a player tremendous leverage during the last series of moves that take place toward the end of a game.

Given the age and popularity of Othello, it should come as no surprise that its game strategies have been extensively researched, analyzed and documented. Here is a fairly readable strategy guide from the French Othello Federation. You can appreciate from this and other Othello guides that pattern recognition, another key element of strategy games, is an essential skill for winning.

Othello lists for $11.99, and will provide many hours of game play for the whole family. It’s also commonly available as a smartphone or tablet app and online. If you’d like to see some of the best Othello players in the world compete, you are somewhat in luck because the 35th Annual World Othello Championship will be held in the US this year.

If you are just discovering this blog, check out Part One of the series on logic games and Part Two on visual-spatial games. We hope that, through this series, you have discovered a new game or two to keep your brain active during these summer months and for years to come.

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In Part Two of our summer series on thinking games, we focus on those that exercise the brain’s visual-spatial abilities. The three games we recommend below will have you shifting, flipping, and rotating objects in your mind and sharpening your problem solving skills.

Katamino by Gigamic

Game Essentials: Katamino is a versatile tiling game that will put your spatial reasoning abilities through a serious workout. The game comes with 12 three-dimensional pentominoes, eight smaller support pieces, a grid-based board, and a booklet full of challenges. A pentomino is simply a shape consisting of five congruent squares that are connected at their edges. In the case of Katamino, each of the 12 main pieces consists of five congruent cubes that are connected at their faces. Gigamic calls these “pentaminos.”

There are variations on how to play, but in the standard solitaire approach, the object is to neatly place a subset of the pentaminos in a rectangular section of the board. If your goal is to tile N pentaminos (a “Penta N”), then the section will be an Nx5 rectangle. A player typically starts with a Penta 3 challenge. Once it is solved, the player adds another pentamino to the mix and rearranges the now-larger set of four pieces to solve the Penta 4. Next is a Penta 5, a Penta 6, and so on. The puzzles get progressively harder as you add pentaminos.

Another neat way to play is to select one of the pentaminos and then use nine of the remaining 11 to create a larger version of the first one that you chose. This can be done for every pentamino. Challenge yourself to replicate all 12. There are 3-D challenges as well where a player uses the pentaminos and support pieces to build the three-dimensional objects pictured in the booklet. Mathematically speaking, the standard Katamino game is two-dimensional but played with three-dimensional pieces for practical purposes. We imagine that flat pentominoes that are hard to pick up would make the game incredibly frustrating to play, not to mention how fragile they would be in little hands.

Katamino may also be played as a two-player game. In the speed game, players evenly divide 10 of the 12 pentaminos (all except for the “I” and the “X”) and all of the support pieces. The opponents then race to see who can tile his or her half of the board first. The strategy game uses only the 12 pentaminos and an 8×8 board included in the booklet. Each player takes a turn placing a pentamino anywhere on the board. The last player to place a pentamino on the board wins.

Recommended Age: The manufacturer suggests ages 3 and up, and we couldn’t agree more. With its colorful wooden blocks, this is just the kind of game to captivate and stimulate young minds. Kids can’t help but be enticed by the colorful assortment of shapes that almost seem to call out, “Build something with me!” And with the eight smaller support pieces, even three-year olds can enjoy the challenge of tiling without any guidance.

Brain Play-To-Price Ratio: Katamino lists for $29.99 but can be found for around $22. There are 500 challenges included in the accompanying booklet, so children and adults of all ages will have no trouble finding puzzles with just the right level of difficulty. After solving the challenges that come with the game, see if you can enumerate additional challenges. This should keep you busy for a while as there are literally thousands more. This is a well-constructed game made of solid wood that will last through lots of rough and tumble play. And kudos to Gigamic for recognizing that a solid wood game, with its extra heft, needs a reinforced box for storage. When your child passes Katamino down to your grandchildren, it won’t be in a box that looks like something out of “The Mummy.”

Multipurpose: Katamino is a great game with which to introduce concepts from Euclidean geometry. Don’t be afraid to use mathematically precise terms such as “polygon” when playing with a child who has not studied the subject. Start by assuming that the pieces are comprised of unit cubes and explain what that means. Then show how to compute the perimeter and area of each face as well as the volume of each shape. Flip and turn the shapes to demonstrate the concept of symmetry. Which pieces have reflective symmetry, and what are the lines of symmetry? Which pieces have rotational symmetry, and what is the order of the rotation?

Another two-player variation is to play a game of balance by using the blocks to build a stack. Each player takes a turn placing one block on the stack. Whoever is last to place a piece on the increasingly unstable stack without causing it to topple is the winner. This is a great way to sneak in some basic principles of Newtonian physics.

Easier Adaptation: Gigamic makes an easier version called Winomino that includes six of the 12 pentaminos and ten additional pieces that are formed by one, two, three, or four cubes. The smaller pieces allow greater flexibility in solving the Penta challenges. The prices for Winomino and Katamino are about the same. If your child is older or is a natural visual-spatial thinker, then we suggest bypassing Winomino and going straight to Katamino.

Noteworthy: Pentominoes belong to a more generic class of shapes called polyominoes, so named to be consistent with the two-square shape of the well-known domino. Use four squares and you get a tetramino, which is the basis for the popular 80’s video game, Tetris. You can play Tetris online.

Shape By Shape by ThinkFun

Game Essentials: In this variation on the traditional tangram puzzle, 14 puzzle pieces must be arranged in a square tray to match the pattern on one of 60 challenge cards. Six orange pieces form the foreground image, and eight yellow pieces form the background. The orange pieces consist of identical pairs of each of the following: square, parallelogram, and isosceles right triangle. The yellow pieces consist of identical pairs of each of the following: right trapezoid, isosceles trapezoid, swallowtail flag, and a five-sided polygon that resembles a boot. To solve a puzzle, a player must place all 14 pieces neatly inside the puzzle tray with no leftovers and no pieces sticking up.

Anyone can try to solve the puzzles by placing the pieces in a haphazard way without much thoughtful planning. In our observations this usually results in more frustration than solutions, and that’s no fun. The real visual-spatial brain exercise and enjoyment comes when you take the necessary time to really think about where each puzzle piece should go. And it’s these mental gymnastics that can improve a person’s ability to handle visually intensive tasks from planning the seating at a wedding reception to designing pharmaceutical drugs to guiding a space-walking astronaut through a complex and unexpected situation from down here on Earth.

While the Shape By Shape challenges are not ranked by level of difficulty, some are definitely easy and others much harder. Take a look at the dog and cat patterns below, and you’ll see what we mean.

The Sad Dog in Challenge 12 is symmetric about the diagonal from top to bottom. Though not always the case, challenges with symmetric images often have solutions that require symmetric placement of the puzzle pieces. Furthermore, the pieces in the dog pattern do not share many edges, so it’s easier to recognize the shapes of individual pieces because they are not part of a larger area made up of connected pieces. For example, the eyes of the dog are obviously the two parallelograms while the nose is clearly one of the triangles. The two yellow areas that are shaped like the swallowtail flags pieces can only be made by those two pieces. Going outward from the eyes to the left and right corners, the yellow areas are most certainly the two “boots”. Once these obvious pieces are put in place, the placement of the other pieces becomes trivial.

By contrast, the Sleeping Kitty in Challenge 14 is asymmetric in every direction, and the pieces in the orange area share a lot of common edges that are in the interior of the cat shape. In kid-speak, the orange pieces are in one big blob. A more mathematical way of putting it would be that the ratio of the area of the cat to its perimeter is relatively high. The same observations can be made about the yellow area. Generally speaking, the higher this area-to-perimeter ratio, the harder the challenge because your visual-spatial brain function has to sort through more combinations of pieces in order to replicate the pattern.

Recommended Age: The manufacturer suggests ages 8 and up, but we think this is an ideal puzzle for much younger kids. Children who are not ready for the puzzle’s pre-defined parameters still stand to gain from the exploratory learning that just naturally happens through play. As a recent academic study indicated, Euclidean geometry is so intuitive that tribal children with no formal education in the subject understand its basic principles.

Brain Play-To-Price Ratio: Shape By Shape lists for $14.99 but can be found at a slight discount. Even at full price, we think this game is a great value. As with all the ThinkFun games we’ve played, Shape By Shape is made with high-quality plastic that’s built to last. The puzzles and the number of puzzle pieces are at just the right level to be challenging but not frustrating for players of all ages and abilities. Sixty puzzles will keep you busy for while, especially if you commit to not looking at the hints on the back of the challenge cards, and you can enjoy the same puzzles again after taking a break. But one of the many cool things about Shape By Shape is that you can challenge yourself to discover new patterns not included with the game. Freestyle play is the one time when starting off with totally random placement is justified. Just go with it and see where it takes you. If you manage to fit all the pieces in the tray, check your pattern against the challenge cards and see if you’ve found a new one. If you’re really ambitious, try articulating the mathematical limits of the shape combinations that would fit in the tray.

Multipurpose: Shape By Shape is another game that is perfect for exploring geometry. Try explaining geometric concepts when discussing observations like the following: The perimeters of the parallelogram and isosceles right triangle are equal, and the perimeters of the isosceles trapezoid, swallowtail flag, and “boot” are equal. The side of the square is equal in length to the shorter diagonal of the parallelogram. It’s also equal to the line segment perpendicular to the triangle’s hypotenuse that connects the right angle vertex and the hypotenuse. Which angles are acute, and which are obtuse? The orange pieces are of equal area, and the yellow pieces are of equal area that is 50% greater than the area of each orange piece. (Can you prove these statements about area rigorously? If not, at least convince yourself visually.) We could go on and on, but you get the point.

Easier Adaptation: A two-part solution is given on the back of each challenge card. If you are working with a younger player, use the first hint to place some or all of the orange pieces. Then go back to placing the yellow pieces without help from the second hint. Unless, of course, you both get stuck and need the second hint. But don’t give up too soon!

Noteworthy: Shape By Shape is one of six ThinkFun games invented by master puzzle designer Nob Yoshigahara. You can read about his work on ThinkFun games here.

Rubik’s Cube by Hasbro

This iconic puzzle has been a part of international popular culture since 1980 when mass-distribution outside of Hungary, home of inventor Erno Rubik, began. We won’t spend much time describing it here. If you really haven’t heard of the Rubik’s Cube, you can explore the official Web site or the many online videos documenting the culture of speed cubing. Here’s one pulled from the oldie-but-goodie shelf. It’s a real throwback, especially for those who remember the 80’s TV show “That’s Incredible.”

Note that the first contestant introduced during the in-studio competition, Holden Thorp, is now the chancellor at UNC Chapel Hill after having earned his PhD in chemistry from Caltech and going on to receive the NSF’s Presidential Young Investigator Award among his many accomplishments.

Robots also enjoy the challenge of the Rubik’s Cube, or at least their human engineers do. You can watch and read about the robot that currently holds the speed record here.

For algebra aficionados, check out these two papers and a book relating group theory to the Rubik’s Cube:
• Group Theory and the Rubik’s Cube by Janet Chen
• Group Theory via Rubik’s Cube by Tom Davis
• Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys by David Joyner

In our opinion, this little gem should be part of every child’s collection, although you should keep it away from little ones due to the small mechanical parts that can be removed. The original 3×3 Rubik’s Cube lists for $11.99 but can often be found for $8 or less. That’s dirt cheap these days for a cool thinking toy that’s also part of history. But if you’re just not into playing games in the physical world anymore, you can still test your Rubik’s solving skills here.

If you missed Part One on logic games, read it here. See you next week for Part Three on strategy games!

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It’s the middle of July. Are your kids bouncing off the walls yet? Then it’s time to play a game! This post is the first in a three-part series on games we like to play at IMACS. Part One of the series will focus on logic games, while Parts Two and Three will cover visual-spatial games and strategy games, respectively. At IMACS we search for games that embody ideas that support successful learning: logical reasoning, focused thought, and fun! In addition, we try to recommend games that provide a good value for parents by being reasonably-priced, made with quality craftsmanship, and fun for all ages.

Chocolate Fix by ThinkFun

Game Essentials: Nine chocolate treats must be arranged in a 3×3 tray based on clues about their shape and color. Each chocolate is a circle, square, or triangle and exactly one of three colors. The current version of the game uses green, white, and brown, while the previous version used light brown, dark brown, and pink. Each puzzle has a set of clues that give incomplete information about the shape, color and relative location of some chocolates. Using the rules of mathematical logic, a single player determines the unique location on the tray of each of the nine chocolates. While Chocolate Fix is designed to be a solitaire game, parents and kids can play together by taking turns with the puzzles or with the clues of a single puzzle. If you like sudoku, then you’ll probably like Chocolate Fix.

Recommended Age: The manufacturer’s suggested age range is from 8 years old to adult, but we feel that talented kindergarteners and first-graders can handle the beginner-level challenges and possibly higher levels.

Brain Play-to-Price Ratio: The official list price for Chocolate Fix is $19.99, but it can commonly be found for about $15, which puts it in the range of a middle-of-the-road Barbie or Transformer. We think this is a bargain for a thinking game that, according to our IMACS students, is tons of fun. As with most ThinkFun games, Chocolate Fix comes with 40 challenging puzzles across four levels of difficulty. This allows the game to remain relevant as a player grows in age and skill. And unless you have a photographic memory, you can enjoy the same puzzles again and again after setting the game aside for a while. But the longevity of a game also depends on the quality of the craftsmanship. You might envision your child playing with it from age 5 to age 15, but will it hold up over a decade of use and abuse? Here we salute ThinkFun for manufacturing games with quality that appears to last. Plus they have a reasonable replacement policy; you can purchase up to five pieces with the first one costing $2.50 and each additional piece costing $0.50.

Multipurpose: With little ones, you can count the chocolates and use them to demonstrate the concepts of same and different. The realistic-looking treats also make for great pretend play. Use them to play Candy Store with your children and practice skills like addition and subtraction. Assign prices to the chocolates and then compute the total amount owed for each purchase and change due.

Easier Adaptation: ThinkFun also makes a similar game called Clever Castle aimed at 5-7 year olds. In this version, princesses, knights, and dragons that are either red, yellow, or blue have been invited to Clever Castle by the king and queen. A player uses clues to help the guests find their rooms. Clever Castle also comes with 40 puzzles across four levels of difficulty, but the higher levels in Clever Castle correspond to the lower levels in Chocolate Fix.

Noteworthy: The newest version of the Chocolate Fix includes shape and color placeholders to help a player remember one of the characteristics of a chocolate that belongs in a certain spot until the player can determine the other characteristic. To the extent that the placeholders help a beginner not give up too soon, we support their use. But once a player gets the hang of the game, we encourage setting the placeholders aside so that building up one’s memory and concentration skills can also be a benefit of playing the game.

Best of all, the Chocolate Fix game rules and challenges were developed by Mark Engelberg, alumnus of Project MEGSSS which was a predecessor program to IMACS! “There is no doubt,” says Engelberg, “that the MEGSSS/IMACS curriculum gave me the logical thinking skills and mental framework that inspired and enabled me to develop the Chocolate Fix puzzle system.”

ColorKu by Mad Cave Bird Games

Game Essentials: We’re big fans of sudoku, and ColorKu is simply sudoku played with colors instead of numbers. The game comes with a 9×9 board and 81 colored wooden balls – nine colors and nine balls of each color. The fundamental rules are the same as number-based sudoku: From a given starting configuration, a player uses logical reasoning to determine the correct position on the grid of each of the remaining colored balls so that no row, no column, and no predefined 3×3 sub-square contains any duplicate colors. As with Chocolate Fix, this typically solitaire game can be played cooperatively among two or more players.

Recommended Age: The manufacturer’s suggested age range is from 8 years old to adult. Talented students of a younger age can handle this puzzle, but as the product warning suggests, children aged three and under should be kept away from this game due to the choking hazard presented by the little colored balls.

Brain Play-to-Price Ratio: The official ColorKu Web site lists the game for $32.99, but you can find it at a slightly discounted price of $30. This is by no means cheap, but for the solid wood craftsmanship of both the board and colored balls, this is a reasonable price that puts it in the range of Nintendo DS games. ColorKu comes with 104 puzzles across five levels of difficulty so that players of different skill levels can play. You can purchase an expansion pack with 104 new puzzles for about $10. Better yet, use the included number-to-color mapping to expand your puzzle set for free by converting any number-based sudoku game that you get from a newspaper, on the Web, or from a smartphone app. If you lose some of the colored balls, replacements start at $4.25 for a set of two of every color and go up to $11.75 for a complete set of 81. Shipping and handling to US addresses runs from about $3.25 to $5.95.

Multipurpose: What else can you do with 81 colorful balls and a grid? Your imagination is the limit. How about counting, bar charts, simple addition, subtraction, multiplication, and division. Play regular tic-tac-toe in one of the 3×3 squares. Improvise a game of Chinese checkers where each player must move his or her nine pieces from one of the outer 3×3 squares to the square on the opposite side of the board. Play marbles. Pretend to run a restaurant and serve “fruit salad” or “vegetable soup.” Challenge your child to name fruits and veggies of each color. If you run out of ideas, we’re certain your kids won’t.

Easier Adaptation: Parents can give younger players a boost simply by filling in some of the empty spots in the starting position of a puzzle with the appropriate balls based on the solution provided. As a player improves, reduce the number of additional clues.

Noteworthy: Mad Cave Bird Games sells sets of 81 balls with just two colors for playing their adaptation of tic-tac-toe. This will set you back another $20, which, if compared to buying unfinished wood balls and painting them yourself, is actually a fair price. However, we recommend that you first look around the house for objects such as small LEGO bricks that are colorful, numerous, and can be used just as effectively to play the tic-tac-toe adaptation.

Mastermind by Pressman Toys

Game Essentials: In this classic two-player game, the code-maker starts by creating a secret code using four pegs that can be any combination of six colors. The code-breaker then takes a series of guesses at the code sequence. With each guess, the code-maker gives the code-breaker feedback on (i) the number of pegs that are the correct color but not in the correct position and (ii) the number of pegs that are the correct color and also in the correct position. Note that under the standard rules, the code-maker does not provide any information as to which pegs in the code-breaker’s guess are either a correct color or a correct color and position. The code-breaker uses logic and reasoning with each new piece of information from the code-maker to improve upon the prior guesses with each successive guess.

Recommended Age: The stated age range is from 8 years old to adult, but again, we think that bright, young kids can handle the challenge. Just be sure to heed the manufacturer’s warning and keep the tiny pegs away from children three and under.

Brain Play-to-Price Ratio: The standard version of Mastermind lists for $15 on the Pressman Toys site but sells for around $13, which, in our opinion, is a tad high for what you get. The quality of the manufacturing seems to have dropped off since Mastermind was introduced in the 70’s, but we recommend it nonetheless because the game itself remains consistently fun and stimulating for talented minds of all ages. There’s a reason it’s been around for 40 years – it really is an excellent thinking game. Just don’t expect to be impressed by its looks or for the cheap plastic and flimsy box to hold up over time. An entire set of replacement pegs costs only about $5 including shipping and handling, which should tell you something.

Multipurpose: Unfortunately, the quality of the pegs leaves us uninspired as to other uses.

Easier Adaptation: Pressman Toys offers an easier version called Mastermind for Kids, but the differences amount to reducing the code length to three colors and replacing the simple pegs with cutesy animal-shaped pegs. We think it’s more cost-effective to just purchase the standard version and reduce the code length yourself. That way, when your kids outgrow the challenge of three-color codes, they can move up to four-color codes and still use the same game board. For another simplifying trick, reduce the set of colors from which the code-breaker chooses to just one more than the number of pegs in the code. While the standard rules allow the code-maker to include pegs of the same color in the code, this can easily lead to confusion. Creating codes with all different colors eliminates this difficulty without making the game less fun. Finally, you can modify the rules so that feedback on the accuracy of peg color and location is peg-specific. This last suggestion works best with the advanced version of the game described below. In that version, the feedback indicators and the code pegs are both arranged in straight lines of five making it easy to match them up, whereas in the standard version, one is arranged in a square while the other is in a line.

Noteworthy: There is a more advanced version called … I’ll give you three guesses and the first two don’t count. If you said Advanced Mastermind, give yourself a pat on the back. This one uses a code length of five chosen from eight colors and costs about $20. If you think that Mastermind is a game that your family will enjoy through the ages, then it may be worth it to purchase Advanced Mastermind from the get-go and just keep working your way up to the maximum level of difficulty. And no, the higher price does not come with better manufacturing quality. Sorry! (That’s a fun game too, but not one for this blog.)

Well, boys and girls, that’s all for this week. If you have a favorite logic game that didn’t make our list, please tell us about it. Then go play!

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