Tag Archives: problem solving

What a Great Gathering!

This past weekend I made my bi-annual trek to the Gathering for Gardner, a four day celebration of recreational intellectualism held in honor of Martin Gardner, who was for many years the Mathematical Games columnist for Scientific American.  Martin is a hero to generations of mathematicians, magicians, metagrobologists (puzzle lovers), skeptics, Lewis Carroll and L. Frank Baum scholars, and assorted polymaths, this conference is a true “gathering of the clans”.  And yes, it is as amazing as it sounds.

Martin Gardner (still going strong at age 95) was a hero to my father; I have vivid childhood memories of the yellow jacketed Mathematical Carnival, Mathematical Circus, and Mathematical Magic Show books that he kept on his bookshelf.  One of my grand ambitions when we started Binary Arts/ThinkFun in 1985 was to someday meet Martin… and one of my proudest achievements has been that we developed Visual Brainstorms 2 with him.  I have visited Martin several times and we are friends… wow!

Making this experience video was a lot of fun, thanks to all who were included.  And, to read more about the G4G9 experience, read the blog post from our own ThinkFun Puzzle Hunter, Tanya Thompson.

How to Spice Up an Algebra Class? Just Add Games!

This post is courtesy of Lisa Kosanovic, a Math Teacher at Holyoke High School, Holyoke, Massachusetts

*Note: The GridWorks game referenced here is the precursor to the current Chocolate Fix game!

I teach high school math in the sixth poorest community in the nation, and for us, math class is too often about passing our state’s standardized tests. While many of my students lack basic skills, I often see a high level of reasoning and problem-solving skills that I want to develop and encourage.

Several years ago, I bought ThinkFun’s GridWorks game (*now Chocolate Fix) for my own children, who loved it. Soon thereafter, I was working through a state test problem with one of my Algebra I classes, and I realized that the problem drew on exactly the same skills that GridWorks did! After several attempts to recreate the game using overhead transparencies, I contacted ThinkFun and asked if they could send me sets of the GridWorks pieces. I knew that if I had a set for each student, I could simply put the challenges on the chalkboard using colored chalk, and my students could work the problems at their desks.

What a success! Even the most reluctant of my students enjoyed using this game, and several came up to me after class to talk about it. One of my Pre-calculus students said she was pleasantly surprised by how much she had to think on the most challenging puzzles (I put 10 challenges on the boards around my room, including the two most difficult), and by how much fun it was to think hard in that way. Another student with serious attention issues insisted on starting with the most difficult problem, and he worked diligently through an entire class period. When he did not finish the problem, he asked if he could come back during the next class to finish, and when he returned, he stayed with the problem until it was completed correctly!

My only regret is that there are not books and books of GridWorks challenges! With GridWorks, I saw many otherwise-unengaged students using math skills to solve problems, and enjoying themselves at the same time. I will use this with my students every year to teach them problem-solving skills and show them that math can be fun!

*Read how another innovative High School math teacher took this same game, now in Chocolate Fix form, and used it to teach his students to make geometric proofs!

Revisiting the Classics…

Need inspiration to start your spring cleaning?  Here’s a great reason to dust off that old collection of classic board games!

A recent article from KnoxNews takes a look at how classic games like Monopoly and Scrabble can serve as powerful learning aids!  In the hands of a creative teacher (or parent for that matter), a game like Candy Land is transformed into a tool to reinforce number sense, early math, and critical thinking skills!

This teacher uses Monopoly to teach money management skills like budgeting and making informed spending decisions.

This article shares results from a 2007 study by Carnegie Mellon University, in which disadvantaged preschoolers played a simple numeric board game four times for 15-20 minutes at a time over a two-week period.  At the end of the two weeks, researchers found students’ knowledge of math greatly increased in four different areas of number sense!

School Counselor Vicki Hill uses games not only for academic support, but also to build social skills. “I use Candy Land for a self-esteem building activity,” Vicky describes, “If the student gets a double color card, he must tell something good about himself. ”  Similarly, with the game Sorry, “if the student has to send someone back to start, he must say something positive to the player that gets sent back.”

Have ideas for ways to revive an old classic as a learning tool for your children?  Please share!

FIRST Robotics Tournament

This past weekend I volunteered as a judge in the New Jersey Regional FIRST Robotics Tournament.  Sixty one teams competed, coming from as far away as Brazil.  The competition was played in three-team alliances, alliances playing against each other to shoot soccer balls through goals with some significant wrinkles thrown in.   The tournament lasts two full days.  Team objectives are to win the tournament and go on to the national championship, and also to compete for more than a dozen FIRST awards celebrating both technical achievement and team attributes.  These are presented at closing ceremonies each day.

The game rules this year were more different from past years than normal, which meant that veteran teams had to change their robots more, to make more fundamental design decisions, than what they were accustomed to.  Early rumors from the practice field were that teams were struggling, that a lot of things weren’t working… and the first matches were indeed low scoring without much action.  Some of us wondered whether the changes had gone too far, if and how the players could adapt during the course of competition.

These issues hit the judges square on during our Saturday working lunch, when we caucused about that day’s engineering quality awards.  What to do with well designed machines that met most of the criteria for an award, but that hadn’t worked on the field?  Would they be performing by day’s end or not?

We needn’t have worried.  Teams scouted the field to learn best practices, shared information, worked together, analyzed and adapted, and the quality of play went through the roof.  In the end the judges struggled this year with too much excellence, we had more teams deserving awards than we had awards to give.

We had grand debates as well.  Should the Entrepreneurship Award go to the young team with the big vision, the experienced team that was rededicating itself to greater service or the team whose written business plan most clearly articulated their plan?  Should the Quality award go to the simple machine that performed at outstanding levels, the more versatile robot that had mastered several game skills or the robot that had outstanding machine quality features but was average on pit quality & team integration?

In the end it was an outstanding experience all around.  If you want to discover the best of young America, get to know more about FIRST!

Attack of the Robot(ic)s!

ThinkFun CEO Bill Ritchie and his video camera have returned from the FIRST Robotics Tournament!

The energy in this video is just incredible (check out the line dancing!), and it’s clear these young engineers are prepared not only to tackle the challenges of tomorrow, but also to inspire the next generation of problem solvers!   For more on Bill’s experience as a judge, check out his new blog Bill’s Big Picture!!

Getting to the Heart of Problem Solving

The following is an article by ThinkFun CEO Bill Ritchie, recently published in ThinkFun’s bi-weekly Classroom Connection newsletter.  To receive these mailings, click here

This weekend I am off to volunteer as a judge at the FIRST Robotics New Jersey Regional Tournament, which I do every year. Founded by legendary engineer Dean Kamen, this is a wonderful program that teams high school students with adult professional engineers. Each team has six weeks to build a robot with special skills such as placing soccer balls into hanging baskets, and then we gather for a big weekend tournament and have a blast! The best teams move on to the National Championship.

FIRST calls this program “The varsity sport for the mind.” To be successful, teams must have strong engineering skills and be well organized. Most basically, though, successful teams are those whose members have learned how to be good problem solvers.

So what makes a good problem solver? For these kids, certainly it involves creative imagination. Should your robot have an arm to lift the ball or a leg to kick it into the goal? Do you focus on offense or defense? And once you decided the big directions, how can you tweak your design to ensure best performance?

A Robot on Display at the 2009 FIRST Tournament

As a non-engineer, I’m not qualified to evaluate the engineering choices teams make. Rather, I serve as a “Team Attribute” judge, which means I ask questions like, “What are you doing to make your community a better place?” and “How are you mentoring younger kids to understand your values and aspire to be like you?” The FIRST organization encourages teams to see themselves as leaders and innovators and to aspire to the strong FIRST value system, and the kids’ responses are just amazing.

Both through their creations and in speaking with these young engineers, I get to see what is in these kids’ hearts. With the most dedicated and inspired teams, I see the same problem solving skills at play. The choices are humanist rather than engineering, and they all involve creative imagination and a blend of strategy, planning, collaboration, and execution. At the underlying core of it all, the decisions these kids make all stem from passion and perseverance… Robotics with heart!

I spend a lot my time thinking about problem solving… and if you are reading this, I bet you do also. It’s a very hard thing to define, and thus a hard thing to measure or test. But it’s really important!

Here’s what I believe: Problem solving starts deep in the emotions. It starts with a drive, a desire to get someplace, a belief that you can achieve. From there, you gain experience, by observing, modeling, trying, stretching yourself. Through this you learn confidence and perseverance, and then you’re on your way!

What do you believe makes a true problem solver? Please share your comments and let’s get the dialogue flowing!

Rush Hour in Cairo Egypt!

Here’s a photo of a real-life Rush Hour traffic jam sent to me by Laura Efinger, a pediatric occupational therapist (and big Rush Hour fan!) in Cairo, Egypt.  Laura writes, “I have attached a picture of some Cairo traffic, which may explain why we love Rush Hour in Egypt! :)  Some is parking and some traffic, but it probably is the worst in the world, and no one follows the lines in the road and rules!”

A Real Life Traffic Jam in Cairo, Egypt

All that’s missing is the Red Car!

A much more enjoyable "Traffic Jam" challenge!

For several years, Laura has used many ThinkFun games, including Rush Hour (which she reports is the hands-down favorite!) in her occupational therapy sessions with children in  Cairo, Egypt.  Laura writes, “I love them [ThinkFun games] as they develop the children’s visual motor/perceptual skills, fine motor, memory and planning skills.”

At a 2008 Occupational Therapy Conference, Laura presented a therapy-based workshop called “Recipes for Fun” in which participants were shown ways to use games like Rush Hour as tools to help children develop academic and sensory motor skills.  Looks like fun was had by all!

Laura is preparing for this year’s Conference which will take place at the end of the month. Here she plans to host a workshop focusing on the benefits of using card games to help children with skills such as attention, sequencing, memory, fine motor, etc.   Stay tuned for an update!

For more on Laura and her work, please visit her Occupational Therapy in Egypt blog!

Can Chocolate Fix Teach Geometry? Here’s PROOF!

The following is a post by guest blogger Sean Gregory, a math teacher at Napa High School, Napa, CA

Games are a normal part of my classroom. I have always loved games personally and believed that I would be a better teacher if I put a part of myself into my teaching. My students from the past 20+ years will remember playing all sorts of gambling games, Jeopardy!, and treasure hunts. I’ve even adapted several off-the-beaten track games like PitchCar, Hamsterolle , and Elchfest into full-room class activities. While these games were vehicles for fun, they were more a source of diversion from the mathematics problems that I loaded the play with.

As a teacher of mathematics, I know that some games come with built in traits that I would love to exploit in class. So, like many others before me, I have incorporated games like Mastermind and Clue into my room to build my students’ deductive skills. I was pleased by the opportunity that I gave my classes with these games, but I also felt that the games did not play well given my restraint on time and my large number of players.

I wasn’t really looking to replace Clue or Mastermind when I went to the ThinkFun workshop at the 2009 NCTM National Convention but that is exactly what happened. ThinkFun’s Chocolate Fix puzzle was a clever, compact, pure deduction puzzle. While its appeal to most people might be the fun that they would have with cute little plastic pieces of chocolate, I saw my opportunity to use it as an aid to my Geometry students who believed they could never produce a deductive proof.

Perhaps I would have seen Chocolate Fix’s application to my class on my own, but the workshop offered  ideas on how to implement the puzzle in a classroom. The activity that spoke the most to me was ThinkFun’s idea that we should not only complete the puzzle, but also share the order in which we used the clues to figure  out the solution. Suddenly I wasn’t playing with a puzzle but was seeing a plastic chocolate manipulative that could help my students prove triangles congruent.

People are natural problem solvers, but in a math class students suddenly lose their confidence, ability, and desire to work things out. Surely if I can finish a Chocolate Fix puzzle and know that I used the clues in the order 3-5-2-1-4, then I can form a geometric proof with vertical angles, SAS, and CPCTC. I was determined to convince my classes that the puzzles they were completing in Chocolate Fix were harder than many of the proofs that they could barely start.

From 9 plastic chocolates, a mathematical proof emerges!

I had no money to put into buying Chocolate Fix games, so  I passed out scissors and had the class cut out pieces to make their own games. It is a tribute to the kids’ desire to play that they eagerly cleared all these hurdles without complaint! The class finished their hour happily working the puzzles.

The next day, I encouraged the students to solve the puzzles with their cut-out pieces. About half the class gave up on the pieces and just made it a pencil and paper thing. Towards the end of the day, desiring some product, I challenged the students to pick a puzzle and share the order that they used the clues AND write about why they made their choice.

A student's written proof provides a map of his problem solving steps!

After school I was shocked at the quality of the written explanations (often with diagrams) I had collected. My Geometry classes do push written explanations but I had never seen such quality so early in the year. It was clear I was on to something.

The class’s excitement for the puzzle grew and grew. They looked forward to our days with it and showed their enthusiasm by giving me frequently spectacular written explanations of their puzzle solving. I put Chocolate Fix questions on exams. I dazzled the class with my own (real) set of the puzzle, and by the end of the first semester had convinced the school’s parent club to buy a class set of 36 puzzles.

As the semester ended, I put my last Chocolate Fix problem on the final exam right next to questions about trapezoids and triangles and nobody seemed to think it out-of-place. I know that I have found the game that will be part of my deductive math classes for the rest of my career.

Three months later my students and I think of Chocolate Fix as “our puzzle,” a game we enjoy playing in class knowing that other math students are not so lucky.

The Power of Praise… is “smart” a bad word?

According to a survey conducted by Columbia University, 85 percent of American parents think it’s important to tell their kids that they’re smart.  To a parent looking to help a child reach his/her potential and feel confident, this seems both a natural and a surefire confidence boost.   However, research in the New York public-school system by psychologist Carol Dweck strongly suggests it may be the other way around.  Giving kids the label of “smart” does not prevent them from underperforming. It might actually be causing it.

For the past ten years, Dweck and her team at Columbia (she’s now at Stanford) studied the effect of praise on 400 fifth grade students in a dozen New York schools.

Dweck sent four female research assistants into NY fifth-grade classrooms. Researchers took a child out of the classroom for a nonverbal IQ test consisting of a series of puzzles—puzzles easy enough that all the children would do fairly well. Once the student finished, researchers told each his score, then offered a single line of praise. Randomly divided into groups, some were praised for their intelligence and told, “You must be smart at this.” Others were praised for their effort: “You must have worked really hard.”

Why just a single line of praise? “We wanted to see how sensitive children were,” Dweck explained. “We had a hunch that one line might be enough to see an effect.”

Then the students were given a choice of test for the second round. One choice was a test that would be more difficult than the first, but the researchers told the kids that they’d learn a lot from attempting the puzzles. The other choice, Dweck’s team explained, was an easy test, just like the first.

Of those praised for their effort, 90 percent chose the harder set of puzzles. Of those praised for their intelligence, a majority chose the easy test. The “smart” kids took the cop-out.

In my own classroom, inspired by my Responsive Classroom training,  one strategy I found helpful for delivering “better” praise was to post sentence starters and key phrases on the walls, both as personal reminders and to help students talk to one another in specific, respectful ways.  These phrases encouraged both teachers and classmates to use encouraging, descriptive language when speaking to and praising one another, such as “I like the way you…” or “Show me how you…”  Here’s another teacher’s account of how changing the way in which she and her students spoke to one another changed the dynamic of the classroom in noticeable and powerful ways!
What are some strategies you’ve used or come across to help deliver effective, genuine  praise?

Read more on this study in Po Bronson’s article: The Power (and Peril) of Praising Your Kids

We Hold These Truths…

Given the current state of education, it’s easy to understand the frustration teachers feel as they are stretched thin and given increasingly mixed messages.  Forced to “teach to the test” while still focusing on differentiating to meet the needs of individual learners. teachers today often find their jobs precariously tied to student test results and feel their instructional freedom slipping away.

These challenges can stack up and feel overwhelmingly discouraging, which is why a recent conversation in a Teacher Leaders Network discussion group was both timely and uplifting.  Bob Williams, Alaska’s 2009 state teacher of the year, commented “It feels unhealthy for me to become defined only in terms of negatives or things that I am against. I’d like to propose that we list up to three things that we support and are convinced will help improve our schools and our profession. ”

From here, the open question was put out to teachers: “What do we believe in?

I found it incredibly inspirational to read these responses. Some that stood out to me:

“Education should honor and prepare students for their own lives in the world of today and tomorrow—not mimic the past educational experiences of policymakers and other adult stakeholders.”

“The single most important thing a teacher can do is to ignite the fire of intellectual curiosity in children, encouraging them to continually ask, “Why?” “So what?” “Now what?” “What if?””

“Children rise to meet our expectations. Children come to us believing in us, trusting we will teach them and help them grow. We must honor their trust and set the bar high for each and every one of them and ourselves.”

“Genuinely hearing, respecting, and incorporating student voices into schools is the single most important thing we can do to help them learn to be good citizens in a democracy… and to acquire other skills they will need for success in school and throughout life.”

“Learning is best when it’s absorbing and enjoyable, and that kind of learning sticks to brains. Learning is meant to be fun. Small children come to us in kindergarten, excited about learning to read, to draw, to add and subtract, to talk about their communities, to sing, to touch frogs, and to play games. We turn all of that natural enthusiasm and curiosity into “subjects.” Shame on us.”

“Our students need to be creative problem solvers. They need to be active collaborators with their peers. They need to be critical thinkers. They need to be challenged to do their very best, and what they can do will expand as their work is shared with peers, critiqued, refined, and reflected upon.”

“I believe in inspiring children at the earliest stages of their education to explore answers to their questions. As they seek answers, children learn to reflect analytically on the world around them… It is this experience that does not just lead them to answers but ignites a proactive energy and an eagerness to know more.”

As a teacher or parent, what do YOU believe in?  Please share your thoughts!

For excerpts from the original discussion, see the summary blog post by John Norton, co-founder and moderator of the Teacher Leaders Network.