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Examples, examples, examples! But, of the right type! - A friendly call-to-duty from the Math Support Gals group

Dear friends,

few days ago the group list of Pulsewire has a newbie: the Math Support Gals.

Our internal URL is

http://www.worldpulse.com/pulsewire/groups/17136

Here are three good reason why you may consider joining the group, and contributing it if you like.

First: Education of girls is an essential element for them to grow and thrive as fulfilled and free individuals. For a social and cultural being as we humans are, education is a right as fundamental as food, water and shelter.

Second: World today is highly mathematical and physical. Applied science rules our lives to an extent hard to imagine just few years ago. And this, globally! To date, being a first-class citizen demands some level of mathematical, physical and scientific knowledge - as a minimum, to be able to comprehend and, when necessary, use a critical attitude.

Third: Traditionally, girls and women are considered "less apt" to mathematics, physics and science, just because they are female. False claim: as a human construction, mathematics, physics and science are accessible to anyone. True: they may be hard to learn, as any other foreign language we encounter. But: they're also fascinating, and we maintain that, if properly exposed and sustained, they may be enjoyed and loved by girls.

The group is primarily aimed at passionate teachers and parents, women and men as well. But, we also understand how important is, to have also the voices of girls heard, here and now. Not forgetting of course the girls you were and in some way you still are.

Apart from the focus on mathematics, physics and science, the group discussion is free. In the very first day of our existence, we touched arguments like different learning styles and how to foster them, or developing girl-friendly examples to present science to them in a compelling and friendly way.

I add a "sample", from a post I've just made, which incidentally is an important problem on which any help, any idea is welcome.

Thank you very much, for the time you have devoted the group by just reading until here.
I hope you will go on, and to greet you in the group.

(A little organizational detail: joining the Math Support Gals requires you to ask joining it; as a general rule, I'll always approve your request - this is just a way allowing me to be advised by e-mail when people ask to join, so that I can maintain my log for future reference; just allow me some time: I'll answer as quickly as possible, but there may be days when I'm out home and without an Internet connection. But, I promise, I'll welcom you as soon as I can).

Cheers

Mauri

-----------------

Why is mathematics and physics so boring sometimes?

The question is hard to answer to me: as far as I've seen in my professional life, mathematics' and physics' applications are widespread and, most often than not, fascinatingly useful.

Just to give an example: if you connect to the site of the environmental protection agency of Lazio, after some browsing you'll discover a wonderful collection of maps illustrating pollution forecasts for the next hours. Like these:

http://www.arpalazio.net/main/aria/sci/previsioni/roma/no2.php

These maps are the results of a sophisticated mathematical models, fed using data which underwent extensive data acquisition and processing work. Behind the scenes, an entire world of scientific knowledge is deployed seamlessly at your finger's command. There is a great deal of physics of the atmosphere, of course. But also, of quantitative chemistry. Of computer sciences.

On the other (darker) side, you open a mainstream high-school textbook on physics and yes, you find a lot of applications, but (in random order):
- About how quickly a soccer ball will travel from a point to another
- On whether a car launched at a crazy speed will stop before or after a (supposedly impenetrable) wall
- If it is better for an artillery round being shot with an angle of more or less than 45 degrees to hit a target
And more on the same line.

In my times you might have be even less lucky: there was no application at all. My high school physics textbook began with a phrase more or less like this:

"Kinematics is the study of the movement of collection of points in the space. A point is a dimensionless object occupying a position in space. Space is..."

If you endured the first lessons, you finally arrived to dynamics where you were told you may deduce anything about "material points" (points "dimensionless", but "with a mass") from few basic "Nature's laws" (your teacher may also have done his best to convince you that anything in the world, made of objects definitely not as dimensionless as points, was also deducible from the same rules).

Well. I hardly know soccer rules. Don't like to take risks when I drive. Prefer discussing (animately, Italian style) with people rather than destroying their lives and properties and killing their beloved with artillery rounds.

And, cordially detest the idea of "deducing physical reality from basic principles".

I'm not so an uncommon type of person, as I discovered! Many friends of mine share the same lack of passion for these things presented as "absolutely compelling".

Is it we lack good examples?

Delving a bit in a (Mauri-logic-style: crank, haphazard and diverging) assessment of common ways of presenting mathematics and physics through examples, I found some common factors I'd like to share. I try exposing them in (apparent) order.

1.Many example are highly gender-stereotyped (that is: unfriendly to most girls and many boys).

More precisely: they deal of arguments assumed to be interesting to boys: cars smashing somewhere, bullets crazily wandering in space, sport events. That they really are interesting to boys, or all of them, is an interesting question (I have some doubts).

Surely to many girls, these example seem contrived, extraneous and uninteresting.

To both girls and boys, they tend to seem marginal and puerile. This leads me to the next point.

2.Where the Real World is?

We all know "human kind has reached the Moon" (vaguely, and with some perplexity, by the generation of who "was not there"): a huge application of physics! We are accustomed to money, a tool of mathematical and quite abstract nature. We know (and sometime expect) weather forecasts - another highly matheatical and physical application.

Very few of these real-world applications are used as examples.

But these are precisely the kind of things mathematics and physics are used for.

Amusingly, to get examples from the real world could be much easier than inventing the next artificial self-standing puzzle: there is literally a sea of scientific and industrial publications from which to get inspiration. All what needed is, presenting things in an interesting way.

3.Why "deducing"?

It takes some time to realize that "deducing physical reality from basic principles" is not exactly the same as "creating reality", and rather is "building a simplified model of it".

Unless you are highly deductive, as a young girl (or boy) you haven't yet realized this conceptual shift. At least, I didn't until early adulthood.

I wonder whether initially teacher would do better to insist on the experimental side of physics and mathematics. Incidentally, this is closer to how science is actually built: collecting and organizing "facts" by experimentation first, then sorting them out and formulating hypotheses to be tested. "Laws of Nature" may emerge when a discipline has matured a lot - but even then they should be considered as nothing more than models, valid until something better is found.

Like what happened with classical mechanics, whose "laws" have been extensively revised in the transition to special and general relativity, and completely replaced by a different thing in quantum mechanics.

Interestingly, classical mechanics has not been "replaced" by relativity or quantum mechanics: these theories (models!) co-exist, and are applied wherever it makes sense to. Sending humans to the Moon and back occurred when both relativity and quantum mechanics were well available and established, but required "nothing more" than classical mechanics.

I'd like to get feedback from "girls of today" (and yesterday, too) about this point.

My impression is, that accepting theories as models required me to mature a lot. I found a very interesting framework for "modeling the acceptance of models" in the wonderful book

"Women's Way of Knowing"

by Mary Field Belenky, Blythe McVicker Clinchy, Nancy Rule Goldberger and Jill Mattuck Tarule (as the title suggests, it's women-centered, but deals of men too - it may be hard following at times, but I found this book inspiring, to say the less).

In their terms, changing your own view so that you accept knowledge as something "constructed" is a relatively late moment. When (if) you reach that stage, it feels just "obvious" considering theories as nothing more, but also nothing less, than models.

But more important, it may be much more compelling to devise example and test cases which allow a great deal of experimentation. Of data-collection, organization, and sorting-them-out. Of distilling provisional truths (all acceptable, provided they can be falsified with some experiment). Of assimilating them "from the inside".

Nice, isn't it? Unfortunately, it collides with this:

4.What a hurry!

In classes we had to complete our works or tests under tight time constraints.

To get to the classes we have to "fight against" a clock ticking all the seconds we lose in traffic during our commute (if you happen to live in Milan).

We always feel the relentless pressure of time and haste.

And many examples seem to convey the same message. They're designed as "puzzles", to be "solved" in some short time (sometimes even specified).

A very competitive way of conceiving examples, that's true. But, not necessarily fostering deep creative thought. Just useful for contests, provided a real usefulness of them can be found (in some cases I've seen, the puzzle was used to build or confirm some pecking order based on some kind of pretended "mental prowess" - almost always by boys in early adolescence).

THen, if you scrutiny just a bit, you notice almost no real world intriguing problem manifests as a "puzzle" to be solved quickly.

Neither they are "competitive", too!
Rather, the more their complexity the higher the need to cooperate with others in organized ways to just even understand them.

In addition to being essentially contrived and unrealistic, examples of "shoot-an-answer" type may be deeply unfriendly to the more reflective and less status-poised people.

My fantasy and competence are limited, and our time scant, so it's better I don't go any further listing reasons. We all will have opportunities to add more.

I may try a synthesis, however: examples as they are commonly conceived tend to be unfriendly to a certain type of people.

These "people" may not form a random sample of the overall population: they are likely to be mostly female.

On average, it is the girls who "stay quiet" in a class, being less impulsive and more reflective. It is also them who, on average, do not get crazy for sport heroes. Again on average, it is girls who love thinking at a calm pace, interacting, trying ideas meanwhile...

The morale of this post may be, we need many more examples.

For them to be inspiring, we may need to deconstruct the way mathematics and physics are presented, and build on the new awareness.

In my opinion, we may try looking for examples which are:
- Taken from real-world, interesting applications
- Presented as open-ended problems, with possibly many, or no, solutions; as medium- and long-term projects anyone may follow at their own pace
- Not imbued of stereotypes on "what the kids would like to learn"
- Very "experimental" in nature, and respectful of the experimenter.

As the "Math Support Gals" group, we may have a role in inventing new examples!

A part of the group's sister site will be devoted to them.

I guess this is not sufficient. Time ago, on Pulsewire, I and my friend Jackie had a very interesting exchange about the subject. She pointed out a very important thing: teaching to girls demands patience. It requires staying in synch with a child time, not pushing, but in a sense (my addition) "pulling" her, gently.

It demands using the proper tone of voice, the sensible pauses, and neglect of the clock.

The reward, you can imagine, is immense. An "oxytocin-intensive" experience.

I realize this may not be easy to do, in the rigid frame of institutional school.

Should we work on this, too?

Cheers to all,
and let's dig the world, looking for interesting treasures!

Mauri

Comments

JaniceW's picture

Math Doesn't Suck!

There is a book by a young American actress who also happens to be a math whiz and has a mathematical physics theorem which bears her name (The Chayes-McKellar-Winn Theorem). Danica McKellar has written several books to help break down the barriers that prevent young people from embracing math including Math Doesn't Suck (Middle School Math) and Kiss My Math (Pre-Algebra). She is currently working on a book on algebra. Both books made it to the New York Times Bestsellers list so I am confident there are methods to teach math and physics in ways that do not have to be boring.

[excerpt from Kiss My Math website]
From bestselling author Danica McKellar, KISS MY MATH makes pre-algebra a cinch, Hollywood-style!

With Math Doesn't Suck, actress and math genius Danica McKellar made waves nationwide, challenging the "math nerd" stereotype—and giving students the tools to ace tests and homework in her unique just-us-girls style. Now, in Kiss My Math, Danica empowers a new crop of girls, taking on the next level in the math curriculum: Pre-algebra. Stepping up not only the math but also the sass and style, Kiss My Math will help mathphobic teenagers everywhere chill out and finally get negative numbers, variables, absolute values, exponents, graphing, and more—concepts essential for algebra and beyond.

Kiss My Math also includes a unique "Math Test Survival Guide" to help students conquer jitters and excel at test-taking—a skill unto its own. Plus, fun extras inspired by today's teen magazines—including personality quizzes, reader polls, and real-life testimonials—ultimately revealing why pre-algebra is easier, more relevant, and more glamorous than readers think. With Danica as personal tutor and coach, girls everywhere can stop dreading pre-algebra and watch their scores rise!

EXCERPT: KISS MY WHAT?
"Math? Are you kidding me?"

In high school, a teacher once suggested that I be a math major in college. I thought, "Me? You've got to be joking!" I mean, in junior high, I used to come home and cry because I was so afraid of my math homework. Seriously, I was terrified of math.

Things had gotten better for me since then, but still—college math? That sounded really hard; I didn't think I could hack it. Besides, who studies math in college other than people who want to be math teachers, right?

Boy, was I wrong. Just ask my friend Nina.

In college, Nina wanted to be a doctor more than anything in the world. She'd always wanted to deliver babies! She was smart, funny, and totally capable of doing whatever she set her mind to—until she found out that calculus was a required course. The idea of taking calculus scared her so much that she dropped out of the pre-med program and gave up her dream!

And Nina isn't the only one. Believe it or not, lots of people change their majors and abandon their dreams just to avoid a couple of math classes in college.

So, what does "Kiss My Math" mean?

It means: "Um, excuse me, I'm going to do whatever I want with my life, and I'm sure as heck not going to let a little math get in my way."

Who knows what you'll do? Armed with math, you might become a cutting-edge scientist and develop your own line of all-natural makeup or therapeutic high heels. You might discover a cure for cancer or travel into space. You might create some cool engineering trick that destroys trash or creates super clean energy and saves the planet!

Something else, perhaps? Doctor, lawyer, clothing designer, architect? Maybe you'll work for a big magazine or your favorite fashion line, or maybe you'll start your own business.

Believe it or not, all of these fabulous careers use—that's right—math.

Check out Stephanie Perry, Jane Davis, and Maria Quiban's real-life testimonials on pp. 37, 71, and 128 to see how studying mathematics gave these ladies a leg up on their competition in the worlds of television, fashion, and magazines. Betcha never knew math could give you power and freedom in those areas.

And if anyone tells you it's impossible to be fabulous and smart and make a ton of money using math, well, they can just get in line behind you—and kiss your math.

Mauri's picture

Great suggestion!

Janice, I checked the books and decided I "must" read both of them.

Thanks to your links, I also discovered Danica has an e-mail address, so I immediately sent a letter from the "Math Support Gals" sister site's e-mail.

Who knows, I imagine how busy she is, but maybe has time to interact with us?

Books like these are compelling and essential resources. I'm also considering to provide a list of them in the sister site!

To all the Gals around: if any of you have their own suggestion, they're welcome!

Hugs,

Mauri

Mwierenga's picture

Perfect!

It is SO great that you started this group! I have always loved Math and Science, probably because it was easier for me. But I was also extremely lucky to have a very supportive Dad who believed so strongly in girls studying these subjects. I could always turn to him with questions. And he stood up for me, too. When I was 15, we lived in Switzerland for a year while my Dad was a visiting Professor. One evening, his "boss/supervisor" came over for dinner. I was doing my math homework and this man came over to look at what I was doing. Then, he turned to my Dad and asked (in all seriousness), "Why is your daughter studying math?" My Dad almost bit the guys head off! He was so mad that someone would say such a thing. That was the first time that I met someone that actually didn't believe that girls should learn math!

I'm very grateful that I had such a supportive family and I thank you for creating this group! I do my best to encourage every little girl I meet to be open to math and science.
Marlies

Mauri's picture

Your support and ideas are welcome!

Marlies, dear,

thanks for having shared your experience, and for supporting the group initiative!
It's so hard sometimes, that people try moving you away from study of math on the ground it is "not necessary".

When this happens, a loving and supportive dad like yours can make the difference.

Would you like to share more? I know of your passion for science and environment, and am very curious to hear from you.

Without obligation!
But if you want to join the group, you are welcome!

Mauri

jap21's picture

My story on math

I never liked math while in school. Only one year, in seventh grade, I had a great teacher with whom I got a good grade in math. Until the day I graduated from high school, suffering very much just to get the smallest grade that allowed me to pass the subject, was the story of my life.

My family never cared very much if I didn´t learn math, maybe because it was usual for me to get straight A´s in everything else. I remember I used to calculate my yearly average grade with and without math. If the top grade was 100, without math I would get somewhere between 95 and 100, whereas with math.... the average fell to anywhere between 85 and 90. To my mom this was not bad, so she didn´t worry. To me, it was awful but I convinced myself that I was a complete wreck for math.

Six years after graduating from high school my life looked really bad and I decided that I needed to go to College. I thought Business Administration didn´t have many numbers in it... until I had my first Calculation class which sounded like japanese to me. Right there I decided that it was truly important for me to make the effort and really learn math. I did this by solving the Baldor Algebra book (all of it), twice, by myself.

To say the least, this has been the most awesome decision in my life, as my way of solving problems was turned upside down. After ffive years of constant math use. I saw the world differently. I was able to find new solutions to every problem, and was willing to study new ways to get better results. People say that when it is hard to do, it is more appreciated. In my case, I began being the worst math student, and with some exciting exercises (I used to repeat every exercise up to five times), I ended up being... the first of the class in the final graduation test!

It is not impossible my friends. I decided to tell you my story so that you will see the opportunities math opens in your life. I hope to reach the readers who don´t like and don´t care about math, to let them know they only need to sit down and practice over and over again, until you master this new way of thinking. Then math will never again pose difficulty. Instead it will become a challenging game in your life!

Why is it worth to acquire math? Because the quality of your decisions will improve dramatically.

Love,

Jackie

Jacqueline Patiño FundActiva
Tarija - Bolivia
South America
www.jap21.wordpress.com

Mauri's picture

Thank for sharing this experience!

Jackie, dear

you gave another moving and inspiring pearl, as so often happens!

It seems me to see you, in another time, while solving the exercises and learning, formula after formula, methodically.
A heartwarming tale from the past - or a present world where some other Jackies, in other places, with different names, also proceed counting on their strength only.

Your experience may be of example to them all. Very precious!

You are so right: mathematics is an instrument allowing people to take better decisions. Better, I mean especially, than intuition might often suggest. You have to collect data, organize them, check priorities, all very rationally. And, arriving at a conclusion.

This is valuable for everyone, even a "mainly intuitive" person like me: even intuition demands good data, time, and calmness to elaborate things. And then, after you get to some valuable point, you have to translate it for others to understand - something requiring a lot of logical thought, sorting, proving...

How could I do, without mathematics?

This is of general importance: real world problems are often so complex that jumping to the first "solution" you foresee is not an option.

So, thank you for sharing your experience!

A practical question: would you like to post it to the MSG group page too? Or (with a bit of time) in the "experience" section of the sister site?

Hugs

Mauri

jap21's picture

Yes Mauri

Please share this all over. I think we might attract more girls to the group if we share everything with more people. Thanks honey!

Love,

Jackie

Jacqueline Patiño FundActiva
Tarija - Bolivia
South America
www.jap21.wordpress.com

Mauri's picture

I try on the sister site!

Thanks honey!

Your post is interesting, and devises a place where it is accessible also outside.

I'll add on the experience I had, and ask from others as well.

Love, and many smiles

Mauri

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