Mathematically Speaking – Good to Great

In upper elementary and middle school mathematics, despite any of the fluff that may have been added to the curriculum in past years, the hard-core topics of instruction revolve (or should revolve) around fractions, decimal, and percents.

A student who moves on to high school without complete mastery of the concepts, procedures, and applications of fractions/decimals/percents is one who will most likely encounter major difficulties in Algebra 2 and beyond.

Every year I bring up baseball batting averages to my classes, as a common application of fractions and decimals. It used to be that a typical seventh grader knew about batting averages and how they’re calculated; that was 40 years ago, maybe. Nowadays, many middle schoolers have no idea what it means for a player to bat .300, or .250, or .279…

Pretty soon the mystery is solved. For a player to bat .300, he (generic “he”, one of the several weaknesses of the English language) must hit a single, or a double, or a triple, or a home run, 300 times out of 1,000 times at bat.

So, it’s easy to conclude that a .250 hitter gets 250 hits for every 1,000 at-bats, and a .279 player hits 279 times out of 1,000 at-bats, and so on.

Bringing up major league statistics, students see that many major league players’ averages hover around .250, while only a relative few are hitting .300 or above. Conclusion: There’s a seemingly insurmountable difference between an average player and a great hitter – 50 big points!

Not so. Three hundred out of 1,000 translates into three hits out of 10 at-bats, or six hits out of 20 chances. On the other hand, a .250 hitter, (250 out of 1,000), is actually getting five hits out of 20.

Isn’t it remarkable that, in the game of baseball, the difference between a great hitter and the average player is only one hit out of 20 times at bat? A player who bats .250 gets five hits in every 20 times at bat, but a .300 hitter gets six hits out of those same 20 times at bat. It is amazing that the margin of greatness is only one more hit out of 20. It takes only a little extra effort to go from good to great.

Most importantly, a young player needs to understand that, if it only takes one more hit to become a star, he should want the bat in his hands, for he is willing to pay the price for success.

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Now let’s go to basketball, specifically foul shooting. In college basketball, a free-throw shooting percentage of 85% is considered outstanding. On the other hand, 75% is mundane; okay, just fine, adequate…

Ten percentage points, seemingly insurmountable, right? Out of 1,000 free throws, 85% means 850 one-pointers, while 75% means 100 fewer points.

Yet 85% means that out of 20 free-throw attempts, 17 are successful; 75%, on the other hand, means that, out of 20 free-throw attempts, 15 are successful.

Another remarkable statistic, and all it takes is simple parallel application of the fractions/decimals/percents concept. The difference between a great college foul shooter and an adequate one is only two free throws out of 20 attempts at the foul line. Consider how many basketball games are decided by five points or less, down to the wire. Consider how difficult it would be for the team that’s behind, with less than one minute to go, to decide which opponent to foul, if every player on the floor were an 85% foul shooter.

I am reminded of how many times over the years I have encouraged my students to concentrate on being better today than they were yesterday. High achievers in any field are committed to continuous improvement.

I need to impress upon my young students the importance of spending an additional half-hour a week going over their class notes one more time, finding and solving additional problems in the textbook or similar resources, or asking for extra “tutoring” time. This might be all they need to propel them from average to good, or good to great.

B pluses are for sissies. If a student can earn an 88% average in math for the term, why not a 92%, a solid A? While five percentage points may seem like a sizable difference, it really is not. Eighty-eight percent means 88 correct answers out of 100 questions, but it also means 22 correct answers out of 25. A student who earns a 92% got 23 out of 25 questions correct. Just one more correct answer, the difference between okay and greatness, between developing the “A” habit on one hand, and being satisfied with being okay on the other.

Similarly, soccer or lacrosse coaches need to impress on team members that making just one more save may have propelled the team to win that last playoff game. This is what teachers and coaches should, **must** do: Use whatever the subject matter may be at the time – whether mathematics, baseball, soccer, chess, lacrosse, it doesn’t matter – to teach those life concepts that do matter.

The difference between good and great may seem huge, impossible, and insurmountable, yet it really is not. It is up to each student, each player, to **decide** to improve. It is up to us, teachers and coaches, to show them what is possible and how to achieve what had previously been regarded as impossible.

The rest is up to them, our students, our players; they’re human beings, endowed with free will to do what is right. Let the ultimate responsibility be on their shoulders.

Great teachers and coaches rest on the laurels of great students and players; they are the ones who make some of us great. Or not.