Women, Education, STEM and a Masculine Mind

"Let it not be said, whenever there is energy or creative genius, 'She had a masculine mind.'" - Margaret Fuller

A few months ago I had an older student ask, "Why aren't there very many women in math?" It was a good question. I've been pondering it, and I think in light of the kidnapped Nigerian girls, I'd try to answer it to my limited ability. I don't really have a complete answer as I am one woman with a limited exposure in math and science, but I have thoughts. Buckle up.

First, I'd like to open up the question to "Why aren't there very many women in STEM (science, technology, engineering and math)?" In college my biology classes were full of women. (The soft science) In chemistry the numbers got lower (The semi-hard science or the semi-soft science) and in physics (The hard science), even fewer. I took engineering physics at one of the top engineering school in the nation. I remember being one of two women in a lab class. The other woman was all, "Girl Power! Let's best these guys!" And I was definitely, "I just want to pass." The numbers of women in my math courses also decreased as the courses became more complex . What's up, Ladies? Where are you?

As for my personal experience, I grew up in a science house. My dad and mom were scientists. I remember dinner conversations that were scientific and completely beyond my understanding. Boy, these peas taste great. Having a science family helped create an encouraging math-sci environment for me. My parents, particularly my dad, believed in equality of the sexes. That helps even more. My dad says with regularity that he grew up in one of the most egalitarian societies in the world. No, it's not here. The only person who told me that I couldn't do something was me. I'm awesome at thwarting my own efforts. Thank you very much. My family, my micro-community, easily negated social messages that said science is for boys or that math is hard. Oh Barbie, even you can learn.*

Educating women is fairly historically new, and it's definitely not global. #bringbackourgirls. Unfortunately, when women have gone against the social grain historically there has not been a celebration or a warm reception. The seas do not part. There is often hostility. It is like cutting a new path through tall grass with a machete. Tiring. Sweaty. A horrible stink. Putting forth great effort often looks like a hot mess. You have to be ready for a pretty crappy time. I am not a trailblazer, nor did I sign up for it, but I find in just moving forward in math and science that the path is not well worn by women. I am so thankful for those who I can look ahead and see, like professors and scientists. What about the women who are themselves pioneers and can not see other women ahead of them? Women around the world being the first to get an education in your family. You are amazing. Take my strength. Don't lose heart.

So I am quoting Margaret Fuller all over the post today. I was introduced to Margaret Fuller in a U.S. literature class in college. She said some pretty profound things in the 1840s. Almost two hundred years later, her quotes resonate. She was an American Transcendentalist who basically said that, of course, every person wants to be an enlightened man; no enlightened man wants to be a women. Why? Because the social position of women has been wife, mother, cook and housekeeper. There was little room for books, philosophy, science and mathematics which involve extended time as well as thought and often a good housekeeper. She was a voice outside of the men's philoshophy club that said, "Hey, I can't find the door." It looks great for the people inside thinking about greater society but what about the greater society that isn't allowed in.

"In order that she may be able to give her hand with dignity, she must be able to stand alone" - Fuller

So back to the question, "Why aren't there are more women in math and science?" There is definitely not one answer. And the factors work together even though they don't plan to. There are collective forces. To name a few...

• Straight up sexism. Just a girl. I'm just a girl in the world.
• Social pressures. Women are marketed for their parts not for their brains. Seriously, marketing parts.
• Gender education. Girls play with dolls. Boys build things. 
• It's challenging. Some sciences are physically challenging as well as mentally challenging. Math is so mental. Letters and numbers, come on.
• Discouragement. Possible and probable failure. Struggling for success is tiring.
• Loneliness. 
• Feeling or looking 'different.' Nerd. Geek. A masculine mind.
• Role models overshadowed by fad models. I love you Mayim Bailik and Danica McKellar.
• People, influential people, telling them the can't or shouldn't. People say dumb things. I am everyday people, btw.
• Thinking how teachers or influential people think about them. Women emote and are empathic. People say dumb things or look us in a way that we take to heart even if they are not true. And it collects in our minds and beings.
• And of course, the tyranny of the urgent. Somebody has to cook, clean, and help fulfill all the other lower properties of Maslow's hierarchy.

There are barriers both real and imaginary. The barriers are internal and external. Thankfully, times, they are a changin'. Let me be clear, not every girl should grow up to be a scientist or a mathematician, but they should have the opportunity to do so if they wish. If they have the talent, we should encourage them and applaud their development. And it shouldn't be so hard for them to find the door. So, Ladies, young and old, if you want to pursue math and science, getting all STEM like, I'll try to clear a path for you.

"We would have every arbitrary barrier thrown down. We would have every path laid open to women as freely as to men. If you ask me what offices they may fill, I reply ---any. I do not care what case you put; let them be sea captains." - Fuller

Smart girlios...stay clever.

*Do you want to encourage some science and math in your home but don't know where to start? Try GoldieBlox or Snap Circuits. Buy a microscope or a telescope. Investigate.

3.14 Ways to Improve Your Mathematical Intuition

When I went back to school to get my math endorsement, my teachers in several classes asked us to use our 'mathematical intuition'. The term caused me to furrow my brow. What is mathematical intuition?

I knew of intuition. Merrill-Webster defines it as a natural ability or power that makes it possible to know something without proof or evidence, a feeling that guides a person to act a certain way without fully understanding why or something that is known or understood without proof or evidence. Going with your gut. Your first instinct. You have a feeling. A sixth sense. Back when I was in the pre-married world and dating, people would tell me, "When you know, you know."* People trust their intuition.

The part of definition that says "without proof or evidence" seems like a contradiction to mathematics. However, after taking a few courses, I understood better what mathematical intuition is. It's building a trust in your own mathematical abilities. In the past we've used words like 'reason' or 'common sense,' but those do not encompass the feeling of confidence that people should have in math and their ability to do math. "That answer feels wrong." "Something doesn't add up." "Something has gone awry." Having good mathematical intuition helps you see when the math isn't right. And with math all around us - life is a story problem- being able to trust your mathematical intuition is important.

So here are 3.14 ways to improve your mathematical intuition:

1. Recognize Patterns: A key part of mathematics and the applied mathematics all around you is recognizing patterns. I'm one of those people who looks at how gas prices move and wonders what was going on in the geopolitical world that caused the movement. I look at big patterns. When are milk prices the lowest during the year? When are certain vegetables in season? How much is packaging and product shrinking? There are also small patterns. How fast do my girlios grow through shoes? How many times does my dog have to bark before someone let's him out? How many calories am I eating daily? We recognize patterns in people's and animal's behavior. Start recognizing patterns in numerical behavior. There is no need to obsess in the patterns. Just recognize them and their anomalies.

2. Estimate: In order to guess better guess often. On the days that we go grocery shopping together, my husband and I over/under the bill. Guess on how much gasoline will fill the tank. Guess on how many steps to the mailbox. Guess on how long it will take you to get to work or school. Guess how much that new phone will cost with its down payment and installments. Make those numbers real. When I was in my science education classes in college I read about the Nobel Prize physicist Richard Feynman.** After Richard and his father read about T-Rex's height in the encyclopedia Richard's father explained to Richard that the dinosaur's head would fit through their second story window. I loved that. Richard's father was making the numbers real. Estimating not only can be used for guessing answers. It can also be used to show ratios, to equate values, to make numbers tangible and to build mathematical intuition.

3. Try and Err: To build some trust in your mathematical intuition, you have to test your mathematical intuition. Just like your regular intuition builds off of what you have already experienced, your mathematical intuition needs some experience. Positive experience. I do a lot of math tutoring on white boards. Why? Because white boards are forgiving. Easy to erase. People have a hard time making mistakes and getting past them. In math, you may have to make a lot of mistakes before getting it right. And when you get it right, you probably won't trust yourself until you have done it enough to feel comfortable with it. This may take some time. Just like breaking bad habits and replacing them with good habits takes repetition so does building your mathematical intuition.

0.14...Don't Fear Fractions: Fractions may not become your friends, but they are necessary. We use them in money without a second thought. A quarter really is a quarter of a dollar, 1/4. Cents are one hundredths. Decimals, which seem to make people much more comfortable, are really fractions in disguise. Decimals are fractions hiding in a base ten system. You often buy things in fractions without knowing it. Milk is sold by the gallon. Meat and vegetables are sold by the pound. Gasoline is sold by the gallon. Those are all fractions. Yes, the word 'denominator' seems like it has the word 'demon' in it, but it doesn't.

Good luck improving your mathematical intuition. Have your pi and eat it too.


*That always caused me to furrow my brow too. 50% of marriages end in divorce. Should I trust my 'know'? Statistically, intuition didn't seem very trustworthy, and yet people often trust it wholeheartedly. There are times when my normal intuition and mathematical intuition collide.

** Richard Feynman's books are fantastic. He's writes well and is very down to earth.

I am sorry that math and science hurt your feelings.

When I started teaching chemistry many years ago, I noticed something at parent-teacher conferences. Parents would come in and share their feelings on chemistry.

“I never took it. I heard it was hard.”

“I loved chemistry.”

“It was hard.”

“The math in it was hard.”

It was interesting to see parents’ reactions. Some portion of the conference would involve comforting them on their chemistry/science/math experience. I told students and parents that students often hit the “wall” in chemistry. It’s their first real challenge. Once they hit it, they had to work to get over it often involving finding help, and I would be there.

Since then I have become a math tutor and teacher, and I have run into the same feelings about math. People have strong feeling on math and science. At some point they have been frustrated, challenged and even angry. Math and science hurt their feelings.

When I was taking math classes myself, I had to deal with these feelings too. As the oldest student and only female in my differential equations class, I was amazed at the feelings it stirred in me. First of all, I never ever thought back in college that I would be able to take, much less pass, differential equations. The first two weeks felt like I was drowning. I had to deal with inadequacy, feeling dumb, frustration, and that “which one of these things is not like the other” feeling when I walked into class. This is for math. Math is systematic, process-oriented, organized and mechanical. I, almost a robot, was battling with feelings as well as the concepts and problems in the course.

In the end, I think I won both battles. I hunkered down. I read the book. I read other books. I did problems. I did more problems. I fell asleep with my math books on more than one occasion. I had to remind myself that failing this class was not a reflection of my self-worth before every class. Every class. I tried to separate my feelings from the material. The material is what it is. Learn it and don’t complicate it.

When asking one of my teachers if she thought I could go on in math, she said, “Well... Yes. You have the brains and the grit.” For most of us, it takes both. So often I hear people blame the first and not try the second. “It does not come naturally for me.” Naturally, whatever that is. None of my children spoke or read out of the womb. They had to learn and practice.

Here’s my point. Math and science are not your enemies. Some of the material has been around for a long, long time and hasn’t changed. Think of math and science like a river. In a classroom setting, the river has a particular current. You may find that it is a struggle to swim and keep up. So, struggle. It’s okay. Practice will make it easier. Put your feelings to the side. Do the work, however much you need to have success. Practice will build confidence and calm your feelings. Find others who swim to help you swim too, like teachers and other successful students.

If the current is too fast, you may have to find a slower current. Thankfully here in the US we offer streams and brooks as well as rivers. In other countries, often if you can’t swim in the current, you are taken out of the water for good. If you want to understand it, there are options available for you to build a strong base at your pace, like Khan Academy and MIT OpenCourseWare.

Don’t stand at the side of the river and curse it. Math and science concepts are involved in every aspect of our lives. We need them, and we need people who understand them. If at first you don’t get it, don’t take it personally.

Embracing My Weakness

It's been all quiet on the Midwestern blog lately. School's back in session for me, and after slacking off a bit, I've finally buckled down. My week in review became a fortnight and then some. Tomorrow I run my first half marathon of the season. Our church's women's retreat is next weekend, which I coordinate, so I've got a big weekend/week ahead of me. Life's gotten busy again. Yesterday, though, we had a snow day.

Big snow. Little dogs.

This past week I learned a bit about myself I thought I'd share. I'm taking two math classes this semester, linear algebra and calculus. One class had been getting a higher billing than the other since the start. Calculus. It just flows with my brain. (Nerdiness previously established) Linear algebra was getting the back seat. In my search for why I realized that I prefer to do math with letters rather than numbers. I'm a terrible number cruncher. When I took trigonometry a few years ago, I had two errors going into the final. One was a copying error, and one was an addition number. Data entry has always been slow going for me. This week I noticed I was favoring my strengths.

When my daughter practices piano I tell her often (borderline nag) to practice the measures she doesn't know as well so that those sections can catch up to the measures she know well. I remind her that if she plays the whole thing over and over again without practicing the weak parts independently the piece will remain unbalanced. Strong parts will become stronger, and the weak parts won't catch up.

This week I took my own advice. I hunkered down and did some number crunching. Lots and lots of number crunching. I'm not much faster, or better at data entry, but I'm more comfortable and confident with the material. Much more balanced.

I am also trying to do this with my fitness. I love running. Love. Love. Love running. However, I can't do more than three real push ups. I'm unbalanced. When I look at my mileage for January, it's lower than I'd like, but it doesn't show my cross training. Yoga, weights, swimming and even resting. And now shoveling and snow shoeing. There have been several days this year that lifting my arms was a bit rough.Striving for balance. Embracing my weakness.

Snowshoeing with the girlios

This is a test...This is only a test...

I'm between tests. I just finished a differential equation exam that really tested me. I can't tell how it went. In a day I'll be taking my math exam to be endorsed as a math teacher in Illinois. Honestly, I was more anxious about the dif eq exam than for the next one, but I still have anxiety.

Anxiety. It's stressful. I don't like what it does to me. I've had a bad relationship with anxiety for a long time. Clinically and thankfully, it isn't disabling. However, it augments my IBS and aggravates my TMJ. It makes me grumpy and impatient.

I know it's a waste of my time and energy. As I meditate on nobler things and verses, I think I can get it out of my mind, but I can't seem to get it out of my body. It gets hold of my temper and my intestinal system. Sometimes, it breaks up my sleep.

Jerk.

Anxiety, let's break up. It's not me; it's you.

I know. You'll be back.

Courage: Moving from Discouraged to Encouraged

So I haven't been blogging lately. I don't feel like I have time. I've fallen into fall and am still waiting to hit bottom. Every week since school started something new has been added on to the schedule. Piano, soccer, homeschool group, college class, work. One huge balancing act. It's the tyranny of the urgent until we get the rhythm down of the fall schedule.

And I have to say I am feeling discouraged. Even now as I am surrounded by a messy house and the girlios are just one phrase away from another fight (or weeping), I feel guilty about sitting down to type. The to-do's call, plead and scream. I've spent most of the day mulling over homework problems for class tonight, and two of them still elude me.

I have a lot to be encouraged about. This weekend during my 20 miler (I only had to do 18) I passed the 600 mile mark for the year. My pace was awesome for me. I am pretty sure the Garmin lies (in my favor). My girlios are healthy and doing well in homeschool. My husband and I still love to cuddle and talk late into the night. We just got a new bed and after a few nights of adjustment, I sleep solid. The weather is cooler. The praise list could go on and on.

I find it amazing, the power of one thing, to undermine my confidence. I am taking another math class this semester. It's a doozy. It's uncomfortable. The material (differential equations) and the classroom environment are uncomfortable. Why can't it be as easy as calculus? Why isn't there another gal in class? Why do I have to be the oldest? Why does it seem to be so cryptic? Why do the problems take so long? It's exhausting. And it's discouraging. You may be saying, as I also say to myself, that the other people in class shouldn't matter. Unfortunately, environment matters. Blocking it out is tiring. For many years, I would have told you that there were no differences between girls and boys. Then I had girls.

Anyway, I've been processing my discouragement. Yesterday, I taught my first day of 5k running and fitness class at our homeschool group. We are doing the couch to 5k plan, and yesterday was day one. I have 17 kids in class. Some are already runners, and some have never run before. My pace puts me near the back of the pack. I am okay with that, but it has to be discouraging for some of the newbies. I am so proud of all of them. So excited! They did awesome, but they may not be feeling awesome. I can think of a few people that may be very discouraged with how it went. I want them to stick with it, see improvement and be encouraged with themselves. I want them to make the move from discouragement to encouragement. Have courage. Do their best and forget the rest. Advice I should take to heart.

Being a teacher and a student at the same time has many privileges. I learn about both sides of the relationship. In November, I will be taking the state certification test for math and if I pass it and this class, I'll be submitting my 24+ hours of math to add a math endorsement on my teaching certificate. Although I am struggling in this class, I am trying to be the student I would want my students to be - asking questions of the teacher, making connections in class and seeking out other sources for a better understanding. I remind myself that it is good for me to empathize with future students that I will have and even current ones. This feeling I have, discouragement, is not foreign to many people regarding math. I really do want to be part of the solution.

So if there is anything in your life right now, like me, that is causing you discouragement, may I encourage you, as I am trying to encourage myself.

Have courage. Be strong and courageous.

On that note I have to go; I have two more problems to wrestle with.