Mrs. Grafaldi,
After teaching mathematics for 20 years, I am sure you are aware of the benefits of self exploration. We have all taught lessons where students draw pictures or maneuver 3-D shapes but we have also all dealt with these pieces becoming a problem in the classroom (being lost, stolen, etc). Technology now allows us to draw pictures and maneuver shapes without tangible objects. There are plenty of math programs (Geometer's Sketchmad, Maple, Mathematica, etc) that allow students to graph equations and change the view of the equation easily. Programs also allow students to quickly draw pictures, measure angles, and test theorems or conjectures.
However, knowing that programs are available simply is not enough. From your own desire and the pressure of the school, you must integrate these technologies into the classroom. The first technology to try integrating is graphing calculators. In fact, you might already be doing this without knowing it! Let the students graph line and calculate the max and min. Let students use the table. Actually, encourage students to use the table. If the students are able to use the calculator to effectively check their work then the students will be more likely to understand what is going on. After the graphing calculator is under control, try moving onto something like Geometer's Sketchpad. I suggest setting up a lesson like this.
1. Introduce the topic such as triangle congruencies with providing basic information and perhaps one or two theorems (depending on the abundancy of theorems).
2. Demonstrate to students how to use the program by having step-by-step instructions on how to create a simplified version of what they will be doing.
3. Give the students the task of creating something (like two triangle with three congruent angles) and have them make a conjecture about their shapes.
4. Have the class join together to see if the conjectures match
5. Have a discussion about why the conjecture is true and perhaps even prove it (depending on the difficulty of the proof) on the board.
If you set a lesson plan up in this manner then students are exposed to a topic both through lecture and exploration without the trouble of pulling out a compass and ruler. Of course, there are technology problems too but most of those can be quickly avoided after trying the lesson a few times.
Most importantly, don't allow the technology to cause you too much stress. Start slow with extremely specific directions for your students. As they become more advanced with the program you will be able to stop providing as many directions. Good luck.
Tuesday, May 1, 2007
More comments
Well, I'm quite sure nobody is reading other people's blogs anymore except myself so I feel relatively safe responding to some other blog entries in here.
Honestly, not even half way through the semester I was extremely unhappy with the quality of work being produced by other students. Not just the work, but the entire attitude toward the class. Yes, I admit, I started out with a really bad attitude toward the class (Andrew and I have had this discussion), and I would like to apologize for how I came across the first few classes. However, to come out and say some of the things that have been said. Saying "I don't like kids" knocks me off my feet. Seriously? Even if you don't typically like being around children, you can surely find something good in each child or even just pick one student and find something you like. Isn't that what teachers have to do? Take even the worst students (and trust me, there are high school students who act like the elementary school kids) and find something good within the student. Without believing that the student can improve, there isn't much hope for improving the kid's life and education. Plus, besides that comment, the amount of late work turned in and homework with little effort put into it was unbelievable. Perhaps the "problem" with the class was not that the work wasn't hard or that the class wasn't demanding but more of the fact that as a class, the students didn't try to learn from it, we didn't take advantage of the class like we could have.
As for the templates for the lesson plans, that was great. Thank you so much for doing that. All lesson plans have some general things required and having a BS in Mathematics did not teach me those things. Without the lesson plan template, I would have been completely without ideas on how to create a good lesson plan. Furthermore, I used the template descriptions to help me create a lesson plan for the summer job I applied for (which I was not hired but only because of my lack of experience with minority high schoolers). As far as I know, all lesson plans are the same with the same standards and you did leave us all the appropriate blanks to fill in to allow for our own creativity in creating our lessons. Requiring us to put a title, our names, the grade level, etc did nothing to hurt our creativity.
As for the typing at the computer during presentations and discussions and such, I honestly don't know how to fix this. I think it completely depends on the class and whether the students are willing to give respect to both the teacher and other classmates. Typing is normally bad but there were cases where a student would say something (such as the graduation rate at Harmony being low) and I tried searching online so I could prove the student wrong. In most cases though, I saw lots of e-mailing, facebooking, and sports scores up on computers during class. Maybe asking students to turn off the monitors more or just plain asking them to be polite and stop the Internet browsing. Surely young adults are capable of being polite for a few hours a week.
As for the educational programs being put onto the computers in the school of education... that seems like a silly request to me. What are all the math programs? NON-educational programs? The math programs, the music programs, in fact, most of the software on the computers could be used for educational puposes if the instructor knows how. Plus there are plenty of educational things to be used on the Internet so why spend money on purchasing them for the computers? However, I personally would have liked to be introduced to a gradebook program of some sort. I am currently keeping track of grades using Excel which is functioning but time consuming.
One last comment is that I'm shocked at the number of times students real names were used in the blog entries. I felt guilty even using the school's name, but to actually use the student's real name with descriptions of problems with the student?! I particularly feel bad for these students because I know I would not want that to be me, with my name out there, even if it was just the first name. I thought the deal at the beginning of the semester was that we could not use the student's real names or take pictures of their faces. Well, the pictures taken never made it off my memory card (oops) but real names were frequently put online. That's not good, is it?
Honestly, not even half way through the semester I was extremely unhappy with the quality of work being produced by other students. Not just the work, but the entire attitude toward the class. Yes, I admit, I started out with a really bad attitude toward the class (Andrew and I have had this discussion), and I would like to apologize for how I came across the first few classes. However, to come out and say some of the things that have been said. Saying "I don't like kids" knocks me off my feet. Seriously? Even if you don't typically like being around children, you can surely find something good in each child or even just pick one student and find something you like. Isn't that what teachers have to do? Take even the worst students (and trust me, there are high school students who act like the elementary school kids) and find something good within the student. Without believing that the student can improve, there isn't much hope for improving the kid's life and education. Plus, besides that comment, the amount of late work turned in and homework with little effort put into it was unbelievable. Perhaps the "problem" with the class was not that the work wasn't hard or that the class wasn't demanding but more of the fact that as a class, the students didn't try to learn from it, we didn't take advantage of the class like we could have.
As for the templates for the lesson plans, that was great. Thank you so much for doing that. All lesson plans have some general things required and having a BS in Mathematics did not teach me those things. Without the lesson plan template, I would have been completely without ideas on how to create a good lesson plan. Furthermore, I used the template descriptions to help me create a lesson plan for the summer job I applied for (which I was not hired but only because of my lack of experience with minority high schoolers). As far as I know, all lesson plans are the same with the same standards and you did leave us all the appropriate blanks to fill in to allow for our own creativity in creating our lessons. Requiring us to put a title, our names, the grade level, etc did nothing to hurt our creativity.
As for the typing at the computer during presentations and discussions and such, I honestly don't know how to fix this. I think it completely depends on the class and whether the students are willing to give respect to both the teacher and other classmates. Typing is normally bad but there were cases where a student would say something (such as the graduation rate at Harmony being low) and I tried searching online so I could prove the student wrong. In most cases though, I saw lots of e-mailing, facebooking, and sports scores up on computers during class. Maybe asking students to turn off the monitors more or just plain asking them to be polite and stop the Internet browsing. Surely young adults are capable of being polite for a few hours a week.
As for the educational programs being put onto the computers in the school of education... that seems like a silly request to me. What are all the math programs? NON-educational programs? The math programs, the music programs, in fact, most of the software on the computers could be used for educational puposes if the instructor knows how. Plus there are plenty of educational things to be used on the Internet so why spend money on purchasing them for the computers? However, I personally would have liked to be introduced to a gradebook program of some sort. I am currently keeping track of grades using Excel which is functioning but time consuming.
One last comment is that I'm shocked at the number of times students real names were used in the blog entries. I felt guilty even using the school's name, but to actually use the student's real name with descriptions of problems with the student?! I particularly feel bad for these students because I know I would not want that to be me, with my name out there, even if it was just the first name. I thought the deal at the beginning of the semester was that we could not use the student's real names or take pictures of their faces. Well, the pictures taken never made it off my memory card (oops) but real names were frequently put online. That's not good, is it?
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