I have taught puzzle math to students in grades three to six. In these classes, I have found that students show a significant positive change in their attitudes toward math after a year of recreational math activities.
This way of using games in education is more commonly used for reading and writing, with games like Scrabble or Hangman encouraging semantic, linguistic and orthographic skills. The two fields, English and Math, seem polar opposites at times in terms of the type of person who is attracted to them, but what's common to both, yet not well recognized, is that both are systems of symbols and therefore have much overlap in the brain regions recruited for their performance.
This may be because neither the ability to read letters nor to calculate with figures are innate human characteristics. We're born with the ability to see (with our fingers if not our eyes, the visual cortex is there to be accessed) and hear and think, which means to analyze and synthesize sensory inputs in our head until they make sense to us, whether we're right or not. We're also born with the ability to observe statistical patterns and make predictive judgements, much much faster than any computer. Fifth and sixth (are you counting?), we have the innate ability to make quantitative judgements and estimate, as shown in studies with infants, and we can parse strings of sound into words and phrases, eventually imbuing them with meaning.
Lastly, we have the amazing ability, not restricted to humans by any means, to form associations, so we can recognize when one thing stands for another--has intentionality, as the philosophers love to say--to know when something is a symbol for something else. In the animal world, that something else can be abstract: when a fawn halts suddenly, ears up, it doesn't think, "Did I just hear a lion approaching?" (in deer thought, of course) but ties the sound it heard to a more general sense of "Danger!" In humans, we have stretched this ability to think in abstractions extremely far--bent it out of shape, some would say-- in our compulsion to understand the world around us, including God, the universe and everything (the answer is 42).*
Along the way we have learned to think outside ourselves, using pen and paper, or quills and parchment, or rocks and pigment, or just by scraping two rocks together. This externalization of our thinking process led to a complex nest of symbolic language, both literary and mathematical, which we now need to pass on to our young, not only to deal with the day to day business of life but, evolutionarily speaking, so that our endless thirst for knowledge can continue to be quenched.
But it is also important to remember, evolutionarily speaking, that until only a few hundred years ago, most people never had to learn this stuff, or at least, not to write it down. The cognitive arsenal we bring to the table is substantial, and certainly up to the task. But working with written symbols to make abstract meaning it is not an innate skill set, not for any of the 3 R's, and some people will simply be better at it than others. As Kulkarni puts it later in his article, commenting on his puzzle strategy:
However, skill improvement among students varies significantly depending on
other factors such as the amount of effort students put into doing homework, as
well as student aptitude.
This is where cognitive games and other thinking strategies come in. By honing a student's aptitude, they sharpen the cognitive tools so that when the time comes, they're ready to apply them. Such access to the mental toolkit has always been around and been put to use by good teachers throughout history. A high level martial arts program, for example, begins by teaching patience, not moves, and among top athletes it is their mental attitude, not their physical differences that gain them the critical split second win.
It is these underlying faculties that 21st century diagnostic techniques are giving us an insight into, and which we should be using to improve our odds, not just for the sake of improving the Gross National Product, but for our very survival.