Showing posts from November, 2011

Measure the Blue Bucket

This was how we kicked off our Math class today.  I put the challenge up on the board and walked off to the side of the room and pretended to read a book, letting them deal with the problem as a group.  While they spoke, I took notes on how their ideas evolved.  Here the rough translation of their sequence of thinking: How do we measure the bucket? What unit should we use? (they choose cm) Group worked together to measure around the bucket Great teamwork Got a piece of string and wrapped it around the bucket, cut it, then measured the string Found that the string was 81cm Hold on, that is just around, how about how deep it is? Another piece of string to find the depth of the bucket One student drew a 3D picture of a bucket on the floor and started to write the measurements onto it Found that the bucket was 21 cm deep Next, do 81 x 21 = 1701 (got a calculator for this) Done! What does this mean?  this doesn't look right You can't times the around part

Assessment as a Collective Activity

We often think of assessment as applying to only a singular child.  What that child knows at that brief snapshot in time.  However, our knowledge is not insular, we are a collective species that relies on the group to help us learn.  The collective (which brings up negative images of the Borg and communist Russia) is, I would argue, the most important part of a learning environment.  We learn more from the group than we could ever do on our own, and the sum of our knowledge is far greater than the individual parts. Collective Assessment Activity With that in mind, I decided to try a summative assessment that required the group to work together and use each others specific (and different) knowledge and perspectives to arrive at an insight or a conclusion that is bigger than the sum of its own parts.  Here is how I tried it, in groups of 4; 1) Each student gets a different colored pencil 2) Around the group there are 4 stations, and at each station there is a single piece of paper with a

An Inquiry into Play, Pt. 1

I recently stumbled across an interesting article from a Linked In group that I am a member of.  The articles basic idea is that Hunter-Gatherer societies educated children in a very different manner to how we do it nowadays.  One of the important aspects of this early form of education was a child's sense of play. This got me thinking.  What is play?  How do children play?  What do children think about play?  Is play an effective pedagogy?  What do the children in my class think of play? With that in mind, I have decided to start a class inquiry into the nature of play.  I have no idea where this is going to go, or how it is connected to any of my curricular outcomes; but at the very least, I hope it will give me a better insight into the children I have with me on a daily basis, and how I can structure activities that they find interesting and engaging. I am looking for other teachers around the world who would like to collaborate and try the same thing with their class; underst

Reminiscing about teachers of the past

My wife and I spent some time reminiscing about teachers we have had in our lives. The detail we can recall is astounding. We have such strong opinions, memories, and characterizations of our past teachers (both positive and negative). Neither of us had any difficulty in remembering any of our teachers, from Kindergarden up to University. I can remember each of one of them. I can remember their strengths, weaknesses, the times in which they helped, and the times in which they did not. I am sure you have similar opinions and thoughts of your former teachers. Remember this the next time you stand in front of your students. They certainly will.

The Success of Failure

Making mistakes in an important part of life.  I make them daily. I tend to forget how old my students are, and I give them tasks that are way above their level.  I make assumptions about what prior background knowledge they are bringing to a task (Islamic Art is a great topic, but most of the kids don't even know what Islam is). Today I gave my students (I teach grade 5/6) a very difficult task.  It was a task that puzzled a real Mathematician over 800 years ago.  His name was Fibonacci.  I read about the problem in Jo Boalers amazing The Elephant in the Classroom , and put in on my list to try.  Today, we dove in. A man puts one pair of Rabbits in a place that is enclosed on all sides by walls. How many pairs of rabbits can be produced from that pair in a year, if it is supposed that every month each pair begets a new pair which from the second month on becomes productive themselves? The real challenge of this problem, and the reason I choose to do it now, is that there are mult

Art as Math Assessment

We are coming to a mid-point in our Geometry unit, and before we switch gears into dimensions, planes and 3D objects, I want to do a summative assessment of the first half of the unit (2D shapes, patterning, lines, angles, etc) Note to Self: I have divided this unit into two sections, I would argue unnecessarily. The next time I do this unit, I would like the 2D world of Geometry and the 3D world to be intertwined, not segmented into distinct sections of knowledge. I need to marry them and teach them both at the same time, not two them in two seperate chunks. This is important for the kids to see how they are inter-related, and by teaching them as inter-related parts of the whole, we can make connections easier. That being said, shouldn't all mathematics be taught in the same intertwined manner? Why am I only doing Geometry once a year? Why can't I teach all strands and topics (Data Management, Geometry, Number, Probability, Algebra, etc) at the same time, simultaneously, not

Emergent Group Dynamics

I really love the website Math Pickle .  There are so many great resources, activities, videos, etc.  I wish there was more! Here is the founder of Math Pickle giving a great talk about problem solving. Inspiring stuff. On of the activities I used to today was their Symmetry search . The kids start with an image like the one below; Next, they have to find all the lines of Symmetry in the shape (rotational and mirror). These include lines and rotations in each individual piece of the puzzle, but also as pices combine to make bigger shapes that have lines of symmetry and rotation. In short, there are a lot. The point of the activity for my students today was not to find lines of symmetry. They know what lines of symmetry are. Today was all about organization. How can you keep track of how many lines you have found, and how can you communicate those lines to your classmates clearly? That was the task. Many of them used tallies, different colored markers, letters to show rotation