I teach Pre-Algebra to students in Special Education, and the geometry skills that we practice are usually very basic. My students have enjoyed working with Pattern Blocks. I have attached the lesson plan (which came from a website) that involves a fun activity. This forces the students to use correct terminology and work cooperatively in order to solve the problems correctly. You can make adaptations to the game by developing your own set of rules, as needed.
Again, this activity is pretty basic, so it may be useful to elementary teachers. The website is:
http://mathforum.org/sum95/suzanne/mission.html
Monday, April 6, 2009
Monday, March 23, 2009
Measuring Height with a Mirror
Just as my students are starting to get that "Spring Fever," I was feeling that way myself. So, I was extremely pleased to hear that we were going to spend some class time outdoors to work on an activity. As I'm always looking for ways to relate this course to my own classroom, I thought to myself, "I really need to get my own students outside to do something like this. They would love it!"
I learned that this activity was not as simple as it sounded when I first read through it. Of course any activity that involves measurement may be inaccurate if any small mistakes are made. There were many important factors that could throw off the results. My group's first answer for the height of the light pole was 11 feet. I thought of my own students and how they would accept this answer and say that they were finished. However, my group knew that the light pole looked taller than 11 feet - we must have made an error or two. We had to re-do the activity and check our measuring points. Then our answer was closer to 14 feet, and this answer was more accurate. I enjoyed this activity and found it to be a valuable lesson.
I learned that this activity was not as simple as it sounded when I first read through it. Of course any activity that involves measurement may be inaccurate if any small mistakes are made. There were many important factors that could throw off the results. My group's first answer for the height of the light pole was 11 feet. I thought of my own students and how they would accept this answer and say that they were finished. However, my group knew that the light pole looked taller than 11 feet - we must have made an error or two. We had to re-do the activity and check our measuring points. Then our answer was closer to 14 feet, and this answer was more accurate. I enjoyed this activity and found it to be a valuable lesson.
Wednesday, March 18, 2009
Article Review
I read the measurement article in Chapter 6, and really enjoyed it. It was easy for me to relate to the common misconceptions which those students had. When I gave rulers to my high school students and asked them to measure a few lines, they stated that it was "baby stuff that 1st and 2nd graders learned". However, they still made many errors! It's very true that a lot of our students do not understand the meaning of measurement, often due to the lack of experience.
I found the article to be a valuable resource because I may need to try some of the same activities in my own class. Our assessment data always shows that students struggle with measurement. This is unfortunate, as it is one of the most "everyday life" skills they will need to possess. This article was actually kind of a wake-up call for me as it made me reflect on my teaching content.
I found the article to be a valuable resource because I may need to try some of the same activities in my own class. Our assessment data always shows that students struggle with measurement. This is unfortunate, as it is one of the most "everyday life" skills they will need to possess. This article was actually kind of a wake-up call for me as it made me reflect on my teaching content.
ISTEP testing
My small school staff of 10 teachers had an interesting discussion the other day regarding the ISTEP test. We were brainstorming for more ways to help prepare our students for those DIFFICULT standardized tests.
I work mostly with 9th and 10th graders in Special Education. The majority of them lack basic math skills, but they are able to catch on to Pre-Algebra concepts when relying on calculators for support. During our meeting, a middle school teacher said, "I'm not really sure what I should be teaching these guys. In order for them to move on to Algebra, they have to know their basic operations. They won't understand Algebra if they don't understand what multiplication means." A few other teachers shared the opinion that it was more important to focus completely on the Algebra skills, because that is what the ISTEP would be testing. This is just another example of the phrase "teaching the test" that we hear so often.
I work mostly with 9th and 10th graders in Special Education. The majority of them lack basic math skills, but they are able to catch on to Pre-Algebra concepts when relying on calculators for support. During our meeting, a middle school teacher said, "I'm not really sure what I should be teaching these guys. In order for them to move on to Algebra, they have to know their basic operations. They won't understand Algebra if they don't understand what multiplication means." A few other teachers shared the opinion that it was more important to focus completely on the Algebra skills, because that is what the ISTEP would be testing. This is just another example of the phrase "teaching the test" that we hear so often.
Master's Project
Since I am a music lover, I plan to work with the music tool in Logo. I am hoping to create songs to go along with images (all created with the Logo program). I may be able to add some animation, so it could almost be like a cartoon with a musical score! However, since I am just starting, I'm really not yet sure how it will all turn out.....we'll see.
Sunday, March 1, 2009
What would you like to ask each other?
In response to Amy Olsen's question (If you teach Algebra, what Geometry concepts do you see?), I teach Pre-Algebra and some Algebra to students with mild disabilities. Our textbook often gives problems involving perimeter, area, circumference, and angles. I must admit that before this class, I often felt that I lacked the expertise in fully explaining these types of problems. I strongly needed to review some basic geometric concepts. Now I often find myself talking about my own learning to my students and having more "geometry" discussions in class.
Now (to go back to your original question), when learning to solve proportions, my students really struggle with using two similar triangles to set up a proportion. Unless they've had some experience with geometry, then these problems will continue to be difficult for them.
Now (to go back to your original question), when learning to solve proportions, my students really struggle with using two similar triangles to set up a proportion. Unless they've had some experience with geometry, then these problems will continue to be difficult for them.
Sunday, February 22, 2009
What are your Spring Break plans?
My Spring Break dates are March 30th through April 3rd. I do not have any confirmed plans, but I may take a few days to visit my dad in Alabama....what a beautiful and peaceful place it is!
Reaction to the Slavit article
This article is clear proof of a very strong point - As I read through the article, I became more and more confused! However, if I were to actually do the activities which I read about, I'm sure I would gain a much better understanding. The author mentioned the educational importance of "doing" mathematics. In geometry especially, the possibilities of teaching through hands-on activities are endless.
I also thought it was interesting how the author continued to build and extend the lesson from using triangles to quadrilaterals, to pentagons, and then hexagons, which led to a deeper understanding. After participating in several ISTEM courses, I've taught myself to extend problems for my own students more often. It's so easy to work a problem, solve it, and quickly move on to the next one. However, I am now more aware of finding those "teaching moments" to pause and have a deeper discussion with my students. This has led to great results!
I also thought it was interesting how the author continued to build and extend the lesson from using triangles to quadrilaterals, to pentagons, and then hexagons, which led to a deeper understanding. After participating in several ISTEM courses, I've taught myself to extend problems for my own students more often. It's so easy to work a problem, solve it, and quickly move on to the next one. However, I am now more aware of finding those "teaching moments" to pause and have a deeper discussion with my students. This has led to great results!
Monday, February 16, 2009
My reaction to the assigned article is ...
While the article had little text to read, I spent a lengthy amount of time on working through the problems. It's great to use real-world examples and I understood what the problems were asking me to do. However, due to my lack of geometry skills, they were difficult for me to solve. I relied a great deal on The Geometer's Sketchpad (GSP) software. As I followed the steps listed in the article, I thought to myself, "I'm not seeing how this will lead to the answer." All of a sudden, the results appeared, and the problem was solved! Now as I compare myself to a student doing this for the first time, I know I would need the teacher to explain why these GSP directions give the solutions. Other than that, I thought the article was a great resource.
I am interested in learning more about ...
Last week we read an article about teaching geometric vocabulary. I strongly agree that our students will gain a much better understanding by exploring and discovering the definitions on their own. The article led the reader through the process of students defining an "angle." I thought the discussions and activities were great. I would really benefit from learning additional ways to help guide my students through more vocabulary terms. There is an excessive amount of terminology in the subject, and I would like to see more examples other than "the angle."
Monday, February 2, 2009
Vocabulary
Reflect on the role of vocabulary in geometry.
The importance of vocabulary in any subject cannot be stressed enough! Just as we learn the Spanish language in Spanish class, we must learn the Algebra language in Algebra class, and the Geometry language in Geometry class. I must admit, I did not do so well in my high school geometry class, nor have I ever taught it myself. Therefore, I feel somewhat like a beginner in this graduate course. I find myself trying to keep up during class discussions because I'm still trying to remember what "corresponding angle" means! Until I strengthen my knowledge of these geometric terms, I will always be behind. The same goes for our own students. Before we teach the concepts, we must be sure that they know and are comfortable with the vocabulary.
The importance of vocabulary in any subject cannot be stressed enough! Just as we learn the Spanish language in Spanish class, we must learn the Algebra language in Algebra class, and the Geometry language in Geometry class. I must admit, I did not do so well in my high school geometry class, nor have I ever taught it myself. Therefore, I feel somewhat like a beginner in this graduate course. I find myself trying to keep up during class discussions because I'm still trying to remember what "corresponding angle" means! Until I strengthen my knowledge of these geometric terms, I will always be behind. The same goes for our own students. Before we teach the concepts, we must be sure that they know and are comfortable with the vocabulary.
Logo Technology
Reflect on the role that the technology is taking as you work with Logo. How does using this program change the teaching and learning of angles and lines?
I have never worked with any program like this before. My first thought was, "My students would love this." I feel that all students benefit a great deal from hands-on instruction. I constantly hear requests to use the computers in my class. My students would enjoy experimenting with the Logo program, mostly because of the simple and concrete directions. After following the lessons in the book, it would become easier to see what the angles actually look like and what image the turtle is creating. Students would be able to see how the image changes when they vary their rotations and directions. Finally, my students would definitely show an interest in this program, which of course, leads to learning.
I have never worked with any program like this before. My first thought was, "My students would love this." I feel that all students benefit a great deal from hands-on instruction. I constantly hear requests to use the computers in my class. My students would enjoy experimenting with the Logo program, mostly because of the simple and concrete directions. After following the lessons in the book, it would become easier to see what the angles actually look like and what image the turtle is creating. Students would be able to see how the image changes when they vary their rotations and directions. Finally, my students would definitely show an interest in this program, which of course, leads to learning.
Tuesday, January 20, 2009
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