Some of the perils of not understanding the concpets of math are demonstrated in the following video.
The Math Lesson
Mathematizing is solving problems, posing problems, playing with patterns and relationships and proving their thinking to fellow mathematicians. It was so fun to see these ideas in action in the classroom video clips from New York.
There is a diference between activity and genuine Problem solving. So we need more than "Hands ON" Discovery Learning.
Classrooms become communities. Children meed in groups and as a class to present and talk about solutions to common problems. There is "no wise one". convincing arguments are made to the group. Knowlege emerges in a community of discovery.
Doing math is like climbing a mountain. You take it one step at a time. Sometime you can take many steps before seeing the vista and all its beauty. For students to continue to climb and enjoy the journey they need to undertake this journey themselves. Only then will they continue to climb instead of staying at one leve
Many techniques were used with the young learners. They were always placed in pairs and the pairs were carefully selected. You did not want to put the best student with your worst a A and Z pairing. You wanted to do a A and C parining so that there was a difference but not a vast gap.
The students would receive a large problem on a large piece of paper and then in pen put their answers to the question. The teacher would choose examples of the student work and have the students present to the class. The students would lead the discussion and ask quesitons to the presenters. The teachers role was to facilitate the conversation to hit petagogical ideas.
Teaching was done in the form of mini lessons to activate strategies and ideas. Learning was always group based and fostered math language skills.
I am looking forward to using these ideas in the fraction unit I am planning.