Taking a geometry course for the the first time in a decade or so, I was nervously optimistic. I always know the math department does an excellent job of making the work in the classroom relevant to our own classrooms as well as enhance us as mathematicians. This semester did not disappoint.
I do not teach a whole ton of geometry to my 7th graders but the unit I do teach in now ten times better than it was before. I have a "toolbox" full of resources I am able to use to enhance and engage my students. The skill I feel will support my teaching the best is Geogebbra. I had little to no experience with the program four months ago, but today I am using in my classroom on a regular bases. I am confident in the foundation skills it uses and am comfortable enough to use it with the students. The readings in the class where relevant to both the classroom and mathematician side. As many of the choices in the class where between a "mathy" article and a classroom article.
The mathematician side of me was strengthened in many ways as well. I was in awe of the many higher level math problems completed in the course. They where presented in a way that was enjoyable and engaging. My eyes were opened to many real world math questions I would not have had an opportunity to have think about without this course. I can not give enough praise for the enjoyment I had coming to this class. I was truly good to escape the rush of daily live and do something I enjoy.
It saddens me the course will no longer be taught at GVSU. It was more productive than any seminar I have every attended. I hope and pray the cyclical motion of education will one day find value in promoting higher learning for its teachers.
Saturday, December 7, 2013
The Great Result: Pt. 2
this blog is a second attempt to an earlier post "The Great Result:"
As I spoke about it in the Celtic Knots blog post, our school has a "Flex" block period where students are placed in classrooms based on data collected from screener assessments. I am able to work with the "high flyers" and we so some enrichment to get them thinking about math beyond the walls of our classroom. I am able to work with students on topics they might not see.
I was bound and determined to have them have the "shock 'n awe" of how amazing the Euler Line was when I first saw it in my MAT 641 class at GVSU. We got the computers out and the students have the Geogebra program on it already so I was going to be able to "kill two birds with one stone." The student could get an introduction to both geoebra and would be able to see math in new way with a new appreciation.
I did a great job of hyping up the concept and gave it my best sales pitch telling them they where going to be "mind blown" by the end of class. So we began, they where having an enjoyable time working with geogebra and creating the different centers for their given triangle. Students were very exited about finding the orthocenter, curcumcenter, and centroid. They had their struggles with geogebra but were very optimisc about what was going on and truly enjoyed the learning the process on finding different centers to a simple triangle. They loved the hands on experience with manipulating the different vertices of the triangle and they would comment on how all the lines would move. They like to see how each center points always worked, how all the lines would change, but the 3 points would but still hold true to their intended purpose.
Then it was time to deliver the big moment, the culmination of the big sales pitch. Students had started to see it after the three points where found and they began to move the triangle into different forms. we then created a line through the three points and continued to manipulate the triangle and we did notice it always works.
Now I didn't receive the overwhelming joy I was hoping like they had just won a state championship but I did spark a little awe in their eyes. A few students thought it was pretty cool that three seemingly independent points of a triangle would form a straight line. So I was relatively excited I had made a few believers. We would continuing the next time we meant I was determined to make more believers.
The next Flex Block class the student continued with questions about the Euler Line so we took second look at it. We improved our geogebra skill by adding icons that hide/showed lines, plus we also introduced the nine point circle. When we where done we noticed the center of the nine point circle also fell on the Euler Line. I had made a few more converts! From where I had began, I made a good majority of my student believe that math was something greater that what was taught in a classroom.
As I continue to become a better mathematician I am in awe about how math is intertwine in everything around us. One thing that I believe I need to do as an educator is pass that love onto my students. Let them know that everything around them is related in some why to what we do in class. Give them the passion they deserve.
As I spoke about it in the Celtic Knots blog post, our school has a "Flex" block period where students are placed in classrooms based on data collected from screener assessments. I am able to work with the "high flyers" and we so some enrichment to get them thinking about math beyond the walls of our classroom. I am able to work with students on topics they might not see.
I was bound and determined to have them have the "shock 'n awe" of how amazing the Euler Line was when I first saw it in my MAT 641 class at GVSU. We got the computers out and the students have the Geogebra program on it already so I was going to be able to "kill two birds with one stone." The student could get an introduction to both geoebra and would be able to see math in new way with a new appreciation.
I did a great job of hyping up the concept and gave it my best sales pitch telling them they where going to be "mind blown" by the end of class. So we began, they where having an enjoyable time working with geogebra and creating the different centers for their given triangle. Students were very exited about finding the orthocenter, curcumcenter, and centroid. They had their struggles with geogebra but were very optimisc about what was going on and truly enjoyed the learning the process on finding different centers to a simple triangle. They loved the hands on experience with manipulating the different vertices of the triangle and they would comment on how all the lines would move. They like to see how each center points always worked, how all the lines would change, but the 3 points would but still hold true to their intended purpose.
Then it was time to deliver the big moment, the culmination of the big sales pitch. Students had started to see it after the three points where found and they began to move the triangle into different forms. we then created a line through the three points and continued to manipulate the triangle and we did notice it always works.
Now I didn't receive the overwhelming joy I was hoping like they had just won a state championship but I did spark a little awe in their eyes. A few students thought it was pretty cool that three seemingly independent points of a triangle would form a straight line. So I was relatively excited I had made a few believers. We would continuing the next time we meant I was determined to make more believers.
The next Flex Block class the student continued with questions about the Euler Line so we took second look at it. We improved our geogebra skill by adding icons that hide/showed lines, plus we also introduced the nine point circle. When we where done we noticed the center of the nine point circle also fell on the Euler Line. I had made a few more converts! From where I had began, I made a good majority of my student believe that math was something greater that what was taught in a classroom.
As I continue to become a better mathematician I am in awe about how math is intertwine in everything around us. One thing that I believe I need to do as an educator is pass that love onto my students. Let them know that everything around them is related in some why to what we do in class. Give them the passion they deserve.
Celtic Knots
At the last MAT 641 class at GVSU, I was introduced to the geometric art of Celtic Knots. I have always had an interest in art and especially math related art. The systematic approach to creating Celtic Knots is very in line with my personality. I am a very linear thinking and process oriented art is right up my ally. I spend some time the next few days after class sharpening my knot art skills and was ready to bring it into my classroom.
In my school we are blessed to have a "Flex" block period that meets twice a week for a half hour. The time is so students can receive the enrichment they need in different subjects. They are grouped up based on achievement level. I am fortunate enough to have the students who are highly successful in math. We are able to do some activities that are not in the curriculum and show them math outside of just structured curriculum. So this past Thursday I introduced them to Celtic Knots. The initial response was "I don't get this," or "this isn't fun," but after continued demonstration and I completed a few on the board they deemed "cool" their interest level increased. After a few minutes, a few students came with smiles on their face and showed me their completed knots. Their passion for math art increased just as mine had when I was introduced to Celtic Knots. Before I knew it the class was silent and everyone had their heads down and where working away.
The greatest moment happened after we talked about adding different walls to manipulate the knots and see what happens. Students tried simple 4x4 knots with one wall. Then the great moment happened. I overheard a student speak to his neighbor, "I don't know what is going to happen but I am going to try it." We stopped the whole class right here and we had a conversation that this is what math should be like. School has become a chore for adolescences and not an inquisitive exploration of gaining knowledge. I was excited and passionate about their level of interest by the end of the hour. It was great to see them take the Celtic Knot and run with it and try it on their own.
In the future I want to wrap my head around some of the math that is involved with Celtic Knots. I have done a little research and spent some time pouring over the articles. I would also like to bring it down to the level where a middle school student can comprehend what is going on and it's application to other real world items.
Tuesday, December 3, 2013
Making Geometry Simpler: "Volume of a Pyramid"
Reflecting on the reading for this week there are some good ideas Masha Albrecht talks about that I can apply to my own class. I am always looking for ideas on Low-Tech "hands on" activities where students can dive into their work.
I always have a hard time with students making the transition with v = lwh in a rectangular prism to using v = Bh. I like using v = Bh because it makes the understanding and application of cylinders and triangular prisms that much easier. We can use the same formula v = Bh for all three 3-D figures instead of switching between independent formulas. Students always have a hard time making that transition. The worksheet that is used and the technique the writer uses makes this transition very fluidly, and in a way middle school students can handle.
I also like how she uses the blocks to understand where the formula for pyramids come from. I believe I can use this for my students as well. We can create the "cube pyramid" and work our way to getting to the 1/3 of the prism formula. Using the technology piece will come in handy but I am having my doubts on how 7th graders of all learning levels will be able to comprehend the formula by Misha uses. I would like them to discover the patter for finding the volume on their own but squaring the side length and adding it to the last pyramid's volume seems to be a little stretch for my students. I will continue looking into finding a more attainable method for 7th graders.
I am excited to use this article in my class. It is the fourth or fifth different resource I will be able to use in the upcoming geometry unit.
I always have a hard time with students making the transition with v = lwh in a rectangular prism to using v = Bh. I like using v = Bh because it makes the understanding and application of cylinders and triangular prisms that much easier. We can use the same formula v = Bh for all three 3-D figures instead of switching between independent formulas. Students always have a hard time making that transition. The worksheet that is used and the technique the writer uses makes this transition very fluidly, and in a way middle school students can handle.
I also like how she uses the blocks to understand where the formula for pyramids come from. I believe I can use this for my students as well. We can create the "cube pyramid" and work our way to getting to the 1/3 of the prism formula. Using the technology piece will come in handy but I am having my doubts on how 7th graders of all learning levels will be able to comprehend the formula by Misha uses. I would like them to discover the patter for finding the volume on their own but squaring the side length and adding it to the last pyramid's volume seems to be a little stretch for my students. I will continue looking into finding a more attainable method for 7th graders.
I am excited to use this article in my class. It is the fourth or fifth different resource I will be able to use in the upcoming geometry unit.
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