Priveat Universe Project In Mathematics Video 3

Problems and Possibilities: Inventing Notations

This video demonstrated how giving students a chance to make their own mathematical notations without providing them with standard mathematical notations can be very surprising. They naturally develop their own system of documenting their possible outcomes. The teacher should be willing to discover the notions the students invent. Look to see how they represent their ideas and the teacher should also learning from the student's. We should take the time to listen to and view what they do. Each group within the video had a different way of reporting their findings. It was interesting to see a teacher express her concern when her students did not initially solve the problem using a list but actually used drawings and other representations She was initially intimidated because they did not solve the problem in the way she visioned they would. However, they still came up with valid answers using the drawings. Teachers must be in tune with what students are interested in and what they would like to do and how they would like to solve a problem. Our way is not the only way.
It was cool to see how some students used blocks to represent pizzas and others used lists. Some students used symbols inside circles and others just used abbreviations. I also like the fact that the researchers intentionally used two topping with the letter P to force students to think beyond just using the first letter of the topping. It really forced them to plan out their problem solving technique. The student who used the 1's and O's to make combinations of pizzas in a chart format was really amazing. He was also able to connect the pizza combinations with the 4 tower combinations.
These videos show that students do not need to be force fed mathematical concepts but given the freedom they can learn concepts on their own. It appears a much more natural way for students to learn and they can develop and discuss their own ideas. "We must give student the opportunity to show us" what they can do.