Tag Archives: Brain Games

Mathematical Thinking at Play (5 year olds are amazing thinkers)

A few years ago I filmed a couple of the Fletcher gang playing  a game I love called “Set”.  Set shows us that challenging means fun.  The game that requires some pretty sophisticated thinking.   Initially, I didn’t know if  my 5 year-old could handle a full game of set, but I thought I would try it anyway.  And… she surprised me.  Even though she just turned 5 a week, earlier, she was capable of so much.  Now,  I’m not saying that she is a genius.  Rather, I make the point that average intelligence is still one of the most powerful forces the universe has ever produced.  We would do well to accept it.  When it comes to intelligence, however one defines it, average means powerful.

Check out the video to see how I worked with the Doo Dah.  The toy company markets Set as “the game of visual perception” but there is a lot more to it.  I use it primarily to encourage a) Planning/Executive Functioning  b) Simultaneous/holistic processing c) control of attention d) fun.  In the video you will notice that I use very little direct instruction.  Instead, I ask questions and encourage the Doo Dah to think for herself.  I could have given her the answer at one point, but that would have stopped her from thinking.  Instead, I  gave her just enough information to allow her to solve the problem for herself.  Watch this video with an eye for the process.  Maybe you do some of this yourself.  What you will see is: 1) I encourage the Doo Dah to survey the task/tell me her plan 2) I prompt her by asking questions/guiding her attention 3) I model for her by talking about my thinking 4) I ask her to summarize her own thinking.

Can Intelligence Be Taught?

How we think is very much a product of our culture and our relationships.  Play often leads to meaningful interactions,  creativity in learning, and new thinking strategies.  Even attention is developmental and  therefore trainable.  If you like, you could try meditation sometime.  You may find that the beginning  sitting practice is tough.  In fact, Buddhists say we have  “monkey mind” because our thoughts and attention bounce around like a monkey.  With practice, however, one learns to sit for longer periods.  One learns to select the breath as the object of attention.  Meditation is the art of resisting distracting thoughts, at least that is what I have learned.

On another note,  I can’t for the life of me understand how “experts” continue to ignore the important role that emotions play in learning.  Any reform that doesn’t place emotions at the center is likely to fail or have limited effects.  In response, several years ago I decided that I would develop video games as learning tools.  Few would disagree that it  is the child’s nature to play.  I go further.  I believe it is the adult’s nature to play, as well.  You might be aware that the average age of the most frequent video game customer is 40 http://bit.ly/brmQA .  If we care to bring the emotions into learning, we would do well to pay attention to video games.  I include play in learning precisely because play brings emotional experiences.  When a person feels intense feelings, he/she often performs better.  Boredom, conversely,  interferes with learning.  Anxiety interferes with learning.  Play, on the other hand, reduces harmful stress.  Video games are play. Video games can teach.

In a short while, my team and I will release what I think will be a very important iPad app.  I hope you will stay tuned so that you might try it.  I will give updates as the release date draws nearer.

For more on the role of emotions in learning, see http://bit.ly/bVRYul , http://bit.ly/aEQeFi and http://bit.ly/b8BYmE .

Can children learn the entire elementary school math curriculum in 30 hours?  For evidence that we might be underestimating what kids can do, see http://bit.ly/c7QETj

I recommend Todd Kashden’s excellent work on curiosity.  Please check it out:  http://www.toddkashdan.com/

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The Psychologist’s Role in Teaching Mathematics

Historically, psychologists have studied math but have been noticeably absent when it comes to doing direct mathematics work with children.   Notable exceptions include Diennes, Bruner, and Vygotsky, but to this day Psychologists tend to assess and make recommendations for treatment.  This surprises me, given the cognitive processing involved and the anxiety that so often appears in achieving and struggling math students.  I have designed and delivered treatment programs for struggling mathematics students for nearly 15 years, and I believe that other Psychologists could really contribute.  Psychologists have a unique and relevant skill set that would add value to a treatment team.  I have used mathematics as a vehicle in promoting a variety of therapeutic outcomes.    The hours I spent working on math may be my most favored memories of my practice.   To learn math for many of these youngsters is to conquer fear.  I offer a few thoughts on the role of psychologists in teaching math.

Psychologists can:

1) Discover the structure of the child’s thought through constructing mathematical models and problems.  Given space, children can do more than simply apply the sometimes confusing rules that might work on tests only to later fail to appear when encountering real world problems.  Psychologists aim to enhance thinking performance which leads to confidence and resiliency.

2) Psychologists might help make sure that math enjoyment survives past 2nd grade.

3) Psychologists get training in helping children use the imagination.  These techniques are well suited to mentally manipulate mathematical relationships, calculation problems and decoding symbols as mental objects.  Psychologists teach visualization, for instance, which goes far in enhancing performance by using visuospatial skills.

4) Help children understanding  concepts,  meanings, and numbers. Math is a language developed for measuring and describing the natural world.  Symbols appear, in part, to prove  underlying ideas, relationships, and concepts.  Physical objects are the reality, the symbols allow us to manipulate it.  (There are exceptions in higher math, of course).

5) Help children use discovery to make math meaningful. Rote Memorization=boredom.  When we play and build math problems, the inherent creative strategies transfer to real life problem solving.

6) Psychologists can make math fun. What if Math were fun? What if Math became an aesthetic experience?  I often repeat “fun is solving a problem mentally” which is how   Raph Koster defines it in his book A Theory of Fun).

7) We feel better by doing better.  The Psychologist might help  through a combination of play, motivational psychology, mindfulness, assessment, talk, and other interactive skills.  The psychologist trades in  building resiliency and helping patients solve problems.

Chime in and let me know what you think.  Have I made a case for it?

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Coping With Math Anxiety Can Be About Perspective

Many children experience discomfort around math, we generally call this Math Anxiety, a fear that math is going to be uncomfortable and full of failure.

Here’s an interesting post via Elizabeth Stevens on Math Anxiety, I wished to share with you all.  Math performance is so important today.  Math is actually fun.  But, we have to approach it in an engaging way.  We can do this and we are doing it.  Thanks to colleagues like Elizabeth.

Let’s remember:

1. Math aptitude is not inborn, math skills can be learned.

2. Math is super creative, there are many different ways to get an answer.

3. Boys and girls can both be great at math, it depends on what we tell children about their experiences with math.

If you wish to delve deeper check out Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School by Thomas Carpenter, et al.

Breathe… and enjoy Dr. Marty

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5 Year Old Discovering Equivalent Fractions

This is the Doo Dah playing math.  Fractions. This is where kids often learn to hate math.  Guess what?  We can change it.  I’ll describe what is happening in this short video.  The Doo Dah is a) seeing what a fraction is b) playing w/ the proper toys/tools to help her discover its meaning c) going from concrete (seeing/touching, etc.) to abstraction (writing symbols, abandoning the manipulatives and doing the math in her head).  I hope you enjoy the short video.  I mainly want you to see how much fun we have doing math.  Math is a puzzle.  Math is a game. But, it is very hard to learn anything if you are not curious/interested in what you are doing.  So, let’s make it a game and play!

Anxiety is first the anticipation of an upcoming event. From that, there is an irrational fear that the outcome will be terrible, horrible, awful, etc.  Math Anxiety is the irrational fear that math is “too hard” and that “I’m going to fail” and “I’ll never get it b/c I’m not smart enough”,  etc.  Nonsense.  Just watch the Doo Dah.  Have fun and Game On.  Also, if you like the blog, please subscribe.  I blog on parenting and education issues mostly.  Thanks, Dr. Marty

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5 Year Old Doo Dah Likes #Algebra

The Doo Dah and I “play math” before she goes to Kindergarten.  We keep it fun, but do some pretty abstract things.  You can really see her thinking as she factors a polynomial.

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Do Not Fight Your Nature

“Accept everything about yourself — I mean everything. You are you and that is the beginning and the end — no apologies, no regrets.” –Clark Moustakas

First of all, I owe my teachers nearly everything good about what I know.   Mr. Smith, for example, is a teacher who touched my life in 3rd grade and I will never forget him.   I’m using it to illustrate a point.  I was in 6th grade when this happened.  Mr. H was my  English teacher and this is one of the few things I remember about him.  I got a paper back and I had misspelled a word and got marked down for it.  I sincerely asked, “Why does the spelling matter?”  His response was an indignant, “I’m going to pretend you didn’t say that.”

I guess I remember it because it reminds me that some of the simple, “stupid” questions are actually pretty good questions.  There is a good answer to that question.  Not so long ago people had no agreed upon spelling.  It is a good story.  Look it up and find out how we got our first Dictionary.   If a question is sincere it is probably a good question.  Stay curious.  Your questions are good.  Be on a good path.  Accept everything about yourself.  Then you can take the next important step.  You will be able to accept others as they are.

 

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Learning What You Have No Interest In

How about you and I start studying geology today?  Let’s spend from 1 to 3 hours a few days per week on it.  Sounds fun, eh?  If you happen to love geology, replace it with something you have absolutely no interest in learning.

Now, let’s turn it around.  Let’s say you finally get to take that dream vacation to Russia.  You have 6 months to learn as much of the language as you can.  Let’s go further, let’s say you even love the sound of spoken Russian.  You imagine having conversations with the people you will meet. It would be a lot easier to learn, no doubt.

I don’t think that this is a bland statement.  Ask a child to describe school using one word.  I do this often and hear the same word: boring!  When I hear something different, it usually involves having a teacher that “makes it fun.”  I do hear that, but not nearly enough.

If I have learned one thing in my professional career it is this:  Most people can learn what they need to know when they need to know it with no penalty.  This especially holds true if the learner really wants to know about something.  Then, it seems impossible to stop them.   So, why not let the kids lead a bit more?

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