Some of us have kids who are quite strong in mathematics. Some will be naturally gifted—their brains just click when it comes to numbers. Some work hard, but they truly enjoy the challenge of problem solving, and their investment pays off. As teachers, we can sense that spark right away: they have an eagerness to answer questions, they are motivated to solve the most difficult problem on the page, and they love to share their the fancy way of calculating something in their head.
It's a joy to see their enthusiasm and to see their talent emerged so young. For them, the mathematical requirements of their grade level might come easier than for other students, and they may complete them with great grades. It may surprise some people to see these kids in tutoring lessons or in supplemental classes when their skills are already so sharp. With exploration, we can discover that there is actually great incentive for them to be there: private tutoring can support the goals of even the most advanced of students.
Math On the Edge
Mathematics has many parallels with athletics. In both fields, one can argue that anyone should have a grasp on the basics. It’s helpful for any adult to have arithmetic skills and a general intuition of the mathematical properties of the world. Similarly, to get the most out of our bodies long-term, it’s helpful to know how to move them and even how to have fun doing so. Both fields allow for natural talents but also require plenty of practice to develop real mastery, and both fields benefit tremendously from enthusiastic and supportive coaching. And at the highest level, even the tiniest edge can tip the scales towards an individual participant.
In any academic or athletic pursuit, for students who are already performing at a high level, it comes down to small, subtle edges of advantage that push them to a new degree of excellence. And it can be quite challenging to get from the 97th to the 98th percentile on a performance metric by sheer willpower and self-direction alone. We can bolster achievement with outside intervention such as coaching, and students who may have thought they reached a ceiling can still find new room to grow. With athletics, growing at this level typically requires extra practices, extra hours, extra coaches, and extra time and resources spent honing those skills.
With mathematics, the exact same principle applies: excellence often requires that little extra push.
Chomping on Challenge
For students who are hungry for challenge, eager to learn, and keen to develop mastery, we can give them an extra arena in which to train that isn’t being supplied at their current level. This can satiate that desire to continue excelling and continue to motivate them further.
For students who are eager, giving them as many opportunities to practice as possible may be the catalyst that enables them to rise above the crowd and practice mathematical skills at the highest level. This could be for fun; these students may find joy and a deep sense of accomplishment in participating in math competitions or contests. Performing well in these contests often requires spending some leisure time on mathematics, and this may provide a great level of satisfaction for these students
In more serious pursuits, our technologically advancing economy continues to need people to specialize in highly advanced mathematical, scientific, technological, computing, and engineering fields. Nurturing the academic instinct while these students are young can turn them into leaders in the STEM fields, or could catalyze accomplished careers in academia and incredible discoveries that keep our collective human experiment rolling forward. To whatever degree they may choose or desire to pursue these kinds of accomplishments, supplemental education can help them refine their skills in an environment that is more suited to them. This can help them develop more precision, more confidence, and more self-awareness, which will set them up to choose the best direction for themselves as they grow older.
Keep On Mathing On
There is perhaps a more fundamental reason to enroll exceling children in supplemental mathematical education. Supplemental education teaches children that there is more work to be done. When they have risen to the top of what's expected of them, there is still more that they can do.
By continuing to provide challenges to excelling kids, we are training them on what to do with excellence. The key here is: the answer is not to coast. When they have fulfilled the requirements of the traditional lanes they're given, they can find their own lanes and continue to grow. They can forge new paths, find new colleagues, and continue to push and challenge themselves until they find something else to master. Supplemental education teaches children that being good at something means you keep working at it. When there is always more challenge on the horizon, we turn a one-and-done jigsaw puzzle into a Tetris game where the player can take the game as far as they would like, or as far as their skills allow.
This is a principle that goes beyond mathematics in education. No doubt every child will find excellence in some area of their lives. By teaching them what to do with that skill once they find it, we open their minds to the limitless possibilities of what they can achieve if they continue to apply themselves. Moreover, that vision can continue to expand as they grow, and this vision in and of itself is an excellent skill to master.
The need for supplemental education goes far beyond the need to be successful at a particular grade level, especially if a student is already achieving more. Let's nurture our children's instincts to climb mountains by continuing to supply them with new heights that they can summit and put in their rearview mirrors.
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