I thought this was a well written article and enjoyed following the activity. The students did a nice job of using maniplulatives to prove or disprove ideas of congruence and similarity. However, he starts the article by saying "The development of intuitive understandings of geometry is highly important at the middle school level" and then moves on with the article. As I am reading, I try to picture this taking place in a middle school classroom that I have taught in. I am amazed by the conjectures that his students are making and can't believe how they are exploring the ideas presented. Then at the end the of the article he says "even though these activities were used in a college classroom, they are immediately adaptable for use in a middle school classroom with little or not change." Hmmm...... Really. You think so, have you taught middle school before....Ok enough with that.
As I said earlier, I think the activity is a great idea and if I ever get the chance to teach geometry again I will try to use parts of this activity to discover the ideas behind triangle congruence. I also agree with Slavit's approach to teaching. He believes that our students should be "doing math" not just "hearing or seeing mathematics." This a difficult law to live by though. It takes a lot of preparation and you have to be willing to face defeat. Not all activities work as well as this one. Despite the difficulty of this type of teaching, if we believe it is best for students, we must persevere.
SPRING BREAK
March 23-27.
I am pretty sure that we are planning on going.....that's right no where. Unless I get a big fat stimulus check in the mail......lots of sarcasm.
Friday, February 20, 2009
Saturday, February 14, 2009
Learning and Masters Project
These two things seem to be connected. I would really like to learn more about the proof process and how I can use GSP and other activities to help students connect to the ideas. Some of my early thoughts have been about setting up a template for a digital dictionary for geometry definitions. I have thought about what format I would use and what things might be with each word. Ideas....
1.) Picture/Sketch
2.) Definition in own words
3.) Formal Definition
4.) Examples and even counter examples
I also would like to build activities that would allow students to discover some of the definitions themselves. I am a little concerned about how many things I can use because many of the activities are already in the GSP activity book. Another concern that I have is availability of a computer lab and the programs that I would be able to use.
Even if I can't make a digital dictionary I would definitely like to find a unique way for students to keep track of the things they have discovered/learned during the year. I would also like to compile and create activities that engage students in geometric thought.
I have been researching different geometry texts this week and I have been looking at the topics covered in geometry. I have never taught geometry so I have been talking with teachers in my building and in Muncie to see what is covered and how they are currently covering the material.
1.) Picture/Sketch
2.) Definition in own words
3.) Formal Definition
4.) Examples and even counter examples
I also would like to build activities that would allow students to discover some of the definitions themselves. I am a little concerned about how many things I can use because many of the activities are already in the GSP activity book. Another concern that I have is availability of a computer lab and the programs that I would be able to use.
Even if I can't make a digital dictionary I would definitely like to find a unique way for students to keep track of the things they have discovered/learned during the year. I would also like to compile and create activities that engage students in geometric thought.
I have been researching different geometry texts this week and I have been looking at the topics covered in geometry. I have never taught geometry so I have been talking with teachers in my building and in Muncie to see what is covered and how they are currently covering the material.
Friday, February 6, 2009
Memory is the residue of Thought!!!!
Response to the Jane Keiser article and an Article from the American Teacher by Daniel T. Willingham.
It seems that the main point from Jane's article is that students need to produce their own definitions first. The concise definitions that we have for terms may not and in most cases do not register with the students. It is very possible that there are words in the definition itself that they don't understand. However, I think the idea goes beyond just definitions. The key is that the students are working with and idea and making discoveries. They aren't being feed definitions and examples. My experience has been that if students discover something themselves they are much more likely to remember the definition, concept, or procedure in the future.
"What Will Improve a Student's Memory?" In this article by Willingham there is a statement the supports the thought of students struggling with an idea, making their own conjectures, and then revising. His statement has nothing to do with mathematics, but definitely applies.
"..., the first principle for students is that memories are formed as the residue of thought." If are students are just given a definition and are not asked to think about the concept or make their own definition there most likely won't be a memory. If a student creates a definition and then defends the definition he or she has definitely devoted thought to the definition. Then as the created definition receives praise or is revised the student is engaging in thought.
Therefore, (sounds like a proof) it make sense that we give students opportunities to think about mathematics through activities and investigations.
It seems that the main point from Jane's article is that students need to produce their own definitions first. The concise definitions that we have for terms may not and in most cases do not register with the students. It is very possible that there are words in the definition itself that they don't understand. However, I think the idea goes beyond just definitions. The key is that the students are working with and idea and making discoveries. They aren't being feed definitions and examples. My experience has been that if students discover something themselves they are much more likely to remember the definition, concept, or procedure in the future.
"What Will Improve a Student's Memory?" In this article by Willingham there is a statement the supports the thought of students struggling with an idea, making their own conjectures, and then revising. His statement has nothing to do with mathematics, but definitely applies.
"..., the first principle for students is that memories are formed as the residue of thought." If are students are just given a definition and are not asked to think about the concept or make their own definition there most likely won't be a memory. If a student creates a definition and then defends the definition he or she has definitely devoted thought to the definition. Then as the created definition receives praise or is revised the student is engaging in thought.
Therefore, (sounds like a proof) it make sense that we give students opportunities to think about mathematics through activities and investigations.
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