CEP 820 Products and Reflection

Developer Notebook Reflection

8/16/2012

Reflections about CMS Course Design

First I would have to say that the developer’s notebook (click here if you would like to see my notebook) is an outstanding tool for tracking progress and the thought process behind any idea that is being constructed.  It is definitely something that I plan to use again.   When using this again I might change the format slightly by defining key areas of concentration first and then adding dated entries as needed below each area.

Critical Design and Pedagogical Decisions

I see the elements of design and pedagogy as being inextricably linked to one another.  For example, my deeply held belief that learning is a social process and that collaborative thinking is therefore essential to quality learning played a vital role in my choice of CMS platform.  I choose Wikispaces as my CMS platform because a wiki is by definition a socially constructed depot for information.  I also feel that having one’s work in the public eye is a strong motivator for producing high quality work. Again, Wikispaces affords this opportunity by allowing the site manager to allow content to be published to the web easily.

Click here to see my project

At the outset I did have a concern about how Wikispaces allowed all users to see every page of a wiki.  This prevents me from being able to use the features of the CMS to assess individual learning.  A student's quiz responses if posted to a page in the wiki would be viewable by all other students.  As my chosen format was hybrid in nature I planned on working around this constraint by having individual assignments done in the classroom (and yes I could have used an additional outside technology like google forms to assess individuals, but that too has its own set of constraints).  After having spent a great deal of time working with Wikispaces on this project, I discovered that they have created a tool which allows me to easily create pages that are viewable only by certain users down to single members.  This allows me to give each student their own page which can be made public or private depending on my needs and thus allows me to work around what I believed was a constraint.

The ability to create pages for individual students also affords another key area of pedagogy to be implemented.  Formative assessment, particularly self reflection on learning by the student, can be done as the student should basically have a journal including assignments that they can use to track their understanding of concepts or materials.  This allows the student to look back on the work that they have done and reflect on the their strengths/progress or areas of weakness/improvement targets.  It is easy to add assignments to a module that require this type of reflection.

One of the things that I continue to struggle with is finding other multimedia resources to incorporate into my module.  While it is easy to find mathematics videos that explain how to complete a particular task, Khanacademy for example, this type of direct instruction goes against my beliefs that students benefit more from making the discovery of new mathematics (new to them) than when they are simply told how to do something.  From a cognitive psychology perspective it removes much of the elaborative process that must occur when students are allowed to construct their own meaning, and most students turn to a purely rote memorization of skills in a direct instruction setting.  This is one of the reasons I have serious concerns about entirely online courses and the reason that I choose to make a hybrid course.  I feel as though my module falls short of using one of the biggest affordances of online instruction, the ability to integrate web content into a class.

If I had this project to do all over again I would have forced myself to create an entirely online course, and I feel like that should actually be the assignment.  The hybridization of my course allowed me to avoid a lot of problems that I would have faced had the course been entirely online, such as the issue of finding multimedia to include.  That is not to say that I didn’t learn from this experience or think about such issues, in fact I am much more aware of them in spite of the fact that did not find solutions to all of them.

If I had to give a piece of advice to a person preparing to make an online course it would be to embrace the good and the bad.  I learned more about my beliefs as a teacher from having to confront difficult situations.  For example trying to find a way to do formative assessments in an online setting made me revisit the reasons for doing this type of assessment and as a result I am certain will have an impact in my real classroom as well as future online classrooms.

CEP800 Technology Integrated Lesson Reflection

The lesson I chose for this project was about discontinuities in the domain of rational functions.  The goal of the lesson was to have students explore and gain an understanding of what causes the domain to be discontinuous so that they would be able to identify functions where this type of behavior is likely to occur as well as at what value(s) the function is discontinuous.  I choose to use the TI-Nspire graphing calculator in conjunction with this lesson.  The technology is not a necessity for students to understand the concept; however, the goal of including this technology with the lesson is to help students focus their attention on the stated goal as opposed to other extraneous, albeit important in previous units, content.

I beta tested this lesson with my wife as my classes will not be working on this for another week.   Just as I hoped she quickly identified that the graph had strange vertical lines appearing in it, representing the discontinuities.  When I directed her attention to the equation I had her enter into the calculator she also quickly identified that the reason that this was occurring was due to the fact that those x-values caused a division by zero which as she noted “you can’t do”.  I created a new equation for her to look at and asked her to predict what the graph would look like.  Again she picked out the values that would cause division by zero.  For our third exercise I created an equation that was impossible to find the zeros of the denominator by inspection.  As it had been years since she solved a quadratic equation, which is not the case for my students, I showed her how to graph the denominator of the equation and asked her what x values made it equal zero.  She estimated the two values from the graph and I showed her that she was correct by demonstrating that the calculator would calculate them for her.  Overall she maintained a focus on the reason for the graphs strange behavior and was able to identify where it would occur, precisely as the lesson had been designed to do.

The lesson did differ from the way I plan to teach to my students in the sense that they have been working with solving quadratics, and finding zeros with the calculator for several weeks.  In this sense the technology should not provide any sort of distraction from the content (i.e. students struggling to use the technology) which has plagued some of my other attempts at integrating technology into my lessons.  As discussed earlier the primary reason for using the calculator is to allow students to focus on thinking about why the function is discontinuous so it is important that one distraction is not replaced by another.

As I thought about this lesson I also discussed whether students should be allowed to avoid having to use mathematics that they have previously learned with other members in my department.  At first, there was a strong sense that the unit on rational functions provided a fantastic opportunity for students to review concepts from previous units, which is certainly the case.  However, when I noted that students seem to get lost when the problems become so long (in the case of a quadratic denominator in simplified form, roughly a half page of written calculations and equation manipulation just to find two x-values) that they lose track of what they are trying to do, several colleagues agreed that the review of old content in this way may be distracting especially when our real goal is to focus on the new content.  I proposed that we may want to consider asking them to do it without the technology at a later time, once the new concept was more fully developed. 

Another interesting idea that came out of these discussion was that by letting students use the calculator to find the zeros of the denominator they are freed up to explore denominators of higher degree (there is no generalizable algorithm for solving polynomials higher than degree four and the generalized solution to degree three and four polynomials is well beyond the scope of an Algebra 1 class).  Hence, our students would be able to subvert these formulas and still be able to make sense of what their solutions mean, even if it was a degree 50 polynomial and have it be almost no more work than if it were a first degree polynomial.

Given the success this lesson was met with when I piloted it with my wife I believe that the overwhelming majority of students will be able to provide a detailed account of what causes discontinuities and how to determine their values immediately after this lesson.  The question that will be more difficult to answer is regarding what the outcomes will be at the end of the unit.  Students typically have a much more difficult time being thoughtful about discontinuities when they are also responsible for determining the x-intercepts, y- intercept and end behavior of a rational function simultaneously.  One other major goal of this lesson is to make sure enough time is spent focusing on the “why discontinuities exist question” that it is never entirely reduced to algorithm and therefore not easily confused with other such algorithms.

CEP800 Digital Story

A video about my experience with the role of scaffolding in the classroom.

Click here if video fails to load.

Student Understanding Interview

Check out my Student Audio Interview!

Wicked Problem Project Part D

Formative: Did the project get implemented as planned?  
There were no major deviations from the original proposed plan.  It was interesting to look at the feedback I had gotten about my plan however.  It seemed clear that I had not explained as clearly as I could have the reasons for and ideas about how to implement my website.  As of right now I have a lot of work to do to get this up and running for next year.  There is a ton of content that needs to be written.  Thankfully I have the help of the teacher that I will be working with next year.

Summative: Evidence of success in addressing the problem of practice.
This is a hard question to answer as this was not intended to go live until the '11-'12 school year.  We plan to enlist the help of some students this summer in gauging their reactions to the work that has already been completed and how it can be bettered.  This is really formative in nature but since I will have no other evidence of success it will have to serve as summative until I can see what really happens.  I can say that my teaching partner for this project was really excited to see the work that I had done and was anxious to add to it.

How would you approach another project of this type differently given what you’ve learned here?
I don't think that I would go about doing much differently that I have.  I believe strongly that this will be a exceptionally useful next year. For my personal sanity, I might have chosen a project with a smaller scope.  It has been really difficult to deal with the vast number of things (different technologies, producing content, aesthetics...) required to produce this project.  However, I think the fact that it was difficult and did force me to think about so many different aspects is what makes it a superior choice to an easier topic.

What are the lessons learned that others might benefit from knowing about?
I think the biggest lesson to be learned is that it is a bad idea to pick a technology and then try to wrap a context around it.  From having watched my group members blog postings it seemed like many of them realized there were some issues with their chosen technology once they reached the TPACK phase of the assignment.  TPACK obviously provided a reflective tool to evaluate whether a proposed solution was good or not.  However, I think TPACK is much better used as a tool to guide me in the construction phase.  I would prefer to see Part C of this assignment exchanged with part B for this reason. 

In what ways will you endeavor to do the same project again, and what will you change or not do?
I have a feeling that I will be busy for some time completing the current project.  I anticipate that it will be continuously revised and refined once we see it in action.  In that sense I am not sure that I will move on to doing another project like this for quite a while. 

Mobile Learning Lab

Alright, I played with Polleverywhere for quite a while.  I could see using it in my classroom as a formative assessment tool for sure.  I liked how quickly it registered responses (I sent several to my own question).  The display as a bar graph for multiple choice questions is very nice.  I have used my TI Navigator system in the same way, but it is cumbersome to set up and get kids logged into.  I am less optimistic about the open response questions.  The data isn't aggregated in a way that is as helpful as it could be.  For example I sent the same response twice because I wanted to see how it would handle the information.  The result was two separate answers that had the same text.  One cool thing about the Navigator system is that if it gets the same response multiple times it shows that in a bar graph by increasing the length of the corresponding bar.  I also don't like that you cant ask multiple questions on one poll.  I see using this as a way to get a quick fix on what students know and don't but prescripting questions might be difficult as I don't always know what direction students will go with a particular topic. Here is one of the polls I made.

Make a live audience poll at Poll Everywhere

On the Classroom 2.0 site people cited other potential issues with using it.  Cell phone reception seemed to be one possible limiting issue as well as those who don't have unlimited text plans.  Also, in reading through the 25 Practical Ideas for Using Mobile Phones in the Classroom there were some other issues raised about students who may not have a cell phone and possibly feeling embarrassed if they can't participate.

I have watched kids take pictures of homework assignments from the board so they didn't have scramble to write it all down.  I have even taken a picture of some students work with my phone so that we could save it to talk about the following day.  I think that there are lots of uses for phones in particular and I think as educators we need to learn how to encourage kids to use them creatively and not in the disruptive "I need to text my friend who's in German class right now" way.  Several of my colleagues refuse to believe that students are capable of doing much other than the former and I keep arguing that the reason for that is that we are not showing them what it means to use them appropriately.  That is a separate issue for now I guess.

Data Visualization Lab

Ok, to be honest I didn't expect much from this lab.  As a math major and physics minor I spent huge chunks of time in college making visualizations to support my work.  This was particularly true in my physics labs.  I decided not to look at visualizations that I was used to working on in those classes and instead looked at some of the flow-charting options that were available. 

I have used MS Visio on a couple of occasions including recently in my Wicked Problem Project and I think it has some great features.  For example if you drag a balloon onto a page with an existing balloon Visio will snap the new object to a grid that aligns it vertically or horizontally with the existing item.  Really this snap feature is useful for drawing arrows between items, crossing out a balloon, etc.  Visio doesn't do a great job with pretty colorful charts.

For this lab I played around with three pieces of free flow-charting software.  Dia (http://live.gnome.org/Diav), Exploreatree (http://www.exploratree.org.uk/) and Gliffy (http://www.gliffy.com/).  Each had their own relative strengths and weaknesses.  I am already thinking that it would be cool to use one to set up a comparison chart.  Here it is, double click to take a closer look..

The winner in terms of functionality is Gliffy.  Presumably that is why it is the only one that you eventually have to pay for.  I actually used it Gliffy to make the chart.  Excel might have been better for this task but still pretty neat.

The real visualization I choose to make is a chart showing the normal/ideal flow of students through our math curriculum. 

Wow, talk about professional looking results in about 40 minutes.  My big ah ha moment with this came when I noticed that as elements are moved the software provides the coordinates of the object.  This allowed me to line them all up neatly.  I later discovered that it was possible to enter the coordinates to locate the object, as opposed to moving them into place pixel by pixel.  Not as nice as Visio's snap feature but very acceptable and better looking results in less time than Visio (at least the antiquated 2002 version that I have).  I will definitely be using this type of thing more often, especially as I continue to put together my website.