MERLOT: Resource Evaluation

Resource:  Eye Opener Series


The link above directs to a page titled, Interactive Mathematics Miscellany and Puzzles.  The introduction and link to the Manifesto provide perspective and a context regarding the intended purposes of the website.  In short, the site seeks to challenge negative perceptions and perspectives pertaining to mathematics using Java applets to prompt discovery and positive experiences with mathematical content.  The author notes in the Manifesto linked above, "I hope to create a resource that would help learn, if not math itself, then, at least, ways to appreciate its beauty."

The following presents an evaluation of the resource with regard to quality of content, potential effectiveness as a teaching-learning tool, and ease of use

Quality of Content

Under the introduction, the contributor organized mathematical  content into categories by either subject or type of resource.  Investigating the "Arithmetic" section, several of the Java applets pertained to grade level content expectations for sixth grade mathematics outlined by the Michigan Department of Education.  Topics in this section related to sixth grade mathematical content requirements and present both visual representations and opportunities to practice skills.


Eye Opener Series presents educationally significant concepts for mathematics.  As noted above, mathematical ideas represented and demonstrated using Java applets related to grade level content expectations.  Also, several of the "Arithmetic" applets introduce mathematical ideas and skills prevalent in many areas of mathematics.  For example, one applet investigates common multiples.  Common multiples reappear with respect to fractions.  More specifically with regard to comparing fractions and common denominators.  Much of the content presented structures foundations for other areas of mathematics.


Personal Effectiveness as a Teaching-Learning Tool

Speaking previously of several "Arithmetic" applets, the following will focus on one particular applet:  Common Multiples and the Least Common Multiple.  After investigating the applet, the content could be situated in the classroom as both a demonstration of an objective as well as a tool for students to manipulate in order to practice finding common multiples.  Upon completion of the applet, students should be able to define and identify both common multiples and least common multiple.  Additionally, students should be able to apply both common multiples and the least common multiple to determine common denominators of fractions.  The target learner benefits and engages from visual representations and hands-on manipulation.  Additionally, the target learner possesses previous knowledge of integers and multiplication.


The Java applet improves the presentation of common multiples by visually showing how multiples change in relationship to each other.  Also, different colored dots help the learner quickly distinguish which numbers are multiples and which are common multiples.  The applet also allows students to explore common multiples with various numbers.  From a teaching standpoint, the applet could be used to provide students with a variety of examples and have students make observations to define common multiples and least common multiple.  Common Multiples and Least Common Multiple readily supports mathematical standards; educators can frame the applet in different ways depending on the content objective addressed.  The lesson presents specific teaching-learning goals; however, the java applet can be used creatively or as a tool for students to practice identifying common multiples and determining the least common multiple.  Educators could design assignments for students to complete using the applet specific to a particular context or the context could be general allowing students choice.


Ease of Use

As noted previously, the Java applet itself provides different colors encouraging the distinction between multiple and common multiple.  The applet itself is easy to manipulate; although, the applet on the webpage is limited in the original number to find multiples of.  Numbers greater than forty-four disappear off the number line pictured.   The applet includes directions and an explanation above allowing users to manipulate easily.  The Java applet does not provide feedback to users outside of the identified multiples and common multiples.  The applet requires little instruction to manipulate and use.  Students may not be used to seeing multiples situated above and below a number line; however, the applet does provide opportunity for students to manipulate and explore multiples in a visual way. 
 

In Progress...

Over the past several weeks, thoughts of effective technology integration lingered in my head.  Seven weeks later, my perspective and strategies on effectively incorporating technology within education have shifted.  Technology remains a tool for educators and learners to enhance discovery and understanding.  To ensure a specific type of technology suits that purpose, a strategy leading to effective incorporation involves investing time to determine the capabilities and limitations of a particular technology.  Focusing on lesson goals and objectives aid in narrowing options for technological tools allowing content to remain the focus of the lesson not the technology itself.  Combined with knowledge of and experience with a technological tool's features, identifying and focusing on lesson objectives enables educators to better evaluate how effectively the tool contributes to the ultimate desired outcome.

The internet presented several opportunities to explore and consider uses for technological tools in education.  Resources and examples demostrated how other educators incorporated specific technology tools in different subject areas.  Additionally, web-based programs often were free to download and experience providing a better picture of the tool's capabilities.  The internet offered easy access to demonstraton videos as well as platforms to communicate with others and engage in conversation regarding technology in the classroom. 

Reflecting on course assignments over the past several weeks, the assignment that stands out in my mind as good teaching with technology is the SIG Group Project.  This project began with a focus area, progressed to research and investigation of a particular technology, and resulted in an evaluation and perspective to share with other educators.  Each step not only incorporated technology but also provided options of technological tools to choose.  The project offered many opportunities to engage and experiment with a technological tool of choice in turn prviding insight into its capabilities.  In addition to providing an opinion about the group's technological tool of choice (Google Earth), opinions and evaluations pertaining to bookmarking and presentation tools resulted.  The process described currently aligns with thoughts regarding effective technology incorporation in education:  research and explore a technology to experience its capabilities, identify and focus on lesson goal(s), and evaluate options of technological tools to determine which most effectively accomplishes the objective.

Reflecting on goals created at the beginning of the course, my evaluation of personal goals sums up in two words:  in progress.  One goal, to learn to effectively incorporate various technology to impact student learning, although not mastered seems addressed with the process described above:  explore a technology, develop skills using the technology, and consider options for integrating or repurposing the technology.  When planning a lesson, identify lesson objectives then sort through available technological tools to determine which will most effectively accomplish the task.  The initial goal has been adapted to continued skill development to add options of technological tools.  A second goal at the onset of the course involved increased awareness of available technology.  The past few weeks exposed several types of technology I had not previously worked with: Twitter, Blogger, Wikis, Google Earth, and Flickr.  The revised task and goal now involves dedicating time to better learn features and capabilities in order to accurately evaluate the technology's effectiveness for adresssing a given objective.  A third goal articulated a desire to gain skill using collaborative technology.  Progress resulted toward this goal with the use of Google Docs, Blogger, Google Earth, and discussion boards for weekly assignments and the course project.

As indicated, the past few weeks evidenced progress toward set goals.  This progress helped reshape initial goals for the fuure as I work to complete the MAET program and contribute to the educational technology community. 

Visual. Kinesthetic. Auditory.

Considering this list of learning styles, I noticed several descriptions that resonated from all three categories listed and wondered if perhaps it's not a question of which learning style I am but which do I favor.  I am an avid note-taker, which from the linked list suggests visual learner.  Concurrently, I am often guilty of reading aloud to process and understand, situating me within the category of auditory learners.  Still, I often need to explore something on my own suggesting kinesthetic learning.  The more I thought about this the question on my mind is:  might our job as educators include enabling students to adapt their learning preferences to a variety of lesson presentations?  A significant emphasis tends to be placed on educators to teach to all learning styles, but the reality seems each lesson cannot be presented in this manner.  That in mind, a classroom should evidence lessons geared toward each learning style but not concurrently.  Imagine a lesson geared toward the visual learner.  How ridiculous would it be to think that I as a kinesthetic or auditory learner would not be responsible for the content?  This connects back to my question of fitting or favoring learning styles.  It seems teachers, without planning three different lessons, could suggest strategies for those favoring other learning styles providing opportunities for all students.  Learning styles are an additional layer by which we need to know our audience.  In this sense know has implications and responsibilities.  Teaching students how to adapt their learning preferences to different learning styles seems beneficial.  This does not eliminate a teachers responsibility to teach using a variety of learning styles; however, it does address the reality that daily lessons may not be presented using all three learning styles. 

Visualizing Vocabulary

Photo Attribution:


Original Image:  "Scattered Geometry"
http://farm3.static.flickr.com/2551/3670244253_a646b14687_m.jpg
By:  Greg Hayter


Released under an Attribution License
http://creativecommons.org/licenses/by/2.0/

After my initial fascination with the image above, my mind quickly worked over ways to bring this image into a mathematics classroom.  My mind immediately recalled a geometry project from last year.  I provided students a list of vocabulary words and asked students to find pictures of them in the real world.  Students were then asked to explain the vocabulary words captured in the image.  The more I look at this image, the more I see transformations and other geometry vocabulary.  The image could be brought into the classroom as a tool for discussion of vocabulary.  This image could also be used to discuss and illustrate area, perimeter, and amount of material extended to total cost.

Here's a link to my Flickr page with a couple images I've used to discuss and visualize vocabulary with my students.