The Reflective Educator

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Month: March 2009

Networked communities and E-learning Opportunities in Mathematics and Science

How can a networked community could be embedded in the design of authentic learning experiences in math or science?

Part of my ETEC 533 course is to examine networked communities, such as Second Life (as an example of a multipersion world simulation), using resources such as PBS Nova Adventures (which provides the ability to hold virtual field trips), and Western’s Integrated Laboratory Network (which allows students to complete a variety of lab experiments online). What these different systems have in common is that they provide a simulation of a real-life learning experience, accessed through the internet.

One immediate question I have is, do these networked communities have any value?  This question is relevant because before one can decide on the "How" one really needs to engage the "Why" question.

It is hotly debated for example whether Second Life is in fact a useful teaching tool1.  Having explored Second Life myself, it seems to me that with proper preparation (read here a LOT of time) one could construct a number of simulations for this faux-world that students could explore.  One could easily represent socio-dynamics and economics using Second Life, but as for Mathematical applications, I think these might be few and far between, and end up being contrived.  There are a number of science communities formed within the Second Life platform, which from a cursory inspection seem to have educational value.  Our instructor had us run through a tour of an astronomical observatory, and although I’ve seen better simulations of the solar system, the ability to communicate live with other students about the simulation probably makes this a valuable learning experience.

The discussion in class of the Integrated Laboratory Network (ILN) brought up some useful points.  The first point, brought up by Nancy was that the fact that the lab time needed to be booked ahead of time meant she really felt like she had to be prepared.  A number of other students in my class agreed with this point, and it would be interesting to see if this effect would happen in a high school settings since of course the preparation would involving learning.  Another valid point, brought up by Ian, was that the simulation felt more like "following a recipe instead of doing science", suggesting that the experiment wasn’t as valuable as a result.  Another student, Tris, reflected that at his school the design portion of a lab was an extremely important part of the experimental process.  My thought was that the use of this equipment physically would be extremely unlikely at the high school level and that if a student created an experiment which required highly specialized equipment, an ILN might be the only way to do it.

As for the simulated field trips, one of the greatest values I can see here is the ability to "explore" a location which is otherwise inaccessible.  I can imagine a time in the not-too-distance future where students would be able to book time using a highly durable robot, and explore Antarctica or Mars, both of which are places that are either extremely expensive or improbable places to visit.  Already there are excellent video field trips of many places in our world which are highly fascinating and learning rich experiences.  One obvious flaw with a virtual field trip is the lack of a tactile experience.  Without taste, smell and touch, the experience would be sensory deprived.

Of these three examples, it seems that only Second Life has a true social learning aspect built into its design.  An ILN or a virtual field trip really lacks that social context which benefits the learning for so many of our students.  It will be fascinating when computer processing becomes powerful enough to allow for multiple users to experience a virtually life-like simulation of a place caught on camera only.  When this happens, and if the people can communicate during the experience, then social learning affordances will be relevant to this type of learning.

Now suppose we wanted to design an actual classroom learning experience which would use one of these tools.  The easiest to do this for would be the ILN, since it has been specifically designed to be an instructional aid for laboratory science.  One would have students design detailed experiments, and then have a wide variety of different tools available to them to complete their experiments, through the use of the Integrated Laboratory Network.  Students would have to discuss their experiments ahead of time and reflect on their experiments afterward to allow for a social context for the activity.

To use the Second Life platform effectively, I think that a simulation could be constructed for the students to access, and then students would be given free reign to experiment within the science simulation (the orbiting of the planets seems like a good example for instance) and discuss their discoveries.  One would lack much control over the specific information learned by any particular student, but it could be a valuable learning experience, particularly for the students who need help visualizing three dimensional objects.

The virtual field trips would allow for hostile locations to be examined by students.  For example one could use footage of an exploration of the deep sea bed and show students how even in an hostile environment, life thrives.  This would make for an excellent learning opportunity in a biology classroom.

None of the resources we have been shown looks like it would be useful for a mathematics classroom without an enormous amount of preparation.  One could imagine that one could show a highly specialized simulation of a concept which involves a fair bit of mathematics, but it seems to me that any such simulations would be too contrived to be useful learning activities.

It is clear that there are uses of these networked communities within education, and even within science education there are opportunities for powerful learning to occur through these communities.  One doesn’t have to look very hard to find examples of things in science worth learning which are for various reasons completely inaccessible for students (imagine setting up a virtual black hole for students to look at for instance).  For this reason alone, I think these network communities are worth exploring, but I think that the inclusion of community needs to be stronger in most of these online systems (Second Life excluded) as this will allow for a strengthening of the learning opportunities available.

References:

  1. Aldritch, C. (2006) Second Life is Not a Teaching Tool, accessed from http://learningcircuits.blogspot.com/2006/11/second-life-is-not-teaching-tool.html on March 31st, 2009.
  2. Cancilla, D. A., Albon, S. P. (In Press) Moving the Laboratory Online: Challenges and Options, Journal of Asynchronous Learning Networks.

 

Online Geogebra training

Hi folks,

I’m planning on doing an online training session, we’ll see if I get anyone to sign up!  The first 20 people to post a comment here will be registered in this free training session in Geogebra.  This limit of 20 people is only because http://dimdim.com restricts the free online sessions to 20 people.  I’m not, by any means, an expert in the program, but I am happy to share what I have learned in 2 years of using the program.

  1. Post a comment to this post indicating what time works best for you.  You need to fill in your email field, which is hidden from everyone except me, the owner of this blog.  I’ll use your email address to send you the Dimdim meeting invitation, so it is important that you include it.
  2. Go to http://dimdim.com and sign up for an account.  You will of course need to use the same email address as step 1.  You should try it out first to check to make sure there are no problems ahead of time.  I’ll of course be testing this myself.   Update: We  might use Mikogo instead, it seems easier to use.
  3. Oh and I suppose I should mention that you really want Geogebra installed.  You can get it from http://geogebra.org and happily, it is free.
  4. I’ll also be putting up some resources on the blog, linked to this post, once I get a chance to organize them.  You should make sure to come back here and download those resources.

Of course this training session is dependent on my internet connection remaining up.  I guess if there are problems, we can always reschedule.  

 

Update:

Hello all,

A little over three years ago I decided I wanted to experiment with online learning, and I decided I would start this experiment with a training session for Geogebra, which is still software I love to use in my teaching. A week after I made announcements everywhere about the training session, my Dad died, and I never ran the session. Three years later, I’m still receiving registration requests for the program so I know there is still interest. At one point, all of you registered for this training opportunity.

I’m still personally interested in what this would look like from my perspective, but I already know of a terrific resource for learning Geogebra for beginners so I see little point in duplicating effort. Linda ran an excellent (and free) course last year, and I recommend using it as a resource for getting started with Geogebra. You can access it here: http://moodlemeets.learnnowbc.ca/course/view.php?id=3

It’s free, but you have to create a login at http://learnnowbc.ca in order to access the course. The course is archived, but there are lots of discussions archived in the forums, and you may find many of your questions answered there.

If you are still stuck, you can take a further plunge and if you have not already done so, sign up for Twitter and then search for #mathchat in the search box on Twitter. Many of the mathematics educators that post with the #mathchat hashtag use Geogebra regularly and may be able to answer your questions. Hopefully you’ve also already found http://geogebratube.com/ which already contains 10,000 Geogebra resources that are free to use and modify as you see fit.

Thank you,

David Wees

 

How can Geogebra be used to help students understand and visualize mathematics problems?

In your inquiry e-folio, reflect upon knowledge representation and information visualization based on your post above and the discussion it generated with your peers. Ensure that you refer to the software you chose to explore.

In my ETEC 533 class, we are in the middle of a really cool unit, and our task of this unit was to share a digital learning tool or resource with everyone else in the class.  I chose to share an open source geometry program I have used a lot, Geogebra.  Unfortunately my post has yet to generate any discussion, possibly because of the large number of other geometry packages available, and the therefore limited interest in this particular one.

This handy geometry package is free, cross platform, and very easy to use. It allows for the creation of geometric objects, which have various properties (including position, color, size, etc…) and which can be either a dependent or an independent object.  Independent objects can have associated dependent objects, and when you modify the independent object, the dependent geometric object is modified as well.

For example, suppose we created two points in the plane as independent objects, and then created an associated line through the two points as a dependent object.  When we move the position of either of the two points the line will change to match this movement.  This allows students to end up with a deeper understanding of the relationship between geometric objects.

This program is very flexible, and can be used to show simple geometric relationships (like for instance the geometric fact that the sum of the interior angles of a triangle is 180 degrees) to very complex geometric properties (the limit of the sum of rectangles which approximate the area underneath a curve is equal to the exact area under the curve).  Geogebra is then therefore useful in a wide variety of different contexts and branches of mathematics.

When students are using dynamic geometry software, such as Geogebra, they invariably end up with a deeper understanding of the material (Pütz 2001).  This is probably because they are given a strong visual representation of the object, that comes associated with a more tactile impression that comes with using the mouse to move and adjust the object.  Obviously there is a "wow" factor involved in the use of any new program, where the students are engaged with an activity simply because it is new, but it has been my experience that the use of these geometry packages ends up leading to a long lasting understanding of geometry.

Another advantage of Geogebra is that it allows the user to export the current file into a web ready format (a java applet) which can then be uploaded to a web server.  This provides the ability for students and teachers to discuss and analyze each other’s work, and allows for the creation of a social discussion about the work. 

Geogebra also allows a "construction protocol navigation bar" to be added to the file, which means that users can step the geometric construction process, one piece at a time.  This is a tremendous advantage of Geogebra as it allows a user observing someone else’s work to have some insight into the process they went through to create it. 

Geogebra allows students to actively and through the sharing of the work online, socially construct an understanding of geometry.  This program allows for simple visualizations of possibly complex geometric concepts, and helps enhance a student’s understanding of those concepts.

References

Pütz, C. (2001). Teaching Descriptive Geometry: Principles and Effective Methods Demonstrated by the Example of Monge Projection, XV Conference on Graphics, Sao Paulo Brazil, November 5-9, 2001.

Hannafin, Robert D. & Scott, Barry N. (2001). Teaching and Learning with Dynamic Geometry Programs in Student-Centered Learning Environments. Computers in the Schools, 17 (1), 121-141. Retrieved March 18, 2009, from http://www.informaworld.com/10.1300/J025v17n01_10

20 reasons not to use a one to one laptop program in your school (and some solutions)

We have a 1 to 1 program right now at the school I’m at, and there are a lot of problems with it.  Initially I was for the program, but I am becoming more and more against it, especially with the current way our program is run.  Let me list the problems I’ve discovered so far:
 

  1. Classroom management while students are "taking notes with their computers" is an issue.  I think installing a gigantic mirror at the back of the classroom would be ideal.
  2. Classroom management issues while the students are supposed to be working on exercises using the CD version of their textbook, or a calculator emulator, when in fact they are searching the internet deciding what shoes they are going to buy on the weekend.
  3. MSN Messenger, Skype, Google Chat, etc… name your poison here.
  4. Transition times between activities increase as you wait for the students to reboot/boot their computer, plug in their power cord, comb their hair etc…
  5. Exceptionally slow internet at our school since every student is actively connected to the internet all the time.
  6. Our wireless hotspots only support 15 active connections.  We have as many as 26 students in a class.  You do the math.
  7. Students don’t maintain their computers properly, leading to the spreading of malware, viruses, etc… through USB sticks.
  8. Since some students have malware installed, our network takes a hit as it has to defend itself against internal intruder programs searching the local network for active ports.  Every day I have 10-12 port scans that my firewall blocks.
  9. Students don’t keep their software up to date.
  10. Students don’t even keep the right software on their computer.  Equation editor is SUPPOSED to be standard in M$ Word, but hey some students have got it uninstalled… heck some students don’t even have a word processor on their computer.
  11. Students don’t have the same software on their computers.  For example, I have seen Firefox 2, Firefox 3, Safari 2, Safari 3, Internet Explorer 6, Internet Explorer 7, Google Chrome, Opera in action, all at the same time, in the same class.
  12. Students don’t know how to do "fill in the blank" on their computer, so class time is spent trouble-shooting rather than on instruction.
  13. Laptops are stolen, about 3% of them each semester.  Combination of laisse-faire attitude by students and poor security at the school.
  14. Students forget their laptops/power cords/brains at home/in locker/in canteen
  15. Three different operating systems in use.  Yes, some students are using Linux.
  16. Of the three distinctly different operating systems in use there are 3 flavours of Windows, 2 of Linux, and 3 of MAC currently in use.  Now I’m supposed to be an expert on all 8 of these flavours and plan my lessons for minor incompatibilities between them because why?
  17. "I just need to print out X for my Y class.  Can I go do it now during your [unimportant] lesson?"
  18. Students forget passwords, even for their own computers at times.  The most common one for the students to forget is the one for the wireless or for my classroom blog.
  19. The laptops are heavy.  Textbooks are heavy.  Some of my students have back problems already at an early age from carrying too much to and from school.
  20. Most teachers lack training on how to use the 1 to 1 program effectively.  We need time to be trained in optimal pedagogical techniques involving the use of technology, provided with classroom management strategies, and shown with some proof that the technology is worth using.
     

There are some simple solutions to these problems.

  1. Don’t let the students buy their own computers.  Either buy all of the computers for the students or require them to buy a specific model.  They need to be using exactly the same software, hardware, etc… 

    Update:
    This is less important now that more applications are on the web or cross platform.
     
  2. Make the school in charge of installing software on the student computers.  This works better if they are actually the school’s computers and you are renting them out to the students for the year.  This way you can ensure that no games, chat programs, peer to peer file sharing programs, http proxy tunnel clients, etc… get installed on their computers. 

    Update:
    This approach is too top-heavy. Recommendation instead is to make sure that teachers are aware of these issues, and then have them focus on effective teaching; which means helping students learn about appropriate timing.
     
  3. Have a way for the teacher to turn off access to the internet when they need.  Could be as simple as a light switch which turns off the nearest wireless box (have one wireless box per room, configure it to a minimum radius, maximum number of active connections).

    Update:
    This seems kind of crazy now. So many of the applications we use are online. 


  4. Don’t use Windows until they can prove that it is as secure as the other Unix based systems.  Go with Linux and a bunch of open source software, or go for Mac and pay through the nose, either way works.

    Update:
    We’ve had many less problems with viruses here at my current school, so I think that either virus protection software has gotten better, or Windows 7 is much more secure than Windows XP.


  5. Have some common sense when planning the layout of your classrooms.  Install electricity outlets in convenient locations, either right in the tables the students are using or on the floor.  Make sure there are enough outlets to go around.  Heck, put an ethernet cable port right next to each outlet and forget about wireless all together.

    Update:
    I still agree with this one. Plan ahead. I think robust wireless networks have gotten easier to set up, and so the ethernet cables are less necessary. Still, it took us almost 6 months to get our wireless network stable.


  6. Make sure students are all given training on how to most effectively use their computers.  It is the job of a school to help students learn how to use these powerful devices, but to be honest, the typical classroom teacher isn’t up to the job, and they’ll be the first to admit it.  This training should happen in an information technology course taught as a core subject.  Each student should take this course each year they are in school.

    Update:
    We integrate technology at my current school without too many issues. We are focusing on teacher training on how to use the technology which seems to be making a difference.


  7. Have a specialist who’s job it is to trouble shoot the computers and make sure they are all running smoothly.  Have students see this specialist outside of class time if possible.

    Update:
    I agree with having a specialist around, but wonder, if a student’s paper wasn’t working, would we let them suffer until the end of the day to get it working again? If it’s a critical tool for learning, it needs to be working.
     

Don’t get me wrong, I’m a strong supporter of technology in the classroom.  I think there are some very powerful, very useful ways it can be used.  However I don’t think it is being used effectively at our school, and I often wish I had the power to can the whole program and start over again, implementing some of my suggestions above. Update: At my current school, I think we are working on improving our use of technology, and for quite a lot of people, it is being used effectively. Obviously, there is always room for improvement.

Update: I wrote this post nearly 4 years ago, when I worked in a very different school, and my own pedagogical approach was different. I think that battery life of computers has improved a lot since I wrote this, mitigating some of the issues, and that I see these more as learning experiences for students and teachers. With more applications being web based (and more applications supporting a wide variety of users), standardization of device and browser is a lot less important as well. Further, students will have these same issues after they leave school, so it is somewhat better for them to have them in school, where they can get some support for later in life.

Questions about Edelson

To help me remember this issue for later, I’ve decided to explicitly post my responses to these questions in my blog.  Those of you who are not interested in my personal responses to a reading for my ETEC 533 course can safely ignore this posting.  🙂

  • Based on the reading, what broader educational challenges have provoked the author to do this research?
    According to the author, teachers are "being asked to teach more content more effectively" and at the same time being required "[that] inquiry to play a much more prominent role in science learning". (Edelson 2000).  This is an issue because both of these requirements of teaching take up more classroom time in a traditional classroom, and Edelson (2000) says that "[t]raditional science teachers often perceive these demands as unachievable."
  • What is the author’s theory of learning?
    Based on this quote, "Learning takes place through the construction and modification of knowledge structures." (Edelson 2000), I suggest that this author is essentially a constructivist where the essential definition of constructivism I am using here is "learning is an active process of constructing rather than acquiring knowledge" as suggested by Duffy, T., Cunningham, D.J. (1996)
  • What are the pedagogical design principles that shaped the development of the WorldWatcher?
    According to Edelson (2000), there are four design principle’s in the development of the WorldWatcher:

    1. "…learning is the process of constructing new knowledge structures and forging new connections between knowledge structures in an interconnected web…"
    2. "…learning can be consciously monitored and directed through metacognitive processes…"
    3. "…knowledge is retrieved based on contextual cues…"
    4. "…an individual must have procedural knowledge that enables him to apply that declarative knowledge, or he must be able to transform it into procedural knowledge…"

    The following table created by Edelson (2000) summarized the pedagogical considerations in the creation of the "Learning-for-use" model.

  • Explain the reasons for integrating digital technology as a key part of this learning experience.
    "WorldWatcher was designed to bring the power of scientists’ computational tools to learners" (Gordin & Pea, 1995).
     
  • How are the pedagogical principles reflected in the design strategies suggested?
    There are 6 phrases or words Edelson (2000) uses to describe the fundamental principles used: "Create demand, Elicit curiosity, Observe, Communication, Reflect, and Apply".  Each of these words appears to lead to an activity used to satisfy this criteria in the WorldWatcher’s program.  A major component of all of these criterion in the program is that computer related technology is used to make the implementation easier.

The second article we were told to read (Learning-for-Use in Earth Science: Kids as Climate Modelers) started off as largely a rehash of this article.  This is probably due to the influence of Edelson as the author of the first article, and a co-author of the second.  However, it then diverses to describe a piece of research by the authors.  First they pretested some 8th grade students on their understanding of the relationship between Earth orbiting around the sun while rotating on its axis, and the seasons on Earth.  Following this, they used some software called the "Planetary Forecaster" to help the students understand this relationship, and finally they post tested the students on their understanding.  Not surprisingly, they discovered that most students understanding of the changing of the seasons had improved dramatically.  A major flaw apparent to me in this research is a lack of a control group, wherein some students are taught using more tradional methods, and some students are taught using their software.  This aside, the software seems very interesting and probably is responsible for a positive effect on the students’ understanding given what appear to be solid design principles.

What both articles have in common is that they are looking at the use of technology to assist in the understanding of geographic principles of Earth.  Students are given training in the use of specialized technology, which is used as a tool in this instance, and guided toward an understanding.  Although the authors claim to be used constructivist methods, it seems apparent that the lessons used are much too guided to allow for true constructivism on the part of the students.  It seems clear to me that the students own prior knowledge is not being used to guide the learning process, and that the direction of the lessons are much too focused.  I don’t mean to say that this is necessarily a bad thing, it is my experience that without sufficient guidance, students will wander aimlessly.

References:

Duffy, T., Cunningham, D.J. (1996). Handbook of research for educational communications and Technology. Association for Educational Communications and Technology.

Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385.

Edelson, D., Salierno, C., Matese, G., Pitts, V., and Sherin B. (2002). Learning-for-Use in Earth Science: Kids as Climate Modelers. National Association for Research on Science Teaching, April, paper presented in New Orleans

Gordin, D.N., & Pea, R.D. (1995). Prospects for scientific visualization as an educational technology. Journal of the Learning Sciences, 4, 249-279.

Curriculum Resources for IB Mathematical Studies

Here are some links to my schemes of work I am currently using for IB Mathematical Studies, for Year 1 and Year 2, created in collaboration with Craig Molla.

IB Mathematical Studies Year 1

IB Mathematical Studies Year 2

I also have my personal unit plans for IB Mathematical Studies Year 2 available:

IB Mathematical Studies Unit Plans