Category Archives: literacy

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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Working memory matters!

For over 20 years I’ve been thinking about working memory in primarily two ways.  We accept  working memory as functioning as a visual-spatial sketch pad and as a  phonological loop.  Put simply, visualizing and rehearsing information by repeating it were the ways in which most of us recognized working memory.  By working memory, we mean that special type of short-term memory that allows us to hold information in mind long enough to solve a task.  For example, think about how you might remember the correct sequence to a new combination lock fiddle with the dial to open your locker.

The Visual-Spatial Sketchpad (VSS) allows us to work with our imaginations in a visual way.  We may remember the shape, color and location of an object as an imperfect picture.  If you are imagining where you need to go while walking down a hallway, then you recognize the  VSS.   The Phonological Loop (PL) works on information which requires a specific order to have relevance or meaning.  Imagine thinking about an unfamiliar  phone number or a series of steps shown to you in an unfamiliar math problem.   We often use the PL as a strategy  when processing language or other auditory information.

In 2000, scientists began to discuss a third type of working memory. This would be known as  the Episodic Buffer (EB).  The EB  helps to  contextualize information in a meaningful way. EB is a short-term working memory function that appears to take place primarily in the frontal lobes.  We use it to suddenly  pull information together in a meaningful way to recall events or complete a task.  The EB can bring information together from many sources to create a single episode or unified memory.

Three ways to enhance your working memory include:

1. Make use of your VSS, practice visualizing things. Hold math problems in your head.  See the quantities, not only the symbols.  You may actually take your finger and draw problems in space and then hold them in your head as execute the operation.

2. SET is a terrific game for enhancing working memory, categorization and strategizing.  I demonstrate the game in a earlier blog post.

3. Poker, bridge, and chess are other ways to practice holding information in your brain and manipulating it for successful output.

4. Physical exercise, especially aerobic activity, has a strong and measurable effect on these types of thinking.

So much learning depends on working memory strategies.  We might consider attention, problem solving and conceptual thinking as depending on working memory . Playing games and practicing strategies can really help. Sudoko to you!

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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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Fly with the eagles: An inspirational story #bullying

What causes a child to bully other children?  It seems natural to wonder about it.  Some speculate it is low self-esteem.  Other research tells us that many bullies have plenty of self-esteem.  I’ve heard people say that bullies bully because “they can”.  I don’t think that tells us a lot.  I’m thinking of one child I met back in 1999.  This situation may not apply to all bullies, but I think it is worth examining.

I became aware of Dean through my conversations with his teacher, Mrs. H.  I was working as a teacher in a local elementary school.  I ran a resource room for Emotionally Impaired (EI) students.  My resource room was located across the hall from her classroom.  Mrs. H. would stop me often, stating that a student in her first grade class was close to forcing her to give up teaching.  She described her frustration to me vividly.  “I can’t teach with this boy in my class,” she would say.  “That boy is going to drive me nuts.”  She stated that she spent much of her time correcting his behavior.

Bully 10

Dean would often interrupt her lessons with questions.  He often moved about the room without permission.  He talked with peers incessantly.  He would, according to Mrs. H., push other students when standing in line.  Recess and lunch time were occasions to “goof off” and behave aggressively.  Other students were avoiding Dean and joining in Mrs. H.’s disapproval for him and his behavior.  I half expected to see a monster.

I met Dean in the hall one day.  Mrs. H. pointed him out to me as Dean was filing in from his bus ride.  He was bundled in a green hooded winter coat.  He was smaller than I expected.  I stopped him and introduced myself.  “Guess what?”  he beamed.  “My guinea pigs had babies.”  He seemed very warm and enthusiastic, unlike the child that she described.  I agreed to have him come to my room when he failed to follow the classroom expectations.  I eventually ended up spending most of my days with him.

Mrs. H. reported that Dean was doing fine academically but I had my suspicions.  While he was fairly good at “sight” words, he labored over blending the sounds in unfamiliar words.  That is another story.  I knew that Dean did not like being seated during instruction.  When I worked with him, I tried my best to let him move around.  We incorporated movement as part of our lessons.  He seemed to enjoy learning this way.  I quickly became fond of Dean and his enthusiasm.  His interruptions seemed too passionate and full of curiosity for me to take offense.  I think he became aware that I enjoyed his company.  He quickly made progress.

While Dean’s reading skills continued to improve, his behavior at lunchtime, recess, and bus rides home were still a problem.  I was baffled.  He would step on loose shoe laces or jostle other students.  I got some insight into this while walking through the hallways with Dean.  His fellow students would often look to me and tell me that Dean was “bad” or that Dean had misbehaved that morning.  Dean would become indignant, saying, “nuh-uh” in protest.  I simply responded that “I see Dean doing very well right now.”

Dean was spending more and more time with me.  He would have several successful hours in class only to misbehave in a serious and potentially harmful way to other students.  For instance, he would push a child down the slide at recess if he wanted to use the slide himself.  As an only child, I suspected that Dean did not have practice sharing with others.  He certainly showed no empathy in these situations.  Despite many serious discussions, Dean would often miss the mark with his behavior.  At an IEPC meeting  the team decided that Dean would spend his entire day in my resource room.  I felt very disappointed that he would not be with his peers.

One day, after carefully preparing–so I thought–Dean for recess, he returned to my room with a note stating that he pushed a boy in a mud puddle.  In my confusion and disappointment I asked “why?”  and “when will it stop?”  I gave Dean a box of crayons and several pieces of unlined white paper.  I asked him to draw a picture of himself feeling what he felt at the moment, his house, and his family.  What he drew that day opened a door for us. He drew a picture of himself in the center of the paper.  There was no ground beneath him.  He drew no arms.  I wrote his words in the margins next to the picture.  He said he felt “bad” and “sad.”  He, without my guidance, offered another picture of himself.  He was all black with red eyes.  Armored spikes covered his body.  He looked like a warrior.  He had a weapon at his side.  “What is he like?” I asked.  “Scary.”  “How do the other children feel about him?”  “They think he is cool,” Dean responded.

Dean drew two pictures of his family.  He included his only parent, his mother.  On his shoulder sat his guinea pigs.  They were all smiling.  He also drew a picture of his couch, living room, and fish tank.  “We love the fish tank” he said.  His last picture was a chaotic and violent scene.  He scribbled in black around a figure of his mother being thrown into a wall.  An ominous figure, named Terry, was beating Dean’s mother.  Terry had red eyes.  Dean drew two pictures of himself in that scene.  One showed him laying in bed.  The other had him pointing a gun at Terry.  He was holding a “Hungry Hippos” gun, pointing it at Terry.  On the ground was debris.  “These are the eagles Terry broke.”  “They hurt my feet when I stepped on them.”

I confirmed that this event, in fact, happened three years earlier.  Dean’s mother tearfully admitted that she had no idea that this had been bothering the child.  Terry no longer lived in the home.  Dean denied that Terry hit others, i.e., Dean, but I received information that suggested otherwise.  Regardless, violence had helped Dean understand his world differently than others.  I consulted the school psychologist, principal, and the entire special education staff.  We held a meeting and Dean immediately engaged in counseling.

I told the staff all of what I knew.  The violence, however, was only one important aspect of Dean’s experience.  The entire milieu  helped to shape his understanding of the world and his place in it.  Dean did not know his father.  His mother worked a full-time job.  Dean had uncles who encourage him to fight when injustice comes his way.  Dean’s teacher was stressed.  Few adults had taken time to build a personal relationship with him at school.  They did not know that Dean wanted to be a veterinarian so he could help repair all the broken eagles in the world.  They had too often seen his behavior and not his heart.

I eventually left that school.  Before I left, I tested Dean’s reading.  He had advanced.  At the time, he was spending most of his day with his peers in his own classroom.  The staff had decided to forego the Emotionally Impaired label.  Mrs. H. insisted that he stay in her classroom.

At the school’s entrance is a trophy case with pictures of all the staff members.  I, having joined the staff later in the year, did not have my picture in the case.  Dean would often notice the oversight and point it out to me.  I would point to a poster of our national symbol and joke, “That’s me, Dean.”  Delighted, he would say, “You’re not an eagle!”  On my last day with the children, they threw me a party.  Dean presented me with a book with messages from all the children.  On the cover, Dean drew a bird flying over trees and toward a yellow and orange sunset.  In his own hand is the message, “Fly with the eagles.”

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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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What music does for the brain: An early Frank Allison recording

Local music fans understand, music enhances brain development.  We are learning more about it all the time as science has taken a keen interest.  Here’s Ghost of some fine girls, with the original line up including Frank, Michael Feeney on bass, Randy Sabo on Drums, and Martin Fletcher on guitar.  I loved this track. We recorded it in Frank’s Dad’s woodworking shop.  I think I was 17 or 18 years old.  Dig the stop and go bass and backwards guitar and heavy tom-tom use.  Very groovy.  Great song by Frank.  Real moody on an 8 Track reel to reel.  Thanks Mikey for sending this to me.

09 Ghost of some Fine Girl 1

The more we learn about music and brain development/rehabilitation, the more I am encouraging parents to get their kids playing music.  Check out Oliver Sacks’ book Musicophilia to begin understanding the mysteries of music LINK

Let me know if you have music tracks or books that inspire you and I’ll be pleased to share with colleagues, family and friends.

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