The first page was fun, and because of it I now understand the base 2 system.  (The system we use is base 10).  Easy peasy.  In the number 11101, the last number is the one’s place, the next to the last place is the 2 place (in this number, that’s the 0), the place right before that is the 4’s, the place before that is the 8’s, the place before that is the 16’s.  So, the number 11101 is  16 + 8 + 4 + 0 + 1=29.  In base 2 there are only 1’s and 0’s.

I moved on to the next page about square roots.  In a matter of minutes, I understood the difference between rational and irrational numbers and understand how to solve simple square root problems.  It’s been so many years since I’ve done anything with square roots and frankly, I had forgotten how.  I had been ashamed at that, but I suspect I am far from being the only person in my 30’s who could not remember what the heck a squre root is.

The next section, Penrose discovers Pancake world, was easy enough to understand. It was about 2 dimensional objects.  I was thinking as I read it that heck, if this is reading about math, then when my boys play Super Paper Mario, they are playing with math.  I love how there is math EVERYWHERE in our world, even in video games. 

In Penrose meets the Fractal Dragon, we get this definition of fractal. “A fractal repeatedly folows a rule and thus continually reproduces copies of itself in various sizes and or directions.”  One example fractal rule was, “always add a square half the size of the last one drawn at its upper left corner”

Perfect inspiration for me to play around with fractals..watch for upcoming posts on that!

I’ll definitely continue reading Penrose and his mathematical adventures.

Other chapters include:

• Penrose discovers the mathematics of soap bubbles
• Penrose learns the truth about infinity
• Penrose meets Fibonaci rabbit
• Penrose watches the puzzling egg hatch
• The polyhedra connect with Penrose
• The golden rectangle dazzles Penrose
• A square becomes a bird right before Penrose’s eyes
• Penrose meets Mr. Abacus
• Penrose discovers the mystery of the triangle of numbers
• Penrose meets the Tangramians
• Penrose solves the case of the missing square
• Penrose sees into the invisible nanoworld
• Penrose loves the games numbers play
• Penrose flips over the Mobius strip
• Penrose discovers mathematics in the forest
• Penrose meets Lo-shu
• Mauritus teaches Penrose a tessellation trick
• Penrose discovers Penrose
• Penrose tangles with the impossible figures
• Penrose learns more number antics

If you missed it, here it is:

I’m so glad for video, because I can watch Ellen lying on those nails and not have to do it for myself! Technology is so cool.

If you are feeling in an experimental mood, you can visit Steve’s website for instructions on how to build a bed of nails for a balloon. http://www.stevespanglerscience.com/experiment/bed-of-nails1

But even after watching the video and reading around at Steve’s website, I still found myself wanting to understand more clearly WHY a person can lie on a bed of nails and not get hurt. The answer is, according to http://health.howstuffworks.com/bed-of-nails.htm , the same reason why a high heel exerts more pressure than an elephant’s foot.

“Pressure is the application of force over a particular area. In mathematical terms, pressure is equal to force divided by area. With more force comes more pressure, and with more area comes less pressure. This is why a person wearing a high-heeled shoe exerts more pressure on the ground than an elephant does. An elephant weighs a lot more than a person, but its feet have more surface area than the pointed heel of a shoe.”

Step on one nail, you put a lot of pressure on the nail. (Ouch!) But spread your body’s pressure out evenly over many nails, none of the nails puncture your skin.

It’s physics, and it’s fun. Yay!

I’ve got some children’s books I think my kids might like, a Lisa Scottoline novel , and a discarded copy of Summerhill: A Radical Approach to Child Rearing that the library is selling for 10 cents.

And then there is the stack of math books. They never used to be a part of my library days. I’m happy I included them!

I’ve been sitting and happily reading Kiss My Math: Showing pre-algebra Who’s Boss by Danica McKellar.

In the introduction, she defines Kiss My Math as “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.”

How many times have I not done something because I DID let a little math get in my way! No more, no more.

In chapter One, she discusses integers, which she defines as “all the counting numbers, their negative counterparts, and zero.” Now, I am a very verbal person. Words excite me. They’re fun, they’re interesting. I remember them easily. But the word integer? My mind draws a blank. I know it’s a math word, but I can NEVER remember what it means. Probably because it reminds me of math class!

So I had to laugh when she said, “I’m sorry, but ‘integer’ has got to be the most boring, sterile word I’ve ever heard. Doesn’t it remind you of, I don’t know, some type of typical instrument used in a hospital? Some doctors say to her intern: ‘Quick, pass me the integer. We have to operate.’ Actually, that’s already sounding more exciting.”

Okay, I can relate. But then she decides since she doesn’t like the word integers, she’s going to start calling them mint-egers, or sometimes mints for short. Okay, that’s a bit…weird.

She said that the higher the positive number, the stronger the good minty taste. But the negative numbers tasted progressively worse, like the booger or vomit flavors in Harry Potter Bertie Botts Jelly Beans [3.5-Ounce Bag]. A really bad tasting jelly bean (say, -6) could be neutralized by adding a really good mint (say +6), so the value is zero. If a -6 icky jelly bean was eaten with a super good +8 mint, it’s the same as if you’d only eaten a 2 mint to begin with.

I didn’t get much from this, maybe because I already knew how to add negative and positive numbers. Yay! I already understand some math! Makes me feel proud. But I think if I hadn’t known how to add positive and negative numbers, this might have helped, quirky and weird as it is. If nothing else, I don’t think I’ll ever be able to forget what the word integer means. So my math vocabulary has been improved. Mint-egers ::rolling my eyes::

Chapter 15 is about exponents. I talked about exponents in this post. I actually like the explanation of exponents in the Kiss My Math book. Not over the top like mint-egers. She talks about a high-powered executive in a corner office on the top floor, who decides to throw an office party and all she has to do is call her assistant. The assistant plans the party, and the high-powered executive doesn’t have to do anything.

The exponent is like that high-powered executive. As Ms. McKellar explained, if you have 4³, “The high-powered executive ‘Ms. Exponent’ is so powerful that all she has to say is ‘3,’ and suddenly the 4 is multiplying times itself 3 times! ”

I like the analogy.

If you can read a book that is very obviously aimed at high school girls and can skip over stuff like, “Most Embarrassing Moments in School!” and “Quiz: Are you a Stress Case?”, there really are some helpful explanations for concepts and terms you might have never fully understood.

My result was:

You are gold. Gold is a precious metal. Gold is beautiful and valuable. It is soft and malleable. It resists corrosion and is a good electrical and thermal conductor. Gold sets the standard for many currencies. Its melting point is an assigned value that is used to calibrate temperature scales. Gold isn’t always ‘gold’… it can be purple or red or other colors depending on the size of the gold particles.

What did you get?  Let me know in the comments section!

This was a book that was mentioned in the geometry class I took in New York. I love how taking one small step in the direction of something I’m interested in leads to interesting books to reads and videos to watch. You don’t have to do it all at once! Just one step at a time, and all the little things you do are building blocks for each other.

In the introduction he talks about the way our children are taught math, using the “drill and kill” method. He says, “If only they could see numbers as the ancients did, as symbols of principles available to teach us about the natural structure and processes of the universe and to give us perspective on human nature.” and “This book concerns mathematics, but not the kind you were shown in school”.

I love it already!

I love nature. I love to think about ideas and to gain perspective on human nature. Love, love, love it! I love that math can help me explore those things more.

The introduction has enticed me with the idea that nature is a text book written in symbols and shapes, and that through studying geometry we can learn to read nature’s text. I am very anxious to continue this book!

Video games, by the way, are excellent ways to incorporate math play into your life!

On his game, there were four switches that needed to be pushed, but we didn’t know which order they needed to be pushed. If we had been at home, we would have looked up an online walkthrough to find out the combination.  But since we were in the car, I decided to figure it out myself.

So I started out with the obvious.

1234.  That didn’t work.

Neither did 4321.

So I said, “Well, let’s see if we start with 1,2.

1,2,4,3.  Didn’t work.

“Okay, How about if we start with 1,3″.

1324 didn’t work.  Neither did 1342.

“Okay, if we start with 1423?”

“1432?”  Ding! Ding! Ding!  Yes!  It worked!

I was prepared to move on to combinations that started with 2,1.  Then 2,3.  Then 2,4.  Then I’d move on to combinations that started with 3,1.  Then 3,2.  Then 3,4.  And so on.

I’ve been missing this blog, anxious to get back into the swing of things.  Anxious to explore more math and science and technology.  And feeling just a bit bad that I haven’t been coming up with new exciting things for me to explore and share here.  But wait a minute!  When I helped my son figure out the correct combination of switches, that WAS math!  It wasn’t using fancy formulas or software and it wasn’t using very large numbers, but it WAS using probability.

I think we sometimes get intimidated with math and feel like we don’t do REAL math because the math that comes up in every day life doesn’t often look like the arithmetic we did in school.  Because playing around with numbers doesn’t feel like school math, we often don’t realize that we ARE doing math.

But imagine if you started realizing that almost every day you do SOMETHING math related. Did you add any numbers or figure out any percents when doing your taxes? Add fractions when doubling a recipe? Add or subtract hours when planning to chat with a friend in a different time zone? It’s all math. If you started recognizing that, you might start saying, “Hey, you know what? I AM a “math person”. I do math regularly!” That attitude might make a more challenging math puzzle less intimidating when it comes into your life.

What math have you done lately without even trying to?

If you have experienced those limiting beliefs and have overcome those limiting beliefs and developed the self-confidence so that you could successfully accomplish something you wanted to do, I would love to consider you to be a guest blogger. Even if the area where you had to overcome your lack of self-confidence was in an area other than math, science, and technology, send me an email. Because really, whether you doubted your ability to solve equations or walk a tightrope, the confidence that you are capable of learning and doing is the important point. Send me an email at sheilakbaranoskillc@yahoo.com and tell me what you would like to write about! I will choose several people to do guest posts, because this is a very important topic to those of us who are overcoming math, science, and technology phobias!

In the meantime, I’m wondering if any of you who downloaded Jewel Quest 2 from Amazon when it was free are finding it as addictive as I am?  Sometimes I can’t get myself to stop playing it, even though when I play in tournament mode I lose a lot more than I win.  (And if anyone has any tips on how I can win more, please let me know!)

Amazon is offering another game for free.  I don’t know how long this offer will be valid.  I can’t link directly to the game, but if you click here to go to Amazon’s Game download page and then type Big Kahuna Reef into their search, you will find it.  When I did that, the first one that came up was Big Kahuna Reef 2, which is 6.99.  The first Big Kahuna Reef, which is the free download, came up second in the search.

By the way, if you didn’t get a chance to download Jewel Quest 2 when it was free, you can still get it from Amazon for 6.99.  Just click the above link to go to Amazon Game Downloads and type Jewel Quest 2 into the search.

To download these games, they will have you download a (free) game installer.  Also, if you don’t already have an amazon account, you have to sign up for one to get the free games. While you’re at amazon, click around to check out some of their other game downloads. A lot of them let you download free trials, where you can play the game for 30 minutes or so to see how you like it.

The cool thing about these games is that they’re fun and they really do get your brain thinking in analytical, mathematical ways without any stress.

Click here to check out the Free Game Downloads from Amazon.com!

In it, he talks about Renee, who was using a computer program  designed to teach students how to calculate the slope of a line.  According to the book, it was eighth grade mathematics.  For anyone who doesn’t vaguely remember slope from math class, that’s the x and y axis thing…rise over run…sounding familiar yet?  Don’t worry, you don’t have to understand it to get the point of this article.  Just know that she was doing a computer program that was math related.

Renee wasn’t a math natural.  She was playing with the program, trying to make sense of a concept, and kept tinkering away at it.  What impressed Schoenfeld, the professor who was observing her, was that she kept at it for 22 minutes before something in her brain clicked and she started to get it.  Schoenfeld said, “If I put the average eight grader in the same position as Renee, I’m guessing that after the first few attempts, they would have said, ‘I don’t get it.  I need you to explain it.”

The book goes on to say, “Schoenfeld once asked a group of high school students how long they would work on a homework question before they concluded it was too hard for them every to solve.  Their answers ranged from thirty seconds to five minutes, with the average answer two minutes”.

While this is an interesting, enjoyable book, I came to some different conclusions about this than the author did.  In chapter 9, he talks about an experimental public school in a poor area of the Bronx.  In the KIPP academy, children go to school from 7:25 am until 5 pm.  After-school activities run until 7 pm.  They have school on Saturdays from 9 to 1.  They have three extra weeks of school in July, when the school day runs from 8 to 2.

A student in a math class might work on a math problem for twenty minutes at the black board.  He will work methodically, carefully, with the participation of the class.  The school is known for its students’ high math scores.  ” ‘What that extra time does is allow for a more relaxed atmosphere,’ Corcoran (a KIPP math teacher) said, after the class was over. ‘I find that the problem with math education is the sink-or-swim approach.  Everything is rapid fire, and the kids who get it first are the ones who are rewarded.  So there comes to be a feeling that there are people who can do math and there are people who aren’t math people.  I think that extended amount of time gives you the chance as a teacher to explain things, and more time for the kids to sit and digest everything that’s going on–to review, to do things at a much slower pace.  It seems counterintuitive but we do things at a slower pace and as a result we get through a lot more.  There’s a lot more retention, better understanding of the material.  It lets me be a little bit more relaxed…’ ”

The author seems to be making a case for helping people get better at math by allowing them to spend more time with math, to take their time doing it, to play with it without being rushed until they get it.  So many times I want to say, “Yes!  You’ve almost hit on the answer.  Don’t make kids go to school!  Don’t make them do things they’re not interested in, but make sure that when they are interested in something, they have PLENTY of time to sit and play with it, unrushed and unpressured.  Model that for your children by playing with math ideas yourself, taking the time to play and fiddle and wonder and tinker.   But he doesn’t come to that conclusion.  Instead, he says, “The only problem with school, for the kids who aren’t achieving, is that there isn’t enough of it.”

The reason the eight graders would have only spent an average of two minutes on the math problem while Renee was willing to tinker for 22 minutes was that the eighth graders didn’t want to be doing the math problem.  They had just spent all day at school, and chances are a lot of them would have preferred to be not be in school in the first place.  They probably hadn’t been given a choice as to whether or not to take that math class, let alone whether they wanted to do that particular math problem.  I bet Renee was given a lot more choice.  I bet Renee wasn’t worried that if she didn’t complete that math problem, and a whole lot of other homework from other classes, and studied a bunch of stuff for tests, and master it all so that she got good enough grades, that her PERMANENT RECORD would be marred.

Chances are, many of the KIPP students had a nicer environment at school than they had at home. Also, the KIPP students had a choice about whether or not to go to KIPP. If the student didn’t sign the form, agreeing to participate in the school, they just continued at their regular school.

In Chapter 9, he also talks about reading scores in young school children. He points out the advantage of being wealthy. “The wealthiest kids come back in September and their reading scores have jumped more than 15 points. The poorest kids come back from the holidays and their reading scores have dropped almost 4 points. Poor kids may out-learn rich kids during the school year. But during the summer, they fall far behind.” He goes on to explain that the wealthier families are taking their kids to museums and summer camp and have plenty of books to read and the parents “consider it their responsibility to keep the children actively engaged in the world around them”.

Now, my conclusion is that instead of saying that we simply need more school, we should encourage the poor families to do what the wealthy families in the study were doing. I put wealthy in quotes because while I agree that wealth has its advantages, I know many unschooled families who are far from wealthy who have plenty of books and interesting things in their homes, go to interesting places, and are actively engage in the world around them.

The answer is not more school. It is giving all people–children and adults–freedom about how and when and where to spend their time.  To give them the opportunity to pursue what interests them.  In other words, the answer is unschooling.

I can’t call myself an unschooler because I’m a 36 year old who spent the compulsory education years of her life in school.  But I can embrace the principles of it.  Explore, indulge your curiosity, honor your heart’s desires when making choices about how to spend your time.  Give yourself pressure-free time to tinker and ponder and wonder, in math and science and everything that crosses your path that calls out to you. Math isn’t about getting the right answer so you score well on the test.  It’s about the process of exploring and tinkering.

Here’s to living life every day the way Renee played with that math problem.