To be honest this has been one of my more difficult courses taken. I’m fairly competent in using the technology which I have needed before (word processors, cell phones, internet, etc). But this course challenged me to work with several new tools each week, and it was pretty hard getting accustomed to all of them. I think the important thing I will take away from this course is knowing that there are endless resources available to teachers, and I just have to find the ones that will work for me and use them in my classroom. In particular I think the SMART technology could be very beneficial to me, but a lot of my technology use depends on my school. The high school I attended had more money than any other school in the county, and I had never even heard of or seen things like SMART boards, Google Reader, or Animoto. All of these things can be valuable to teachers, but I think that not all of them are available in every school. My focus is to learn to use those technologies available to me in my school, and learn to use them as well as I can. I think this class has helped me to learn to use new resources quickly, although it can be very challenging. In the end, I will probably not use many of the tools which I learned in this class. But I have practiced learning and using new tools, and that kind of adaptability will help me more than anything as a teacher.
Here are four resources that could be used in high school math classrooms.
http://player.discoveryeducation.com/index.cfm?guidAssetId=53795D9B-2EBD-41AA-B087-1CAD8E9C92FA&blnFromSearch=1&productcode=US
This link is to a video from Discovery Education about basic terms and definitions in geometry. I envision using this video at the beginning of a geometry course. It covers a lot of the definitions used in geometry, and it does so in a very understandable way. I would probably show this and then have a discussion about the nature of the items listed in the movie, and where these things occur in nature. When students have a solid understanding of these fundamentals of geometry, it makes learning theorems and proofs a lot easier.
http://player.discoveryeducation.com/index.cfm?guidAssetId=5907606C-E098-4F41-A4E3-45A326649C4D&blnFromSearch=1&productcode=US
This video is also from Discovery Education, but it deals with simplifying fractions which involve algebraic expressions. It is a nice short video for introducing the basics of simplifying such fractions. It draws on prior knowledge of simplifying fractions, and shows that simplifying any fraction is essentially the same process. This might be good to show at the beginning of a class before going into a more in-depth lesson, but I would not rely on this movie alone to teach this concept.
http://education.smarttech.com/ste/en-US/Ed+Resource/Lesson+activities/Notebook+activities/Browse+Notebook/United+States/Secondary/10-12/Math/Powers+II.htm
This link is to a lesson for SMART Notebook on raising integers to positive, negative, and fractional powers. I really like that there is an interactive slide on which one can actually calculate n^(m/p), and you can use this to see patterns on how exponents behave. It’s pretty good stuff, and it’s a fairly complete lesson. Of course it would have to be supplemented with the right assignments and assessment, but it has a lot of good examples and ways of demonstrating how exponents work.
The following are some “stories” on the different themes of digital citizenship. I think it’s amazing how many resources are available online like these. There is so much one can do in digital storytelling by using such tools. I think I liked Animoto best, because it was a really cool way to take little clips from several videos and make a short story. It was also pretty easy to use. I had a lot of trouble with embedding my VoiceThread, so I think that was my least favorite to use. I’m not really sure how much I will use digital storytelling in my classroom, but I’m glad I know about these tools which can help me. Anyway, recall that the themes of digital citizenship (according to http://www.digitalcitizenship.net/Nine_Elements.html) are these:
Digital Etiquette
Digital Communication
Digital Literacy
Digital Access
Digital Commerce
Digital Law
Digital Rights and Responsibilities
Digital Health and Wellness
Digital Security
This is a post from Paul Bogush’s blog, Blogush. It addresses the issue of teachers using technology, and whether we should make teachers change their teaching styles to incorporate the technologies available to them. Below is a short audio response to the post.
This actually isn’t much of a blog by Mike Falick, but I found the video it pertains to interesting. It’s a short video, only about three minutes in length, but it presented some interesting ideas. I think that generally calculus is indeed the pinnacle of the math we learn up through high school. But this isn’t to say the math we learn cannot be used in and of itself, or in statistics and probability. Perhaps we shouldn’t expect everyone to take calculus, because like he says, not everyone will consciously use it in their daily life. But the algebra and geometry we learn before calculus can still be applied to nearly everything. I don’t think that probability should replace calculus, but students should have the opportunity to take courses in both during high school. This will give them a better idea of how they can use math after high school and give them more opportunities to use math in their daily lives. I remember wishing my high school offered a course in statistics and probability, because it had been taught there before I was old enough to take it. That doesn’t mean I would have avoided calculus, but I wanted to experience as many applications of math as possible before graduating. So I definitely agree that students should be taught statistics and probability in high school, but not as a substitute for calculus.
Below is a talk by Bill Gates, and my focus is the last section, from roughly 8 minutes in through the end. I was shocked to find that top quartile teachers make such a large difference in comparison to their colleagues. It seems hard to imagine that the United States could be ahead of the world in test scores after four years if every teacher was of the quality Bill Gates describes in this talk. But this is very concerning because it means we are not producing the quality of teachers we need, nor are we retaining the ones we seek. I know there isn’t much I will be able to do right out of college, but this inspires me to take care of business on my end. And many of the things he says make sense intuitively, so it seems obvious what good teachers must do. Things like keeping students engaged and involved only make sense, and I think this will be one of my main priorities as a teacher. I also want to analyze those things I am doing well to help myself and my coworkers to do things well. At the same time, I want to examine those things which I do poorly, whether I detect them myself or if others see them for me. As with any profession, it is important to get sufficient feedback so that one can make adjustments and always work to improve over time. And I think we can do all these things without being handcuffed by standards and test scores. And I think the biggest thing to be concerned with regarding teacher quality is complacency. I think that every teacher experiences this to some degree after gaining tenure. I think that as teachers continue in the profession it is important to keep analyzing what they can do to serve their students’ learning and not get too comfortable. Of course I’m getting ahead of myself, so for now I will just focus on what I can do to learn the profession and to help students.
In the video below, Ken Robinson talks about several really important ideas concerning creativity and education. The purpose of schools is to prepare students for life in the future, a future that is unpredictable. He says that we are born creative beings, but schools often direct us away from that because creativity is not as valued as skills in the core areas of education. He argues that this should not be the case, because intelligence is diverse and dynamic, and not limited to these few subjects. He also makes an interesting point that children are not afraid of making mistakes until they wrongly learn that mistakes are bad. As a future teacher I think it’s important to not only understand this point, but for it to be manifest in my classroom. No one does everything perfectly the first (or nth) time, and I really need my students to know this. I need to help my students be confident and unafraid of making mistakes. The best environment which I can have in my classroom is one in which students are willing to try anything I ask of them. They need to be comfortable with me, their classmates, and themselves to try anything, and to accept that mistakes are part of learning. I also need to help students look for ways to apply math in their life and in their future. Problems that arise in real life typically do not tell you exactly what kind of math technique/s to use. It is important for me to teach them skills in algebra and calculus, yes. But more importantly I need to teach my students to think mathematically, and to look for patterns and clues that point to the skills I teach them. In doing this I will better prepare them to use what they learn in school, because they can use what I teach them in whatever challenges and problems they have beyond my classroom.
I think the primary role of any teacher is to teach students a specific curriculum the best way they see fit. The only way we can ensure this is by giving teachers all of the resources they want to incorporate into their classroom. For example, if I think it will be beneficial to use Geometer’s Sketchpad to teach rules about triangle congruence, then schools should (within funding limitations) do everything they can to make that possible. Likewise if I think that teaching my students to solve simple algebraic equations without a calculator is the best way, then I should be free to do exactly that. A teacher must own his or her classroom. Teachers deserve freedom and support to guide students’ learning in the ways they see fit. Of course every teacher must follow the standards of their profession and content area, but we should not place more limitations on them unless they are necessary. I feel that if two teachers choose different means of teaching one lesson (for example, one with technology and one without), and they both have similar success, then we should leave those teachers to decide on their own methodology. Therefore I completely believe that technology use should be left to the discretion of individual teachers. One cannot force a teacher who depends on technology to abandon it, and one cannot thrust technology on a teacher who refuses it. This is not to say that students do not need proficiency in technology. I feel that every high school student should have at least one course in keyboarding, and another general course on computers and the internet. In addition to these courses, students learn many things about technology outside of specific classroom assignments. In many cases students know more than their teachers about new technologies anyway, because so much learning takes place outside of classrooms. All of these things considered, I claim that it is not only okay, but preferred that teachers are left to decide on matters of using technology in their curriculum.
