It’s been called the “Queen of the Sciences” but many prefer to view math as more of a liberal art than a STEM subject even through the “M” in STEM stands for Mathematics.
In FIRST LEGO League this year we saw a number of simple and complex applications and potential applications of math including: calculating circumferences from radii, linear distance traveled as a function of angular wheel rotation, proportional line following, calculating rotational angle based upon single or dual motor angular wheel rotation, estimating E-W alignment with the Robot Arm Mission based upon differential left and right color sensor readings of the slanted green line, etc.
A great part of the math learned in FIRST LEGO League is how we could experiment with, quantify and physically measure the abstract math concepts we were using. For example, early in the season we began with an AA Alkaline powered NXT robot but switched to a NiMH rechargeable pack powered eV3 robot. Our countless trail runs and experimentation gave a physical reality to the graph below when it came to the robot power output, speed, turning and linear travel distance. Understanding this concept and adopting technology with a better power output curve led us to a more accurate and reliable robot performance.
There is the potential for a wide variety of applications of math to the study of this year’s FLL Challenge Trash Trek: economic analysis, energy flow modeling, optimization of transport and logistics, etc. We are only limited by our imagination and mathematical abilities and interests.
I’ve been advocating for starting Math League in the local schools for several years now and led a group at a local private school last year when my oldest was first eligible in 4th grade. It’s was difficult with the recent introduction of Common Core and greater emphasis on testing like the PARCC exam to not view Math League as yet another competing claim on limited class time.
Fortunately, Math League is more complimentary than competitive with the Common Core as content is entirely grade-level appropriate and practice is done outside class time. Although it is a multiple choice exam, the Math League exam emphasize analytical skills needed to solve some of the more difficult multi-part style PARCC math questions (minus the large expository writing).
Math League is one of the largest math competitions for kids as young as 4th grade and is designed to spark kids interest in math and quantitative problem solving. Kids take a 30 question exam around March or April. Several months prior they systematically review questions from exams of previous years in a group setting to prepare.
To allow all kids to demonstrate some mastery, questions are divided into 10 easy, 10 middle and 10 hard questions. Sixth grade kids and older with top scores are given an invitation to a gifted summer math program hosted by Stanford University. An interesting and more elaborate math competition called MathCounts consists of a number of individual and team math contests competing in tournaments up through the national level.
Because FIRST LEGO League was so demanding and ran 3 months longer than we initially anticipated, I wasn’t able to volunteer with the Math League group from last year. However, I have been able to help with another group briefly due to an unexpected absence. Although it’s a bit of a self-selected group, it is still good to see kids get excited about math.
Although I didn’t major in math I’ve always admired the power and beauty in it. With just the fundamentals of math, one can begin to see beyond the immediate to grasp a logic, order and eternal nature to all existence (or proposed existence). To be unable to perceive the world in mathematical terms would be like seeing the world without color or even vision itself. Life would be a drastically impoverished experience if we had no mathematical intuition to view and understand the world around us.
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A good analogy of expressive power of math would be with the power of good writing and speaking. Although it seems natural that writing and speaking are more fundamental to human perception and needs, technological progress is rapidly elevating the value of quantitative skills like math. Even jobs that were not quantitative a generation ago, are rapidly becoming so (eg marketing and medicine via big data analysis). When employers say schools are not graduating students prepared for today’s work force, they are often critiquing quantitative skills as much as verbal skills.
Both language and math rely upon foundations that will either open up opportunities or foreclose them. Native language acquisition seems a more innate human aptitude. It appears more flexible in terms of things like the correlation between adult proficiency and the age of first reading (e.g. Finland). On the other hand, Math seems less innate, cumulative and influenced by early exposure like learning a foreign language or perfect pitch in music.
As Barbie maladroitly said, “Math is hard”, but Ken could’ve said it as well. Math can be incredibly hard for anyone who ventures far enough into the deep end of pool. One of the hardest aspects of math to reconcile with our modern Western conception of humanity is how math quantifies us, reduces us to a number and clearly defines our cognitive limits with unforgiving logic. It seems to deny our uniqueness, ignore the subtleties of beauty beyond the obvious facts and leave no room for interpretation or intangibles.
In contemporary America, we are particularly ill-equipped to deal with the blindingly harsh and unambiguous judgements a field like math imposes. However, a scientist and engineer (and increasingly everyone in our technology driven society) absolutely need clear-eyed humility in the midst of this cultural age of hubris.
The good news is that the most interesting and broadly useful aspects of math are the lowest hanging fruit. Even with probability and statistics and the simple math underpinning it one can immensely improve their lives with everything from school choice to auto insurance. A simple undergraduate program that covers math for scientist and engineers would probably equip graduates with the math chops to tackle 98% of the high-demand and high-paying knowledge jobs in our economy from economics to programming to medical research.
Just because one cannot create beautiful poetry, music or mathematics does not preclude one from exploiting the benefits and gaining enrichment from those who can. Although it helps, most people who use advanced statistical analysis in software packages to measure the efficacy of a medical trail or financial models could not derive models from first principles yet they are able to produce valuable results.
Learn as much math as your interests and abilities take you and enjoy the experience. Like music, I’ve never met an anyone who regretted learning too much math – quite the converse. Go math.