Lesson Design Project

At this time, I do not have a specific topic that I want to cover for my lesson deign project. I do know that it will be a mathematics topic, more specifically geometry, and I will incorporate elements of inquiry or exploration and collaboration.

The technology I intend to use for the inquiry/exploration element is Cabri Jr., a visualization app that can be loaded onto Texas Instruments (TI) calculators. I have a classroom set of TI-83 graphing calculators which makes this technology available to all of my students, at least during hour and a half that they are in my classroom. Therefore, the inquiry/exploration element will need to be completed while the students are in class.

For the collaboration element, I hope to use Knowledge Forum 4.8 which is a knowledge-building computer environment or community. I am currently in the process of exploring Knowledge Forum, therefore, I do not yet know if it will be an effective technology choice. I still need to consider its availability (e.g. cost), user-friendliness, and support systems. If I need an alternate technology for the collaboration element, I know that wikispaces or Google docs will suffice.

Classroom Tools - Geogebra and Cabri Jr.

The Texas educational standards or Texas Essential Knowledge and Skills (TEKS) consider technology to be one of the techniques¹ for working with spatial figures and their properties, as well as, one of the underlying processes for all mathematic content areas. Therefore, TEKS for high school geometry specifies that students use technology “to solve meaningful problems by representing and transforming figures and analyzing relationships” and “in problem solving contexts.”

Acceptable forms of technology include, but are not limited to, calculators with graphing capabilities, data collection devices, and computers. Data collection devices often require that they be used in conjunction with a graphing calculator or computer, whereas, a computer or a graphing calculator can work independently of each other. However, all three can be combined and work as a single system to increase the capabilities of the devices.

There are also software packages, internet tools, and apps available to facilitate the integration of technology into the curriculum itself. In the context of geometry, these tools are referred to as dynamic geometry software (DGS) because they are able to represent figures, illustrate transformations and demonstrate how certain relationships will respond to manipulations.

With numerous factors that must be considered, the choice of which technology or DGS to use is by no means an easy decision. The very first factor that I consider is accessibility. Will all of my students have relatively easy access to a particular DGS? Furthermore, will my students have to purchase the DGS or special hardware to run the program?

My first choice will usually be a software package that is free. If a school or district has a considerable population of economically disadvantaged students, purchase packages become a matter of accessibility and, by extension, equality². What is more, some software packages that are available for free via the internet are still not accessible to all students (i.e. economically disadvantaged) because they cannot afford internet access at home. This must also be considered in the decision process. However, if a purchase package is available to students at the campus computer lab, the cost of purchase and accessibility from home becomes a non-issue in most cases.

The next factors I consider when choosing a software package are available features and ease-of-use or “user-friendliness”. What does this DGS offer that others do not? Is the extra feature absolutely necessary? How much training will my students need before they can use a particular DGS? How much training will I need before I can use a particular DGS? The quality and/or features of a particular DGS versus another DGS must be considered because it can be a matter of quality and equality of education, especially when associated with a difference in price.

The final factor that I will discuss is support. What kind of technical and/or user support will be provided with a particular DGS? What kind of training will be available for students or will they have to figure it out on their own? What kind of training will be available for me? I find few things as wasteful as money spent on technology that sits idle because teachers and/or students simply do not know how to use it.

I could see the Cabri Jr. app and Geogebra being used in my classroom. All of my students have access to TI-83+ calculators (during classroom time) which would provide them access to the free Cabri Jr. app. This would offer students the opportunity to explore transformations, constructions, and manipulations on their own. Although the graphic quality is quite low, the dynamic nature of the illustrations can do more for student understanding than a static image. Also, the simplicity of the app makes it very user-friendly which would allow students to spend more time exploring and less time trying to figure out how to make it work.

I do not have enough computers for each of my students. I do not even have enough computers to allow my students to work in small groups. Therefore, I would use the free Geogebra package as a presentation tool to illustrate dynamic, geometric relationships. Using Geogebra I would create illustrations that I could share with the entire class. The example I think of is showing the relationship between the unit circle and trigonometric functions (see Technology-Supported Mathematics Learning Environments chapter 10).

Endnotes

¹   the mathematical techniques and underlying processes include: multiple representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), technology, applications and modeling, and numerical fluency.

²  “equality” refers to quality of education. Are all students receiving an equitable education regardless of socioeconomic status?

Using Twitter Resources

            Today, using Twitter is as common as having a cell phone and as vogue as having a Facebook page. It is a simple way to stay connected with your closest friends and your favorite celebrities. As more and more people use Twitter, more and more uses are being discovered or, perhaps more appropriately, explored.

            One use I have recently been exposed to is using Twitter to gather resources for research. With as many people and companies using Twitter, there must be equally as many opportunities to find whatever it is you may be looking for.

However, with as many people and companies using Twitter, there equally as many opportunities to be inundated with pointless and mindless tweeting. That has been my experience over the last two weeks. I have received countless tweets and re-tweets with blurbs and links.

Perhaps if I had countless hours to explore each tweet I could find nuggets of useful information. But like you, I have to balance my time between my family, work, grad school, and the myriad other things I have to do every week. I have found that using blog alerts is much more effective use of my time. Blog alerts also provide me with blogs and articles that do not meet the criteria that I am researching, however, they are much easier to sift through and skip over.

For that reason, I will continue to use blog alerts and recommend the use of blog alerts.

Collaboration Tools

Web 2.0 is a fundamental shift in the nature of the Web based on a set of principles and practices intended to connect the collective intelligence of its users (O’Reilly, 2005; 2009). It is not a piece of software or hardware.

The internet in the era of Web 2.0 provides collaboration tools that allow the formation of communities on a global scale. These new communities are then able to interact and learn together. Furthermore, some of the most important tools for education are technologies that support online collaboration, called online collaborative environments. These technologies have been designed to connect people around the world for sharing information and creating new content together (Johnson, Smith, Levine, & Haywood, 2010).

This is due to the belief that collaboration is an essential skill in today’s workplace. The Partnership for 21st Century Skills (2009) lists Global Awareness as an essential 21st-century interdisciplinary theme, with collaboration skills as necessary outcomes for success in a global economy.

It should be mentioned that not everyone shares the same positive beliefs about the social networking technologies that make these online communities possible. “Hargadon (2010) suggests the term educational networking to describe educational uses of social networking technologies, recognizing that some educators may have negative views of social networking” (Jonassen, Howland, & Marra, 2011).

A significant trend in technology is shifting to the process of constructing and sharing knowledge. Along with this shift is a change in the idea of knowledge itself as (NMC, 2005). It is believed that learners are more willing to participate in knowledge construction. The results of this shift are technologies enabling social networks and knowledge webs that offer a means of constructing knowledge by facilitating collaboration and teamwork. This is possible because technology plays a key role in knowledge-building communities by providing a medium for storing, organizing, and reformulating the ideas that are contributed (Jonassen, Howland, & Marra, 2011).

In light of this shift toward knowledge building, I find Scardamalia’s and Bereiter’s (1996) statement provocative and insightful:

…schools inhibit, rather than support, knowledge building by: (1) focusing on individual student’s abilities and learning; (2) requiring only demonstrable knowledge, activities, and skills as evidence of learning; and (3) teacher-hoarding wisdom and expertise. Students’ knowledge tends to be devalued or ignored, except as evidence of their understanding of the curriculum.

According to Scardamalia, Bereiter, & Lamon (1994), the goal of knowledge-building communities is to support students to “actively and strategically pursue learning as a goal”—that is, intentional learning. These knowledge-building communities, also called online collaborative environments, are environments where students produce their own knowledge databases in their own knowledge-building community. Knowledge building communities create an environment where student knowledge can be “objectified, represented in an overt form so that it [can] be evaluated, examined for gaps and inadequacies, added to, revised, and reformulated” (p. 201).

Two examples of knowledge building communities I plan to explore are Computer-Supported Intentional Learning Environments (CSILEs) and Knowledge Forum. In these knowledge-building environments, users contribute ideas in the form of text, graphics, movies, or attachments. Pedagogically this is significant because students are providing the multiple representations of ideas, therefore, the key to learning lies with the students.

These ideas, which are central to the knowledge-building process, become connected, expanded, and refined as the individuals in the community question, add to, reference, and annotate each other’s thoughts (Jonassen, Howland, & Marra, 2011).

References

Jonassen, David H.; Howland, Jane L.; Marra, Rose M. (2011-05-18). Meaningful Learning with Technology (4th Edition) (Kindle Locations 3350-3351). Pearson HE, Inc.. Kindle Edition.

 

Classroom Tools - Geometer's Sketchpad

            Dynamic Geometry Software such as Geometer’s Sketchpad is a helpful tool for visualization. This helps not only the students but the teachers as well. Having a visualization tool available helps teacher explain concepts and ideas, which are difficult to put into words, in a way that is easier for students to comprehend.

            For example, Geometer’s Sketchpad can be used to illustrate the dynamic relationships between trigonometric functions (i.e. sine, cosine, tangent) and the unit circle. Trigonometric functions are taught at the high school level, usually introduced in Geometry (tenth grade) or Algebra II (eleventh grade) and explored more rigorously in Pre-Calculus (twelfth grade).

            I have just been introduced to Geometer’s Sketchpad so I am still learning its capabilities and exploring its potential. Unfortunately, one major drawback to Geometer’s Sketchpad is its price tag¹. Since the district I work for does not own a license for the software I have limited opportunity to familiarize myself with it.

            However, Geogebra is a completely free DGS with similar capabilities to Geometer’s Sketchpad. I will discuss Geogebra in my next blog.