Mathematical Adventure

When I step back and take a look at the past ten or fifteen years, I am absolutely amazed how much technology has changed.  I remember having a computer in high school and college.  They were expensive, large, and very slow in comparison to what is available today.  The internet was starting to become very popular, but it was used more for research and email communication.  Email and Instant Messaging was so liberating because I was able to communicate with people all over the world and I could do it from any computer that had internet access.  I have to laugh as I remember submitting my first paper to my professor by an e-mail attachment.  Telephones were still attached to the walls with the answering machine as a separate piece.  We did have car-phones they were very large (they would be plugged into the cigarette lighter) and were used for emergencies only because each call was very expensive.   Education looked much like it did ten years before that, but computer labs were being added and library card catalogues were all on the computer.  Although I enjoy looking back and reminiscing about the past, I do remember the frustrations with the slow speed of computers or with losing documents I had typed and not saved on the computer.  I also remember writing a rough draft of papers by hand and then typing them on the computer. 

Needless to say, we have already come a long way, but I can’t wait to see what the future holds for us.  In the year 2020, I don’t think students will have text books for each class anymore because printed material is so quickly outdated (this will be great for their backs!) and each child will be required to have a lap top computer.  Laptops will be very small, light in weight, extremely fast, and inexpensive.  Text book companies will have all of their material online and students will be able to access them from anywhere.  Students will also be able to complete homework and assessments through the online textbook and the online text book will be able to give students immediate feedback about their work.

Students will have more choices and options about what direction they want to take their education in.   Although there will be more opportunities to take online courses, I do think that many courses will require a physical meeting time as well.  Perhaps some students’ education will be composed of primarily online courses, but school buildings will still be needed for the perhaps weekly meetings of the online courses, for families who need child supervision, for students who are not motivated or self disciplined enough to take online courses and need the structure of a classroom.  A student who wants to learn Spanish might be able to enroll in a course in Spain.  A student who finds a Multivariable Calculus course in Japan that meets his needs might enroll in that course and meet with students and professors either by webcam or in person in smaller local groups (with a local teachers assistant).  I am finding that today more and more students have IEP’s in our classrooms, which just reinforces the fact that every child is different and has different needs so finding the placements that work best for each child is better than providing the same instruction to every child in the classroom 25 different ways (which we all know is physically impossible, but yet this is what is required of us).  A child will be able to work at their own pace through each subject in school.  For Instance, a child may be working through a 6^th grade reading class while taking an 11^th grade math course.  The great thing is the fact that there will be choices to be made by each family as to the education that fits their children best.  There may be a federally mandated high school diploma exam to make sure each child has a basic level of understanding before entering college, but the path to the diploma will not necessarily be confined to a particular building that you need to hop on a school bus to get to. 

With choices comes responsibility.  Both the parents and children will need to make sure they balance their time with all of this emerging technology.  Making sure kids get physical activity during the day will be even more important as we enter a world where much of what we need we can do through a computer.  Perhaps physical education classes will be required daily no matter if you choose to take online courses or attend your local school.  Parents will need to be concerned about their child’s health and the repercussions from using so much technology- weight gain, vision problems, carpal-tunnel syndrome, etc.

Being a high school teacher, I tend to think of the older children, but I imagine elementary school will be different as well.  There may not be as much demand for online courses at that age, but computers will be an integral part of the classroom.  Children may learn to read through specially designed programs that measure their level and provide level appropriate material for them.  Memorizing lists of spelling words will not be necessary because of spell check programs.  For the most part students will attend a school and have a classroom in 2020 just as they do today because the teacher-student interaction and student-student interaction is so important in building appropriate social skills.

For teachers, education will be different too.  Our classrooms may be in the school building much like they are today, they may be cyber-classrooms, or perhaps a mixture of both.  Wireless access will be available throughout the country, so teachers will also have more options about where and how they want to teach.  The classroom will be much more student centered and less teacher centered.  The teacher will act as a facilitator instead of the source of knowledge.  Because technology is changing so rapidly, teacher training courses will increase and teachers will perhaps be required to take at least on course a year to stay up to date. 

The changes that are taking place are incredible.  If I would have tried to imagine 10 years ago how things would be today, I would have never been able to dream up that we would be blogging, podcasting/video casting, working collaboratively on projects with students in different states/countries on wikis, and being able to access information instantly through computers, cell phones, and IPods.  It seems overwhelming to think that I entered a career that in 2020 will be in many ways very different the career I thought I was entering when I graduated from college.  I get a lot of satisfaction from the interactions I have with my students and watching them grow, I hope that no matter how technology changes I continue to enjoy teaching students.

I think the idea of a paperless class is wonderful and I think that is the direction that schools are heading.  I really like that there is still an opportunity to meet as a class in the seminars for discussions because I think the social interactions and connections that occur are also very important.  The paperless classroom puts more responsibility on the student to access the information needed to complete the assignments.  It makes the classroom a more student centered environment.  It will not be long before students will no longer bring textbooks for each class in their backpacks, but perhaps a laptop with wireless access will be required instead.  For students, there would be no reason to memorize facts that could be looked up easily online, instead they will need to learn good researching skills and appropriate ways to give credit to their sources.  It will be the teachers responsibility to provide guidance, teach research skills, and safety for using the internet.

As a teacher I will probably spend my time in class guiding students in the right direction through their projects instead of lecturing as much.  I see this as a great opportunity to differentiate instruction and provide opportunities for all different types of learners.  I will probably spend more time leading discussions on class forums.  I know many English teachers in our school are already using sites such as turnitin.com to have students turn in their written work.  Students have access to thousands of articles and papers through the internet to use as resources for their work which is wonderful, but it also makes it very difficult for teachers to know that the work belongs entirely to the student.  The great thing about turnitin.com is that it checks to make sure that the work turned in is the work of the student and not taken from someone elses work off of the internet.  Also, there is a time and date stamp when they turn in their work which enables the teacher to accurately determine if work was turned in on time. 

            Measuring learning will probably be done using rubrics, much like we do now, but the work will be turned in online.  I like the fact that assignments can be completed and turned in on students own time.  Students will need to learn responsibility and good time management skills to be able to complete their work without having a teacher reminding them daily of what they need to complete.  I see this as a good thing, but I think that will be very difficult for many students.

            A paperless space makes it easier to build a learning network.  Students have so many resources to access and often experts are willing to respond to students or teachers.  In an English class, students could read a book and contact the author.  In a Foreign Language class, students could learn about the culture in class, but also contact students in those countries by e-mail or skype (what a wonderful penpal experience that would be).  The possibilities are endless as we head toward a paperless classroom.

Information is so accessible to students that I have definitely seen a shift in teaching practice in the last 9 years of teaching.  Where I remember memorizing facts throughout my education and even a poem every week in 6th grade, students these days are not expected to memorize anything and will often even question why I am asking them to memorize even one formula for a test.  I hear colleagues often discussing the idea that information is so accessible that there is no need to have students memorize any facts that they can instantly look up on a computer or cell phone.  Our school allows students to bring study sheets into their midterm and final exams, some students are allowed to bring multiplication charts, and all students can use calculators on most assessment.  Students often use their cell phones or iPods as mini computers to look up information instantly, so the need to memorize facts seems unimportant, but I do sometimes see the negative side of this as well.  Students become dependent on the technology and panic or have complete melt-downs when the technology fails them.  I am a little worried that they are not thinking on their own enough and when the technology does not work that they don’t know how to think.  I realize that I have the very important job of making sure students use the technology in a way that also makes them think and reason.

Skype is a wonderful tool that I first heard about on Oprah.  Oprah uses Skpe on a regular basis on her show.  She is able to connect with people from all over the world to find out their views on the topics being discussed.  No longer do they need to pay for expensive flights and hotel rooms to be a guest on the show. 

In the classroom there are so many great possibilities with Skype.  I would think  Social Studies classes or Foreign Language classes could connect to people in the countries that they study and learn about their culture without ever leaving the classroom.  In an English class it would be wonderful to talk to the author of whatever book the class is currently reading. 

Students could even collaborate with students in other schools on group projects perhaps.  I hope to try to include Skype in my classes this year in this way.   I would like to contact a teacher from another school and put together an activity that the students could do with a partner from the other school.  It sounds like a lot of fun and it really extends the classroom outside of the classroom walls.

Another way I could use Skype in the classroom is to talk to experts.  What a great thing it would be if a stuent asked, “when will we ever use this?” and I could say, “let me see if I can get my friend the architect or an accident reconstruction investigator to answer that question for you.”  What a great way to bring a speaker into the class.

It is amazing how much technology has really changed so many aspects of our everyday living and how quickly this has all happened.  It is incredible that we are so dependent on the technology and many are very lost without it.  I think the changes are not happening fast enough in our schools for many reasons, funds being one reason, but perhaps confusion as to what this all means is also holding schools back.  George Siemens attenpts to make sense out of it by offering a new learning theory called Connectivism. 

Siemens has some interesting views, but I am not convinced that Connectivism is a learning theory.  Group C discusses the idea that “learning is individual to the person and their perception of the material.”  It is an internal event that occurs.  We have plenty of places where we can store information, quickly access it, and even share information, but we have had that for many years (books, magazines, research papaers, televisions, radios, telephones, etc.), just our ability to access it was not always as quick as it is today.  Now that we have faster access to it does not mean that we are learning differently, we still need to make meaning of all of this information (maybe even at a faster pace) which is the idea of Constructivism. 

http://bce-summer2009.wikispaces.com/Group+C+Against+-+Karisti%2C+Susan%2C+Julie

I found a great podcast that I can see myself using in my classroom.  Dan is a math teacher who has created a series of podcasts in which he discusses various math topics in a very clear and succinct way.  I chose this particular podcast becuase I really enjoyed his description of direct and indirect proofs.  This would be great for my geometry students to listen to to pick up the vocabulary and the examples he gave.  He covered other areas of mathemetics such as trigonometry and algebra II, with parabolas and arithmetic sequences and series.  I could use these podcasts as discussion starters in class.  For example, instead of asking students to do a reading to prepare for a discussion, I could ask them to listen to a podcast and perhaps even write a reflection before the next days lesson.    

One of the obstacles that I as a math teacher struggle with most is getting students to talk math.  For some reason there seems to be a disconnect between the math the students write down on paper and their ability to communicate it.  Students commonly misuse vocabulary and lack the vocabulary to express their thoughts about math- I think this frustrates them.  The pod cast series that I found might be a way for them to hear the vocabulary and in turn be able to understand math in a very different way then they were used to before. 

Check out the podcast below: 

http://cdn3.libsyn.com/dansmath/dansmathcast_032.mp3?nvb=20090703180728&nva=20090704181728&t=032dfeb668ab7e5511621

Flickr is a great way for students to use artwork to express themselves.  I think its’ usefulness in a high school math class may be limited, but I see many possibilities for English, science, history, and art classes.  My favorite idea that I came across is randomly choosing a picture and then writing about that picture (Will Richardson calls this “random writes”).  What a fun journal activity that would be.  In a math class, I could see the pictures being used to perhaps embellish a project or create a power point presentation.  All of the resources I read made mention of the fact that Flickr images could be used in a math class, but I did not find that there were many examples given for the high school level.  Has anyone who has used Flickr successfully in a math class at the high school level?  Please share your ideas. 

Richardson, Will.  Blogs, Wikis, Podcasts, and Other Powerful Web Tools for Classrooms. Second Edition. Corwin Press 2009.

Image Citation: 

elb the prof. (2008, September 12).  Cauliflower fractals…  Retrieved July 3, 2009 from http://www.flickr.com/photos/elb_the_prof/2851361270/in/photostream

I have really enjoyed creating a wiki this week.  I think I can definitely see myself using wikis in my lessons.  Students can be in charge of being the experts about a specific parts of a unit and create a wiki as a small group for their particular part just like we did.  I love that idea because it gives students another opportunity to be exposed to the ideas of the lesson and it forces them to consider the main ideas of the lessons. 

One of our group members had worked with a wiki before, so he immediately assumed the role of the leader.  The other group member and I felt relieved to have someone who could help us and take the lead.  The most difficult part of creating the wiki was assigning roles.  It would have been nice to have an initial meeting with my group members.  An idea was thrown out to the group on the discussion board as to what our sub-topics should be, and then we each picked one.  The person who checked their messages last ended up with whatever topic was left.  Also, at one point two people were working on the same section because of a miscommunication.  In the end, I think our wiki came together nicely with no major problems.

Social bookmarking could be a very useful department tool, although it is still very new to me and I am not completely sure I understand all of its’ capabilities.  The internet can be extremely overwhelming, but now there are ways to organize the websites that you find to be most useful.  This can be a great professional tool.  I could find interesting websites, tag them and then share the tags with the department or with those who teach the same subjects and they could share their tags.  This would be a great way to collaborate and organize useful information.   Even students can be part of the process if we allow them to be.  It would be nice to have some more time to explore the options to see what would work best for our department.