Sunday, July 17, 2011

1510 Post #6: Simple Subtraction

I know that many of my posts have been involved in one way or another with differentiated instruction. Part of me believes this is so because until I started my journey as becoming a teacher, I did not even think about differentiated instruction. I was not for or against many methods for mainstream ideas and how to get to the same place using different paths. I grew up in a very vanilla school that taught an idea one way and that was the way we needed to know. If a student had a hard time trying to grasp a concept, they were sent for special help. I do not know what happened in those rooms. Perhaps there they were being introduced to the same concept as I, just in a different way to help them understand.

I love the idea that students are so diverse and keeping teachers on their toes. When we started to discuss the different methods for subtraction, I assumed that it was going to be a short section. I was wrong, the depth that some of the methods goes into seemed to be a little long winded for me. That being said, I can see how that same long winded (to me) could spark that thought in a students mind. Expand using powers of 10. Perform using expanded notation, scratch method, the rules and probabilities; there is so much to what I thought was simple subtraction.

Again, I am going to suggest online game sites for additional help both inside and outside of the classroom. What I have learned in the last few weeks of taking a college math class has been that little in the classroom has stayed the same in regard to math content from the time when I was in elementary school. The changes are for the best and the additional support from both inside and outside of the class should increase the cognition of the student.

1512 Post #6: Euler's Formula

One of my favorite things about math is that it is what it is. There is little room for conflicting answers when everyone is following one path with the same information. Some of these formulas, like trying to calculate the measures of dent angles, can become very involved and tricky for adults. I cannot imagine what it is like for high school students, much less the students who are younger than that and picking it up.
Amidst the number spiral I kept getting sucked into; I found an "eye" for the hurricane in the sections of work that dealt with Euler's Formula. This site gives information on both polyhedrons, Euler, and the formulas that he inspired or conceived during his lifetime. V-E+F=2. If one takes the number of vertices in a shape and then subtracts the number of edges, and then adds the number of faces; the person should get an answer of 2. This formula can be flipped around to find the missing information if one of the three fields is blank. One example would be V+F=E+2.

Of course there is always a possibility for error when starting to deal with shapes that have many different faces, vertices, patterns, edges, etc. Continued practice is one way to ensure that the students will keep the information fresh in their minds. Many websites such as this one, offer lesson plans that other teachers have organized to provide different levels of depth to their class and freshen up assignments as well. Being able to introduce material like this is a good break from the mind confusion that is geometry.

Saturday, July 16, 2011

1512 Post #5: Cartoons

We have been taught that teaching is a combination of head, heart, hand, and humor. I think that often times educators are so concerned with spreading the head, heart, and hand that they often forget about humor. What we know is that we remember the times that we laugh. We do not remember the boring lecture or the spiral bound notebook filled with notes. We also know that engaging the class is a great motivator for increased learning.

Being able to find ways to reach your class, present ideas, and open a discussion is through cartoon strips. This is an idea that can be applied inter academically and can be used as group projects as well. The math class I am currently taking has required the class to come up with cartoon strips that are relevant to what we are learning. While I was puzzled about why we needed to make cartoons for a class about teaching math in elementary school, I kept an open mind through the process.

These cartoons can bridge the gap between student and teacher. It can also allow the teacher a different way to present the new material to the class. Additionally, it is a great way for the teacher to apply humor to their class. Most importantly, these cartoons may be a source of "A-ha!" for some students. At the very least, it will break up the day for the class and provide them with a brain break.