After our class this week focused on thinking about geometry, and then the reading, "The Rationale for Using Manipulatives in the Middle Grades", by Dana M. Freer Weiss, my understanding of geometry understanding has definitely increased.
In class I learned about the Ban Hiele Levels of understanding geometry, and that visualization is the first. This makes sense to me because anytime I am doing any kind of mathematical thinking I am visualizing. I really start running into trouble when my visualizations start becoming just memorized number rules because then I've lost the meaning, I don't have those mathematical ideas connected to anything else, so when I try to build some new information in I don't have anything to connect that to either, it has to have its own isolated little spot and isn't very useful then.
In the 1st/2nd grade class today the students were struggling to find the differences between 2-digit numbers and were getting frustrated because their fingers weren't getting them very far and drawings were taking forever. As I moved through the students trying to help and wondering how to best suggest manipulative to my master teacher, I remembered the 7th grade math classes I was I was in this past fall and how the teacher always encouraged them to use manipulatives, even on tests, and the students at that school were some of the highest achieving math students in the district. Probably not just because of the manipulatives, but I bet there were part of it. I am fully convinced, whatever time I spend finding and learning to effectively use manipulatives with students will be worth it.
Finally, I am just wondering about geometry. How can it make sense all the time? Is it because it is all repeated patterns? Is it because of the physical properties of the universe, like a plant growing straight up from flat ground makes a right angle and if another is close by and a leaf lays across the two you have a rectangle and it's properties just because that's how it is? Is there any geometry that hasn't been explained yet or has it all made sense to somebody sometime?
In class I learned about the Ban Hiele Levels of understanding geometry, and that visualization is the first. This makes sense to me because anytime I am doing any kind of mathematical thinking I am visualizing. I really start running into trouble when my visualizations start becoming just memorized number rules because then I've lost the meaning, I don't have those mathematical ideas connected to anything else, so when I try to build some new information in I don't have anything to connect that to either, it has to have its own isolated little spot and isn't very useful then.
In the 1st/2nd grade class today the students were struggling to find the differences between 2-digit numbers and were getting frustrated because their fingers weren't getting them very far and drawings were taking forever. As I moved through the students trying to help and wondering how to best suggest manipulative to my master teacher, I remembered the 7th grade math classes I was I was in this past fall and how the teacher always encouraged them to use manipulatives, even on tests, and the students at that school were some of the highest achieving math students in the district. Probably not just because of the manipulatives, but I bet there were part of it. I am fully convinced, whatever time I spend finding and learning to effectively use manipulatives with students will be worth it.
Finally, I am just wondering about geometry. How can it make sense all the time? Is it because it is all repeated patterns? Is it because of the physical properties of the universe, like a plant growing straight up from flat ground makes a right angle and if another is close by and a leaf lays across the two you have a rectangle and it's properties just because that's how it is? Is there any geometry that hasn't been explained yet or has it all made sense to somebody sometime?
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