"Chasing Vermeer"

We have discovered a new readaloud author! Not only does she write thought provoking prose but we get to do art history and maths at the same time!As one reviewer comments:"

Secrets, lies and mysteries surround the work of one of the greatest artists of all time. Moonlit chases, hidden hiding places, and even a secret code help to solve the mystery."

 There are clues in the art work that help you solve the mystery. The art work itself is worth close investigation.The author has her own site with games and puzzles and even downloadable pentominoes for you to work with! 







The book also has plenty of scope for writing projects:"Is writing the most accurate way to communicate, investigate",  "Research letter writing by asking people to describe a piece of mail that changed their lives and then,write me a letter I won't be able to forget ". "At the beginning of chapter three Petra "window gazing" from a train is described, write about a changing scene you have observed on a journey." Then there are descriptive writing examples including the children's narratives of famous paintings(but not just these!) that beg to be used as jumping boards for further discussions/projects.     This is a book we will remember for a long time. And the good news? The author has two more in the series along similar lines. No we haven't read them. Yes we are looking forward to doing so!                                                                                                                              

Penrose the Maths loving cat

Another readaloud! This one we are reading just before individual maths time. Master 13 is really working well with mathsonline and a little bit of help from his sisters.He is working at the Yr9/10 level.

Master 9 is using MEP and really enjoying a different way of working with the same problems. Although he has completed Addison Wesley book 5 I am using the rest of the year as consolidation of concepts and fun stuff like Penrose!

We read about real numbers and then "from Auckland" we learned about Pythagoras(and his school of the Pythagoreans)who believed in the literal reality of numbers. They were so shocked when one of their number discovered irrational numbers that they kicked him out of their school.

Curvey lines

For maths today we had a lot of fun making curves from straight lines.










When straight lines are put through at least two points in a pattern, Bezier curves emerge, giving the illusion of rounded shapes, when in fact no curved lines are used.We're off to find some coloured string to try it like this next

Telling Mathematical Tales

In English a car can circle a building but it can’t do any rectangling or pentangling; at least not without a switch to another language. But there are other languages says Associate Professor Bill Barton, Head of the Department of Mathematics at the University of Auckland where shapes do behave as verbs, and it is possible to speak of pentangling, and a rectangle is seen as something that rectangulates. One is the Navaho people of North America.,
If we imagine then, as Bill does, what sort of geometry might emerge from a language where shape is seen as an action, we are likely to concede that it could be quite different from the geometry we learned at school. The chances are it would be more dynamic, perhaps with the basic unit as a moving circle rather than a straight line.
If maths is a creative human activity rather than a set of finite rules waiting to be discovered, this has pedagogical implication. An important one in Bill’s view, is that “play” and exploration need to be more highly valued at all levels.
Play is encouraged at the elementary level of arithmetic in primary grades, then vanishes to be replaced throughout high school and through undergraduate studies with an unremitting focus on acquiring knowledge and skills. It emerges only at postgraduate level and beyond, where for mathematical researchers, it becomes the centre of the creative part of their work.
“Mathematics is a created world, a world of the imagination a kind of academic Middle earth,” says Bill. “Research mathematicians play with abstractions. They make things up. And then they manipulate things in their made-up world to see what happens. It’s much more creative than making up a game. Often they’re making up the playing field as well.”
“Mathematical thinking is about relationships between abstractions. Teachers aim to help learners manipulate abstract concepts. But what do we do when children have trouble with maths,” says Bill “we go back to the concrete.” A much more useful approach Bill believes would be to give learners more practice with the abstract, perhaps by drawing maps, or plans of houses, or playing games with sequences of numbers, to see what happens and find patterns but without any expectation of a “correct” result.
“Learners need to get used to numbers being things to play with, because that’s what mathematicians do.”

(extracts from an article by Judy Wilford in "Ingenio et Labore: the University of Auckland Alumini Magazine")

Numbers of things

“You can’t really want to do these ghastly sounding sums,” said Hal.
“They’re not ghastly when you understand them.”
“But can you?”Hal asked it doubtfully. It did not seem to her that anybody could.
“I could if they were explained to me.I have to. They’re…they’re my language,” said Una.
“The Peacock Spring” by Rumer Godden

I am one of those who see the study of Mathematics as just that; a foreign language. However I have a daughter who just as Una said “speaks” in Mathematics(and probably dreams in it too) Years ago when we were new to this homeschooling business I worked my oldest two children at the same level and pace in Maths. My oldest plodded away at it(when his mind wasn’t drifting away to a ‘national Geographic article he’d “successfully” hidden behind the text). He couldn’t do much more though, because like me, it wasn’t his language. His sister only sixteen months younger probably cut her teeth on numbers! She tells me now how there was never enough Maths in our schoolwork. Still it took a work of fiction to make my language orientated brain understand this!