Are You a Rocket Girl?
Do you love math?
Do you love science?
Do you like to solve problems?
Figure things out?
If you answered “yes” to three or more of these questions, you just might be a Rocket Girl.
Are You a Rocket Girl?
Do you love math?
Do you love science?
Do you like to solve problems?
Figure things out?
If you answered “yes” to three or more of these questions, you just might be a Rocket Girl.
It’s been 4 weeks since Hillary Clinton lost the presidency to Donald Trump’s electoral count win - currently, in the counting, Clinton’s popular vote lead has grown over 2 million. I have to admit, I’ve been having a really hard time with this. Experts say there are five stages of grief. And I feel like I’ve been manically flip-flopping among them. I’m still going through the first two stages— denial and anger — though my denial has waned. I’ve even grown to accept what I can’t change — the fifth of the five steps.
10 Top Children’s Book about Numbers
Does your child love numbers? Do you want your child to love numbers? Then stock your library with these 10 reads, from preschool titles to middle school. Read them with your child and you’ll get as big a kick out of them as she does. Maybe even more.
1. Math Curse by Jon Scieszka and Lane Smith
Math Curse is about a student whose math teacher claims that everything can be seen as a math problem. Everything in her life becomes a math problem which she learns to solve to absolve herself of the “math curse.”
Number sense refers to "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996). In other words, people with number sense can do the following:
Perform calculations in their head
Judge the relative magnitude of numbers
Recognize part-whole relationships among numbers
Understand place value concepts
So much of science (and life) depends on one’s ability to manipulate numbers that addressing any weaknesses in any one of the above areas is as important as reading and writing.
How to address weaknesses in number sense:
1. Study Khan Academy’s Number Sense lessons: https://www.khanacademy.org/math/on-sixth-grade-math/on-number-sense-numeration. Khan Academy breaks number sense down into six categories:
Each category contains lessons and practice problems that tailor themselves to your individual progress. And, of course, it’s free.
2. I would add to the list of skills above, learn to:
3. Use your calculator as a last resort. Estimate all answers before plugging numbers in your calculator.
Obviously there are higher-level math courses that you will need to master to become a scientist, such as Trigonometry, Calculus and Statistics, but these are useless without a firm basis in the skills I listed above. Use these fixes to address your number sense issues, and you’ll be calculating with the big girls yet.
10 Steps to Developing a Growth Mindset
Carol Dweck, noted Stanford psychologist and author of Mindset, tells us that the only thing standing in our way of learning is our beliefs about our ability to learn.
“In one world, effort is a bad thing. It, like failure, means you’re not smart or talented. If you were, you wouldn’t need effort. In the other world, effort is what makes you smart or talented.” – Carol Dweck, Mindset: The New Psychology of Success
Want to get smarter? Want to get better at something? The only thing standing in your way are your thoughts about yourself and your abilities. Want to become a math person? Want to get an “A” in science? Want to study at MIT? Then change your brain. It’s easier than it seems. And it starts with your own self-talk.
1. Recognize that your brain and its neural connections are elastic.
As you continue to learn, new connections are made. Those who think they know all there is to know, or even enough, risk atrophy. Brain cells are always dying. In fact, the only part of the brain that continues growing new cells after the age of 2 is the hippocampus, the center of learning and memory. You will grow new cells as you learn new things, and make excellent use of the ones you still have.
2. Acknowledge your weaknesses.
Admit to yourself what you don’t know. Now go and learn it. Learning a difficult subject is a lot easier than spending your life in fear of what you don’t know.
3. Improve your vocabulary: “Failing” is “learning.”
When you make a mistake or get a bad grade on a test, learn from it. Nothing can teach you better than your own missteps.
4. Stop seeking approval.
What others think of you and what you know or don’t know is none of your business. Your business is to be better today than you were yesterday. Treat everything as a learning opportunity. There will always be those who support you and those who deride you. Those who put you down are projecting their own of not being good enough. It has nothing to do with you.
5. Stop apologizing and/or berating yourself.
Don’t preface your questions or your fear of not knowing with an apology or worse yet, a self-deprecating comment. “I’m sorry. I know I should know this, but… “ We tend to do this so as to get the approval of those whose help we are seeking. Refer back to #4 “Stop seeking approval.”
6. Celebrate your process.
Theodore Roosevelt said it best: “Nothing in the world is worth having or worth doing unless it means effort, pain, difficulty… I have never in my life envied a human being who led an easy life. I have envied a great many people who led difficult lives and led them well.”
Learning something new and all the more so difficult takes time and effort. Praise your effort, not your results. Effort consistently applied will move you in the direction you wish to go.
7. Seek out criticism.
Ask for feedback. We believe when people criticize something we do or say, they’re criticizing us. This is a direct result of having a “fixed mindset." In other words, if I believe that something is my absolute best work, then a criticism of my best work is a criticism of me. The truth is, my best work hasn’t been done yet, because I get better every day. Ask for feedback. Welcome constructive criticism. And if you agree with it, take steps — even baby steps — to improve. A "growth mindset" person might respond to constructive criticism, “Cool, now I know how to get even better.”
8. Cultivate grit.
The natural result of a “growth mindset” is the realization that learning and growth take effort. Cultivate your ability to make real and consistent effort. And, while you’re at it, be sure to celebrate your effort. After all, your effort is all you really have control over.
9. Set realistic expectations of the time and effort required.
We are notoriously bad at estimating how much time something will take, especially learning a new skill or subject. Remember Parkinson’s Law says that “work expands so as to fill the time available for its completion (Wikipedia).” I would add an addendum saying that, work expands to take more time than allotted. Be patient with yourself. Try to overestimate the time something will take and be pleasantly surprised.
10. Don’t compare your “bloopers” reel to others’ “highlights” reel.
Know that people’s social media status updates and those of the stars you follow are not even half of the story. When you watch only their “highlight” reel, you tend to believe that success comes easily to others. No one reaches the top of her field because it was easy. J.K. Rowling cites many rejection letters before procuring a literary agent for Harry Potter.
To one of her Twitter followers, Rowling confirmed her “Growth mindset”: “Believe me, neither @RGalbraith nor I walk around thinking we’re fab. We just shoot for ‘writing better than yesterday'."
Mozart was quoted posthumously saying that his ideas flowed best and most abundantly when he was taking a walk or alone in bed at night, “and provided I am not disturbed, my subject enlarges itself, becomes methodized and defined, and the whole, though it be long, stands almost finished and complete in my mind, so that I can survey it, like a fine picture or a beautiful statue, at a glance.” Putting it down on paper for Mozart was almost an afterthought, he said, “and it rarely differs on paper from what it was in my imagination.” Wolfgang Amadeus Mozart, Allgemeine Musikalische Zeitung, or “General Music Journal,” in 1815, vol. 17, pp. 561–¬66.
Most of us have heard this or another similar version of Mozart’s creative method; how a symphony or concerto would just appear to him, in its final form. In Peter Schaffer’s 1979 play “Amadeus,” Mozart is portrayed as a foolish prankster with an effortless God-given gift that he plops onto staff paper, whilst his nemesis Antonio Salieri works laboriously day and night on his talentless compositions.
Unfortunately, or fortunately for us mere mortals, this letter is a fake. Mozart’s biographer Otto Jahn proved way back in 1896 that this letter was not only a false representation of Mozart’s process, but that Mozart never wrote it.
Mozart’s real letters — to his father, to his sister, and to others — reveal his true creative process,” writes Kevin Ashton in his book How to Fly a Horse: The Secret History of Creation, Invention, and Discovery. “He was exceptionally talented, but he did not write by magic. He sketched his compositions, revised them, and sometimes got stuck. He could not work without a piano or harpsichord. He would set work aside and return to it later.... His work was exactly that: work.”
A similarly fanciful tale colors our perception of the scientific process. The first “Eureka!” moment is attributed to the Greek mathematician Archimedes, who was charged with the task of determining whether Hiero of Syracuse’’s gold crown was pure gold or an amalgam of gold and silver that his goldsmith was attempting to pass for pure gold. One day while working on this problem, Archimedes noticed how the water level of his bath rose as he submerged himself in it, promptly causing him to exclaim “Eureka!,”” jump out of his bath, and run naked through the streets of Syracuse.
This well-known story does not appear in any of Archimedes' known writings, and is first recorded two hundred years after the fact, in Vitruvius’s Book of Architecture. As such, its accuracy cannot be verified, and chances are, it never happened. We hold onto it, however, because it fits well with our myth of how science works, replete with lone geniuses, toiling away until that fateful “Eureka” moment.
Scientific discovery, just like works of great art, rarely happens in a bold stroke of inspiration, but as the outcome of fits and starts, failures and dead-ends, small successes and gradual conclusions. “Eureka!” is a moment born of a lifetime of effort.
Roald Hoffmann, the 1981 recipient of the Nobel Prize in Chemistry, explained his process to me:
“It is not as romantic, it is always piecewise knowledge, hard-won, and you don't see the totality until a couple of years later, 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.”
As with other creative endeavors, doing science is work – hard work. Those of us who’ve ever struggled in an advanced level science course can attest to that. But creative? Hard to imagine. After all, scientists are the epitome of left-brainedness.
So I asked the “Father of String Theory” Leonard Susskind whether he believed his scientific outpourings were creative, he almost instantly ascribed creativity to artists; not to scientists like himself.
"An artist thinks to himself, ‘How do I create something new and different that will excite an aesthetic sense?’. I think for me it's quite different, although I have a very strong aesthetic sense what constitutes a good explanation or a good mathematical explanation of something. Nevertheless, I don't go into a thing saying, ‘Let me create something new.’ I go into a thing saying, ‘How does it work?’”
And yet that kind of thinking is arguably creative by definition.
“When I was a young person, I wanted to do something creative. I wanted to do something new and something nobody else had done or something that I could create. When I was younger I thought of trying to be a composer, a musician, and compose music and compose poetry. Unfortunately, didn't have the talent. I could play the violin, but I couldn't compose original music. I tried poetry and I like poetry, and I like reading it, but I didn't really have a big talent for it. When I got into science I had more of a talent for that. What I tried to do is use my interest in creating something new in science and medicine.” - Kilmer McCully, Chief of Pathology and Laboratory Medicine Services for the United States Department of Veterans Affairs Medical Center and father of the homocysteine theory of cardiovascular disease.
Science mines for and interprets data. This is where creativity comes in. What do I want to know? Is it worth knowing? How could I design a method to find answers to my question? How can I interpret what this data tells me? Creativity is the underpinning behind all stages of the scientific process.
Astronomer Clifford Stoll: “Ask simple questions to start the creative ball rolling, such as ‘‘How does this work?’ And ‘Why?’ Find questions that interest you. Then start digging for answers. In the search for answers, you just might find better questions. And, isn’t that what science is, in the first place?”
Oblivious to my need to keep to my unrealistic schedule, Max, then 3, asked, as I was rushing him out of the car and into school, "Is that the parallax effect?"
“What are you talking about Max?” I responded, hurrying him into the classroom.
“The moon stays in the same place, even when we’re driving.”
I was watching the clock the entire drive. My son was watching the moon.
Children observe. They take it all in. So many things about the world are new to them.
By the time these children reach adulthood, however, they’ve learned to filter almost everything out. This is too bad, because what makes for a good scientist is to hold onto that ability to observe the world, well into adulthood.
Though Rutherford received the Nobel Prize in 1908 for his discovery of the radioactive emission of alpha and beta particles, his interest lay in the effects these particles caused. And in order to study this, he had to first figure out how many particles were given off by his uranium sample. So he and his assistant, Hans Geiger, counted. They had found out earlier that a screen coated with zinc sulfide emitted a flash of green light every time it was hit by an alpha particle. So they counted the number of flashes of light.
This was no easy task, and rumor has it that Geiger did most of the counting. With such an arduous task, the two of them sought any way to simplify the process. They soon realized that the beam of alpha particles would scatter more when covered by a thin piece of foil, making the tiny flashes of green light easier to detect and, therefore, easier to count. They prepared the thinnest piece of foil they could, gold foil, approximately 0.004 mm thick and measured the angle of scattering of the alpha particles.
This worked, and the tiny green flashes of light were easier to count. But if these particles could be scattered at an even larger angle, it would work even better -- and be a little easier on Geiger's eyes. Rutherford posed a side project to one of his research students, Ernest Marsden, to see if he could diffract the particles through an even larger angle. Marsden rose to the challenge and was able to deflect one out of approximately every 20,000 particles at a larger than 90 degree angle.
More than 90 degrees? This was impossible. Or was it? Rutherford, in describing the results years later, remarked: “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."
Rutherford published his findings a few years later, attributing the large diffraction of only a few particles to the presence of an infinitesimally small, dense and positive center in each atom, known as its nucleus. To this day, we have yet to see an atom, let alone its nucleus. But from the consistent day-to-day observations of a handful of scientists, we have a good understanding of this black box that is the essential ingredient of all matter.
Observation is tedious. It takes time. And patience. Many of the traits that working parents and teachers with state-mandated pacing guides have very little of. Though it’s a trait we each are born with. And it’s a skill our children have mastered.
Roald Hoffmann, recipient of the 1981 Nobel Prize in chemistry, was born in 1937 to Jewish parents in Złoczów, Poland. Soon after Germany invaded Poland, he and his family were interred at a labor camp, from which he, his mother, an aunt and two uncles bribed a guard to escape. From there, they hid in the attic of a Ukrainian neighbor for a year-and-a-half. Hoffmann’s father remained behind in the camp, highly valued in his capacity as civil engineer, until he was eventually tortured and killed. Five years after the war, at the age of 11, he and his family immigrated to the United States. He describes his first years in American school:
When you're an immigrant and you don't know the language well -- English was my 6th language when we came to the United States -- I had studied it the year before in a class, but I really didn't know it. I think English opened up for me with a Tarzan comic book on a boat coming to the United States. The immigrant experience, when you don't know the language, I was ahead in math, and so you're an outsider. You stand out and you very quickly learn the language. You can see that among immigrant children. But you stand outside and you watch. You watch trying out to figure out what are the niceties or regularities of behavior among students with respect to each other. It sounds much more formal than what it is. You want to fit in, so you watch, you observe and you know, there's something about watching and observing and not knowing the language that's a little bit like science. Now if you put that in the context of watching and observing nature, just watching from outside, I don't want to push the analogy too far, but to me it's a little bit of what has led many immigrants into science. And you can see this in other ways. They first go into science. It's usually also because the mathematics is what is cross-cultural, and that they bring where they're ahead to that group. And so it's natural that they utilize that. So I think the immigrant experience, being an outsider, is actually helpful.”
Another example is Galileo, who night after night, month after month, observed and sketched the moon. Only through such precision and persistence did he discover that the moon was not a perfect sphere as his contemporaries believed, but a landscape replete with mountains, valleys and craters. When he turned his telescope to Jupiter, he came to realize that the stars he observed weren’t stars at all, but moons -- moons that revolved around Jupiter just like our moon revolved around Earth. And he found support for Copernicus’ theory that, rather than the Sun revolving around the Earth, the Earth and all other planets revolved around the Sun.
In an era of instant gratification and measurable outcomes, observation for observation’s sake and science for science’s sake are difficult selling points. We value only what we can measure. Hence, we test our children for measurable educational outcomes when the most important outcomes of a good education are immeasurable. And we defund NASA because we are unable to assess the value of what we learn today on the technology of tomorrow.
We are so conditioned to observe in order to act, to listen in order to respond.
Great scientists, however, observe in order to see. And listen in order to hear.
In her 2011 blog post in Scientific American about physicist and Manhattan Project alum Robert Wilson, Jennifer Ouellette recalled his 1969 testimony before the Congressional Joint Committee on Atomic Energy about whether to fund a new particle accelerator in Batavia, Illinois.
Then-senator John Pastore asked, "Is there anything connected with the hopes of this accelerator that in any way involves the security of the country?"
Wilson responded: "No sir, I don't believe so."
Senator: "Nothing at all?"
Wilson: "Nothing at all."
Pastore: "It has no value in that respect?"
Wilson: "It has only to do with the respect with which we regard one another, the dignity of man, our love of culture. It has to do with: Are we good painters, good sculptors, great poets? I mean all the things we really venerate in our country and are patriotic about. It has nothing to do directly with defending our country except to make it worth defending."
With the challenges that even the scientific community faces in following its own credo of “Just the facts ma’am,” how much harder is it for children to think for themselves, especially when they are bombarded hourly with unrelenting social cues to be like everyone else?
Recall that I wrote in an earlier article “Thinking Independently is Risky,” how birth order can influence whether one follows the status quo (mostly first-borns) or is a revolutionary (mostly later-borns). Keep in mind that these are trends and not absolutes. However, by garnering clues from the parenting practices toward first and only-borns and those toward later-borns, we can learn a lot about how to raise independent thinkers.
First-borns tend to receive a lot more parental attention than later-borns, especially since they were only children for part, if not all, of their childhood. As such, parents tend to exert greater pressure on first-borns to succeed, especially through the established pathways provided by higher education. This is especially true among immigrant children, whose parents regard education as the shortest path to climbing the socioeconomic ladder. Parental attention, parental involvement and even parental pressure often mold children to follow the traditional path of hard work and higher education.
As additional children are born to them, these same doting and involved parents naturally become more lenient and accepting. Their later-born children then, given more latitude and often being less overscheduled, grow up more independent, finding ways to engage themselves and stand out that may not always be the most traditional or accepted.
Raising a scientist means raising an individual who values and follows her curiosity, has the patience to see her hard work through fruition and the independence to follow her findings to their natural conclusions, regardless of the opinions of others. Raising a scientist, then, means combining the best parenting practices of both first-borns and later-borns.
In other words, give your child plenty of attention, while at the same time, allow her the freedom to explore her own interests.
Encourage and involve yourself in her education, while disengaging yourself from the outcome. Your daughter does not need to go to Harvard or Stanford to be a successful scientist, nor does she need to become a scientist to live her life’s purpose.
Cut back on her afterschool commitments. Allow her more playtime.
Guide her without directing her. Share experiences with her.
Share your interests with her.
Let her share her interests with you.
Listen to her.
Follow her lead.
You may be surprised where she takes you.
“It's easy to stand in the crowd but it takes courage to stand alone.” - Mahatma Gandhi
Scientists, charged with the mission of following the evidence wherever it leads, are ironically often too well-entrenched in their own status and a priori beliefs to accept it. In other words, the established scientific community that devotes years and lifetimes doing the work that inspires scientific revolutions, may also be the last to accept these very same revolutions.
Rocket Girls know when to stand alone.
In order to address the epidemic of infanticide among illegitimate children in nineteenth century Europe, free maternity clinics were established to care for underprivileged women and their infants. Ignaz Semmelweis, a Hungarian physician serving in a “chief resident” capacity at the First Obstetrical Clinic of the Vienna General Hospital, worked at one of these maternity clinics in his off hours.
He found that the four percent mortality rate due to puerperal fever, a form of sepsis of the genital tract, of women in the poor clinic was considerably lower than the ten percent mortality rate at Vienna General Hospital. This discrepancy was so well known, that some women preferred to give birth in the street rather than be admitted to the latter, more established, hospital.
Dr. Semmelweis investigated the possible causes of these discrepant events, one by one, following the evidence wherever it lead. He eliminated differences in religious practices, overcrowding – because the clinic was far more overcrowded than the hospital -- and climate, as the two institutions were close to each other. The only difference he could find was that the hospital trained medical students, whereas the clinic trained midwives, only.
When his friend Jakob Kolletschka died in 1847 after being accidentally poked by a student’s scalpel during an autopsy, Semmelweis discovered a pathology in his friend similar to that of the women who were dying from puerperal fever.
Semmelweis proposed a connection between working with cadavers and then attending to childbirths, without washing in-between, and spent the remaining years of his life, canvasing for antiseptic medical procedures. The subsequent scorn he received from the medical establishment eventually landed him in an insane asylum and early death. Germ theory wouldn’t catch on until later that century, ushered in by the work of Louis Pasteur.
As physicist Maxwell Planck wrote in his autobiography, “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die.” In the end then, good science does triumph over the status quo, even if the status quo has to die off first. Still, scientists must be willing to “follow the evidence wherever it leads,” though it may lead to the occasional post-operational death, bruised ego, or ulcer in its wake.
By challenging the Church’s doctrine of a geocentric universe, Galileo spent the last years of his life under house arrest. From our vantage point 400 years after the fact, it is hard to reconcile the immutability of the Church’s dogma in the face of “the ultimate arbiter of truth,” observation and experimentation. Unfortunately, even to this day, scientific findings that challenge “a priori beliefs” are still criticized and ridiculed, even among other learned scientists. I offer up a few contemporary examples here.
Dr. Kilmer McCully, the founder of the homocysteine theory of arteriosclerosis, was ostracized from his own Harvard medical community because of his findings that cholesterol and clogged arteries were not the causes of heart disease, but rather the symptoms of it. Dr. McCully gave me permission to quote from his essay “Pioneer of the Homocysteine Theory”:
When the Atlantic Monthly article ‘Beyond Cholesterol’ was published in 1977, there was a flurry of attention paid to the striking conclusions of the article in the conventional media, especially the Boston Globe and Time Magazine, but also in the tabloid press, including The National Enquirer. When Robert Lees was questioned by a reporter from the Boston Globe about the article, he labeled the approach as ‘errant nonsense,’ and ‘a hoax perpetrated on the public ’.”
Dr. Barry Marshall, unable to convince the medical community of his research findings that ulcers were caused by the bacteria Helicobacter Pylori, and not stress, downed a petri dish full of the bacteria to prove it. In his Nobel Prize address, he recalls, “On the morning of the experiment, I omitted my breakfast but took 400 mg of cimetidine, believing that the infection might be easier if my stomach acid level was lowered,” he notes. “Two hours later, Neil Noakes scraped a heavily inoculated 4 day culture plate of Helicobacter and dispersed the bacteria in alkaline peptone water (a kind of meat broth used to keep bacteria alive). I fasted until 10 am when Neil handed me a 200 ml beaker about one quarter full of the cloudy brown liquid. I drank it down in one gulp.”
Thinking independently is risky behavior, and is rarely espoused in compulsory education. In fact, quite the opposite is true. Students who follow the rules, do what they’re told and perform well on tests are rewarded with good grades, glowing recommendations and prestigious college acceptances. These are my favorite students to teach. It may very well be, however, that the students who challenge the status quo, break the rules, and make regular visits to the principal’s office are the ones who will move the world. Does this mean that the good student will not or cannot move the world? No, not at all. It’s just that the latter are more risk-adverse. In fact, Adam Grant espouses in his book Originals that achievement motivation, the drive to succeed, interferes with original, independent thinking. While the drive to succeed is responsible for many of the world’s achievements, it often simultaneously crowds out original thinking. According to Grant and the research he cites, “The more you value achievement, the more you come to dread failure.” And failure is the necessary prerequisite to innovation.
Interestingly, the research suggests that birth order has much to predict about one’s willingness or unwillingness to take risks. First-borns are more likely to to follow the status quo, to be motivated by parental approval and school and professional achievement. Later-borns, on the other hand, tend to take greater risks, be more independent, fun-seeking and socially engaged. Later-borns are more likely to challenge a priori beliefs, while first-borns wait patiently for indisputable and time-tested evidence to sway them. Frank J. Sulloway, psychologist and preeminent UC Berkeley Researcher on birth order, describes how accepting the theory of evolution fell along birth order lines. Prior to Darwin’s findings, 56 out of 117 later-borns believed in evolution, compared to only 9 of 103 first-borns. Sixteen years after Darwin’s findings, the acceptance of the theory of evolution increased to 56 out of 103 later-borns, and actually dropped among first-borns. Apparently, the more accepted and established evolutionary theory became, the less favor it received among the more rebellious later-borns.
It would seem then, with all this talk of birth order, that Nobel prize-winning scientists are predominantly later-born. This however, is where their similarities to other original thinkers meet the proverbial fork in the road, and where we get a real sense of what makes for great scientists. Out of 118 Nobel Prize-winning scientists surveyed, 14 were only-borns while 47 were first-borns, the two categories comprising 57% of the recipients. Scientists, unlike thoroughly original thinkers, are bound by the evidence, to follow it wherever it leads. Their original ideas, their independent thoughts, come not from brief flashes of inspiration, but from flashes of insight born of painstaking and often tedious experimentation over many years, a preponderance of failures, and an undying passion to follow their curiosity. Yet when the evidence guides them unmistakably toward a conclusion, they’ll drink the Heliobacter “Kool-Aid” to prove it so.