Hidden Figures

by Margot Lee Shetterly

I had been putting off going to see the much-talked-about film Hidden Figures until I finished reading the book, which with my full-time teaching position and my newly 10-year-old son, took longer than I expected.

I’m going to talk about the book here, after which I’ll see and report back on the movie.

The book Hidden Figures is the debut work of Margot Lee Shetterly, about the role African-American women mathematicians played in the United States Space race.

Colleges with the Highest Average GPAs of Incoming Freshman

Which colleges have the highest average GPAs among their incoming classes?  Here are the Top 100 Colleges as determined by Forbes, sorted by average GPA, average SAT and average ACT scores of their incoming classes.

RankingNameGPASAT MathSAT CompositeACT
45University of California, Los Angeles4.29690137028
33California Institute of Technology4.23790156034
36University of Virginia4.22700140030
5Yale University4.19770154033
3Stanford University4.18760152033
22Duke University4.17780154034
39College of William & Mary4.16700143030
20University of Chicago4.16760152033
80Scripps College4.13710145030
63Washington University in St. Louis4.13770152033
15Columbia University4.13760152031
13University of Notre Dame4.11750148033
93University of Maryland, College Park4.11700137030
16Northwestern University4.11760150033
14Dartmouth College4.1760151032
57Harvey Mudd College4.1780151034
1Pomona College4.08750150032
32Rice University4.08760151033
24Tufts University4.06750149031
7Swarthmore College4.06740149031
2Williams College4.05740149032
8Brown University4.05750149032
9Amherst College4.04740149032
6Harvard University4.04770154034
30Carleton College4.03750148031
25Cornell University4.01760148032
19Haverford College4.01740148032
18Claremont McKenna College4740147031
28Vassar College3.99730147031
29Washington and Lee University3.97720145031
23Georgetown University3.96730146031
26Wellesley College3.96710145030
34Middlebury College3.96720145031
90Georgia Institute of Technology3.95740143031
51Hamilton College3.95720145031
65Grinnell College3.94730142030
12University of Pennsylvania3.94750150032
37Boston College3.92720143032
4Princeton University3.91780154033
54Smith College3.9700141030
31Davidson College3.9670140030
48Kenyon College3.9660140030
52Reed College3.9690144031
70Bates College3.89700141031
67Macalester College3.88700141031
75Brandeis University3.87710140030
27United States Naval Academy3.86700139029
72Villanova University3.86690137030
92Connecticut College3.86690140030
35University of California, Berkeley3.86740144031
42Barnard College3.86690142030
86Wheaton College3.856341230
64Bryn Mawr College3.85700140029
59Wake Forest University3.85700138030
61Colorado College3.84690140029
74Lehigh University3.83710137030
38United States Air Force Academy3.83700137030
68University of Illionis, Urbana-Champaign3.83760139028
55College of the Holy Cross3.82670138029
41University of Michigan, Ann Arbor3.82730143030
69University of Wisconsin, Madison3.81700135028
58Franklin and Marshall College3.81740136030
21Bowdoin College3.8750150033
11United States Military Academy at West Point3.8670134029
99University of Richmond3.8690137030
60University of Rochester3.8720141030
98Rhodes College3.78650135029
81Trinity College3.78660136028
76University of Washington3.76660129028
47Vanderbilt University3.76770152033
17Wesleyan University3.76730147032
87Dickinson College3.75660135029
79Emory University3.75720143030
78DePauw University3.75630127027
50Whitman College3.74660138029
62Johns Hopkins University3.74740147032
83University of Florida3.73650134028
71University of Southern California3.73740145031
56Carnegie Mellon University3.72760147032
77New York University3.71700141030
88Skidmore College3.71640132028
82University of Texas, Austin3.71660133028
89Centre College3.7630131028
95Mount Holyoke College3.66670140029
85Santa Clara University3.66670134029
40Colgate University3.66710141031
44Colby College3.66710141031
84Sewanee - University of the South3.62640133028
96Denison University3.6650132029
73Cooper Union3.6710140031
94Occidental College3.6690139029
91Boston University3.59690137029
66Union College3.5931
46Oberlin College3.59700144030
43Bucknell University3.54690137029
97Wofford College3.54610125026
100Trinity University3.5650132028
53Lafayette College3.46670135028
49University of North Carolina, Chapel Hill3.29550105222

These statistics were appended from the following sources:




And the individual schools' websites

Biology Books for Kids (Ages 6 and Up)

Here are recommended books on biology topics for rocket girls aged 6 and up,

Coral Reef Animals. Francine Galko. (6-8 years) Heinemann (2003). Describes coral reefs, where they can be found, the animals that inhabit them, and how to protect them.

Nature’s Adventures by Mick Manning and Brita Granstrom (ages 6 to 9)
The authors give simple advice to budding naturalists about what to look for at home, at the beach, or in a forest.

When in Doubt, Choose “C”

Two weeks ago I eliminated all multiple choice assessments. Mind you, this was a double-edged sword. Both the test prep and the grading for a written assessment puts an enormously time-consuming strain on my already bulging-at-the-seams schedule. Still, the more the students protested, the more confident I was in my decision. Students have been taught how to take multiple-choice tests; they can work backwards from the answer choices, the quickest among them can “guess” the right answers, and the least ethical always seem to “find” the right answers. Students and well-intended test-teaching “gurus” often tell me that, when in doubt, choose answer “C.” Of course, in written assessments, there are no answers from which to choose, and no letter “Cs” to bubble in.

Rather, the answers must come from within the students themselves.

One student whom I usually see brazenly copying someone else’s homework at the beginning of each class period told me how he spent three hours studying for the new written exam, thinking his effort alone could convince me to bring back the beloved multiple choice. Rather, it strengthened my resolve.

I estimate it will take me eight hours to grade all 120 written exams, whereas a multiple choice exam grades itself and makes for happier students (and often parents). The path I have chosen is the path of fools, I know. After all, most students don’t care about chemistry. They care about the grade.

But the thing is, I care about chemistry. And not in the way you may think. Yes, it’s both scientifically and spiritually satisfying to realize that you, I, and all the stars are made up of the same handful of elements -- carbon, hydrogen, oxygen, and a preponderance of metals -- which differ only in the number of positively charged protons housed in their infinitely tiny nuclei. The difference between hydrogen and helium is just one proton, and yet a rigid airship made of the former resulted in the Hindenburg disaster, and an airship made of the latter continues to hover over sporting events advertising tires.

But it’s not about chemistry, really. Rather, it’s about what chemistry teaches. Chemistry teaches you to work methodically through problems whose level of difficulty at times rises exponentially faster than your ability to solve them. Chemistry teaches you to stay the course, make daily effort, even when the effort seems to be fruitless. Chemistry teaches you to show up, be willing to be wrong, and be even more willing to learn from your mistakes. Chemistry teaches you that error is not something to be embarrassed about, but quantified, and learned from. Chemistry teaches you to struggle without the guarantee of ultimate victory. And chemistry teaches you that, if you do show up daily and work through the struggle, the challenge, the failure and the uncertainty, you will master a life skill that no multiple-choice exam in the world can assess, not even letter “C.”

Because the answers must come from within the students themselves.

Which, as we all know, is the only place to find them.

Failure IS an Option

As summer vacation ends, teachers observe the annual ritual of returning to school days ahead of their students, to be indoctrinated in the school district’s goals for the new year. The latest education fad is tossed out and replaced with newer education initiatives, which are usually older education initiatives spiffed up and redressed under new acronyms. After all, no matter how far we stray, we always return to the fact that improving reading, writing and arithmetic can cure most educational deficiencies.

A handful of years ago, while participating in one such “welcome back” ritual, I was introduced to our newly-adopted district-wide motto, “Failure is Not an Option.” A fitting corollary to No Child Left Behind, “Failure is Not an Option” was to inspire us to succeed with each and every student, so that no student would fail, literally. Of course, no one ever required or asked us to give all students a “passing” grade, but as teachers, we were expected to give each student unlimited opportunities to pass. And regardless of the district’s gentle shove, most teachers will do almost anything to get a student to show up, pay attention, do the work, struggle with the material, and learn, and pass.

But something funny happens when failure is taken off the table. Success falls right off the table with it, along with true and lasting learning. Watch any child learn to walk, and you see that child fail again and again. She first learns to pull herself up to her feet, using a table or the side of a chair or sofa. She lets go, and she falls. She tries again. She may cry. Yet she tries again. With a little practice, she gets good at standing while holding onto something. Soon, she attempts to move her feet, still holding on. She takes two steps forward, and falls backward. She pulls herself up again. She learns from the last fall what not to do this time. Soon, she is walking unassisted, though she still falls. She is laughing more than crying now. Because she’s got this. And falling isn’t so bad. And failure is her best teacher.

Fast forward a few years. My son won’t learn how to ride a bike for fear of falling. And my students won’t attempt to solve a chemistry problem without my constant reassurances that they’re doing it “right.” Yes, learning is risky, but these are measured risks. I’m right there alongside them. They may fail, but the fall isn’t so bad. And the learning that comes with it is priceless.

My son is afraid of getting hurt. And my students, of getting a “B.” So they won’t try unless all possibilities of failing are taken off the table. And yet, without the willingness to be “wrong,” and to learn from their mistakes, their treasured “A” remains elusive, and my son never learns to ride a bike.

We are all familiar with Edison’s purported retort to the reporter asking him how it felt to fail 1000 times, “I didn’t fail 1000 times. The light bulb was an invention of 1000 steps.”

Any scientist can tell you that learning is slow and arduous. And, in scientific research, there are no “right” answers at the back of the book, because the book hasn’t even been written yet. As my teacher and Nobel Prize recipient Roald Hoffman told me, “It is always piecewise knowledge, hard-won, and you don't see the totality until a couple of years later. There are often not single ‘Aha’ or ‘Eureka!’ moments, there are little pieces of understanding that slowly fall into place.”

It took 100 years since Einstein predicted their existence and twenty-two years after construction began on the Laser Interferometer Gravitational-Wave Observatory (LIGO) to find the compressed squiggle, the telltale sign of gravitational waves, on a computer screen. Sometimes it takes more than a lifetime of failed attempts to find what you’re looking for.

Learning anything new requires risk, frustration and the occasional “B.” And yes, failure, and plenty of it. Because, when it comes to learning, failure is not only an option, but a prerequisite.

Are Teachers to Blame?

I’ll admit it. I’m first in line to fault teachers — English teachers all the more so — on poor grammar, written or verbal, poor spelling, and lack of depth in their subject areas and breadth across others. I guess I got a little of the “teachers are to blame” gene from my mom, who threw a massive fit when I told her, as I was finishing up my senior year at Cornell, that I wanted to take a year or so off from pursuing a medical degree to teach. “We didn’t send you to Cornell so you could become a teacher!” she yelled over the phone, seeing her dreams for me crashing down all around her. But when I published my latest blog post on why students need to work hard to succeed in both comfortable and uncomfortable subject areas — namely math — I got a lot of teacher finger-pointing in response. “My teacher did me a disservice.” Teachers “ignored me.” My teachers “let me down.”

And I’ll also admit, I felt a little defensive. After all, I hear it every day from my own students. “You don’t teach us,” they mutter under their breath, or sometimes brazenly out loud. “No one gets this,” individual students remark beneficently on behalf of everyone. And so I struggle. Every day. Every class. Every interaction. To figure out how to make the complex subjects of chemistry and physics both understandable and engaging to each and every student. To the ones who are staring into their laps, attempting to hide their cell phone usage. To the ones using chemistry class to cram for another class’s test. To the ones furiously copying someone else’s homework so they can get full credit. To the ones getting a jump on tonight’s homework by working ahead. To the ones whose girlfriend or boyfriend just dumped them. To the ones whose parents just announced last night they’re getting a divorce. And to the one whose mother died earlier that week. And, to the most difficult students to reach, the ones who are absent from class altogether.

And I know that, if they just put it all aside for a moment, and fully engaged with the struggle, armed with pencil and calculator, each and every one of them would learn. And I also know that, if they truly attempted the homework, no matter how complicated and confusing it was, and were willing to bask in the discomfort to figure it out, they would grow wings. Yes, wings. Because nothing can stop a child who has learned for herself how to face challenges and work through them. But going to school, expecting to learn without putting in the work, is like joining a gym expecting to build muscles without doing the exercises.

I read a Washington Post article yesterday by a noted psychologist on why telling children they can be anything they want is doing them a disservice by creating undue pressure on them. I totally disagree. The only disservice is making them believe it’s easy. And that there are shortcuts. And “right” answers. The American dream has never been more accessible. To the ones willing to do whatever it takes. To the majority of students, however, it’s just “too many steps.” And they don’t “learn” because their teacher doesn’t “teach” them. So they return to class with copied homework, or blank homework amid protestations of “I don’t get it.” Of course they don’t get it. Because the only way to get from here to there is through, and “through” is an uncomfortable, time-consuming and frustration-laden preposition.

Does a Science Have to be Good at Math?

Does a Scientist Have To Be Good At Math?

The short answer is “It can’t hurt.” The physical sciences, such as Physics, Astronomy, Chemistry, all require a great deal of math to master. That is often why these disciplines are referred to as the “hard sciences.” When it comes to high school sciences, however, the level of mathematics knowledge required is relatively minimal. One could successfully complete AP Chemistry with only seventh grade algebra skills and an understanding of base ten logarithms. High school and AP Physics require algebra, plus a facility with the trigonometric functions sine, cosine and tangent. It is only AP Physics C that requires Calculus (AP Physics 1 and AP Physics 2, both of which only require Algebra and the trigonometric functions sine, cosine and tangent).

However, it has been my experience that a student who is not at or above grade level in mathematics will struggle in these courses, not because she hasn’t been exposed to the prerequisite skills, but because there is either some aspect of number sense that has not yet been fully developed, or the perpetuated belief that they aren’t good at math. If at any point in his/her elementary years a child is falling behind in mathematics, get her the help she needs immediately. Chalking it up to “not being good at math” is the greatest disservice you can do to your child’s education, and will stunt the budding scientist within her.

There are some fields of science in which math is not paramount, such as many of the biological sciences. Whereas I firmly believe that mathematics facility can only serve a biological scientist well, high school Biology will place few to minimal demands on a student’s math skills. In college and beyond, where research is a necessary component to biology, mathematics competency will prove itself not only valuable buy necessary many times over.

With that said, there are exceptionally successful biologists who claim that good math skills are not a requirement, offering themselves as living breathing examples. Two of whom come to mind are E.O. Wilson and Temple Grandin.

“Many of the most successful scientists in the world today are mathematically no more than semiliterate,” claimed E.O. Wilson in an article he wrote for the Wall Street Journal. E.O. Wilson, “Great Scientist ≠ Good at Math,” Wall Street Journal, April 5, 2013. “Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. Eureka moments require hard work. And focus,” not necessarily math.

E.O. Wilson explains that is far easier for a scientist to collaborate with a mathematician than for a mathematician to find “scientists able to make use of their equations.”

To Thomas Edison has been attributed the line “I can hire a mathematician but a mathematician cannot hire me.”

“If your level of mathematical competence is low,” explains Wilson, “plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have. Think twice, though, about specializing in fields that require a close alternation of experiment and quantitative analysis. These include most of physics and chemistry, as well as a few specialties in molecular biology.”

“For every scientist,” Wilson continues, “there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.”

Temple Grandin, the great animal biologist, professor of animal science at Colorado State University, and outspoken hero for autism, attributes her college and graduate degrees to the absence of an Algebra requirement.

“Tutoring me in algebra was useless,” writes Grandin in Thinking in Pictures, “because there was nothing for me to visualize. If I have no picture, I have no thought.”

Grandin barrelled through her required finite math courses with the help of tutors and devoted hard work in order to achieve her science goals.

In short, if math isn’t your thing, then make it your thing. After all, any skill can be mastered through diligence and hard work. Then, whether or not math is an essential component of your scientific career, it will not be your stumbling block.

Is Genius Innate?

There was a famous study in the sixties by Robert Rosenthal and Lenore Jacobson, known in most circles as The Pygmalion Effect. Certain students with normal IQs were identified to teachers as having higher-than-normal IQs – referred to as “spurters” – and could be expected to do better that year than their peers. Not only did the mean IQ of the entire group improve at the end of the year, but the students identified as “spurters” showed statistically significant gains. In other words, children rise to the expectations we set for them. A belief that “I am not good at math” is self-propagating. A not-good-at-math person assumes his math incompetencies limit his ability to succeed in math, thereby avoiding opportunities to learn math and improve his math skills, further eroding his math skills.

The belief that you are not a “math person” is a greater determinant of mathematics competence than some innate gift, or lack thereof.

Intelligence research identifies two distinctive orientations toward intelligence. Incremental orientation says that intelligence is acquired incrementally with increased effort. Entity orientation says that one is born with a fixed amount of intelligence that does not increase with effort. If you believe on the whole that intelligence is something you’re born with, as opposed to something that can be acquired, you absolve yourself of the responsibility to improve your skills.

And it’s an issue somewhat unique to our American individualistic ideals. Noted Stanford psychologist Carol Dweck, the guru of the “Growth Mindset,” has devoted the bulk of her career researching, writing and lecturing on how to develop a “Growth Mindset,” the belief that intelligence is acquired, not something you’re born with. In the 2007 Stanford Alumni magazine article “Effort Effect,” Dweck explains how other cultures do not luxuriate in the limiting beliefs of fixed mindsets. A college physics teacher wrote to her explaining that, where she was educated in India, “there was no notion that you had to be a genius or even particularly smart to learn physics. ‘The assumption was that everyone could do it, and, for the most part, they did’.”

And look where it’s gotten us. The 2013 Skills Outlook Survey published by the Organization for Economic Co-operation and Development (OECD), places young Americans dead last, out of 24 advanced countries, in numeracy and problem-solving skills. Even among Americans who have graduate degrees, Americans performed far worse than their counterparts. Poorer countries recognize math as difficult, just as Americans do, but simultaneously see math as the key to economic advancement. Rather than chalking it up to “I’m just not good at math,” these poorer countries add more courses to the curriculum to move their children to proficiency.

While this is all somewhat convincing, we know from first-hand experience that intelligence is also something you’re born with. We have all met certain precocious children that learn tremendously quickly, read from an early age, and display advanced vocabulary. We have seen, or at least heard of, music prodigies, math prodigies, artistic prodigies.

What we rarely see, however, are the hours and years of work involved in educating a child with a “gift.” Olympic gymnasts, concert pianists, ball players, chess champions have put in countless hours of dedicated training and practice to get where they are. “Gifts” alone only go so far.

“I've always hated the word prodigy,” says chess prodigy Josh Waitzin, author of The Art of Learning. “I think it's dehumanizing. I think that when you're labeled ‘genius, prodigy, wunderkind,’ it denies the human struggle against adversity which is at the center of my relationship to success. I think that anybody can become tremendously successful at what they do as long as they approach the learning processing a way that isn't self-paralyzing.”

An intelligence “gift” may open a doorway, but hard work and perseverance provide the legs to achievement. Further, time and again we’ve seen that hard work and perseverance, without the “gift,” can open doors themselves.

This is all the more true in scientific research. “It is always piecewise knowledge, hard-won, and you don't see the totality until a couple of years later,” describes Roald Hoffman, recipient of the 1981 Nobel Prize in chemistry, “but the process is interesting. There are often not single ‘Aha!’ or ‘Eureka!’ moments. There are little pieces of understanding that slowly fall into place.”

How “Smart” Do You Have To Be To Do Science?

When I listen to noted scientists Steven Hawkings and Neil deGrasse Tyson, or try to comprehend the immense impact of the recently discovered gravitational waves, I quickly get overwhelmed by both the subject matter and its preceptors. I am in awe of the intense genius that came up with these ideas in the first place, the brilliance of those who disseminate it, and grapple with how far short my above-average mind falls. Scientists must be really, really smart, I think to myself. And if I’m thinking it, you can bet my students are too.

“I’m just not good at math,” they explain.

In the classroom, math mistakes result in low grades. At NASA, math mistakes such as not converting between English and metric units cost the loss of a $125 million dollar Mars Climate Orbiter spacecraft. For both students with high aspirations and scientists alike, neither of these consequences is acceptable.

So, just how smart do you have to be to become a scientist?

The better question is, “How hard am I willing to work to become good at science and math?

There’s a belief in the United States that there are two types of people – those who are good at math, and those who aren’t. And yet, studies have shown very few, if any, genetic differences between a strong mathematician and someone “not good at math.” The reason is clear. Everyone has the capacity to be successful at math. However, by labeling ourselves from an early age as either “good at math” or “bad at math,” these labels become self-fulfilling prophecies. Sure, on occasion, there have been extreme math geniuses in our midst, but for the most part, math skills are the direct effect of two things – diligence and confidence.

I used to teach in a rural largely Hispanic high school. Halfway through the year, a new student from China joined our Physics class. My students teased the class’s top student that he would now be relegated to second place. Clearly, they were invested in the Asian stereotype, even if they had never met an Asian person before. Joining a new school in the middle of the school year is difficult for any student, especially one with a poor command of the language. I sent everyone home with a new assignment that day, that built on a previous lesson. The new Chinese student asked me questions after class about the homework assignment, making it apparent that he had very limited prior content knowledge. Imagine my surprise when he returned the next day with the completed assignment in hand. It was all the more surprising when only one other student in the class completed the assignment, the “formerly” top student. To my students, the Asian myth was perpetuated, commenting in awe about the new genius in their midst.

From my vantage point, I saw something totally different. I saw a student, unfamiliar with the subject matter or the previous lesson, who did what was necessary to learn the new material and return to school prepared.

In the book Intelligence and How to Get It, Richard E. Nisbett writes about how Chinese, Japanese and Korean educational systems focus more on hard work than on natural abilities. Here are some of Nisbett’s findings.

Children in Japan go to school 240 days a year, as opposed to the 180 days our American students attend. Further, Japanese high school students in the 1980s studied at least 3 and a half hours a day, which is likely to have increased over time. American students, on the other hand, spend more of that time online, using social media and chatting with friends.

Asian students see intelligence as malleable, meaning that it can be acquired. American students see intelligence and aptitude as something you’re born with.

When Asian students perform poorly, they work harder at it. When American students perform poorly, they often blame the test, the teacher, or their own inabilities. Rarely do they attribute poor performance on lack of effort.

Finally, Asian culture values persistence in the face of failure, and criticism as a guiding force toward self-improvement. American students, especially the most privileged, are rarely allowed to fail, thereby lacking the valuable lessons that failure teaches, and ward off criticism as attacks on their fragile self-esteem.

The truth is, assuming you are not good at science or math is a much easier path than the alternative one of hard work. So, how smart do you have to be? Smart enough to know that the only way to get there from here is through hard work, persistence and the ability to pick yourself up after you fail, which is all but guaranteed.