Thursday, May 26, 2011

Web Conferencing

Our group used WebHuddle to conduct our web conference.  One appeal of WebHuddle was that the program is web based requiring no downloads.  Investigating further, WebHuddle offered ease of registration and creating meetings.  WebHuddle offered options for creating meetings such as naming the meeting, describing the meeting, the inclusion of audio, and recording.  The site also provided a link to easily invite others to join the conference.  The complications began once everyone entered the conference.


Watching our recording, one quickly observes the level of experimentation the conference involved.  As the initial moderator, I attempted to give group members microphone rights.  As it turns out, WebHuddle only allows one person to have microphone rights at a time.  Additionally, two of our group members were unable to be heard in the conference even with microphone rights.  The group spent some time troubleshooting the microphone issues and decided, after a significant amount of time passed, to share the microphone between the two who could be heard in the conference and all depended on the chat feature to communicate.  Our group found and referenced a user guide as we worked through complications during the conference.  Options were given for all members to experience the conference as a moderator and as a team we experimented with the question feature, blank slide screen, and screen share.  WebHuddle allows for uploading of powerpoint files as well as .gif and .jpeg image files.  The question feature allows  the moderator to select from yes/no, true/false, multiple choice, or essay.  Questions, once submitted, are displayed for all participants.  Results can also be viewed within the program.  The blank slide screen acts similar to a paint program allowing for color, shapes, and writing to be shared.  WebHuddle does store recorded conferences on the user homepage under "recordings."  The only option other than "delete" and "merge audio file" is to download the zip file.  Unfortunately, the file is not saved to each participants account.  To share the recording, the file was uploaded to an ftp server and the link distributed.


For future use as a conferencing tool, the microphone dilemma requires addressing.  One microphone produced a significant amount of static while mine an incredible amount of feedback.  To use the program in the future, I would need more time to figure out the audio settings.  I later realized my microphone produced so much feedback because the level was turned so high to hear another group member.


WebHuddle could be used by student groups.  Since non-moderating participants possess little control over any of the features, this tool could be used in situations where one student is responsible for communicating information to the rest of the group.  WebHuddle could be used in the classroom for project presentation and evaluation.  Conference participants could offer constructive feedback, suggestions, or concerns through the chat feature as well as the Q&A feature.  The Q&A feature allows participants to ask questions of the moderator.  The moderator can then share the questions with the entire conference if desired.  Another suggestion for use might be as a medium for tutorials.  For similar reasons as those listed above, students could view presented information as well as ask questions and provide feedback.

Wednesday, May 25, 2011

Part B: Application of TPACK

Technological Pedagogical Knowledge
The Algebra Balance Scales  virtual manipulative, an instructional 
technology, supports the teaching methods and strategies intended for this intervention activity.  The applet scaffolds solving equations, an important strategy for the students participating in the intervention.  The solving process is modeled step by step for students both visually and symbolically simultaneously.  Student response followed by immediate feedback demonstrates another strategy supported by the manipulative.  Students begin by placing the blocks on the scale to model the equation.  When students believe the model is correct, a continue button at the bottom moves students on to the next phase of solving the equation or states, "The two sides don't match the equation," pictured above.  Additionally, students have the visual feedback that the scale lacks balance.  Students have the immediate opportunity to compare the created model and the equation before proceeding to solving.  This virtual manipulative allows for connections and observations to be made regarding how changes effect all representations of the equation, an advantage over a physical manipulative to investigate solving equation.  As blocks are moved to keep the scales balanced, a visual representation, the equation(s) in the boxes above evidence the operations symbolically.  The technology selected also offers the flexibility to create equations to be solved.  This supports the teaching method of giving the equations context.  Students will investigate solving equations in a real world context.  The "create" feature allows the technology to support the instructional decision to provide students with real world problems.  The manipulative also offers an opportunity for students to create a scenario for the given equations.  As an extension or future use of the applet, students could create the context for the given equation and then solve.


Technological Content Knowledge
"Meaning does not reside in tools; it is constructed by students as they use tools."
Herbert and Colleagues (1997)

Quoted by Suh in Third Graders’ Mathematics Achievement and Representation Preference Using Virtual and Physical Manipulatives for Adding Fractions and Balancing Equations
Not only does the Algebra Balance Scales virtual manipulative support the instructional strategies, the manipulative also works with the content.  The two learning objectives for the activity include:
  • Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution (A.FO.06.12)
  • Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solutions (A.FO.06.13)
The Algebra Balance Scales helps make the content accessible by providing linked, multiple representations.  The visual representation of the scale and blocks helps address student misconceptions regarding coefficients.  The picture links to the symbolic representation by clarifying what coefficients actually mean.  "One," is a common response from students when given an equation such as 3x+7=13 and asked how many "x's" are on the left side.  The manipulative helps address this misconception by providing verbal and visual feedback during the modeling phase.  Students have the opportunity to recall prior information, or experience for the first time, that multiplication is repeated addition.  Simultaneous manipulation of the scale and symbolic representation contribute greatly to the applet's support of the content and increased accessibility to students.  The manipulative prompts students to work between both the visual and symbolic representation.  As one representation is changed, students evidence how the change effected the other representation.  As students enter in the appropriate steps to solve the equation, the visual representation supports the learning objectives.  Students watch as blocks are added, taken away, multiplied, or divided and the scale remains balanced.  The differences in the two images below show the linked representations described.  The applet provides students an image of the intended learning goals. 
To solve for x, subtract 4 from both sides.
The scales remain balance yet four less unit blocks are present on each side


Pedagogical Content Knowledge
Lastly, the instructional strategies used for this intervention activity also support the content much like the selected technology supports both content and pedagogy.  Students ability to solve equations depends largely on a developed understanding of the symbolic representation.  The misconception regarding coefficients discussed previously relates to the essential understanding of symbolic representations.  Scaffolding supports the content by ensuring students have appropriately modeled the given equation.  The scaffolding continues after the modeling phase also.  This links to the importance and understanding of order of operations.  Immediate feedback then continues the support of the content.  Students proceed through the scaffold to solve the equation with appropriate mathematical moves; however, the feedback redirects students with a little hint to reconsider and manipulate the equation differently.  Both symbolic and visual representations of equations further support the content's accessibility to students.  As noted previously, verbal and visual feedback helps connect and develop an understanding of what manipulating an equation actually does to the equation.  Again, the visual feedback contributes and supports the learning objectives by showing a balanced scale emphasizing the equality of both sides of the equation.  Scaffolding, providing feedback and multiple representations, along with student manipulation of the applet all assist in making the content more accessible to students.

Sunday, May 22, 2011

Part A: Description of Need or Opportunity

I.  Educational Need or Opportunity
Solving algebraic equations represents the focus of the educational need to be addressed with this project.  Algebra represents a significant number of grade level content expectations for the sixth grade students I work with.  Specifically, this project targets the following algebra standards:
  • Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution (A.FO.06.12)
  • Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solution (A.FO.06.13)
Reflecting on my students performance through the unit on algebra and solving equations, revisiting the content and representing the ideas in a way different than students experienced in their respective math classroom would benefit student understanding and skill development.  I intend to use this project as an intervention to address student misconceptions related to solving equations as well as promote a deeper understanding of algebraic equations.


II. Proposed Technological Solution to Educational Need
I intend to use the Algebra Balance Scales applet from The National Library of Virtual  Manipulatives to address the educational issue articulated above.  The balance scales applet will be used to investigate solving equations of the first degree with whole number coefficients.  The applet provides students with a visual representation of the equation; students model the given equation on the scale by placing blocks representing the variable (x) and the number of unit blocks on each side.  Student users receive visual and verbal feedback from the applet.  If students attempt to continue to solve before the equation is modeled correctly, a message appears noting that the scales are not yet equal.  Visually, the scales shift left and right as blocks are added to both sides until equal also indicating to students the need to adjust the blocks on the scales.  After correctly modeling the equation, students proceed  to solving the equation.  Students must decide which operation to perform and the amount to add, subtract, multiply, or divide in order to keep the scales balanced.  Again, verbal feedback prompts student thinking lending consideration to how equations can be manipulated.  The Algebra Balance Scales applet offers students a link between visual and symbolic representations.  As students manipulate the blocks on the scale below, the display box above manipulates the equation.  Students have the opportunity to see the connection between what happens on the scale and what happens to the equation.  The applet is free to use and requires only an internet connection to access.  Additional technology to be used includes audacity and windows movie maker for students to produce a tutorial describing how to solve equations.  This use of technology encourages students to process and reflect on the activity and additionally create a new resource collaboratively with a group demonstrating new understandings about solving equations. 


III.  Logistics
The Algebra Balance Scales applet will be used during one hour sessions in the computer lab by two student groups on my caseload.  The eight students identified for the intervention will be provided time to work independently with the applet after brief instruction of how to manipulate the applet.  The technology will be used to reteach solving equations by providing and connecting multiple representations.  Screenshots will be captured as students work through solving equations keeping the scales balanced for use in the final student created tutorial.  The students on my caseload are sixth graders identified as at-risk at a public middle school in Kentwood, MI.  Students will document responses on an assignment sheet and will also complete journal reflections related to the use of the applet.


IV.  Relevant Research and Resources
Research suggests the use of virtual manipulatives increases student understanding of mathematical ideas and  concepts.  I tagged resources "Wicked" on my delicious page relevant to the educational need identified.  Initial findings helped clarify what constituted a virtual manipulative.  Moyer, Bolyard, and Spikell (2002) articulated that virtual manipulatives are, "an interactive, web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (p. 373).  The Algebra Balance Scales applet does fit this definition in representation as well as opportunity for students to construct and model mathematical concepts.


A study by Suh and Moyer entitled Developing Students' Representational Fluency Using Virtual and Physical Algebra Balances used the Algebra Balance Scales applet to compare student understanding of solving linear equations based on instruction using either physical or virtual manipulatives.  The authors state, "The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen their understanding" (p. 155).  This study showed manipulatives enhanced students understanding and concluded, "Different representations, including those increasingly available through technology, can facilitate the teaching of these fundamental ideas." (p. 172).  In this case, research supports the use of the Algebra Balance Scales applet to help increase student understanding of solving equations.  This article also provides suggestions for implementing the technology effectively as the students evidenced increased understanding when following the implementation method described in the study.


Further support for using the Algebra Balance Scales applet comes from Suh's dissertation (2005) entitled, Third Graders' Mathematics Achievement and Representation Preference Using Virtual and Physical Manipulatives for Adding Fractions and balancing equations, summarized from (Dorward, 2002):
"The creators of the National Library of Virtual Manipulatives designed the virtual manipulatives in hopes that it would add to some of the benefits of using physical manipulatives in the classroom and eliminate some of the drawbacks such as:  classroom management, structuring activities with manipulatives, connecting manipulative use with symbolism, and lack of resources and professional development."
The Algebra Balance Scales applet, contained in the National Library of Virtual Manipulatives, was created to address some of the concerns with using physical manipulatives in the classroom.  The applet was designed with the intent of fostering connections among representations for students encouraging a conceptual understanding of solving equations and promoting transfer of ideas to be applied in a variety of scenarios.


An identified resource, Computer Technology for Math Excellence, cited research answering the two questions below which offered perspective related to virtual manipulatives as a solution to the defined educational need:
  • What is a virtual manipulative
  • What role can virtual manipulatives play in the classroom?
The site noted, "Virtual manipulatives provide that additional tool for helping students at all levels of ability "to develop their relational thinking and to generalize mathematical ideas"" (Moyer-Packenham, Salkind, & Bolyard, 2008, pg. 204).  With specific regard to the Algebra Balance Scales, this statement suggests the applet will assist in developing student understanding of solving equations.  


Further research exposed a theory called Dual Coding.  According to the Dual Coding Wiki, this theory states that verbal and visual representations are processed and stored differently.  The Algebra Balance Scales applet provides both verbal and visual representations for students while engaging with the mathematical content.  Quoting Suh and Moyer (2007) who referenced (Rieber 1994):
"...it is easier to recall information from the visual processing codes than the verbal codes because visual information is accessed using synchronous processing rather than sequential processing," (p. 158). 
Again, this lends support to using the virtual manipulative Algebra Balance Scales to help students learn how to solve equations since it provides visual representations and additionally connects the different representations present.


The findings described above and the list of resources linked above were found initially using Google Scholar.  The search began with keywords such as:  solving equations with virtual manipulatives, using technology to teach solving equations, and examples of teaching math with technology.  After the preliminary searches, a few articles seemed worth investigating further.  Dissertations and research studies provided a wealth of literature and research reviews.  I used the reviews attached to the studies in order to find additional resources specific to the defined educational need.  To locate online versions of articles and documents, I often copied the citation and entered that in the search engine.  Locating articles used within studies and dissertations proved difficult at times to find a viewable copy.  Often times the articles were available for purchase of either the specific article or a membership to a database housing the articles.  In these instances, I resorted to using the synthesized information as found in the research review.  In the future, I would utilize similar strategies.  I would additionally add the search engines and subscriptions available through Michigan State University's library.




V.  Implementation Plan 
Students participating in this intervention to readdress solving equations will participate in two computer lab opportunities prior to the end of the school year.  During those times, students will work with the Algebra Balance Scales applet in order to increase and solidify their understanding of solving equations.  Additional meeting time will be used for students to reflect on and discuss the completed tasks using the virtual manipulative.  Also, students will respond to journal prompts regarding their experiences working with the applet.  Time permitting, students will compile screenshots of working with the manipulative, reflections from journal entries, and thoughts from discussion to create a tutorial to share with both math classes.  The tutorial will include an explanation of how to solve equations including links between the representations.  The tutorial may be created after the course depending on availability of lab time and permission from my students' teachers.  Additionally, the tutorial will be shared with the different math classes after the completion of the course.  


VI.  Indicators of Success
Successful learning of solving equations with the Algebra Balance Scales applet will be evidenced ultimately by the created tutorial.  The tutorial will present accurate methods for solving algebraic equations as well as mathematically correct explanations of the steps.  Additionally, students will correctly connect and link the different representations modeled by the applet.  Student discussion of their experiences in small groups prior to creating the tutorial will also be an indicator of success as well as offering another opportunity to clarify and discuss any remaining misconceptions.  The discussion group also serves to help students articulate the learning which took place while using the applet. 

Sunday, May 15, 2011

A brief introduction,


The above links to a brief introduction.  The introduction begins with my website and then transitions through a few pictures.  The first image is of my family at my brothers wedding in January.  The next image captures a moment in my former classroom.  Students learned vocabulary for geometry in a charade fashion using themselves to represent the term.  The third picture highlights a few of the things I enjoy most.  The picture of the trees represents my love of photography and all things outside.  The race bibs show some of the races I've run in the past few years, the passport representative of my love of traveling, and lastly my team the Detroit Red Wings.

The Google Earth clip shows a view of the middle school campus I work at.  The wiki created for my sixth grade students appears after that with pages to each of the core content areas.  Each content page links to students respective teacher pages as well as provides access to some interventions created for specific instructional units.  Lastly, a link to two technologies of interest are posted for reference.

Friday, May 6, 2011

In Progress: Final Reflections

Brophy stated, "Effective teachers allocate most of the available time to activities designed to accomplish instructional goals."  This quote reflects current learning and personal perspective with regard to effective strategies for integrating technology in the classroom.  The statement seems a given and the thought taken for granted about the importance of beginning by articulating instructional goals.  No doubt most educators would agree on the significance of starting the planning process with goals and objectives.  Adding technology to the equation and reflecting back it seems, although the obvious place to begin, in some instances the emphasis turns to the technology and away from the instructional objectives.  As an educator, I need to be mindful of technology's place:  as a tool used to support content, instruction, and objectives.  Thus to effectively incorporate technology within the curriculum and classroom, educators must know what needs to be accomplished to help select the best tool (technology) to support student learning.  With respect to UDL principles, technology remains a strategy and tool to provide students with multiple representations of concepts, options for action and expression, as well as increasing student engagement.  Technology tools serve to enhance lessons in the previous three areas while helping eliminate barriers for all students to engage in the curriculum.


Recent work with WebQuests, http://www.merlot.org/, http://www.wikispaces.com/, http://www.weebly.com/, and the creation of a StAIR helped process through which of the listed technologies and tasks constitute an online learning experience and which might be used in a face to face environment to enhance lessons.  Creating projects and pages with the technology listed above provided opportunity to think through ways to accomplish technology standards and requirements.  One use of the created wiki which served an excellent purpose was storage for the created StAIR to reteach fractions for some students.  The project, created with Powerpoint in kiosk mode on the computer in my office, was unavailable to the group of students I needed to work through the activity.  Uploading the program to the class wiki provided an access point from any computer lab with internet in the school building.  WebQuests and StAIR projects reinforced the importance of the educator testing and working through the activity prior to asking students to complete the task.  Additionally, I thought more about how to use the resource in class with students (individually, small group, pairs, etc.).  Also, evaluating a WebQuest confirmed how important clear, thorough directions and modeling are, especially when students are expected to complete the task individually.  When considering evaluating a technology, the question which initially comes to mind is, "How does this activity help accomplish the objectives?"  MERLOT offered a structure and method for evaluating submitted resources based on three considerations:  quality of content, potential effectiveness as a tool, and ease of use.  These three categories provided multiple lenses to view a web-based technology; however, these three areas of consideration transcend technology tools used in education.  "Internet brought about 'information pumps' and lessened effectivity of lesson/instruction," stated Merrill.  MERLOT's evaluation guide offers educators a way to sort through the overwhelming number of resources on the internet to find a resource that will effectively help accomplish instructional objectives.


Part of my decision to complete the MAET program emerged from an excessive amount of available technology and a fear the technology was not being used to its potential as a tool in my classroom.  In progress describes the status of my current pursuit of learning how to effectively integrate technology.  In truth, I would not mind "in progress" describing that goal for a significant amount of time indicating continued learning about how to implement technology effectively in the classroom.  Exposure to UDL principles helped see areas to include technology within lessons to help eliminate barriers for all students.  Effectively using technology in the classroom requires experience with the tools in order to discover the technology's limits and capabilities.  I had the opportunity to create a wiki, website, and StAIR.  This exposure either introduced a new program or feature of a program such as kiosk or interaction mode.  Discovering more options such as the ones presented provide opportunities to assess and evaluate when a technology will be most effective when considering instructional goals.  Additionally, the instructional design format helped organize key aspects of planning in order to utilize technology as an effective instructional tool. 


New goals at the conclusion of this course relate to specific technologies.  One goal I have is to familiarize and experiment with glogster, voice thread, web-based quiz and feedback platforms, and look into a platform for WebQuest creation.  I identified some of the technologies while working through weekly session material.  In other cases, I encountered the technology by checking the resources provided by peers in StAIR projects.  The goal remains to explore these technologies to become familiar with features and limitations; additionally to form an idea of how the technology could effectively be implemented and enhance curriculum, instruction, and student learning.