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.

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Student Understanding Interview

Check out my Student Audio Interview!