Wednesday, May 30, 2012

Don’t worry so much about being the right type of science role model

Role models: How do they look? (Source)
[Today we have a wonderful guest post from Marie-Claire Shanahan, continuing the conversation about what makes someone a good role model in science. This post first appeared at Shanahan's science education blog, Boundary Vision, and she has graciously agreed to let us share it here, too. Shanahan is an Associate Professor of Science Education and Science Communication at the University of Alberta where she researches social aspects of science such as how and why students decide to pursue science degrees. She teaches courses in science teaching methods, scientific language and sociology of science. Marie-Claire is also a former middle and high school science and math teacher and was thrilled last week when one of her past sixth grade students emailed to ask for advice on becoming a science teacher. She blogs regularly about science education at Boundary Vision and about her love of science and music at The Finch & Pea.]

What does it mean to be a good role model? Am I a good role model? Playing around with kids at home or in the middle of a science classroom, adults often ask themselves these questions, especially when it come to girls and science. But despite having asked them many times myself, I don’t think they’re the right questions.


Studying how role models influence students shows a process that is much more complicated than it first seems. In some studies, when female students interact with more female professors and peers in science, their own self-concepts in science can be improved [1]. Others studies show that the number of female science teachers  at their school seems to have no effect [2].


Finding just the right type of role model is even more challenging. Do role models have to be female? Do they have to be of the same race as the students? There is often an assumption that even images and stories can change students’ minds about who can do science. If so, does it help to show very feminine women with interests in science like the science cheerleaders? The answer in most of these studies is, almost predictably, yes and no.


Diana Betz and Denise Sekaquaptewa’s recent study “My Fair Physicist: Feminine Math and Science role models demotivate young girls” seems to muddy the waters even further, suggesting that overly feminine role models might actually have a negative effect on students. [3] The study caught my eye when PhD student Sara Callori wrote about it and shared that it made her worry about her own efforts to be a good role model.


Betz and Sekaquaptewa worked with two groups of middle school girls. With the first group (144 girls, mostly 11 and 12 years old) they first asked the girls for their three favourite school subjects and categorized any who said science or math as STEM-identified (STEM: Science, Technology, Engineering and Math). All of the girls then read articles about three role models. Some were science/math role models and some were general role models (i.e., described as generally successful students). 


The researchers mixed things even further so that some of the role models were purposefully feminine (e.g., shown wearing pink and saying they were interested in fashion magazines) and others were supposedly neutral (e.g., shown wearing dark colours and glasses and enjoying reading).* There were feminine and neutral examples for both STEM and non-STEM role models. After the girls read the three articles, the researchers asked them about their future plans to study math and their current perceptions of their abilities and interest in math.**


For the  most part, the results were as expected. The STEM-identified girls showed more interest in studying math in the future (not really a surprise since they’d already said math and science were their favourite subjects) and the role models didn’t seem to have any effect. Their minds were, for the most part, already made up.


What about the non-STEM identified girls, did the role models help them? It’s hard to tell exactly because the researchers didn’t measure the girls’ desire to study math before reading about the role models.  It seems though that reading about feminine science role models took away from their desire to study math both in the present and the future. Those who were non-STEM identified and read about feminine STEM role models rated their interest significantly lower than other non-STEM identified girls who read about neutral STEM role models and about non-STEM role models. A little bit surprising was the additional finding that the feminine role models also seemed to lower STEM-identified girls current interest in math (though not their future interest).


The authors argue that the issue is unattainability. Other studies have shown that role models can sometimes be intimidating. They can actually turn students off if they seem too successful, such that their career or life paths seem out of reach, or if students can write them off as being much more talented or lucky than themselves. Betz and Sekaquaptewa suggest that the femininity of the role models made them seem doubly successful and therefore even more out of the students’ reach.

The second part of the study was designed to answer this question but is much weaker in design so it’s difficult to say what it adds to the discussion. They used a similar design but with only the STEM role models, feminine and non-feminine (and only 42 students, 20% of whom didn’t receive part of the questionnaire due to an error). The only difference was instead of asking about students interest in studying math they tried to look at the combination of femininity and math success by asking two questions:
  1. “How likely do you think it is that you could be both as successful in math/science AND as feminine or girly as these students by the end of high school?” (p. 5)
  2. “Do being good at math and being girly go together?” (p. 5)
Honestly, it’s at this point that the study loses me. The first question has serious validity issues (and nowhere in the study is the validity of the outcome measures established). First, there are different ways to interpret the question and for students to decide on a rating. A low rating could mean a student doesn’t think they’ll succeed in science even if they really want to. A low rating could also mean that a student has no interest in femininity and rejects the very idea of being successful at both. These are very different things and make the results almost impossible to interpret. 

Second these “successes” are likely different in kind. Succeeding in academics is time dependent and it makes sense to ask young students if they aspire to be successful in science. Feminine identity is less future oriented and more likely to be seen as a trait rather a skill that is developed. It probably doesn’t make sense to ask students if they aspire to be more feminine, especially when femininity has been defined as liking fashion magazines and wearing pink.
Question: Dear student, do you aspire to grow up to wear more pink? 
Answer (regardless of femininity): Um, that’s a weird question.
With these questions, they found that non-STEM identified girls rated themselves as unlikely to match the dual success of the feminine STEM role models. Because of the problems with the items though, it’s difficult to say what that means. The authors do raise an interesting question about unattainability, though, and I hope they’ll continue to look for ways to explore it further.

So, should graduate students like Sara Callori be worried? Like lots of researchers who care deeply about science, Sara expressed a commendable and strong desire to make a contribution to inspiring young women in physics (a field that continues to have a serious gender imbalance). She writes about her desire to encourage young students and be a good role model:
When I made the decision to go into graduate school for physics, however, my outlook changed. I wanted to be someone who bucked the stereotype: a fashionable, fun, young woman who also is a successful physicist. I thought that if I didn’t look like the stereotypical physicist, I could be someone that was a role model to younger students by demonstrating an alternative to the stereotype of who can be a scientist. …This study also unsettled me on a personal level. I’ve long desired to be a role model to younger students. I enjoy sharing the excitement of physics, especially with those who might be turned away from the subject because of stereotypes or negative perceptions. I always thought that by being outgoing, fun, and yes, feminine would enable me to reach students who see physics as the domain of old white men. These results have me questioning myself, which can only hurt my outreach efforts by making me more self conscious about them. They make me wonder if I have to be disingenuous about who I am in order to avoid being seen as “too feminine” for physics.
To everyone who has felt this way, my strong answer is: NO, please don’t let this dissuade you from outreach efforts. Despite results like this, when studies look at the impact of role models in comparison to other influences, relationships always win over symbols. The role models that make a difference are not the people that kids read about in magazines or that visit their classes for a short period of time. The role models, really mentors, that matter are people in students’ lives: teachers, parents, peers, neighbours, camp leaders, and class volunteers. And for the most part it doesn’t depend on their gender or even their educational success. What matters is how they interact with and support the students. 
Good role models are there for students, they believe in their abilities and help them explore their own interests.

My advice? Don’t worry about how feminine or masculine you are or if you have the right characteristics to be a role model, just get out there and get to know the kids you want to encourage. Think about what you can do to build their self-confidence in science or to help them find a topic they are passionate about. When it comes to making the most of the interactions you have with science students, there are a few tips for success (and none of them hinge on wearing or not wearing pink):

§   Be supportive and encouraging of students’ interest in science. Take their ideas and aspirations seriously and let them know that you believe in them. This turns out to be by far one of the most powerful influences in people pursuing science. If you do one thing in your interactions with students, make it this.
§  Share with students why you love doing science. What are the benefits of being a scientist such as contributing to improving people’s lives or in solving difficult problems? Students often desire careers that meet these characteristics of personal satisfaction but don’t always realize that being a scientist can be like that.
§  Don’t hide the fact that there are gender differences in participation in some areas of science (especially physics and engineering). Talk honestly with students about it, being sure to emphasize that differences in ability are NOT the reason for the discrepancies. Talk, for example, about evidence that girls are not given as many opportunities to explore and play with mechanical objects and ask them for their ideas about why some people choose these sciences and others don’t.
There are so many ways to encourage and support students in science, don’t waste time worrying about being the perfect role model. If you’re genuinely interested in taking time to connect with students, you are already the right type.
__________________________________________________________
* There are of course immediate questions about how well supported these are as feminine characteristics but I’m willing to allow the researchers that they could probably only choose a few characteristics and had to try to find things that would seem immediately feminine to 11-12 year olds. I still think it’s a shallow treatment of femininity, one that disregards differences in cultural and class definitions of femininity. (And I may or may not still be trying to sort out my feelings about being their gender neutral stereotype, says she wearing grey with large frame glasses and a stack of books beside her).
**The researchers unfortunately did not distinguish between science and math, using them interchangeably despite large differences in gender representation and connections to femininity between biological sciences, physical sciences, math and various branches of engineering.
[1] Stout, J. G., Dasgupta, N., Hunsinger, M., & McManus, M. A. (2011). STEMing the tide: Using ingroup experts to inoculate women’s self-concept in science, technology, engineering, and mathematics (STEM).Journal of Personality and Social Psychology, 100, 255-270.
[2] Gilmartin, S., Denson, N., Li, E., Bryant, A., & Aschbacher, P. (2007). Gender ratios in high school science departments: The effect of percent female faculty on multiple dimensions of students’ science identities.Journal of Research in Science Teaching, 44, 980–1009.
[3] Betz, D., & Sekaquaptewa, D. (2012). My Fair Physicist? Feminine Math and Science Role Models Demotivate Young Girls Social Psychological and Personality Science DOI: 10.1177/1948550612440735

Further Reading
Buck, G. A., Leslie-Pelecky, D., & Kirby, S. K. (2002). Bringing female scientists into the elementary classroom: Confronting the strength of elementary students’ stereotypical images of scientists. Journal of Elementary Science Education, 14(2), 1-9.
Buck, G. A., Plano Clark, V. L., Leslie-Pelecky, D., Lu, Y., & Cerda-Lizarraga, P. (2008). Examining the cognitive processes used by adolescent girls and women scientists in identifying science role models: A feminist approach. Science Education, 92, 2–20.
Cleaves, A. (2005). The formation of science choices in secondary school.International Journal of Science Education, 27, 471–486.
Ratelle, C.F., Larose, S., Guay, F., & Senecal, C. (2005). Perceptions of parental involvement and support as predictors of college students’ persistence in a science curriculum. Journal of Family Psychology, 19, 286–293.
Simpkins, S. D., Davis-Kean, P. E., & Eccles, J. S. (2006). Math and science motivation: A longitudinal examination of the links between choices and beliefs. Developmental Psychology, 42, 70–83.
Stout, J. G., Dasgupta, N., Hunsinger, M., & McManus, M. (2011). STEMing the tide: Using ingroup experts to inoculate women’s self-concept and professional goals in science, technology, engineering, and mathematics (STEM). Journal of Personality and Social Psychology, 100,255–270.

Monday, May 28, 2012

How to find science near you


(Source)


By DXS Chemistry Editor Adrienne Roehrich

For scientists, finding science going on nearby seems to not be an issue. If they don’t wish to spend time in their own lab, they can generally walk down the hall to speak to a colleague. But to those who don’t know scientists in their daily lives (or don’t think they know scientists), finding a place to discuss your interests in science can be a daunting task.

Where can you find like-minded people to discuss science? There are a number of local groups in any location that may help you satisfy your science craving.

The big one, Science Online, is an annual meeting in North Carolina of scientists, science educators, science communicators, and science enthusiasts. The next meeting (in 2013 as of the writing of this post) has a planning wiki up, and a Twitter account. Science Online has spawned several local science online groups. According to the Science Online Now site, NYC, Seattle, Vancouver, and the Bay Area are having regular meetings, and tweet-ups occur in NYC, DC, and NC Tri-Cities area. There are also two conferences, one for teens in NC, and one in London.

Another way to get your science fill is to attend a “science café.” Science cafés are live events, usually hosting scientists to speak in a pub, coffee, shop, or other gathering spot, to discuss nifty science. These are not just oral presentations, they are also discussions. There’s not a state in the union without one of these events, although many occur in the more highly populated areas.

Meetup.com may be a place to see if there is a science group meeting near you. However, you must have a meetup account to view these possibilities, and a search for “science” may get you a lot of woo, too.

Maybe you aren’t looking for a discussion, but a place to do some hands-on science. Science Centers exist all over the world. Some are geared for children, but some include adults (and I enjoy playing with the kids science activities as an adult.) A listing as of 1999 exists here. However, googling “science centers” and your location (or a location you are visiting) will hopefully provide a more up-to-date result. Please comment if you know if another way for someone to find science near them.

Friday, May 25, 2012

Happy belated birthday, Mary Anning!


Mary Anning and a small, non-fossilized dog. (Source)

[Today, we're featuring a post by Mike Rendell, author and keeper of Georgian Gentleman, a blog chronicling aspects of 18th century life. Mike spent 30 years as a lawyer--poor fellow--before he retired to time travel in his mind back to the 18th century, where he has set up mental shop permanently. By what he calls a "curious stroke of luck," he has all of the 18th century papers of his great-great-great-great (that's four) grandfather, including diaries, accounts, letters, and even shopping lists. In 2011, he published the story of this ancestor's life as a social history, "The Life of a Georgian Gentleman,' and thus, a blog was also born. We thank Mike for having graciously given us permission to publish his post here because we are huge fans of Mary Anning, who, as was typical, did not receive recognition from or entree into male scientific society of her day. We have added in a few explanatory links, too.]
Today the spotlight is turned not on a well-educated man, or a wealthy daughter with aristocratic connections, but on a girl who was amongst the poorest of the poor; who in many ways led a miserably hard and short life; who could barely read and write, and yet was someone who amazed the scientific world in the first half of the nineteenth century.
Her name was Mary Anning, born in Lyme Regis in Dorset on 21st May 1799. She cannot be said to have had an auspicious start in life. She was one of ten children – but eight died in childhood. An elder sister had already been called Mary but she had perished in a fire when her clothes were ignited from some burning wood shavings. Our heroine was born five months after this tragic death, and was named Mary in memory of her dead sibling.
Mary had luck, of a sort, on her side. When she was eighteen months old she was being held in the arms of a neighbour called Elizabeth Haskings who was in a group of women watching a travelling show. A storm sprang up and the group took shelter beneath an elm tree, but a bolt of lightning struck the tree, killing three of the women including Elizabeth. Yet Mary was apparently unscathed. Fate had something quite remarkable in store for the young girl…
Mary’s parents were Dissenters, meaning that education opportunities were limited and the family were subject to legal discrimination. A member of the Congregationalist Church, she attended Sunday School and here learned the rudiments of reading and writing. The Congregational Church, unlike the Anglican Church, attached great importance to education, particularly for young girls, and she was encouraged in her development by the pastor Revd James Wheaton. Her prized possession was apparently a copy of theDissenters’ Theological Magazine and Review in which the good Reverend had apparently written two articles; one reiterated the importance of understanding that the world was created by God in seven days, and the other, somewhat curiously, suggested that a study of the new science of geology was to be encouraged.
Father was a carpenter and cabinet maker and business was tough. Even worse, her father died when Mary was eleven, leaving the family without any apparent means of support.
After the father’s death the destitute family eked a living finding fossils along what is now termed the Jurassic coast in Dorset. In 1811 Mary’s elder brother Joseph found a fossilized skull of what was thought to be a crocodile protruding from the crumbling cliffs of Blue Lias. Mary was given the task of slowly exposing the ancient creature, uncovering not just the skull but 60 vertebrae. It was difficult work, scrambling to reach the exposed rock face, at risk from the tides and rock falls, but the young girl showed an aptitude for the work. Besides, there were rewards: the skeleton was bought by the local Lord of the Manor called Henry Hoste Henley for £23. He in turn sold it to a private collector called William Bullock, and he exhibited it in London with the rest of his fossil collection in his Museum of Natural Curiosities. In 1819 it was bought as a ‘crocodile in a fossil state’ by the British Museum, for £45. The creature was eventually called Ichthyosaurus (‘fish lizard’) by the scientists Henry de la Beche and William Conybeare. It was the first specimen of Ichthyosaurus ever recorded, and both men went on to make their name on the back of Mary’s efforts.
The find was to change Mary’s life and, in time, her studies of anatomy, geology, paleontology and scientific illustration were to propel her to considerable fame (but never fortune). The world of scientific discovery was not just dominated by men, it was dominated by Anglicans, people of good education and usually privilege. An ill-educated, impecunious, girl from her background was never going to find acceptance easy.
She did however have supporters. Her big break came in 1820. Lieutenant-Colonel Thomas James Birch had previously got to know Mary and her brother Joseph and had bought a number of items from them. He decided to auction off some of these specimens and the sale generated huge interest from all over the country and indeed throughout Europe. The specimens were sold for £400, a huge sum at the time, and the generous Lieutenant-Colonel handed the entire proceeds over to Mary.
In time she became the focus of attention – not just collectors and scientists would visit her tiny beach-front shop, but also socialites keen to see and speak with this witty, knowledgeable but poorly-educated woman.
Throughout the 1820’s and 30’s she hammered away, discovering the long-necked plesiosaurus or sea dragon in 1823, a ‘flying dragon’ i.e. the pterodactyl (in 1828) and hundreds, upon hundreds of other fossils. Squaloraia a cross between a shark and a ray, was discovered in 1829. In the winter of 1830, she found a new, large-headed Plesiosaurus, and sold it for £210. She became an expert on the delightful subject of bezoar stones (now known as coprolites, that is to say, fossilised faeces!). She also proved that belemnite fossils contained fossilised ink sacs, by grinding up the fossilised remains and mixing them with water to produce an inky substance similar to sepia ink in squids. Her brother Joseph demonstrated this with his drawing of one of Mary´s fossils, shown here.
She helped show the astonished world what marine life looked like in the Jurassic period, some 140 to 200 million years ago, before mammals ruled the earth. Scientists such as Henry de la Beche helped her financially when he handed to her the proceeds of sale from his engraving entitled Duria Antiquior, a more ancient Dorset – a scene of prehistoric life based upon fossils which she had found and identified.
Not everyone accepted her without question: the French anatomist Georges Cuvier dismissed one of her finds as a fake, but Mary was able to refute the allegation of forgery and, in fairness, Cuvier acknowledged his error and became a fan of hers. For some, they simply couldn’t bring themselves to give credit to the achievements of a mere woman – and a poorly educated one at that. Even her own gender seemed amazed at her skill and knowledge, as in this diary entry, made in 1824, by Lady Harriet Silvester, after visiting Mary Anning:
“. . . the extraordinary thing in this young woman is that she has made herself so thoroughly acquainted with the science that the moment she finds any bones she knows to what tribe they belong. She fixes the bones on a frame with cement and then makes drawings and has them engraved. . . It is certainly a wonderful instance of divine favour – that this poor, ignorant girl should be so blessed, for by reading and application she has arrived to that degree of knowledge as to be in the habit of writing and talking with professors and other clever men on the subject, and they all acknowledge that she understands more of the science than anyone else in this kingdom.”
Ah, so that was it: Divine favour, not skill and hard work ….
For years she carried on chipping away at rocks with her hammer, accompanied by her faithful dog Troy, who always appears beside her in paintings of the day. Eventually in 1833 Troy was killed in a rock-fall when the tide undermined the ledge he was standing on, but Mary was unharmed. She was however distraught at the loss of her constant companion. She knew only too well the irony that it was the really high tides in winter which revealed the fossil deposits, just as it was the same tides which made the rock face unstable and liable to collapse.
Hers was not to be a long and happy life. She died of breast cancer at the age of 47 on 9th March 1847. In her lifetime success and recognition evaded her. She had been barred from admission to the Geological Society on account of her gender (women were not admitted to their ranks until 1904). At one stage she wrote “The world has used me so unkindly, I fear it has made me suspicious of everyone” and only one journal ever published anything from her – and that a letter to the editor, not an article. And one, only one, other geologist named a specimen after her in her lifetime, when the Swiss-American naturalist Louis Agassiz named two fossil fish after her, Acrodus anningiae and Belenstomus anningiae.
The gravestone marking where Mary & her brother are buried.
In fairness to the Geographical Society they did help her financially through her final illness. She was buried in St Michael’s Church in Lyme Regis.
The Mary Anning window
Recognition came after her death: three years later the Geographical Society paid for a stained glass window at the church in her honour. The inscription reads “This window is sacred to the memory of Mary Anning of this parish, who died 9 March AD 1847 and is erected by the vicar and some members of the Geological Society of London in commemoration of her usefulness in furthering the science of geology, as also of her benevolence of heart and integrity of life.”
Finally, more than a hundred and fifty years after she died, the Royal Society included her in their 2010 list of the ten British women who have most influenced the history of science. Some might say: better late than never.
Many happy returns of the day, Mary!
Post script: I particularly enjoyed doing this post because my ancestor Richard Hall was an avid fossil collector. I still have some of the items he collected along with his booklet of fossil drawings. I especially liked the way that he believed that the ammonites were actually long worms, curled up in death, with their mouths in the centre of the spiral, turned to stone. More details appear in The Journal of a Georgian Gentleman.
                    

Wednesday, May 23, 2012

Excerpts from Sophie's Diary: A Mathematical Novel

Today we enjoy a bit of math, as told in Sophie’s Diary: A Mathematical Novel. Written by Dr. Dora Musilek, this novel was inspired by the French mathematician Sophie Germain, an important contributor to number theory and mathematical physics. Her correspondence with some of history’s great mathematicians such as Lagrange, Legendre, and Gauss are known while her life prior to that is shrouded in the unknown. Dr. Musilek explored Germain’s early life and uses the concept of an adolescent’s diary to discuss how Germain may have taught herself math while dealing with the social upheaval of the French Revolution, which occurred at this time in her life. Read on for an engaging lesson in math.

Monday | January 2, 1792

I begin the new year with more determination and a renewed resolve to study prime numbers. One of my goals is to acquire the necessary mathematical background to prove theorems.

Prime numbers are exquisite. They are whole pure numbers, and I can manipulate them in myriad ways, as pieces on the chessboard. Not all moves are correct but the right ones make you win. Take, for example, the process to uncover primes from whole numbers. Starting with the realization that any whole number n belongs to one of four different categories:
The number is an exact multiple of 4 : n = 4k
The number is one more than a multiple of 4 : n = 4k + 1
The number is two more than a multiple of 4 : n = 4k + 2
The number is three more than a multiple of 4 : n = 4k + 3

It is easy to verify that the first and third categories yield only even numbers greater than 4. For example for any number such as k = 3, 5, 6, and 7, I write: n = 4(3) = 12, and n = 4(6) = 24; or n = 4(5) + 2 = 22, and n = 4(7) + 2 = 30. The resulting numbers clearly are not primes. Thus, I can categorically say that prime numbers cannot be written as n = 4k, or n = 4k + 2. That leaves the other two categories.

So, a prime number greater than 2 can be written as either n = 4k + 1, or n = 4k + 3. For example, for k = 1 it yields n = 4(1) + 1 = 5, and n = 4(1) + 3 = 7, both are indeed primes. Does this apply for any k? Can I find primes by using this relation? Take another value such as k = 11, so n = 4(11) + 1 = 45, and n = 4(11) + 3 = 47. Are 45 and 47 prime numbers? Well, I know 47 is a prime number, but 45 is not because it is a whole number that can be written as the product of 9 and 5. So, the relation n = 4k + 1 will not produce prime numbers all the time.


Over a hundred years ago Pierre de Fermat concluded that “odd numbers of the form n = 4k + 3 cannot be written as a sum of two perfect squares.” He asserted simply that n = 4+ 3 a2 + b2. For example, for k = 6, n = 4(6) + 3 = 27, and clearly 27 cannot be written as the sum of two perfect squares. I can verify this with any other value of k. But that would not be necessary.

And now we skip ahead to another excerpt where differential calculus is described.

Wednesday | February 27, 1793

I feel strong enough to resume my studies. My mind is clear again to meet the challenges of a new topic that at first seemed insurmountable. I resumed my studies of differential calculus.

There is something magical about Infiniment petits. I went back to the basic definition: “a derivative of a function represents an infinitesimal change in the function with respect to whatever parameters it may have.” The simple derivative of a function f with respect to x is denoted by f’(x), which is the same as df/dx. Newton used fluxions notation dz/dt = ż, but it means the same, so I will use f’ or df/dx from now on. Well, I can now take the derivative of certain classes of functions because I just follow certain rules.

If my function is of the type xn, I use the fact that d/dx(xn) = nxn−1. So, if I have f(x) = x5, its derivative should be 5x4. This is easy. If I analyze trigonometric functions such as sin x and cos x, then I use the derivatives d/dx(sinx) = cos x, and d/dx(cosx) = − sin x.

Taking derivatives is so easy! I could spend hours deriving more complicated functions. However, I wish to learn also how to see the world through mathematics. I must find the connection between differential equations and physics. I am eager to explore this applied aspect of mathematics.

Let’s start with a differential equation, an equation involving an unknown function and its derivatives. It can be relatively easy such as
or a bit more complicated such as the linear differential equation:
or even a nonlinear equation such as this: 

A differential equation is linear if the unknown function and its derivatives appear to the power 1 (products of these are not allowed) and nonlinear otherwise. The variables and their derivatives must always appear as a simple first power. Nonlinear equations are difficult to solve and some are impossible.

First I need to master linear equations. Some mathematicians use the notation y’ for the dy/dx derivative, or y’’ for d2y/dx2, and so forth. Thus, the previous linear equation would be written as (x2 + 1)y’ + 3xy = 6x. I need to keep these differences of notation in mind, since I am studying from five different books.

I studied the properties of differential equations and learned to solve them. Now, I must learn how to apply differential equations. But how do I translate a physical phenomenon into a set of equations to describe it? It is impossible to depict nature in its totality, so one usually strives for a set of equations that describes the physical system approximately and adequately.

Say that I want to predict the growth of population in Paris. To do it, I can use an exponential model, that is, an equation that represents the rate of change of the population that is proportional to the existing population. If P(t) represents the population change in time (t), I write
where the rate k is constant. I observe that if k > 0, the equation describes growth, and if k < 0, it models decay. The exponential equation is linear with a solution P(t) = P0ekt, where P0 is the initial population, i.e., P(t = 0) = P0.

Mathematically, if k > 0, then the population grows and continues to expand to infinity. On the other hand, if k < 0, then the population will shrink and tend to 0. Clearly, the first case, k > 0, is not realistic. Population growth is eventually limited by some factor, like war or disease. When a population is far from its limits of expansion, it can grow exponentially. However, when nearing its limits, the population size can fluctuate. Well, I think that the equation I use to predict the rate of change of population can be modified to include these factors to obtain a result closer to reality.

Aristotle thought that nature could not be expected to follow precise mathematical rules. But Galileo argued against this point of view. He envisioned the experimental mathematical analysis of nature to be used to understand it. Newton was inspired by Galileo and later developed the laws of motion and universal gravitation. Newton, Leibniz, Euler, and other great people then created the mathematics that help us converse with the universe.

Oh, how glorious it is to speak such a language and understand the whispers from the heavens and the world around me.

Dr. Dora Musilek is a research scientist and also lectures on the role and contributions of women scientists and mathematicians. She holds a Ph.D. in aerospace engineering. You can learn more about Dr. Musilek and her novel at sophiesdiary.net You can learn more about Dr. Musilek’s writing process at MAAA Books Blog.

These views are the opinion of the author and do not necessarily either reflect or disagree with those of the DXS editorial team. 

Friday, May 18, 2012

We gotta watch out for feminine role models wearing pink


Beware blonde, feminine role models wearing pink.
(Source)

Today's guest post comes to us courtesy of Sara Callori. She is a physics Ph.D. candidate at Stony Brook University in Long Island, NY. In the lab, Sara loves working with x-rays and even has a Bragg diffraction tattoo. She would eventually like to focus on science teaching and outreach because she loves to get people to stop being intimidated when they think of physics.

This may sound odd, but I never aspired to be feminine until I became a physicist. I grew up playing sports and getting short haircuts. There were phases when my mother would have had to tranquilize me to get me into a dress (this was infrequent as my tom-boy qualities seemed to come from her own lack of femininity). As I got older, I started to develop some style, but it was more comfort over fashion, especially when it came down to 8 am classes in undergrad. When I made the decision to go into graduate school for physics, however, my outlook changed. I wanted to be someone who bucked the stereotype: a fashionable, fun, young woman who also is a successful physicist. I thought that if I didn’t look like the stereotypical physicist, I could be someone that was a role model to younger students by demonstrating an alternative to the stereotype of who can be a scientist.

This week researchers at the University of Michigan released findings that dashed my hopes for being the cool physicist that younger girls want to emulate. In a paper titled “My Fair Physicist? Feminine Math and Science Role Models Demotivate Young Girls”, psychology researchers Diana Betz and Denise Sekaquaptewa found that women presented as both successful in science/technology/engineering/math (STEM) careers and possessing “feminine traits” negatively affected how young girls viewed science and math.

When I read the summary of these findings, I was dismayed. I became even more disappointed when I read that for feminine traits they used “wearing make-up and pink clothes, liking fashion magazines”. Gender-neutral women were given traits such as “wearing dark-colored clothes and glasses, likes reading”.

The assignment of these traits bothered me on several levels. The most immediate was how narrow the study’s concept of “feminine” seemed. If you asked me if I considered myself feminine, I would say yes. I like colorful dresses during the summer and own too many purses -- but I also wear glasses, play rugby, and have tattoos. Most real-life women, including women in STEM, also possess traits from a mix of “feminine” and “gender-neutral” categories. It is important to remember these are the women younger students will encounter when they are introduced to female scientists.  

Additionally, the researchers’ idea of “feminine” seems to play into another set of negative stereotypes common in popular culture, what you might call the “Legally Blonde” scenario. In the movie, the protagonist is a woman who could easily be described as “wearing make-up and pink clothes, liking fashion magazines”. The story builds around how someone with those traits is perceived as unintelligent and unsuited for work that requires a strong academic background. While throughout the story, the main character shows she isn’t just a pretty face, there are still many people who will associate these types of feminine traits with unintelligence. 

This association is at odds with women in STEM fields and it makes me wonder if some of the girls’ negative associations of feminine STEM professionals were due to those traits being perceived as incompatible with women in STEM careers. (To briefly address the finding which showed that femininity could be compatible with overall school success, the “success” descriptions seem to be generic enough that they could be interpreted as encompassing non-academic accomplishments as well; e.g. being well liked by classmates or elected to the student council.)

This study also unsettled me on a personal level. I’ve long desired to be a role model to younger students. I enjoy sharing the excitement of physics, especially with those who might be turned away from the subject because of stereotypes or negative perceptions. I always thought that by being outgoing, fun, and yes, feminine would enable me to reach students who see physics as the domain of old white men. These results have me questioning myself, which can only hurt my outreach efforts by making me more self conscious about them. They make me wonder if I have to be disingenuous about who I am in order to avoid being seen as “too feminine” for physics.

Overall, that this study could be useful as a springboard for improving discussion and ideas for motivating girls in STEM. However, I think that their idea of “feminine” is too narrow to apply these findings broadly. Rather than work in the black and white “feminine” vs. “gender neutral” cases, why not build further ideas, research, and programs around much more realistic types of women who are currently succeeding in many STEM fields.

These views are the opinion of the author and do not necessarily either reflect or disagree with those of the
DXS editorial team. 


Tuesday, May 15, 2012

Motherhood, war, and attachment: what does it all mean?



The antebellum tales
Scene 1: Two fathers encounter each other at a Boy Scout meeting. After a little conversation, one reveals that his son won’t be playing football because of concerns about head injuries. The other father reveals that he and his son love football, that they spoke with their pediatrician about it, and that their son will continue with football at least into middle school. There’s a bit of wary nodding, and then, back to the Pinewood Derby.

Scene 2: Two mothers meet on a playground. After a little conversation about their toddlers, one mother mentions that she still breastfeeds and practices “attachment parenting,” which is why she has a sling sitting next to her. The other mother mentions that she practiced “cry it out” with her children but that they seem to be doing well and are good sleepers. Then one of the toddlers begins to cry, obviously hurt in some way, and both mothers rush over together to offer assistance.

Scene 3: In the evening, one of these parents might say to a partner, “Can you believe that they’re going to let him play football?” or “I can’t believe they’re still breastfeeding when she’s three!” Sure. They might “judge” or think that’s something that they, as parents, would never do.

But which ones are actually involved in a war?

War. What is it good for?
I can’t answer that question, but I can tell you the definition of ‘war’: “a state of armed conflict between different nations or states or different groups within a nation or state.” Based on this definition and persistent headlines about “Mommy Wars,” you might conclude that a visit to your local playground or a mom’s group outing might require decking yourself out cap-á-pie in Kevlar. But the reality on the ground is different. There is no war. Calling disputes and criticisms and judgments about how other people live “war” is like calling a rowboat on a pond the Titanic. One involves lots of energy release just to navigate relatively placid waters while the other involved a tremendous loss of life in a rough and frigid sea. Big difference.

I’m sure many mothers can attest to the following: You have friends who also are mothers. I bet that for most of us, those friends represent a spectrum of attitudes about parenting, education, religion, Fifty Shades of Grey, recycling, diet, discipline, Oprah, and more. They also probably don’t all dress just like you, talk just like you, have the same level of education as you, same employment, same ambitions, same hair, or same toothpaste. And I bet that for many of us, in our interactions with our friends, we have found ourselves judging everything from why she insists on wearing those shoes to why she lets little Timmy eat Pop Tarts. Yet, despite all of this mental observation and, yes, judging, we still manage to get along, go out to dinner together, meet at one another’s homes, and gab our heads off during play dates.

That’s not a war. That’s life. It’s using our brains as shaped by our cultural understanding and education and rejection or acceptance of things from our own upbringing and talks with medical practitioners and books we’ve read and television shows we’ve watched and, for some of us, Oprah. Not one single friend I have is a cookie cutter representation of me or how I parent. Yet, we are not at war. We are friends. Just because people go online and lay out in black and white the critiques that are in their heads doesn’t mean “war” is afoot. It means expressing the natural human instinct to criticize others in a way that we think argues for Our Way of Doing Things. Online fighting is keeping up with the virtual Joneses. In real life, we are friends with the Joneses, and everyone tacitly understands what’s off limits within the boundaries of that friendship. That’s not war. It’s friendly détente.

The reality doesn’t stop the news media from trying to foment wars, rebellions, and full-on revolutions with provocative online “debates” and, lately, magazine covers. The most recent, from Time, features a slender mother, hand on cocked hip, challenging you with her eyes as she nurses her almost-four-year-old son while he stands on a chair. As Time likely intended, the cover caused an uproar. We’ve lampooned it ourselves (see above).

But the question the cover asks in all caps, “Are you mom enough?” is even more manipulative than the cover because it strikes at the heart of all those unspoken criticisms we think--we know--other women have in their heads about our parenting. What we may not consider is that we, too, are doing the same, and still… we are not actually at war. We’re just women, judging ourselves and other women, just like we’ve done since the dawn of time. It’s called “using your brain.” Inflating our interactions and fairly easily achieved parental philosophy détentes to “war” caricatures us all as shrieking harpies, incapable of backing off and being reasonable.

The real question to ask isn’t “Are you mom enough?” In fact, it’s an empty question because there is no answer. Your parenting may be the most perfect replica of motherhood since the Madonna (the first one), yet you have no idea how that will manifest down the road in terms of who your child is or what your child does. Whether you’re a Grizzly or a Tiger or a Kangaroo or a Panda mother, there is no “enough.”

So, instead of asking you “Are you mom enough?”, in keeping with our goal of bringing women evidence-based science, we’ve looked at some of the research describing what might make a successful parent–child relationship. Yes, the answer is about attachment, but not necessarily of the physical kind. So drop your guilt. Read this when you have time. Meanwhile, do your best to connect with your child, understand your child, and respond appropriately to your child.  

Why? Because that is what attachment is--the basic biological response to a child's needs. If you’re not a nomad or someone constantly on the move, research suggests that the whole “physically attached to me” thing isn’t really a necessary manifestation of attachment. If you harken to it and your child enjoys it (mine did not) and it works for you without seeming like, well, an albatross around your neck, go for it.

What is attachment?
While attachment as a biological norm among primates has been around as long as primates themselves, humans are more complicated than most primates. We have theories. Attachment theory arose from the observations of a couple of human behaviorists or psychologists (depending on whom you ask), John Bowlby and Mary Ainsworth. Bowlby derived the concept of attachment theory, in which an infant homes in on an attachment figure as a “safe place.” The attachment figure, usually a parent, is the person who responds and is sensitive to the infant’s needs and social overtures. That parent is typically the mother, and disruption of this relationship can have, as most of us probably instinctively know, negative effects.

Bowlby’s early approach involved the mother’s having an understanding of the formational experiences of her own childhood and then translating that to an understanding of her child. He even found that when he talked with parents about their own childhoods in front of their children, the result would be clinical breakthroughs for his patients. As he wrote,
Having once been helped to recognize and recapture the feelings which she herself had as a child and to find that they are accepted tolerantly and understandingly, a mother will become increasingly sympathetic and tolerant toward the same things in her child.
Later studies seem to bear out this observation of a connection to one's childhood experiences and more connected parenting. For example, mothers who are “insightful” about their children, who seek to understand the motivations of their children’s behavior, positively influence both their own sensitivity and the security of their infant’s attachment to them.  

While Bowlby’s research focused initially on the effects of absolute separation between mother and child, Mary Ainsworth, an eventual colleague of Bowlby, took these ideas of the need for maternal input a step further. Her work suggested to her that young children live in a world of dual and competing urges: to feel safe and to be independent. An attachment figure, a safe person, is for children an anchor that keeps them from become unmoored even as they explore the unknown waters of life. Without that security backing them up, a child can feel always unmoored and directionless, with no one to trust for security.

Although he was considered an anti-Freudian rebel, Bowlby had a penchant for Freudian language like “superego” and referred to the mother as the “psychic organizer.” Yet his conclusions about the mother–child bond resonate with their plain language:
The infant and young child should experience a warm, intimate, and continuous relationship with his mother (or permanent mother substitute) in which both find satisfaction and enjoyment.
You know, normal biological stuff. As a side note, he was intrigued by the fact that social bonds between mother and offspring in some species weren’t necessarily tied to feeding, an observation worth keeping in mind if you have concerns about not being able to breastfeed.

The big shift here in talking about the mother–child relationship was that Bowlby was proposing that this connection wasn’t some Freudian libidinous communion between mother and child but instead a healthy foundation of a trust relationship that could healthily continue into the child's adulthood.

Ainsworth carried these ideas to specifics, noting in the course of her observations of various groups how valuable a mother’s sensitivity to her child’s behaviors were in establishing attachment. In her most famous study, the “Baltimore study” [PDF], she monitored 26 families with new babies. She found that “maternal responsiveness” in the context of crying, feeding, playing, and reciprocating seemed to have a powerful influence on how much a baby cried in later months, although some later studies dispute specific influences on crying frequencies.

Ainsworth also introduced the “Strange Situation” lab test, which seems to have freaked people out when it first entered the research scene. In this test, over the course of 20 minutes, a one-year-old baby is in a room full toys, first with its mother, then with mother and a strange woman, then with the stranger only (briefly), then with the mother, and then alone before the stranger and then the mother return. The most interesting findings of the study came from when the mother returned after her first absence, having left the baby alone in the room with a stranger. Some babies seemed quite angry, wanting to be with their mothers but expressing unhappiness with her at the same time and physically rejecting her.

From her observations during the Strange Situation, Ainsworth identified three types of attachment. The first was “Secure,” which, as its name implies, suggested an infant secure and comfortable with an attachment figure, a person with whom the infant actively seeks to interact. Then there’s the insecure–avoidant attachment type, in which an infant clearly is not interested in being near or interacting with the attachment figure. Most complex seems to be the insecure–resistant type, and the ambivalence of the term reflects the disconnected behavior the infant shows, seeming to want to be near the attachment figure but also resisting, as some of the unhappy infants described above behaved in the Strange Situation.

Within these types are now embedded various subtypes, including a disorganized–disoriented type in which the infant shows “odd” and chaotic behavior that seems to have no distinct pattern related to the attachment figure.

As you read this, you may be wondering, “What kind of attachment do my child and I have?” If you’re sciencey, you may fleetingly even have pondered conducting your own Strange Situation en famille to see what your child does. I understand the impulse. But let’s read on.

What are the benefits of attachment?
Mothers who are sensitive to their children’s cues and respond in ways that are mutually satisfactory to both parties may be doing their children a lifetime of favors, in addition to the parental benefit of a possibly less-likely-to-cry child. For example, a study of almost 1300 families looked at levels of cortisol, the “stress” hormone, in six-month-old infants and its association with maternal sensitivity to cues and found lower levels in infants who had “more sensitive” mothers.

Our understanding of attachment and its importance to infant development can help in other contexts. We can apply this understanding to, for example, help adolescent mothers establish the “secure” level of attachment with their infants. It’s also possibly useful in helping women who are battling substance abuse to still establish a secure attachment with their children.

On a more individual level, it might help in other ways. For example, if you want your child to show less resistance during “clean-up” activities, establishing “secure attachment” may be your ticket to a better-looking playroom.

More seriously, another study has found that even the way a mother applies sensitivity can be relevant. Using the beautiful-if-technical term ‘dyads’ to refer to the mother–child pair, this study included maternal reports of infant temperament and observations of maternal sensitivity to both infant distress and “non-distress.” Further, the authors assessed the children behaviorally at ages 24 and 36 months for social competence, behavioral problems, and typicality of emotional expression. They found that a mother’s sensitivity to an infant’s distress behaviors was linked to fewer behavioral problems and greater social competence in toddlerhood. Even more intriguing, the child’s temperament played a role: for “temperamentally reactive” infants, a mother’s sensitivity to distress was linked to less dysregulation of the child’s emotional expression in toddlerhood. 

And that takes me to the child, the partner in the “dyad”
You’re not the only person involved in attachment. As these studies frequently note, you are involved in a “dyad.” The other member of that dyad is the child. As much as we’d like to think that we can lock down various aspects of temperament or expression simply by forcing it with our totally excellent attachment skills, the child in your dyad is a person, too, who arrived with a bit of baggage of her own.

And like the study described above, the child’s temperament is a key player in the outcome of the attachment tango. Another study noted that multiple factors influence “attachment quality.” Yes, maternal sensitivity is one, but a child’s native coping behaviors and temperament also seem to be involved. So, there you have it. If you’re feeling like a parental failure, science suggests you can quietly lay at least some of the blame on the Other in your dyad--your child. Or, you could acknowledge that we're all human and this is just part of our learning experience together.

What does attachment look like, anyway?
Dr. William Sears took the concept of attachment and its association with maternal sensitivity to a child’s cues and security and… wrote a book that literally translated attachment as a physical as well as emotional connection. This extension of attachment--which Sears appends to every aspect of parenting, from pregnancy to feeding to sleeping--has become in the minds of some parents a prescriptive way of doing things with benefits that exclude all other parenting approaches or “philosophies.” It also involves the concept of “baby wearing,” which always brings up strange images in my mind and certainly takes outré fashion to a whole new level. In reality, it’s just a way people have carried babies for a long time in the absence of other easy modes of transport.

When I was pregnant with our first child and still blissfully ignorant about how little control parents have over anything, I read Sears’ book about attachment parenting. Some of it is common-sense, broadly applicable parenting advice: respond to your child's needs. Some of it is simply downright impossible for some parent–child dyads, and much of it is based on the presumption that human infants in general will benefit from a one-size-fits-all sling of attachment parenting, although interpretations of the starry-eyed faithful emphasize that more than Sears does.

Because much of what Sears wrote resonated with me, we did some chimeric version of attachment parenting--or, we tried. The thing is, as I noted above, the infant has some say in these things as well. Our oldest child, who is autistic, was highly resistant to being physically attached much of the time. He didn’t want to sleep with us past age four months, and he showed little interest in aspects of attachment parenting like “nurturing touch,” which to him was seemingly more akin to “taser touch.” We ultimately had three sons, and in the end, they all preferred to sleep alone, each at an earlier and earlier age. The first two self-weaned before age one because apparently, the distractions of the sensory world around them were far more interesting than the same boring old boob they kept seeing immediately in front of their faces. Our third was unable to breastfeed at all.

So, like all parents do, we punted, in spite of our best laid plans and intentions. Our hybrid of “attachment parenting” could better be translated into “sensitivity parenting,” because our primary focus, as we punted and punted and punted our way through the years, was shifting our responses based on what our children seemed to need and what motivated their behaviors. Thus, while our oldest declined to sleep with us according to the attachment parenting commandment, he got to sleep with a boiled egg because that’s what he wanted. Try to beat that, folks, and sure, bring on the judging.

The Double X Science
Sensitivity Parenting (TM) cheat sheet.
What does “sensitive” mean?
And finally, the nitty-gritty bullet list you’ve been waiting for. If attachment doesn’t mean slinging your child to your body until you’re lumbar gives out or the child receives a high-school diploma, and parenting is, indeed, one compromise after another based on the exigencies of the moment, what consistent tenets can you practice that meet the now 60-year-old concept of “secure” attachment between mother and child, father and child, or mother or father figure and child? We are Double X Science, here to bring you evidence-based information, and that means lists. The below list is an aggregate of various research findings we’ve identified that seem reasonable and reasonably supported. We've also provided our usual handy quick guide for parents in a hurry.
  • Plan ahead. We know that life is what happens while you’re planning things, but… life does happen, and plans can at least serve as a loose guide to navigation. So, plan that you will be a parent who is sensitive to your child’s needs and will work to recognize them.
  • Practice emotion detection. Work on that. It doesn’t come easily to everyone because the past is prologue to what we're capable of in the present. Ask yourself deliberately what your child’s emotion is communicating because behavior is communication. Be the grownup, even if sometimes, the wailing makes you want your mommy. As one study I found notes, “Crying is an aversive behavior.” Yes, maybe it makes you want to cover your ears and run away screaming. But you’re the grownup with the analytical tools at hand to ask “Why” and seek the answer.
  • Have infant-oriented goals. If you tend to orient your goals in your parent–child dyad toward a child-related benefit (relieve distress) rather than toward a parent-oriented goal (fitting your schedule in some way), research suggests that your dyad will be a much calmer and better mutually adapted dyad.
  • Trust yourself and keep trying. If your efforts to read your child’s feelings or respond to your child’s needs don’t work right away, don’t give up, don’t read Time magazine covers, and don’t listen to that little voice in your head saying you’re a bad parent or the voice in other people’s heads screaming that at you. Just keep trying. It’s all any of us can do, and we’re all going to screw this up here and there.
  • Practice behaviors that are supportive of an infant’s sensory needs. For example, positive inputs like a warm voice and smiling are considered more effective than a harsh voice or being physically intrusive. Put yourself in your child’s place and ask, How would that feel? That's called empathy. 
  • Engage in reciprocation. Imitating back your infant’s voice or faces, or showing joint attention--all forms of joint engagement--are ways of telling an infant or young child that yes, you are the anchor here, the one to trust, and really good time, to boot. Allowing this type of attention to persist as long as the infant chooses rather than shifting away from it quickly is associated with making the child comfortable with independence and learning to regulate behaviors.  
  • Talk to your child. We are generally a chatty species, but we also need to learn to chat. “Rich language input” is important in early child development beginning with that early imitation of your infant’s vocalizations.
Lather, rinse, repeat, adjusting dosage as necessary based on age, weight, developmental status, nanosecond-rate changes in family dynamics and emotional conditions, the teen years, and whether or not you have access to chocolate. See? This stuff is easy.
                                                          
Finally
As you read these lists and about research on attachment, you’ll see words like “secure” and “warm” and “intimate” and “safe.” Are you doing this for your child or doing your best to do it? Then you are, indeed, mom enough, whether you wear your baby or those shoes or both. That doesn’t mean that when you tell other women the specifics of your parenting tactics, they won’t secretly be criticizing you. Sure, we’ll all do that. And then a toddler will cry, we’ll drop it, and move on to mutually compatible things.

Yes, if we’re being honest, it makes most of us feel better to think that somehow, in some way, we’re kicking someone else’s ass in the parenting department. Unfortunately for that lowly human instinct, we’re all parenting unique individuals, and while we may indeed kick ass uniquely for them, our techniques simply won’t extend to all other children. It’s not a war. It’s human… humans raising other humans. Not one thing we do, one philosophy we follow, will guarantee the outcome we intend. We don’t even need science, for once, to tell us that.

By Emily Willingham, DXS managing editor

These views are the opinion of the author and do not necessarily either reflect or disagree with those of the
DXS editorial team.