Tuesday, August 21, 2007

Fosnot and Dalk Mathematizing Institute Day 1

What a terrific day I had today. With the exception of the fire alarm that interrupted the afternoon session great learning was had by all. Here is my recap...

Fosnot Institute Day 1

Starting to use math with context. It is important for students and teachers to learn math with a context. Allow students to be mathematicians learning and explaining. For too long teachers have been the be all know all.

Here is the context. The teacher poses this question to the class.

A rectangular lot in neighbourhood A is 50m by 100m. Of this lot ¾ of it will be a playground. Of this playground 2/5 will be blacktop.

A rectangular lot in neighbourhood B is 50m by 100m. Of this lot 2/5 of it will be a playground. Of this playground ¾ will be blacktop.

Which Park has more space for blacktop?

In pairs you now attack this problem. As a teacher you stand back and take notes on the conversations happening between the students. This thinking time is important for the mathematical ideas to take place. A push or prompt needs to be held in instead of giving that helping hand.

Here are some photos of our finished work

It was fun to work with a partner and talk math. Together we worked out the problem and were chosen to speak for the math congress. Hmm not bad for my first day back thinking about math.

Following this work time students post their work which had been done on chart paper for a gallery walk. During this time students are encouraged to post notes using post-its on the other pieces of chart paper.

Students need to be trained to have good gallery walks. Choose similar and different solutions. Teachers need to use guided questions to start this process.

· What was done similar to your solution. Is it clearer on this paper?

· What do you not understand on this solution. Is there something missing?etc

Next to the congress. This is a part of the lesson where students become the teachers. You could call it double learning. Students are reinforcing their learning when they are teaching the rest of the class.

The teacher based on the gallery walk chooses examples that will further the learning process. This does not necessarily mean the best examples but examples that add more context to the topic.

During the congress it is important for the teacher to remain on the side lines. Instead of asking Do you get it? The teacher needs to ask;

How many people and put in there own words what this group has said?

Giving a group a second chance to explain a topic will give them another chance to reinforce their knowledge. The second time around concepts are easier to explain or at least seem to be more coherent.

During this congress after the group presented there was time for a pair talk. Are 2 fifths equivalent to 4 tenths. Questions that arise during the congress are the avenues to deeper contextual understanding and avenues to further discussion and scaffolding.

It is not the presenting groups responsibility to explaining the new topics arising from the congress. Other students take turns explaining using their own words and pictures on the assignments hanging up throughout the room.

If students get bogged down in these instances the teacher then jumps in and tries to rephrase the topic. (pictures can be a powerful manipulative)

The congress develops a sense of community in the classroom. It is important to recognize the importance of math to students. Celebrate questions and explanations explaining to students the mathematizing they are doing.

Side note Create a classroom space for working and congresses. Find a way to separate the two pieces of the problem.

From the congress here were some things I heard… Lets prove it.

Of means multiply
(use pictures that are out there in the congress)

  • to prove it you need to disprove it. Find a math sentence that uses of in a different way other than x.
  • two of 5 or 2 out of 5
  • groups of means x?

The use of arrays proves this …?

Facilitator needs to stop this and give this as homework journal. (blog it)(move it back to the individual level instead of the group)

Multiply numerators and denominators the demomenators give the number in the gird(array)the numerators multiplied gives you the amount of the whole.

Communicative Property 2 times 5 is the same as 5 times 2

All the above were ways in which we took the contextual problem and stretched it further our understanding.

Take away the AHHA’s and kids will never want to be mathematicians.

Petagogy… make the kids do the explaining. Take your time and have them do the explaining…double learningl.

In the afternoon we broke up into two groups. We were with Maartin D talking about the landscape of learning. This landscape takes into account

  • Building the landscape of learning.

  • What do children really think and do….

  • What is it that I as a teacher want my students to talk about

  • Building context…what content can I steal….

  • What is the order

  • Big ideas take time to create

  • What models are used

In their supplemental material that is provided Fosnot and Dalk give many examples of teachers and students interacting in mini-lessons and math congresses. This gives educators a chance to see this mathematizing in action. The CD's have the ability to cut and paste video lessons and parts of video lessons into your own customized clips which you can then add to your landscape of learning for the unit you are creating. We went through this task in the afternoon and I was pleasantly surprised with the ease at which we started to create our own landscape to improve our learning experience.

As you watch the many different video clips that are provided you will be able to deduce for yourself,
  • What is the role of the teacher
  • What are the children saying and the math behind it(this is how you neeed to see the footage we watch)
  • What is the big idea being discussed in the video blip?


As we watched the first video clip it was clear that the students were doing most of the teaching and the learning. The teacher was merely a guide to facilitate the learning.

You want the students to start to use the model with a context to understand a variety of different situations.

I went home with a positive attitude and a desire to return the next day and continue my journey into mathematizing and the joy of seeing students be key instruments in their own learning.

Message of day one... Context is important, kids need to be mathematicians.

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