Tessellations

Today, thanks to The Adventures of Penrose the Mathematical Cat, we took a closer look at tessellations as math and as art.  M.C. Escher was a world-renowned graphic artist who was Dutch-born but did much of his work in Rome.  (M.C. stands for Maurits Cornelis, by the way).  Mr. Escher was fascinated with impossible spaces and the division of planes in unique ways.  He was fond of using tessellations in his art.  If you have never seen any of his symmetry work, you should take a gander!  He certainly saw things differently.

We started with the lesson in Penrose the Mathematical Cat on tessellations and then tried our hand at making our own tessellations by warping rectangles, cutting them out and then arranging them into a design. Penrose gives a short and easy description of how to do this.  Then we moved to a website about M.C. Escher and spent some time looking at his amazing art!  By all means, go to his official website (Mr. Escher died in 1972, but his foundation maintains a website of his work) at: 

http://www.mcescher.com/

His works of symmetry can be viewed by clicking ‘Picture Gallery’ and then ‘Symmetry’.

While searching for more information on tessellations we ran into this very fun website; it’s a treat for the eyes and you can download several Java applets to fool around with various designs (yes, long address, isn’t it?)  The shortened version or home page is www.bugman123.com – from there you can click on “Math Artwork”.

http://www.google.com/imgres?imgurl=http://www.bugman123.com/Math/Color.jpg&imgrefurl=http://www.bugman123.com/Math/Math.html&h=202&w=350&sz=64&tbnid=Dxp5T60GulBgAM:&tbnh=69&tbnw=120&prev=/images%3Fq%3Dtessellations&usg=__YEuG76R2xFlxZ8s1pQGDfVZ3EVY=&ei=WzILS5ztIJHgswPjmok4&sa=X&oi=image_result&resnum=5&ct=image&ved=0CA8Q9QEwBA

And finally, we happened to have a tessellation puzzle of bugs, so worked with that for a while at the kitchen table.  Max was better at fitting the pieces into clumps; I could only seem to get them into a long line.  He is definitely more spatially oriented than I am.  I would not have made for a very good dentist!  The Busy Beetle puzzle can be found here:

Here are some other fun tidbits that are tessellation-related:

A coloring book.

 

Slow Parenting

This morning over breakfast I read an article in this week’s Time Magazine titled ‘Can These Parents Be Saved?’  It’s a riveting romp through the past generation’s parenting habits and how some moms and dads have turned into anxious helicopters buzzing a continuous circle just over their children’s heads lest they fall down or make a mistake, or worse, eat something with partially hydrogenated soybean oil in it!  The author, Nancy Gibbs, did an outstanding job of compiling seemingly harmless events such as a school auctioning off the right to cut in front in line with the car and drop a child off directly in front of the school building, or the development of the leash and harness systems you’ve seen some toddlers wear, or groups of parents lobbying to get jungle gyms off of playgrounds, or worse yet, schools cutting out recess to use that time to improve test scores with parent approval, or some preschools offering Mandarin Chinese lessons - she compiled these into a much bigger picture of what is going on with us crazy parents.  Alone, these events seem rather benign, but put them together and they paint a rather startling picture.  She’s right!  She states, “we were so obsessed with our kids’ success that parenting turned into a form of product development”.  A child was something we could truly sink our teeth into – like a project!  She is also pointing out how our worries are sometimes getting the best of us and rendering us ridiculous.  She stitches words together more precisely than I can to convey the message and she’s good at it – read the article if you can here because I don’t feel like I’m doing a good job getting to the heart of her premise:

http://www.time.com/time/nation/article/0,8599,1940395,00.html

It got me to thinking about those of us who homeschool and how we might or might not lean in this direction of over-parenting.  Of course we want our children to be successful in life, but what does that really mean?  Are we secretly aiming for CEO positions with multi-million dollar a year salaries for our kids?  Is that success?  In whose eyes?  Why are we homeschooling anyway?  Why are we pouring so much of ourselves into our kids and their educations at home?  Is this about them, or……could it possibly be about us?? 

Please don’t misinterpret what I’m saying.  I’m not trying to be accusatory.  I’m just trying to encourage some thought about all of it, to help us all stay balanced and therefore raise balanced kids, because I think the slope is slippery and we can easily tumble down it and hit a rock at the bottom.  Ouch.  I’ve been thinking about it all morning – it’s a rather eye-opening subject.

She brings up the idea of s….l….o…..w……p….a….r….e…n….t….i….n…..g; some call it free-range parenting.  Loosening the grip, letting kids be.  Letting kids have ample time to play so they can tap their natural imaginations and learn to problem-solve.  How about dropping some of your children’s activities?  Slowing down the pace.  She points out that due to our national economic situation, many families have had to scale back all of the running around and much to their surprise, they are learning that they like it!  Their relationships with their children have even improved.  Less car time, more face-to-face time. 

We homeschoolers can benefit from some self-examination in this arena, too.  We are in a very unique situation, one where we spend an awful lot of time with our children (not time spent awfully, just a lot of it!)  Of course we want the best for our kids.  We pulled them out of school or we decided to homeschool them from birth, for deeply personally reasons.  We need to be aware, though, of how much of ourselves we are asking our kids to become in our hopes and dreams for them.  How much pressure are we applying on a daily basis for them to pull ahead, for them to learn everything about a subject we can possibly get our hands on?  I would wager that some parents might use the level to which their children excel as a direct measure of their success as parents – an affirmation of sorts.  Then it becomes an issue about us, and not the children and their best interests. 

I struggle with this concept internally as I put together materials for Max to learn from.  I have to be very, very careful that I stop to think about life from his perspective, not mine.  The last thing he needs is pressure from me, whether it’s real or imagined, for him to learn something or worse, my expectation that he needs to excel at it.  There is a fine line between a genuine interest in a subject on his part, and my excitement to teach him said subject. My excitement could easily overpower his desire to learn – and then I’ve blown it.   As a relatively new homeschooling mom, I am concerned about this for Max’s sake. 

We purposely opted to not sign up for classes or co-op events for a while so that we could feel our way through homeschooling.  I am so glad I resisted the urge to jump at the science class, the art class, the web-based opportunity that meets every Tuesday and Thursday at such and such a time, etc.  Our days have taken on a peaceful rhythm, one that I am reluctant to trade in for more activities.  We have lots of breathing room, many casual hours in which to read, draw or just hang out.  The only threat to Max’s well-being I would wager, is well……me!  And my desires for him.  I am so glad I picked up Ms. Gibbs’s article this morning and read it through.  Maybe it was just good timing – sometimes that happens.  You’ll be mulling over an issue in your head at various levels and then along comes a book or article that helps you sort it out.  This appears to be one of those times.  Please post your thoughts, even if you disagree.      

 

Covert Detectives in the Neighborhood

Originally we began tackling geography by learning the major mountain ranges, rivers, continents, deserts, oceans, etc. along with various geographical terms.  Necessary information in my mind, but it was dry and dull – working on blackline maps, working on the spellings, reviewing and then quizzing.  It was as good a place to start as any, but a very good thing happened a long the way:  I stopped to think about it!  Sometimes that’s the answer.  Stop.  Think.  Move forward, perhaps in a different direction.

As a grownup, I am learning that I’m making assumptions about Max’s knowledge base.  Well, doesn’t everybody know that north is that way?  And if you turn in this direction, you’ll be facing to the west, where the sun sets, right?  Basic information which when I stopped all the noise to think, is probably not a part of Max’s internal world.  So what’s the point of trying to cram in places in the world when he doesn’t understand some of the basic underlying concepts?

Brown Paper School to the rescue!  The Book of Where:  Or How to be Naturally Geographic by Neil Bell:

 

This book cuts to the chase with activities designed to help you figure out where you are in space, where you are in  your world.  No better place to start than in your own house!  We blindfolded ourselves and tried to find a pretend piece of hidden gum under the third couch cushion in the living room.  Next the ‘gum’ got moved across the house to the master bath’s top drawer on the left sort of scenario.  The point they were trying to teach is that we can use all of our senses to determine where we are at any given time.  With our sight taken away, we had to rely on photographic memory and a few bumps here and there to help us get where we needed to go.

Next we learned about the importance of drawing things to scale.  Max chose to measure his room and a few things in it (like the bed) and he drew a bird’s-eye view of that room on graph paper using a scale of 1″=2 feet.  Now we have a better understanding of distances on maps and the realization that even though Texas looks like it’s ‘right over there’, it takes forever and a day to drive there.  Bummer and wonderful!

Yesterday we went on a stroll about the neighborhood and pretended we were helping a private eye by the name of ‘Detective Oh No’ case the neighborhood.  We followed along with the story and in the process began learning our city’s numbering and naming system for streets.  We took a clipboard along and Max diagrammed out the streets and the house numbers, learning as he went.  After we safely avoided the 10-ton garbage masher with the meanest looking driver this side of Cleveland and a granny in a wheel chair wearing combat boots and a beard, we made it back to the ranch to look at the data.  I think Max has a better appreciation for our mail carrier now since finding all of those numbers and houses can be confusing! 

Next week we’ll be making our own compass and will take a look at how the earth and sun interact.  It’s going back to square one and building from there, which is, well……….brilliant!  And so much more applicable at this stage.

Assembling a New Unit Study

Tonight I started preliminary research for a new unit study on whales and dolphins.  Max informed me he is also interested in sting rays, manta rays and possibly creatures that are in the deeper parts of the ocean like the Lantern Fish.  This ought to be interesting!  I’m planning a three-week study with nice broad strokes, so maybe we can hit most of what he’s wanting to learn about.  A few days ago we went to the aquarium and saw the sting rays getting fed their crab rations – ick.  But they seemed to like it very much!  I was more tuned in to the two seagulls who have permanent wing damage – they were stationed on the fake rocks next to the sting ray pond.  They hang out there all day and don’t seem to realize they are hanging out on fake rocks near a fake ocean.  They even jump in and paddle around with the sting rays. 

So, am finding lots of neat stuff pertinent to the subject at hand.  We might even watch Free Willy!  Nova has a good film out about whales and dolphins and there is an IMAX movie available, too.  I usually use the week in between each six-week school block to catch my breath and put together the next six-week block, so that’s the process I’m starting now.  First I start off with an Internet search and try to find unusual, intriguing resources and ideas.  Next I’ll head to the library and see what’s available there.  Sometimes I forget to check what’s already on the bookshelves around here – this time I won’t forget.  If given enough time, we generally have more than enough items to pick from for the three to six week studies we’ve been doing. 

After looking at a bunch of resources and ideas, I try to take a step back and look at the big picture, trying to determine what aspects of the subject are the most important to offer.  In this particular study, I can think of a number of topics such as whaling and its history, what whaling has obviously done to the whale populations (interject my own agenda there, huh?), the properties of sound and echolocation (how whales and dolphins communicate), migratory patterns, cool facts, rescuing beached or stranded whales, which of these mammals are endangered, regions of the earth they inhabit (geography), marine biologists and what they do, mother/baby relationships, size comparisons, etc.  I’ll have to think about this some more.  It’s easy to see some science mixed in there, along with geography and history.  Pulling spelling and vocabulary words will be easier once I have some of the materials in-hand. 

Then I have to take a step even further back and remember that Max has a genuine interest in this subject, so I’d best not stomp on his interest and kill it.  Too much is too much.  Always searching for that balance in our learning so as not to overpower him or turn him off.  That’s not an easy thing to establish, believe me. 

So, making my way through the beginnings of another unit study, one which I’m looking forward to.  It’s a bit of a break from the history tangent we’ve been on thus far, but that’s okay.  Should you have any ideas about resources for this one, could you let me know?  Thanks!!!!!! 

I’m also searching for one or two good literature sources that incorporate whales or dolphins.  These are read-aloud books so we can both enjoy them.  An interesting coincidence this week – having spoken with two moms about reading aloud to their children, two moms who expressed their doubts.  I am a huge proponent of engaging in this activity for as long as you can, even if you have a fourteen-year old seated next to you!  Reading aloud to a child does magical things for vocabulary, for comprehension, for his/her imagination, not to mention it’s a wonderful way to nurture your child.  Who doesn’t love this kind of attention?  The best we have to offer our children is a gift of ourselves and reading aloud to them is where it is at.  Plus you often get caught up in the story, too!  And there are some awesome stories out there.  You’ll be amazed at how quickly your voice gets stronger.  At first I got hoarse.  Now I can read three or four chapters at a time without a problem.  Sometimes if we’re snacking and I’m eating, I’ll ask Max to take over and read for a while until I finish.  Somewhere that perfect book about a whale or a dolphin will pop up and we’ll stumble upon it.  One I can recommend that was read over the summer is Grayson by Lynn Cox:

    

It’s a heartwarmer about a girl who meets a lost baby Gray whale while out on her daily ocean swim; beautiful imagery!  You’ll get attached to all of the mammals……..

Back to the search! 

Math Adventures – Part B

Just a reminder to not forget about all of the math books offered through Marilyn Burns and the Brown Paper School.  You can see those books in two previous posts, one titled ‘Heading Math-Induced Whining Off at the Pass’ and the other, ‘Brown Paper School’.  I opted not to re-post them here, but they are definitely books not to be missed when thinking about a living math approach!

Feeling somewhat more energetic this evening, thank you very much, so I can tackle eleven or twelve more math adventure resources.  Remember, these are based on a ‘Living Math’ approach, which is a different take on teaching math.  This approach helps to establish a working foundation upon which a child can build; it helps the child see quite clearly that math is basically everywhere, that it seems to be one of the guiding forces of our universe.  It also establishes the realization that math is interesting!  Even if the concepts seem way over a child’s head, it doesn’t hurt to introduce them – and there are plenty of cleverly written ways to accomplish these introductions.  Tomorrow Max and I are taking a look at the Möbius strip – not an in-depth examination, but a smidge more than a cursory glance.  We’re going to play with one, pretend we’re a bug crawling on one and trace it’s path, and do some cutting to see what we end up with.   The lesson should take about 15-20 minutes.  If he has energy or interest left to look at what Penrose has to say about nature’s use of probability in redwood tree growth, well then, we’ll head in that direction.  If not, that’s okay.  I am completely comfortable following a gentle, curving path through math concepts right now instead of a pointed in-your-face-learn-this-because-you-are-in-fourth-grade tactic.  It just doesn’t FEEL right – I say this even as I am stifling the urge to pull out the multiplication worksheets again!  He has a grasp of the multiplication tables, but is not lightning fast with his answers – he’s tried to stick the facts into the crevices of his memory and it’s just not working for the time being.  My response has been to step back and not pressure him.  I don’t think his difficulty with the times tables is unusual and would surmise that many children experience a similar period of time.  And that’s all it is – it’s a period of time in which multiplying is not important in his world.  When he is ready, I’ll know and we’ll take it from there.  There are several resources listed below to help teach multiplication in a fun way.

Okay – more resources!

Click on the book if you’d like to learn more about it.

Young Robert’s dreams have taken a decided turn for the weird. Instead of falling down holes and such, he’s visiting a bizarre magical land of number tricks with the number devil as his host. Starting at one and adding zero and all the rest of the numbers, Robert and the number devil use giant furry calculators, piles of coconuts, and endlessly scrolling paper to introduce basic concepts of numeracy, from interesting number sequences to exponents to matrices. Author Hans Magnus Enzensberger’s dry humor and sense of wonder will keep you and your kids entranced while you learn (shhh!) mathematical principles. Who could resist the little red guy who calls prime numbers “prima donnas,” irrational numbers “unreasonable,” and roots “rutabagas”? Not that the number devil is without his devilish qualities. He loses his temper when Robert looks for the easy way out of a number puzzle or dismisses math as boring and useless. “What do you expect?” he asks. “I’m the number devil, not Santa Claus.” (Ages 10 to adult).

Yes!  A pleasant blast from the past, only this one’s not grammar related.  This DVD would be something I would look for for Max when we’re ready to revisit those tables of numbers.  Join the Schoolhouse Rock team as they explore math and multiplication with their unique style of irresistible melodies. This classroom edition DVD includes favorites such as Three is a Magic Number and My Hero Zero. Includes a bonus interactive assessment activity to reinforce key learnings, Public Performance Rights, and a printable educator’s guide.

Hilarious reproducible stories and follow-up problems, reinforce essential fraction skills: addition, subtraction, division, multiplication, decimals, ratios, and more. Includes annotated answers.  By Dan Greenberg.  Louis Lewis, Fractional Private eye is a character in the book as is Texarkana Bernstein, the world’s greatest adventurer and her trusty dog, Woovis.

We have this one and will pull it out eventually.  Another Dan Greenberg humorous take on math.  He has other comic strip math books, too.

From a homeschool mom reviewer:  “Many children struggle learning and recalling multiplication facts, and need other techniques rather than rote memorization to master these skills. Eugenia Francis’ workbook utilizes wonderful, strategies and methods to do so – such as learning to recognize and attend to patterns for the multiplication tables, using memory tricks/mnemonics, and other engaging and fun techniques. I recommend Teach Your Child the Multiplication Tables as a helpful resource for children to learn the math facts and understand the principles of multiplication.”

This is in my shopping cart at Amazon as a reminder to buy it or find it.  For the auditory learners!  Some reviewers said the songs are corny, yet the writers took the time to really think about this strategy and came up with a tool that works.  Yes, you can move on to Division Unplugged when you are finished if you want to.

Another multiplication option.  In this one the numbers are connected to different characters and then stories are told about the characters.  It’s a picture method of learning the facts.

More songs.  I guess the accompanying DVD wasn’t that good, but the songs are catchy.  They can also be purchased as MP3’s via Amazon.  Did you know that some penguins can rap?  The song isn’t too bad, so don’t worry.  Listeners will learn about our world, music, art, history and science while practicing math because the writers incorporated layered learning throughout.  And this is interesting as I’ve not heard this term before – it received the 2005 carschooling award.  Carschooling.

Science fiction, teenagers, mathematical absurdity and problems in the fourth dimension.  This book is more suited to older kids, sixth grade and up, maybe even older.

Activities, math concepts and math history.  The subtitle is “100 Ways Parents and Kids can Share the Wonders of Mathematics”.

This book is structured in a question and answer format, with the questions having been submitted by actual students trying to understand pre-algebra.  Dr. Math answers the questions in a non-threatening, often easy manner that many younger kids will be able to understand.  This is a good reference, too, for those of us who have been distanced from algebra for sometime and are now faced with teaching our children!  Dr. Math to the rescue to help explain things.  Whew.  Dr. Math can also help with geometry.

I think I included this book  in another post awhile back.  A more-toward-middle-school-age book.  Join the Cryptokids as they apply basic mathematics to make and break secret codes. This book has many hands-on activities that have been tested in both classrooms and informal settings. Classic coding methods are discussed, such as Caesar, substitution, Vigenère, and multiplicative ciphers as well as the modern RSA. Math topics covered include: – Addition and Subtraction with, negative numbers, decimals, and percentages – Factorization – Modular Arithmetic – Exponentiation – Prime Numbers – Frequency Analysis. The Cryptoclub presents a number of different systems of encryption and methods of breaking them. Each type of cipher is presented in detail and exercises are included allowing students to apply the techniques presented. The Cryptoclub also includes short descriptions of famous examples of secret codes, including the Beale Ciphers, the Zimmerman telegram, and the German Enigma cipher.

Herein ends the current tour through Math Adventures.  Be sure to refer to Julie Brennan’s site www.Livingmath.net for more information.  My next post will likely be about math games!

Math Adventures – Part A

I spent a couple of hours last night tooling around the Internet, continuing to search for a certain type of math book, the type that exhorts a covert ‘math through the back door’ approach.  In the past Max has been keenly aware of my efforts to help him become solid on his multiplication tables or some similar mathematical task.  He resists those efforts as if they were the cause of the plague!  Hmm.  Maybe he knows something I don’t.   He has hypersensitive ‘math-dar’ on board and proceeds to shut down if I pull out some flashcards or place a worksheet in front of him.  Even when he attended a small charter school, math worksheets and workbooks flipped his switch to OFF.  He saw them as drudgery, something he must endure (I feel that way about most variables of housework.)  Math was quickly becoming a minefield, one that I had to carefully pick my way through lest a meltdown occurred.  I have a feeling this might be a common reaction in bunches and bunches of kids out there, too.

We reached a critical point of resistance and something just didn’t  ‘feel’ right.  Intuitively I knew that I was going about this the wrong way and he had picked up on my ridiculous anxiety about learning rote memorization math facts.  Children are our barometers – they are intrinsically linked to us and are most certainly aware of our anxieties.  Not to mention the fact that he just plain hated worksheets.  That’s what was probably going on – not the psychobabble stuff.

Truth be told, it wasn’t Max’s problem.  It was mine and I needed to change my philosophy about all of this math business.  I needed to RELAX and let him absorb those math facts when he was darn good and ready, when he saw a logical use for them.  Right now they mean nothing to him and he could care less.  Relaxing is precisely what I am trying to do.  Well, sort of.  Okay, maybe I’m just a smidge more relaxed about it than I was a couple of months ago.

Thus the task has fallen to me to help him see that math can actually be quite an amazing subject, one that is fluid and exciting, one that encompasses a vast body of cool stuff way beyond division, fractions and percentages.  One that makes a difference in daily life or helps us to understand the world around us, one that helps us to see differently.  I needed to let go of my own preconceived notions about math and try to carve out a fun journey through the subject.  Julie Brennan’s website, www.Livingmath.net helped me begin to light the way.  Reading about her philosophy radically changed my thinking and my behavior.  I set out to fill my Amazon wish list with ample resources, resources I’ll eventually have to weed down to a more reasonable number at some point, but I piled them in there so I can share them with you, too.  While reading some of the descriptions and comments about a few of these books, my heart began to beat faster!  Never, ever did I think I’d become excited about math books.  That’s what is so surprising about life – our philosophies can gradually shift and mold themselves to suit us as we change and grow.  We surprise ourselves.

So……here are some examples of a more well-rounded, less tactical, much more fun approach to teaching and learning math.  Julie recommends taking it slowly to see how your child responds to the shift in philosophy.   I could not be happier nor more relieved to report that it’s working for Max.  So far he’s enjoying looking at math through the eyes of Penrose, the mathematical cat, as well as the books written by Marilyn Burns and company.  See the post on how to head whining off at the pass under the math category for more information about those books.  I’ve included excerpts from comments readers have left about the books below because many of these I do not yet own or have not yet checked out from the library; they are on this list because there was that magical something about the book that flipped MY switch to on!

I would be amply pleased to spend our entire year on just these books and maybe toss in some math games here and there.  In my view, this is laying a unique and thoughtful foundation for more math to come later on.  If we don’t look at another worksheet for the rest of the year, then that’s fine.  Really – it is!

These are not organized in any particular fashion – just random craziness, which generally works for me on most days.

Please click on the books to find more information about them and as always, check your library for them first!

I need to start out this section with a cheer for Penrose and his mathematical mistress, Theoni Pappas.  We are almost finished with this book and will be moving on to more Penrose shortly.  Max nearly always asks me to keep reading into the next section – we have been introduced to some fascinating concepts through the eyes and ears of a cat.  It’s very cool.

Here’s the continuation of Penrose’s journey.  I would be remiss not to mention Penrose.

More.  Can never have enough!

Poetry dances with math in poems for two voices.  Reviewers say it’s a lot of fun and kids seem to take to it.  Theoni Pappas is fab!

Again by Theoni Pappas.  Mathematical vignettes.  It got blasted (and I mean blasted) by one reviewer, but this person seems to have been struggling with a superiority complex?  Bent the whole review on pointing out the flaws.  That said, the book is meant to be an introduction to various concepts.

This book contains wonderful illustrations of a boy and his unforgettable dog, Frank. The boy, as he’s referred to in the book, uses Frank as a unit of measure.  The boy also calculates fascinating and interesting facts about peas (his least favorite vegetable), humpback whales, his father and the bathtub.  It inspires readers to reconsider measurement and allows them to laugh at the same time.  It is a wonderful book full of interesting, if sometimes seemingly useless, facts about numbers, calculation and one amazing dog named Frank!

Greg Tang, the author of this whimsical collection of math adventure books, gets bonus points just for thinking hard about his titles!  Mathterpieces:  the Art of Problem Solving utilizes artwork from famous painters to help the reader problem-solve via grouping.

Greg Tang again.  Here you get a rousing dose of poetry to help you solve some tricky grouping problems.

Mr. Tang uses his mastery of riddle-making to develop skills in grouping, pattern recognition and orderly thinking – blink-of-an-eye problem solving because it teaches you to perceive patterns.

A book with a similar theme as his books listed above; this on is suited for a younger set, maybe ages 4-8.

In this book, ‘W’ stands for ‘when are we going to use this stuff anyway’, which in MY book fits where my kiddo is at right now.  What’s the point?  A reviewer writes:  G is for Google explains complex math concepts in a palatable format. From “abacus” to “zillion,” detailed descriptions are combined with fun cartoons and illustrations that bring math concepts down to earth. Even adults can learn a thing or two from this book: for instance, how the German city of Königsberg, with its seven bridges, came to demonstrate the network theory. How many grown-ups really know the quantity of a google, the two ways of writing a google, and how this number got the name “google” in the first place.”  It’s a non-threatening, fun way to start laying a foundation for math concepts.  I like that approach – like it a lot.

This book is probably more suitable for a younger set, ages 4-8 maybe.  Cute book.  The main character uses her dog, Penny, to learn the difference between standard and non-standard measurements.

A review states, “Did you ever wake up to one of those days where everything is a problem? You have 10 things to do, but only 30 minutes till the bus leaves. Is there enough time? You have 3 shirts and 2 pairs of pants — can you make 1 good outfit? Don’t worry — it’s just the Math Curse striking! An amusing book about dealing with numbers in everyday life.”  Younger kids will see the silliness, older children will likely pick up on some of the funny subtleties woven into the text.

Math Appeal is Greg Tang’s sequel to The Grapes of Math.  His books encourage kids to think creatively and cleverly.  This one contains riddles that give clues to solve problems.

An out-of-control popcorn popper, a professor and his dog help to teach kids about the power of 10 and some exceedingly large numbers.  Author is David Schwartz.

I heard tell that this is an entertaining workbook for learning about big numbers.  David Schwartz’s attempt to increase math literacy sounds pretty effective.

Word problems gets some words added to become short stories of the mystery variety.  The hero/detective is Ravi, a fourteen year old who can examine a crime scene and use math to solve the ‘who dunnit’ part.  Classic deductive reasoning, maybe targeted to a middle  school or high school audience.  But definitely one to keep on the wish list until your child reaches that age group!

This is a book wrought with metaphorical mathematical magic.  A reviewer says, “Wendy Lichtman has created a fun mystery involving main character Tess, whose unique view of life has her imagining everything around her as it relates to math. Chapter headings include concepts such as “Graphs,” “Tangents,” “The Additive Property of Equality,” and “DNE” just to name a few.”  Please note that there are references to a possible suicide in this book and of course, the obsession over boys that teenage girls experience.  This might be a very good read-aloud book.

More teen life, metaphors and math.

When a school district opts to ban math, of all things, from its curriculum base, most of the kids faint from sheer joy.  Not Sam and Jeremy, however.  They set out to prove that math is useful and necessary in art, music, science, architecture, nature, patterns, etc.  One-page biographies of famous mathematicians are sprinkled throughout the book along with thoughts on chaos theory and probability.  This is a wonderful example of a Living Math approach.

A good resource to teach about the factor of scale.

A reviewer and teacher said, “I purchased this book as a way to provide my 6th grade math students with some fun ways to understand shapes. What I liked about this book was that it wasn’t just discussing shapes, but covered perimeter and area as well. The “magic tricks” made the class sit up and pay attention when I read them to the kids. And, they all wanted to try out the “tricks” themselves!”  Zachary, the main character, keeps forgetting that Friday is math show-and-tell, so he has to use ingenuity and everyday objects to demonstrate math concepts.

Imagine waking up one morning to find a cat permanently affixed to your cranium.  The cat will only go away if you can win a game of probability.

This author (Cindy Neuschwander) has produced a number of books in this series – highlighting a medieval plot mixed with a math concept.   This particular book helps to explain place value.

This is a ‘must have’ book for me, along with the second volume.  Volume one focus on moments of mathematical discovery experienced by Thales, Pythagoras, Hypatia, Galileo, Pascal, Germain, and still others. Volume Two dramatizes the lives of Omar Khayyam, Albert Einstein, Ada Lovelace, and others.

Because I’m getting tired…….I’m going to cut and paste reviews that are not copyrighted here to give you an idea about the rest of these resources.  “Here’s a delightful little book that combines the joys of mathematical recreation with some fine storytelling. It follows the Arabian adventures of a man with remarkable mathematical skills, which he uses to settle conflict and give wise advice. The tales of his travels involve the solving of mathematical puzzles and sharing insights from the minds of some of history’s great mathematicians. In reading it, you can almost smell the spices and feel the desert wind. You just don’t find this kind of atmosphere in books about mathematics.”

Okay, all signs are pointing toward my bed.  My energy reserves have officially left the building.  I can no longer see straight or think well.  I will pick up where I left off with many more fantastic books about math adventures!

Upcoming Posts

I feel compelled to share all of this wonderful information – and believe me, there is much more to share!  I kind of need to take a breath and get my bearings again so I can stay organized and focused.

I’m currently working on posts about the following:

Math Adventures (changing your philosophy to embrace a whole new and entertaining style of learning math)

Math Games (those clever game makers are at it again; they’ve been at if for awhile, actually)

Literature (where to get the good stuff and once you find it, what to do with it)

Language Arts (fun with words and beyond)

Probably won’t post anything until next week – going to take the weekend off to play and get back to my camera.

Art, Artists and Art History – Beginning to Search

I want Max to play with paint.  I want to get all ooey gooey, messy, artsy with him and let him explore that side of himself.  Art is a HUGE topic because it can go in so many varied directions.  I’m a photographer drawn to bright colors; I used to do a fair amount of drawing and have experimented with other forms of art.  Time spent in this way has provided me with an immense amount of pleasure and a very therapeutic outlet.  We humans are meant to work with our hands and many of us don’t take the time to experiment with art because we may think  it’s cheesy, it’s intimidating, it’s for sissies.  No it’s not to all three counts.  Don’t wait for the planets to align, for all obstacles to clear themselves out of your way.  JUST DO IT.  Go get some paper and some paint and let er’ rip.

Art in a homeschool situation takes a bit of planning because you need some materials.  But remember, art doesn’t always have to consist of a messed up kitchen table, dribbled paint on the floor, glue on the chair.  You can come at it from different angles and use literature to learn about art and artists, too.   I’m looking for resource materials to help us at least be a little directed and here’s what I’ve come up with so far………I will keep searching and will post about the treasures that are out there.  Am looking for a good set of art cards (reproductions of masterpieces), but can’t seem to locate any just yet.

Stellar.  Have it.  Use it.  Love it.  Painting in Van Gogh’s style is gratifying – it’s the first project.  A perfect mix of art history and styles – some twenty plus artists are represented.  I had a hard time being honest with Max about the fate of Van Gogh.  I did mention him cutting off his ear, but not the suicide part.  Lots of master artists struggled with mental illnesses but I feel he doesn’t need to know that Van Gogh shot himself at the end of a long and depressing life.  I just said, ‘he only sold one painting and then he died’.  And felt guilty.

Got 33 five-star reviews on Amazon, so it must be worth looking at.

Lives of the Artists:  Masterpieces, Messes (and What the Neighbors Thought) by Kathleen Krull.  Sounds juicy!  This is available as a cassette tape or a CD (and as a book as well).  The CD/cassette is about 3 hours in length.  “From Da Vinci to Warhol, each of these 20 artists is respectfully exposed for their idiosyncracies as well as their contributions to the history of art.  What they ate, what they wore, who they loved and who their friends were – it’s all here.”  Quote taken from an audio book site.  This might be just the ticket to help kids make connections by learning about those idiosyncracies.  Ms. Krull has other similar offerings about writers, musicians, presidents, athletes and extraordinary women (hey, wait.  Aren’t we all extraordinary??)  You can read more about those here:  http://www.kathleenkrull.com/wrtintro.html

Good basic foundation for design.  Simple yet it gets the point across.

These are fun to color because you can manipulate the design by varying colors.  Pictures within pictures.  There are many offerings in this series – even a stained glass type that can be hung in windows to let the light shine through.

From the Mixed Up Files of Mrs. Basil E. Frankweiler is about two children who run away to spend a week in the Metropolitan Museum of Art in New York and come face-to-face with a mystery surrounding a statue potentially crafted by Michelangelo.   Three-hundred-twenty-eight reviews and it came out with 4 1/2 stars.  Won a Newberry Medal in the late 60’s.

Marvin lives with his family under the kitchen sink in the Pompadays’ apartment.  He is very much a BEETLE.  James Pompaday lives with his family in New York City. He is very much an eleven-year-old boy.  After James gets a pen-and-ink set for his birthday, Marvin surprises him by creating an elaborate miniature drawing.  James gets all the credit for the picture and before these unlikely friends know it they are caught up in a staged art heist at the Metropolitan Museum of Art that could help recover a famous drawing by Albrecht Dürer.  But James can’t go through with the plan without Marvin’s help.  And that’s where things get really complicated (and interesting!). This fast-paced mystery will have young readers on the edge of their seats as they root for boy and beetle.  In Shakespeare’s Secret Elise Broach showed her keen ability to weave storytelling with history and suspense, and Masterpiece is yet another example of her talent.  This time around it’s an irresistible miniature world, fascinating art history, all wrapped up in a special friendship— something for everyone to enjoy.

by Justin Denzel and is about a boy who is a talented cave painter in the era of the Cro Magnons.  We read Denzel’s Hunt for the Last Cat as part of the unit on prehistoric man and enjoyed his style of writing.

Part of a review:

“Based on “thin threads” of truth, I, Juan de Pareja explores the relationship between famous 17th-century Spanish painter Diego Velazquez and his black slave, Juan de Pareja. Written in first person as if Juan is really telling his story, it is the chronicle of much of Juan’s life and his colorful experiences as apprentice to a master painter.

There are many excellent aspects of this book, yet I think that the “strength” of the character of Juan is the book’s biggest asset. Many books that are simply first person narratives are dry and boring, yet one could never complain of boredom while reading I, Juan de Pareja.  Juan’s intelligence shines through in every page and his intuitiveness fills the book with detail. Also, his struggle to paint (because Spanish slaves at the time were forbidden to practice the arts) is fascinating, suspenseful, and ultimately inspiring. This book would not be a 5-star read without a strong character like Juan.

Historical detail also adds great richness to the book. Author de Trevino has captured the mood of 17th century Spain perfectly, and her accounts of Juan’s Italian travels fascinate the reader as well. Art facts and descriptions are well-placed, and the reader will find themselves interested in the rich history presented in the book, rather than bored by it.”

A story about the bronze horse that Leonardo Da Vinci never got to complete for the Count of Milan.  A group of modern-day artists picked up where Leo left off and finished his project.

On with the search!  Please comment if you know of other great resources for art.

 

Brown Paper School

“Accept no substitutes for fun.”  Quote taken from the back of a Brown Paper School book.  I just ordered some used copies of a few more titles out of this series and am anxiously awaiting their arrival from Amazon – some of them were a penny each, so it seems these have been around for a while – and have been well-read.  What I am struck by in the reviews of these books is that when someone read these during childhood, the ideas and information stayed with the person into adulthood and made a lasting impression.  One person stated that Marilyn’s books impacted her attitude about math to the extent that she became a mathematician when she grew up!  Many have read these books over and over, gleaning new and wonderful things each time, I’m sure.  I am entirely impressed with their books on math and time and wanted to add more of them to the collection.  They list ages 9-12 as the most appropriate, but surely forty-year olds can fit under that umbrella, too!

I’ll list the titles that I know about in this post.  Try the library first – see if you like them, and then by all means, buy them for your shelves.  These are often available on eBay.  Here is the rest of the verbage taken from the back of the This Book’s About Time book:

“The Brown Paper School is a series of small books about big ideas, written and designed for kids and grownups together.  The series comes from a group of California teachers, writers, and artists who get together every now and then to work on stuff for kids and to have a good time.  They believe that learning can happen anywhere, and that it doesn’t require fancy tools.  This book and the others in the series are dedicated to anyone who thinks so, too.”

On with greatness!  Here are the titles I’m aware of, but you can bet I’ll be hunting for more……..

Click on the books or the pictures to link to Amazon for more information

And the titles for which I could not locate pictures:

Beastly Neighbors:  All About Wild Things in the City, or Why Earwigs Make Good Mothers

The Big Beast Book:  Dinosaurs and How They Got That Way

Gee Whiz!  How to Mix Art and Science, or The Art of Thinking Scientifically

The Book of Where:  How to Be Naturally Geographic

The Reasons for the Seasons:  The Great Cosmic Megagalactic Trip Without Moving from Your Chair

Make Mine Music!

I am Not a Short Adult:  Getting Good at Being a Kid

Only Human:  Why We Are the Way We Are

Word Works:  Why the Alphabet is a Kid’s Best Friend

And finally, here is a link that leads to a page containing most, if not all, of the math books for kids by Marilyn Burns.  She is a cornerstone in the Brown Paper School book movement, a teacher, and an author.  She teaches teachers how to teach math and is well-known and respected as an educator.

http://home.avvanta.com/~math/burnsbooks.htm

If you’d like to learn more about Ms. Burns, you can find that information here:

http://teacher.scholastic.com/products/authors/burns.htm

(funny how Scholastic doesn’t mention her involvement with Brown Paper School publishing…hmm)

My, How the Week Flies

A week of school around here looks something like this:

MONDAY~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Not the best, most productive day of the week because apparently, those two out-of-the-routine weekend days throw my child wildly off course.  When I reveal the first order of business for school on Monday morning, I am usually greeted with angst.  It’s the same reaction every week.  Now that I recognize the pattern, what to do about it?  Not sure.  He thrives on routine; I’m more of the by-the-seat-of-your-pants kind of mom, so each day is different in my world.  I let my moods and ambitions drive me and have never been able to stick to much of a routine.  Weekends are generally carefree affairs where we go with the flow as a family and don’t really plan things.  We eat when we are hungry, sleep when we are tired – that kind of mentality.  Mondays are the days when we become painfully aware of my inability to be disciplined with time-management and keep the days consistent.  Monday is also the day when I secretly believe that I can change and that I CAN master the art of routine – I can do this!  I can keep it together more or less for about five days, but even by Thursday I’m beginning to slip.  Max would rather that I were more structured and predictable, I think.  Will keep working on that.  We always should have things to work on about ourselves………and sticking to a routine is my monster to tame.

So……here’s what Mondays usually look like as far as homeschooling subjects:

Grammar is a decent subject in Max’s mind and he rather likes it.  He’s good at it, too.  We usually start out with two sheets of Daily Grams – short and sweet daily reviews of capitalization, punctuation, grammar concepts and all kinds of nifty stuff.  It’s subtly repetitive, meaning once you learn a concept, it get’s inserted into work that you’ll tackle a few days down the line, so you’re always solidifying what you learn.   It gradually builds in its difficulty level and I think it is spot-on appropriate for his level of understanding at this point.  I like it, too – it has helped remind me of all the details I used to be a whiz at out of Strunk and White.  Big fan of Daily Grams.  There is a teacher’s manual that you can purchase, but you can have success just looking up terms on the Internet and helping your child over humps that way.

Checking account

We did a unit on money at the beginning of the year and decided to expand upon the topic of money.  Why not start teaching him real-world applications?  I set him up with a mock checking account and a register that was made in Excel with really big spaces so he has plenty of room to write; he has another register to keep track of savings, and he has a credit card with a limit of $20 with simple interest of 5%.  Each Monday he collects his allowance (payday) and has to figure out what to do with it.  He can do extra chores to earn extra money, but has thus far avoided that opportunity.  A minimum set amount has to be deposited into his savings account and he has to take care of any unpaid credit card bills along with the added interest.  He does the math and by now has begun to realize that using his credit card on impulse purchases is not working out so well for his checking account (hooray!)  If he learns nothing else all year, this realization is golden!  At any rate, it causes him to stop and think before he decides to spend on something.  I really try to take a natural consequences approach with this one – let him make choices and then……..face the credit card bill.

Next comes the spelling and vocabulary words for the week, usually numbering from 15-20 words.  These are taken from whatever unit study we happen to be focusing on.  Some are challenging, some are a lot easier.  He has a spelling notebook in which he writes down the new words.  One week I let him choose his spelling words – words which he mastered the first day because they were too easy!  I’m back in charge again, but will occasionally do that and let him make some decisions.

Whatever geography we’ll be working on for the week gets introduced on Mondays too.  I put up several large maps running down a hallway, so we’ll go take a look at those or use blackline maps or the Brown Paper School book about geography (which is grand, by the way.)

Math – please see my post about a Living Math approach (‘Heading Math-Induced Whining off at the Pass’).  On Mondays we’ll do some reading about math.  No math worksheets, though.

History is covered in a unit study format, so it’s broad and enjoyable.  Whatever we might be in the mood for, be it a DVD, a site on the Internet, a library book or two or a game – Mondays always have a history component.

The day gets topped off with reading, either Max reading to himself or me reading aloud.  He is reading the Harry Potter series and will get lost in that, or together we are reading a novel from the library that is specific to whatever unit study we’re working on at the time.  We’ve been able to cover about a book a week with me reading aloud.

TUESDAY ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Back into the rhythm by today, thank goodness.  Tuesdays are always smoother than Mondays.  We start out with Daily Grams, practice spelling words and go over definitions.  Maybe a short stint with the cursive writing practice book.

In math I’m using a ‘Living Math’ approach which is one of the best decisions I’ve made thus far in our homeschooling curriculum.  It is with a great sense of relief that I’ve been able to introduce Max to math concepts without frustration or force.  We are reading books – lots of them.  Math adventures, books about a cat named Penrose whose mistress is a mathematician, books by Marilyn Burns and her team that are engaging and royally entertaining, and others.  Today we learned about the Pythagorean theorem and who conceived it and practiced Roman numerals up to 1,000.  We play math games, do logic puzzles, or…..read!

Tuesdays and Thursdays are science days.  Meaning we are either working from a kit, reading about a concept, or trying an experiment.  Science is the area that needs more fine tuning, but it will get there.  I am probably going to utilize Science Jim as a resource (see www.sciencejim.com).  He has video classes and workbooks that are organized around science and physics topics – he seems to be a lot more pulled together than I am when it comes to a homeschool science program, and he is a funny guy, which is a big plus.  He likes to incorporate silly into his webclasses.  I’ve downloaded his workbook on forces, but have not yet cracked it open.  In January we will likely be joining a science co-op and will work with other families to teach science.  For now I’m kind of shooting from the hip and listening to Max’s interests.

This is the writing program I chose for this year.  You can find it by clicking on the book – it’s available at Currclick.com (which stands for Curriculum in a Click).  So far it’s been a good program.  It’s not boring drill work – it gets you thinking and imagining.  There are three levels you can work under – startup, intermediate or advanced writer.  Tuesdays are the day wherein writing is concentrated on.  During other days Max might send an email to a friend or write a letter to his cousin or write down some thoughts about a book he’s reading.  Not structured writing.  The best part is this is a downloadable program in PDF format, so you don’t need to wait for the book to arrive in the mail.  And it’s super cheap!

WEDNESDAY~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

By order of the homeschooling authority (um, that’s me), Wednesdays have been declared FUN DAY!!!!!!  This is Max’s favorite day of the week.  ArT, PaIntInG, fIeLD tRiPS, FrEE PlaY, ReADiNg, wAlKS,  – whatever we are in the mood for.  Trips to the zoo, to museums.  Computer games that have at least some educational merit.  We still practice spelling and do the Daily Grams, just out of habit.  On Wednesday nights Max takes karate lessons at a studio just up the street.  In the afternoon he either has a friend over or heads over to a friend’s house for several hours – to get away from MOM!  We spend an awful lot of time together .

THURSDAY~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More math, science, literature, spelling, grammar and history.  Drum lessons and another karate class round out the day.

FRIDAY~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First thing he gets a review of the week’s work.  It’s non-intimidating and I try to provide silly multiple choice options for him to pick from, or creative/thoughtful ways to see whether he understands something we worked on.  A spelling test and then vocabulary words are usually provided in a cross-word puzzle format.  This way he has to spell the words correctly TWICE (once on the spelling test and again in the puzzle).  Isn’t that sneaky?  So far he hasn’t noticed what I’m doing.  Plus I’ll throw in questions about math concepts or what we might have learned in history or geography.  It serves to pull the week together and let him see how much he picked up over the course of four days.  Daily Grams, more math, literature and history usually round out the week.  On Saturdays and Sundays we generally don’t do any school work, unless he can’t stand to wait to find out what happens in a book – then we’ll read or watch a DVD pertinent to the unit study.  As mentioned, these two free days serve to send him into a tail spin on Monday mornings.  Argh.

That’s the week.  We are already ten weeks into this school year and I can scarcely believe that much time has gone by already.  I guess this must be working?  I think it is!

I don’t wig out if we have a slack day and don’t get much accomplished.  If that’s the case, we’ll incorporate some work into Saturday and Sunday to even it out.