MathNook

A blog about MathNook, math, math games, and more.

Prefrontal Cortex Should not be Bothered

July23

PROCESS:

Prefrontal cortex recognizes need for data

Math fact data “delivered” to prefrontal cortex

Prefrontal cortex combines fact recall with rules and patterns, resulting in skilled problem solving

Pictures at www,mathnook,com/blog

Why Fact Games Work

Readers of this column know that we at www.mathnook.com believe that there is value to rote memorization, but that “skilling, drilling, and killing” students with facts and procedures simply kills kids’ motivation to learn, or even to try. It seems like an impossible dichotomy, but in fact, there is a simple analogy to something we all encounter on a daily basis. Do you have an old computer, a warhorse relic from ten or more years ago? Other than warning you to check continuously for viruses on your XP machine (please don’t pass your viruses to us!), I want you to remember what it is like to try to stream a movie, write music, or develop your own graphics with a machine that was built long before Netflix and the Adobe Creative Suite™.

You are sitting there fuming as your machine keeps saying things like, “Adobe Creative Suite (not responding).” You are tempted to yell at it, “You’re a machine! Stop ‘not responding,’ respond!” Finally, you slam down Ctrl-Alt-Delete and find out that your CPU usage is stuck at 100%. Permit me this geek moment, but I can explain just why this is happening.

Let’s say that your computer has something like 2 gigabytes worth of random access memory (RAM). Adobe Creative Suite™ requires almost all of that for the program to work. The closer you get to full utilization of your computer’s RAM, the more your CPU (central processing unit) takes over the work, which slows your computer down like the carapace on a giant turtle.

Is your child, or your classroom if you are a teacher, trying to compute with too little RAM? If so, the part of the brain that we think is responsible for storage and recall of math knowledge is underutilized, while the parts which should be retrieving the data from centers like the parieto-occipital sulcus, is busy pretending to be RAM. You can buy more RAM quite cheaply for your computer. Why not buy some more RAM for your problem-solving centers to query, by getting the math facts out of the way? Relegating facts to the random-access memory part of the brain frees the prefrontal cortex to organize itself around problem-solving, not fact recall.

For an example, let’s look at the long division algorithm. On the left of the table below, you will find the step, and on the right, the brain processing step that should go into applying stored data. We are going to assume a neurotypical student with at least an adequate storage for math facts and rules.

Step Brain Process
1. set divisor outside the box and dividend inside it Rule recall
2. Estimate how many times the divisor will fit into the dividend, or into the appropriate place value of the dividend Higher-order processing
3. Multiply the divisor by your estimate in step 2 Fact recall; maybe recall of multiplication subroutine
4. Subtract result in Step 3 from dividend Fact recall, application of place value (higher order knowledge) and regrouping rules
5. Repeat (iterate) steps 2-4 until there is no remainder or the desired level of accuracy is reached Higher-order processing, fact recall, and assimilation of rules, facts, and applications.
6. Report the results Mathematical language

Even as I look at this, I’m astonished that some students who manage to become proficient at math remain unable to zap you with “42” when you ask them, “Seven times six?” If you have to work out the staggering number of math facts in every long division problem, by the time you reach algebra, your prefrontal cortex is going to be like that dinosaur computer running Windows XP that we met at the beginning of this entry.

The games at www.mathnook.com don’t claim to train your prefrontal cortex for higher-level functions. A regular visitor to this site will, however, reduce the cognitive load on the part of the brain that needs to send out data requests and integrate the responses into an answer.

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Apples and … Basketballs?

July14

Apples and…Basketballs? I recently had the opportunity to talk with Alfie Kohn, one of my favorite theorists of education. In fact, I asked him if he might have a look at some of the games on our site. It was with a sense of dread that I opened up his email later that afternoon.

Mr. Kohn (If he holds a Ph. D., he is self-effacing enough never to mention it, even on his blog, www.alfiekohn.com) is a leader in a counterrevolution in American letters, whether kindergarten mathematical reasoning or applied political philosophy. He’s a fan of situated learning, which is to say, giving children tasks that are inherently worth doing, and working the specific fact learning in at the margins. I appreciate his point of view, and I really, really wish that American education would have taken that course when it played with going that direction in the post-McCarthy Era through the Sixties. Situated learning is associated with thinkers like John Dewey, and it brought us victory in the Space Race with the Soviets – that same empire that is piecing itself back together over the bodies of Ukrainians, and before that, Georgians (that is, the kind whose last name ends with “-vili,” not the kind that keeps winning the National League East). Clearly, setting children loose with meaningful tasks is a great way to help them think about math, and at www.mathnook.com, we mostly turn fact recall and algebraic problem-solving into a matter of rapid-fire muscle memory.

So would Alfie (as he prefers) rip me a new one, given that what we have done on Mathnook.com has nothing in common with what he proposes as a way to educate students to be able to apply mathematical reasoning to real problems great and small? No. He said, “While in principle I think that this kind of game is counterproductive, it is so only if the game is used to replace situated learning, not to supplement it (emphasis mine).” In other words, the corporate education system is screaming for kids to learn math by rote so that they can fill in those bubbles quickly and accurately, which Alfie rejects (see the abstract from “The Schools Our Children Deserve” on his website at http://www.alfiekohn.org/teaching/math.htm), but at www.mathnook.com, we don’t prepare kids to do that! We simply take advantage of the fact that anything that sucks you in and grabs your attention is going to make an impression.

Is it “worthwhile mathematics” to know by fast-twitch muscle response that 7×6=42, or equally hateful, that 7×8=56? Well, no. However, if the student who could devote an hour to Candy Crush Saga spends it instead on the mastery of math trivia to the point of not having to spend a scintilla of effort on how many sides in a hexagon, the product of 7×6 (or 7×8, for that matter), or what x makes 3x-1=20 true, might that student be free of “skill, drill, and kill” forever and be free to explore math in context of life? I think so. The second-youngest President of the United States attributed his ability to succeed at what mattered to his ability to routinize everything that doesn’t. You would never catch this man dead designing his daily workouts, figuring out what to eat for breakfast, mixing and matching his wardrobe, or any of a host of tasks in which you and I sink precious energy.

So what about comparing apples to basketballs? Last week, we discussed the fact that a highly complex math simulator, DimensionM (not a Mathnook product, alas), has been shown in at least one peer-reviewed study to increase skill, aptitude, and interest in high-school level algebra among middle-school students, family background and economics factored out. DimensionM is a highly sophisticated simulation that has more to do with James Cameron’s Avatar than with the simple designs that allow me to get so many games up so fast. Yet, I get similar results. Why? Let’s say that DimensionM is an apple, crisp, cold, and healthy. If you want a healthy math mind, you want to evangelize DimensionM and similar products as opposed to wasteful social media and mindless entertainment – the potato chips and Milky Way bars of consumer electronics. However, developing a healthy math aptitude requires a good diet and a healthy dose of exercise. Consider Mathnook.com the basketball. Let’s play!

P. S. For those of you who want to teach oddball facts like 7×6 and 7×8, let me give you an idea. Two, actually.

1) Divide and conquer. Most people have 7×3=21 and 7×4=28 (fewer this one) committed to memory, and may even be able to produce an array of seven rows and three or four columns. Using the associative property, 7×6 = (7×3)x2, or (7×3)+(7×3) = 21+21 = 42. Similarly, 7×8=(7×4)x2, (7×4)+(7×4), 28+28, or 56.

2) Nearest square: Most people can give you 6^2=36, 7^2=49, and 8^2 (chessboard) = 64. Adding one more six to 36 depends on knowing what multiplication means, but I am all for learning the meaning before practicing the facts. Similarly, adding a seven to 49 or subtracting an eight from 64, while a little more arithmetically cumbersome, amounts to the same thing.

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STEM Teachers in a Box

July9

How many science, tech, engineering and math (STEM) teachers do you think enter the US workforce every year? A few hundred thousand? Surely, at least fifty thousand, right? Try again. Since 2004, both the present Democratic administration and its Republican predecessor have begged Congress to enact into law a plan to graduate a measly 10,000 new highly-qualified (more on that term in a future posting), jolted me out of my chair when I read it; the US actually falls short of even that modest goal. The persistence of the 10,000-a-year goal for STEM educators demonstrates how hard it will be to develop even this human resource.

On the other hand, games like Worlds of Warcraft reach millions of new users every year (in the case of WoW, four million in 2012, according to www.statista.com ), and Food Force, the food security simulator from the UN got played a million times in its first six months after launch. Who does the student listen to more, the poor algebra teacher (who might not have as much as a math minor in college), or the flashing, blaring, addictive video game (see last week’s post on “Addicted to Math?”). Many people are lining up on the side of the video game here, noting the smashing success of Khan Academy and the “flipped classroom” model – homework in class, lectures at home from Khan.

What about effectiveness? Surely, the personal touch does better than the Max Headroom approach. Well, maybe not. A far more complex game than we offer (yet!) at www.mathnook.com, DimensionM, recently received a peer-reviewed grade by a major UK journal. The gamers showed a lasting boost in algebra skills and yes, in interest. Interest in math! Even math teachers report that their worst day of the year is that dreaded “What do you like or dislike most about math?” day. That’s the day when students get to kill their math teachers, lumping them in the category of oral surgeons at the dental clinic. Just the very possibility that electronics might dissolve the emotional barrier against STEM learning has us tickled and giggling (for a counteropinion, albeit earlier than the Dimension M paper, click through to this paper which thinks math games are a mixed lot).

Another research paper raises a more pithy question: “How can learning design maintain a sense of the wonder and joy of learning, minimize math anxiety, and improve performance on standardized tests?” No, really. They wrote that last clause, not us. The point is that we have to find ways to teach that fit the brain’s natural way of learning, which means that “development of left-brain skills that depend on sequential action and thought (reading, writing and arithmetic) must be complemented by development of the holistic, creative processes by means of right-brained activities such as visual support, story-telling, and role playing.” This includes dealing with the emotional component of learning, too. There is a negative feedback loop between seeking behavior and fear, anger, and panic. Seeking behavior is reinforced by play and attention, creating a positive feedback loop with more seeking as the result.

READERS RESPOND: What are the STEM fields if not the epitome of seeking? If you find this question pithy enough, visit us and let us know.

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What are the Best Ways to Increase Intelligence?

May13

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While some individuals may be born with a naturally elevated intellectual capacity, intelligence is not necessarily solely an innate trait. Most smart minds develop overtime through proper care, exercise, and routine maintenance. Though schooling absolutely enhances cognition, going to school is not the only means by which one can strengthen mind function. Are you interested in heightening your intelligence? Here are a few of the best ways to increase mental capacity.

 

Meditation: Meditation calms the mind, while also, as research shows, changes the structure of the brain, increasing memory capacity, and improving focus and attention span. Meditative practices can vary person to person, but focusing on the breath is a great way for mediators to begin moving into their practice. Overtime, regular daily mediation can teach your mind how to work for efficiently, thereby increasing your mental speed and capacity for varied thought.

 

Get Healthy: Daily exercise and proper diet benefit both body and mind. The physical condition of the body directly affects cognition. If the body is in poor shape, the blood stream heavily populated with toxins from poor diet or low exercise levels, it becomes more difficult for oxygen to reach the brain, siphoning off vital fuel, thereby decreasing mental functioning. Incorporating a regular exercise regimen into your daily life, and maintaining a healthy and organic based diet can help your keep your body, your mind’s home and feeding ground, in its best possible condition for proper mental function and intellectual growth.

 

Sleep: Regular sleep is a vital variable in the equation for a well-running mind. Researchers actually surmise that during sleep, the unconscious mind files and organizes thoughts from the prior day, readying the mind for what lies in store for the future. Brains without regular sleep suffer from memory impairment, decreased motor skill function, and weakened focus. Lack of sleep can also increase anxiety levels. To give your brain its best shot at expanded intelligence, be sure to get at least eight hours of sleep nightly.

 

Brain Exercise: As all body parts need regular exercising and strengthening to maintain proper functioning levels, so too does the brain. Exercising your brain can be as simple as alternating your teeth brushing hand, or driving a different way to work. Doing math exercises or playing games like Sudoku are also great ways to keep your brain in shape for extended cognitive capacity and increased function.

 

Are you interested in exercising your brain? Math Nook offers fun and educational math computer games to work out your brain and increase intellectual capacity.

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Why Does Your Child Struggle with Math?

April29

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For some children, math class is the most daunting forty-five minutes of their day. Whether they are learning algebra, geometry, or calculus, some children really struggle in this particular educational subject due to a variety of reasons. From inadequate teaching methods to unfair overcompensations, here are some reasons why your child may be struggling with math.

Memorization: Do you remember memorizing information for a test? Do you also remember forgetting all those valuable facts right after that test? When math teachers teach through memorization, mathematic information often holds residency in the short-term memory temporarily, and then slowly exits, never making much of an indent in a child’s long-term memory.

Furthermore, encouraging kids to simply memorize their times tables or other algebraic equation results in rote learning, inapplicable to varied situations. As adults, we know that math affects our real lives in very different ways than how we learn its skills in school. Learning math by rote makes it nearly impossible to apply these skills beyond the set number of memorized equations. If teachers, instead, take the time to teach children how addition, multiplication, subtraction, and division work, why these tools work in these ways, and who to quickly perform these operations in a variety of different ways, children’s math skills not only improve, but they become more applicable later in life, exponentially increasing cognitive development.

Teaching to the Test: Standardized tests have negatively affected teachers’ ability to tailor lesson to their individual student needs. Instead, schooling systems measure teacher success by good standardized test scores, rewarded in continued school funding. However, the lessons on these tests are often just more memorization tricks rather than true exercises in understand critical thinking principles. This skewed system values school funding over children’s education needs, ultimately harming our children.

Tutoring: Instead of fixing the flaws in our educational system’s math classes, parents are compensating for these flaws by hiring their children tutors. While this can be helpful for those children whose families can afford tutoring, unfortunately not all families can. Thus, education becomes for those who can afford it, rather than for all. If parents instead put this money into improved schools rather than extra tutoring , more children could benefit.

Are you looking for fun ways to teach math to your child? Math Nook offers a wide variety of awesome math computer games and worksheets to teach our children the mathematics they need for later in life.

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This is a blog about Math Nook, math games, math and other fun and educational subjects.
Math Nook is owned by Jan and Tommy Hall.

Jan is retired from education where she spent 30 years in various positions ranging from classroom teacher to math specialist. She now spends her time working on the website and raising MathPup.

Tommy works full time but spends his free time utilizing his math degree and love of games to create some of the math games found on the website.