My Project Fall 2013

After reviewing Jen's aMAZing Geogebra program and reviewing her Unit Plan. I am going to write my own unit plan or at least get a good start on one. I am going to incorporate the many different topics taught in the MAT 641 class.

The link that follows are the CCSS I am going to achieve for this unit. 7th Grade Geometry Standards

I am starting to piece together topics that can be used.

• Vocabulary - Turning Origami into the Language of Mathematics
• Euclid - Book I
• Patty Paper - http://www.michaelserra.net/weblog/patty-paper-geometry-1.html
• Geogebra - Compass - straight edge
• Incorporate Euclid into unit plans.  

Some items I still need assistance with are 3 - dimensional drawings (quadrilaterals, polygons, cubes, and prisms) - I am thinking this would be a good place to incorporate Geogebra tube. 

I have started a Unit Plan on Google Drive - Geometry Unit  

Patty Paper vs. Compass/Straight Edge

Last weeks class my eyes were wowed to the idea of creating figures using patty patter. You know, the paper between your frozen hamburgers. For 2 hours my classmates and I constructed basic quadrilaterals squares, rectangles, trapezoids, rhombus, parallelograms, and also basic bisecting properties. I have had zero past experience with patty paper and was very impressed with the ease of transformations.

My thoughts are with the patty paper, the students understand the ideas behind the constructions a lot better. For example. When creating an angle bisector, you take an angle and you fold the two sides of the angle on top of one another. When you create the crease were the fold line happens you then get the bisecting line of the angle. Or take for example the perpendicular bisector of a line. Fold the patty paper on itself so the line on the paper is exactly on top of itself including the two end point on one another. From here you really understand the idea that a perpendicular bisector is a perpendicular line in the middle of an original line. The thought of the topic becomes so clear on what this vocabulary is and the student is not lost in the process. Which happens when we construct objects with compass and straight edge.

Why would we use a compass and a straight edge then. One of my philosophies as a teacher is, "I teach students with math, I don't teach math" Compass and straight edge are a great tool for teaching fine motor skills. Using these items takes practice and more practice. Students can fine tune these skills and become very good at creating simple constructions. My fear is students become lost in the idea of creating the figure and don't focus on what they are trying to achieve. For example a simple reflection of a figure over a line with a compass and straight edge takes 4 or 5 different actions for each vertices of the figure. If you are reflecting any quadrilateral the student is constructing 20 different movements.  They loose sight of the idea that the image is "flipped" over a line. With patty paper it is simple and obvious. The figure is drawn and you make a fold over the line and copy the figure to the other side of the figure.

What is the conclusion then? I believe there can be a balance of the two. The skills compass and straight edge provide working side by side with patty paper can be the best for student's learning. This way we are getting the best of both worlds. We can even can throw in technology constructions for a well for a rounded learning experience that differentiates to all students.

Jen’s aMAZEing GGB

While looking through through the weeks activities on what is required. I was able to tap into my inner child. Any time you get to play with a maze, it is hard to pass up the opportunity. I spent the first five minutes with the maze just trying to find my way through the difficult sequences to be successful. It was a mighty challenge turning left and right especially when the car got faced the up-side-down (opposite way of start). I often found myself hitting the wrong direction and crossing over the walls and having to restart.

After continued failures I started to become more reactionary. The left and right movements no longer became left and right. I was getting the sensations I as in the car and moving forward with the vehicle itself. My errant turns became less problematic and I was successful more often, completing the maze quickly and flawlessly. 

After mastering the craft of rotational translations, I decided to give a few 7th graders a crack at it. Much like my experience they continued to turn the wrong direction and cross the walls. I was interviewing them about their experience and asked them what was making it so hard? The response was almost always carelessness. The students did not pay any attention to the writing on the buttons signifying turn left or turn right. 

I pondered why they would not pay attention to the scrip on the buttons. My conclusion is, video games. Especially the older the video game the more alike to the aMAZeing program, games like Pack-man come to mind. Many of the original NES games where you control a character on a 2-dimensional map moving up, down, left, or right are also similar to the maze. Maybe there are some benefits to videos games, I'm going to look into more ways to incorporate them into math class. 

At the end of my reflection with Jen's aMAZeing GGB I looked at her Unit Plan which included the maze program. I was shocked and taken back with her lessons. Her incorporation  with history is "amazeing." Being certified to teach history as well as math, I have always wanted to incorporate the great mathematicians of the past into lessons. I need to start doing this more. I am assuming she is not using a textbook for this lesson. Seeing this amazing unit plan has motivated me into looking at dropping our new textbooks for a self created unit. I'm going to use my time in MAT641 to do this, more to come....

Jen's aMAZEing GBB: http://www.geogebratube.org/material/show/id/48117

The Great Result:

The great result in education is passed by for so many students. How can I compete with Hollywood when everyone is trying to be out "shock" the general public, how can a math lesson complete with a Meat Suit or an interesting Mickey Mouse outfit at an awards show. 

After leaving my MAT 641 class at Grand Valley, I was in awe with the Euler line (see http://www.geogebratube.org/material/show/id/52099 ). How can the line found by finding the curcumcirlce, orthocenter, and incircle of a triangle form a straight line.  It was amazing these three different points found inside and around a circle where so closely intertwine. It was almost beautiful how they worked. 

I was so moved by the Euler Line, I showed  my advanced class this amazing piece of math when they finished their quiz. I created the work using geogrebra in front of them so they could see the complexity of each of the points. Once I completed the work, I was glowing with anticipation to show them the true meaning of Math. When I hit the climax, ready to move the vertices around showing the Euler's Line always holds true. The response I got in return was, crickets, nothing, not even a, wow that's kind of cool.

Was I over hyping an idea only Math Geeks would enjoy or was my delivery wrong. I pondered my conundrum over the weekend. My conclusion is that if you don't see the beauty in math when it hits you right in front of your face your not going to get it. Similarly if you pass a 1971 GT 500 Mustang and you don't turn and watch it drive away. I blame you and not the car. But how can we fix it so all students can have a love for a subject in which they seem is dislike.

My mission this year is to have students see the beauty in math. It is so much more than adding fraction and converting between different units and finding roots. Math is an art that should seen as breath taking  ideas ideas and thoughts. I want them to enjoy the great result that is mathematics.