Looking Back

I am on a journey to learn how to effectively use technology to enhance teaching and learning.  The final destination of this journey is an elusive, currently undefined, technologically enhanced Math classroom based on the disruptive-innovation theory.  But since my goal is so far off in the distance that it appears to be a mere mirage, it is time to stop and take stock, to contemplate how far I have come, to look back to the beginning of this journey, in the hopes that this reflection will stave off despair and feelings of being overwhelmed, replacing these overwrought emotions with courage and strength to continue the journey.

So let’s flashback to ten years ago.  I am working in a segregated school in Abu Dhabi.  There is a big wall down the middle of campus separating the boys from the girls.  The Math office is on the boys’ side, so if the girls want to see me for extra help, they have to send a message to me.  Then I cross to the girls’ side to meet with them.  In my classrooms there is a chalkboard or whiteboard, coloured chalk (on a good day), and an overhead projector.  If I want to demonstrate calculator key strokes, the class goes one key stroke at a time, pausing to ensure everyone is ready to push the next key before we move on.  There is a computer lab down the hall for the computer classes and we have one computer in the Math office, shared by 8 of us.

Now speed forward to today.  I work in a one-to-one laptop school.  My tablet, smartboard, and projector are everyday tools.  When I want to demonstrate keystrokes on the calculator, I bring up my TI Smartview on the smartboard.  Students can watch me press each key on the huge projected calculator.  The tri-window view lets them know what all my background settings look like while the key stroke recorder allows them to work back through previous steps.  This is especially helpful for Algebra 1 students who may be using a graphing calculator for the first time.  These are tools that I now consider essential.  But if you add to that all the other accessories that are now utilized, even if on a less regular basis the list grows exponentially.  There is a document camera used to display and record exemplars of exceptional student work.  Numerous graphing software programs are used to bring clarity to messy, hand-drawn graphs (Padowan, Winplot, and Mathematica to name but a few).  Youtube videos are used to demonstrate concepts in a dynamic manner.  Java applets are used for both demonstration and investigation purposes.  Wikipedia and a host of internet sites allow for rapid gathering of information and tidbits to supplement and enhance the mathematical content.  Geometer’s Sketchpad, Geogebra and Sketchup provide dynamic tools for visualizing and understanding key mathematical concepts, such as parallel lines and planes, centers of triangles, and three dimensional figures.  The dynamic nature of these programs accomplishes understanding and engagement for students in a way that traditional methods of teaching never could.  When talking about volumes of revolution in Calculus, understanding dawns as students see the 3-dimensional shape develop as a curve rotates around an axis.  A recent addition to this list of tech tools used is Skype.  Students who were quarantined last year due to H1N1 “attended” class by having a friend call them on Skype and turn their laptops so the camera was facing the front of the room.  They were able to ask questions and follow along with the lesson.  What a change from ten years ago!

 This list of some currently utilized resources is not comprehensive, but it does encourage me to continue the journey.  Who knows, maybe that radically transformed math classroom is not so far away!  At least let’s hope it isn’t!

Shortcomings … and Hell Freezing Over

“No, I won’t post my class notes on the OLC.  If I did, you guys would not listen during class.”

Ouch … I cringe as I hear myself say those words again.  What am I so afraid of … really?

In my last post, I was beginning to contemplate the benefits of having a class blog; this lead to some online searching and the discovery of some internet content that further challenges my thinking.  The Techticker site maintained by Mike Bogle, Educational Technologist at the University of New South Wales contained one entry in particular that has inspired me:  “Student Engagement and Technology in the Classroom”.  Mike Bogle uses Richard Buckland as an example of how “the combination of an engaging instructor and empowering technology can have incredible results for student participation.”  Richard Buckland did what I am afraid to do.  Having identified that students were not taking notes in his classes and therefore had trouble recalling details in the future, he began to post his notes on a wiki.  Richard’s presentation “Wikis for Collaborative Learning and Teaching” on this problem can be accessed through The Techticker or directly from Youtube.  This presentation intrigued me because Richard Buckland began with some of the same fears that I have, yet his courage to open his notes to the world enhanced the learning experience for students in his class.

The idea of having a class blog for reflection and collaboration was only just beginning to take shape as a feasible option for me.  So would a blog serve the same purpose as a Wiki?  Richard addressed the issue of a wiki versus a blog by saying (14:43 – 15:00) “… Wikis are not for discussion … For discussion we use forums and emails … Wikis are a repository for recording information that should be objective and factual.”  This means there is a place for both a wiki as the keeper of information and a blog for reflection.  One of the problems I struggle with is that my notes, say for BC Calculus, contain every detail, including worked out solutions for every question.  Richard addresses this by providing only the skeleton of his notes and having students flesh them out.  This would mean students are engaged in the classroom as they collaboratively seek to write the notes during class and tidy them up after class.  The students are also taking ownership of the material (13:57 – 14:02).  Because Richard was able to access the wiki, he was able to identify misconceptions and mistakes (19:40 – 20:40).  What really intrigued me was his response to these mistakes.  Rather than jumping in and “fixing” everything, he waited.  He had faith that another student would come along and correct it.  What he found was that students not only made the correction, they explained why they were doing it.  This generated discussions in the forum.  So the collaboration that I see as so beneficial yet difficult to foster was naturally occurring.  Learning was enhanced and understanding was deepened without direct teacher involvement.  (Reminder to self:  there are benefits to releasing control and trusting students.)  If the mistakes were not corrected, it gave Richard fast feedback that there was a misconception from his lecture and he could address it in the next class.  Collaboration and feedback in a fast cycle.  Cool!

Richard Buckland has apparently had wonderful success with wikis in his University courses.  Dealing with a younger crowd there may need to be more preparation time early in a course.  This would be time spent establishing appropriate guidelines and boundaries for wikis: wiki etiquette or what Richard calls Wiki Nature (15:39).  Students may need practice atwriting and posting notes, seeing what counts as good notes, and discussing  how these notes will be useful to them.

To make this dream a reality, there are a number of other issues to explore.  The challenge of how to have students solving problems using appropriate notation within the notes would need to be addressed.  I can see how a wiki would help to counteract an issue that I deal with on a regular basis in a math course:  students need to show me all the steps that go into solving a problem and thus the logical process they followed.  Generally, students want to do this work in their head without writing it all out.  In a wiki of class notes, the value of showing all their work would be inherent as peers will be using the notes to help them understand the process and solve their own questions.  An investigation of  the mathematical notation possible in a wiki would be necessary.  Many students find it time consuming to type correct mathematical notation.  One of the most commonly used tools for this is  Math Type.  This is a fabulous tool, but can take time to use, especially for those who are unfamiliar with its capabilities.  So does the wiki support Math Type?  If students have a tablet, it would be easy to have them include their processes for solving math problems as they could ink their solutions and post a screen shot of their work.  If student work and notes were going to be accessible to their peers on a wiki then students would hopefully be intrinsically motivated to show all their work.  Others could then also edit the notes or show different methods of solving the same question.  I can see this collaboration being very beneficial for students and especially for those who are struggling to understand the material.  They would have the content in the form presented in class, as well as supplemental material where their peers rephrase the ideas in their own language and at their own level.

So if you check my OLC, you won’t find my notes posted there yet.  I am still cautious, but I am considering the possibility of change.  See … miracles do still happen … and I think you will see “my” notes, as generated by students in my classes posted long before Hell freezes over!