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Showing posts from September, 2011

Mathematics History Inquiries

Once a week I dedicate a period of our math study to looking at famous stories, paradoxes, inquiries and problems that real mathematicians have gone through in the past.  I approach it through the following general outline;


 Recreate the historical story, understand who the players were and define the problem
 Have the students attempt to work through the problem and come to their own conclusion on the outcome
 Show the students how the actual mathematician solved the puzzle, and compare it to their own solution
 Connect the concept studied to the larger picture of the history of math, society and how it shaped life and knowledge

So far, we have looked at the following problems this year;


The Case of the Lady Drinking Tea - Dr Ronald Fisher is at a party and serves a lady a cup of tea, however she declines and says she prefers her tea with the milk added first, not second.  He does a scientific test to see if she can actually tell the difference. The results of that test are the foundations…

Organizing your Math Work

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During our presentations today on our most recent Fermi problem (blog post about that coming soon), one thing that emerged from our discussions is just how important organization is; not just when presenting your work, but also during the process of solving the problem.  Several students had too many calculations on their page and they got lost and confused and mixed numbers up.  As a result, one student suggested we make a poster to help us remember some good points for organizing our work.  As a class we brainstormed and then went onto Powerpoint and made a little digital poster.  I printed one off and stuck to the wall next to the carpet, but I also printed some smaller ones off and the students use them as bookmarks in their math journal.



Here is the PDF Version;

Organizing our Math Work




Meta-Cognition in the Classroom

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Hello all. I have a request for resources. I am looking at incorporating more meta-cognition and reflection into my classroom, and was wondering if anybody could share any great resources or books? Also, I am working through my Masters degree, and this will be a major component of my dissertation, so if you know of any theory based work, and practical based work, that would be great.

Thanks in advance if you can help.



The Librarian Who Measured the Earth

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This really is one of the best picture books I have ever read related to math and critical thinking.  It is the story of Eratosthenes, who was the Head Librarian of the great library of Alexandria.  He was also an incredibly curious, and multi-talented scholar who did a bit of everything.  However, his work that he is best known for is measuring the circumference of the Earth.  He did this over 2000 years ago, and his calculation was within 200 miles.  How did he do it?

That is where a great inquiry math lesson pops up, because the book doesn't give you the answer quickly, it builds it up, step by step, stone by stone.  And what I love about this book is how you can take your students along for the ride with Eratosthenes.

It also covers a broad range of other subject disciplines and can be stretched out and kneaded into so many different shapes.  History, language, science, social inequalities, law, government (it has a bit of everything).

How I use it (and how I describe it below) i…

Moving Learning into the Stone Age

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This post is inspired by a wonderful post over on What Ed Said.  Thanks Edna for some inspiration!  Keep up the good work, I am a fan of your site.

We will be starting a UOI on Ancient Civilizations in the coming weeks.  I sat down with myself and I, and we had a bit of a brainstorming session.  We decided that we need to move the unit back to the Stone Age.  I looked at the old unit plan and re-tinkered it to meet our modern, past tense focus.  The only way to go forward is to go really far back.

What has changed?



They used to...... use Lego to make a stop motion video about what a day in the life of an early human was like.

Now, we will go outside for a day and live it.

They used to..... use timetoast to create a timeline retelling the history of their civilization.

Now, we will find a large rock, make our own paint, and tell the story through cave-painting art.

They used to..... use Google Sketch Up  to make a 3 dimensional model of an ancient dwelling.

Now, we go out into the woods, gathe…

Translating our Thinking

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I have this little boy in my class who is very, very good with math.  He gets everything, he can apply it, and he does it in his own way that makes sense to him.  The problem is, and his major goal for the year, is to be able to explain to others how he does it.  I am not to concerned with operations or calculations, but rather how he explains his thinking.  How he makes it visible for us to see.

Today, instead of getting him to explain his thinking in more detail, I got another student to do it for him.  One of my ultra-neat, super-organized girls took his scrawling mess of a piece of paper and sat down to try and translate how he had got to the solution.  With help from the little boy (it was a great mathematical discussion) she was finally able to organize his work into something coherent.

This was a valuable lesson for both students.  For the boy, he had to describe his thinking to another person on a one-on-one basis, without the pressure of the social group staring at him.  He kne…

The Noisy Math Class

Kids like to be noisy, and teachers like to make them quiet.  Line up in rows.  Sit down with your hands on your desk.  Five point check.  No talking in the halls.  Stay in a straight line.  Show me how you listen.  I could go on.

***Aside Rant: Where else in society is it an expectation to start at attention in rows and wait to be given orders?    I can think of one.  So, why do we make it an expectation in school?*** 

I like a noisy classroom.  I like incessant chatter like the drone of a million cicadas (I love the sound of Cicadas in Japan, get outside the cities and it is an amazing wonder).  I have been thinking a lot about listening and sound (great TED Talk), and the impact it has on our lives.  With that in mind, I came up with this lesson today;



We did a mental math activity today.  I had the students walking around the room practicing how to show their thinking.  Instead of doing it in a notebook (a messy one!) we did with words.

Teacher:  Question one; what is three hundred an…

Being messy with Math

We were working on Mental Math strategies today, and I had the students attempting to show their thinking on paper.  First, we try to think of all the steps we do in each problem we try mentally.  Instead of doing this in our heads though, we write down what we see in our heads as we see it (not always an easy task with grade 5/6!).  For example;

134 + 143

In my math notebook I would write

134 + 140 = 274

274 + 3 = 277

These are the two steps in which I followed to do this problem in my head.  We have been working on writing our thoughts on paper as they come into our heads.  During the exercise, I noticed something funny going on, so I called an emergency math congress on the carpet.

Me:  Unicorns (I call them unicorns), I want you to look closely at the following two notebooks, and tell me which one you think is better.

Notebook One was immaculate and neat, everything was lined up in a row and written in perfect numerals, however, under the perfect script were remnants of erased numbers, b…

Henry Climbs a Mountain

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I found this picture book in a second hand store in Canada for about 0.50 cents.  It is the story of Henry David Thoreau, and how he spent a night in jail in protest over the governments acceptance of slavery (he didn't pay his taxes).  The artwork is brilliant.  It is very cool to see how the cell transforms from a plain white space into an area of natural splendor.  I personally love Walden and Civil Disobedience, and it is great to see the general philosophy from those books brought to a level that young children can understand.  There are a lot of big ideas to chew on in this book as well;

Is it right to break a law that you feel is unjust?  Does everybody have the same perception on what unjust means?  What do you think unjust means?  Did he accomplish anything by going to jail?

Henry Thoreau is a colorful and interesting character, and we will certainly come back at some point this year and make some more connections to him.

If you are working in a PYP school, and have a UOI on…