Understanding Geometry Understanding

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?

Singapore is Super Neato

Singapore is super neato.  In 2006 I stepped into that country as I entered Asia and had my mind totally blown.  This week's social studies method's reading reminded me of my short-circuited nerve synapses, especially in the Parker text's printing of the Singapore pledge of allegiance (p. 3-c):

We, the citizens of Singapore, 

pledge ourselves as one united people, 

regardless of race, language or religion, 

to build a democratic society based on justice and equality 

so as to achieve happiness, prosperity and progress for our nation.

No wonder they have the best firework shows on earth!  Plus, the reading included how students there are guided to learning about all of the cultural groups that make-up their unique country in a way that cultivates with and unifies under respect while valuing diversity.  

It hasn't been until recently that I have really put lots of thought into how it is every teacher's responsibility to help students learn democratic values.  Also, in the social studies text, the incredible writer, James Baldwin, said that "if children are not educated to live democratically, they may well become apathetic or worse: They could become the next generation of people to commit a Holocaust such as the one in Germany in the 1930s and 1940s... Baldwin observed that the perpetrators of these crimes against humanity were very well educated and knew a great deal about reading, writing, literature, math and science, but in spite of their education, they could not live democratically" (p.62).

Although I feel like my own school education lacked way too much consideration of democratic values and thinking, I still was fortunate enough to have parents who modeled and discussed democratic values with me.  It baffles me when the people around me are less than passionate about what is happening in our society.  Because I didn't experience very much democracy in my schooling I am somewhat intimidated about teaching it myself, but I understand, intimidated or not, it is my responsibility because I know the importance of it.  I will do my best to help.  It helps me to know there is a lot out there, including people, that will support teaching democratic values, and, that I am so right, "Idiots were (are) citizens who paid no attention to the common good...They placed personal concerns far out in front of community concerns and, in this lethal act of imbalance, threatened the freedoms and rights they were so eager to enjoy" (p. 61).  I am excited to try to help catch-up to super neato Singapore.