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.

Delicious Stacks

I have wanted to share these links for some time. I was able to organize and share them by creating "stacks" using delicious.com, a social bookmarking site. My hope is that you will find these links, not only helpful, but useful as well. Please share these stacks with your friends and contribute other links that you have found to be helpful and/or useful.

 
web tools - communication

web tools - presentation

web tools - publication

web tools - community

web tools - video

Visualization Tools

            Visualization tools have been created because humans have no natural mechanism for visually representing ideas apart from mental images and dreams, which can be very difficult to communicate. Necessarily, they help people to visualize ideas and share those images with others.

In the classroom technologies are available and have proven useful for visualizing mathematical ideas and concepts. This is because, on a human level, visual images are effective facilitators of meaning. For many people, visualizing something helps them to make sense of it. This is especially true for the abstractness of mathematics. Furthermore, the ability to visualize ideas will prove particularly useful in clarifying and correcting common misconceptions of mathematical concepts. On a technological level, visualization tools automate some of the manual processes for creating images for those that lack the artistic skills necessary for generating original images.

There are two predominant roles of visualization tools. The first is interpretive, which helps “learners view and manipulate visuals, extracting meaning from the information being visualized.” The second role is expressive, which “helps learners to visually convey meaning in order to communicate a set of beliefs.”

In mathematics, dynamic geometry software (DGS) such as Geogebra, Geometer’s sketchpad, and Cabri Jr. app help learners to construct and manipulate geometric objects. Learners are also able to make conjectures about the relationships of objects and then test them for correctness.

I teach high school geometry but I am sad to say that I have never used any of these DGS packages. I hope to explore them in coming weeks to make my lessons more effective for all of my students.

Technology Alert - Week of Feb. 19th

            A new online tool has been developed to help math teachers assess the numerical reasoning and conceptual understanding of students. The Math Reasoning Inventory (MRI) serves as a web-based formative assessment. During the 10 minute process, students solve math problems and explain how they arrived at their answer, an indicator of deep understanding.

            MRI was developed and created by a team of master teachers and financed by a $2.2 million dollar grant from the Gates foundation. The best part is the tool will be available online and free of charge to all teachers. The tool itself is intended for incoming middle school students but could prove very useful for high school teachers that want to ensure that their students have a proper mathematical foundation. See the links below for the full article and the MRI website.

http://www.prnewswire.com/news-releases/its-not-only-the-answer-its-how-students-solve-the-problem-that-counts-in-new-math-assessment-for-the-common-core-139218279.html 

https://www.mathreasoninginventory.com/ 

Meaningful Learning WITH Technology

Meaningful learning asserts that “the nature of the tasks best determines the nature of the student’s learning” (Howland, Jonassen & Marra, 2012). Therefore, the five major components of meaningful learning engage students in tasks or activities which are active, constructive, intentional, authentic, and cooperative (Howland, et al., 2012).

Likewise, when incorporating technology into learning, technology must foster the components of meaningful learning by engaging and facilitating students’ thinking not by delivering information (Howland, et al., 2012).

The intentional and constructive component of meaningful learning can be fostered using simple technology such as weblogs. For example, my geometry lessons begin with an essential question that students must be able to answer by posting a blog. This task makes students, not only accountable for their own learning but makes them deliberately reflect on their knowledge to assess their learning and require that they articulate what they understand not what the teacher understands. Students can personalize their blog which further engages them in the learning process.

Click the following links to see blogs posted by my students.

                        http://deborahsgeometryblog.blogspot.com

                        http://swisschels.blogspot.com

                        http://bianqaadenisee.blogspot.com

References

Howland, A., Jonassen, D., and Marra, R. 2012. Goal of technology integrations: Meaningful Learning fourth edition. San Francisco: Pearson.

Technology Alert - Week of Feb. 12th

The state government of Kerala, India will launch an open educational web portal which is free for students in the state. The web portal will serve as an “online multimedia virtual classroom”.

This project, the first-of-its-kind in the country, targets high school and higher secondary school students. Students will have access to “interactive multimedia modules” (IMMs) for math and science classes on the state website http://www.sietkerala.gov.in from anywhere, at any time. Modules for vocational classes¹ will also be available via the portal.  

All of the IMMs include animations, graphics, text-overs, and voice overs. Informative games, designed for the students, and reference links to other educational websites will also be available on the portal. Babu Sebastian, director of State Institute of Education Technology (SIET) Kerala, says this about the portal:

“A multi-sensory learning process is being offered to make the studies perfect as the traditional model of learning by hearing is getting obsolete … It is a leap that we are making through this project in the educational system of Kerala. We hope that this project would later lead to a text book-free system.”

Endnotes

¹     The vocational classes will include subjects such as like agriculture, clothing and embroidery, civil construction, domestic nursing, office secretaryship, travel and tourism, and medical lab technician

Technology Alert - Week of Feb. 5th

This is the first post in a series of weekly updates that explore the use of the Apple iPad and web tools in the math classroom. Be sure to check back every week or just subscribe to my blog.

Early this year Apple introduced iTunes U for the iPad. Of course iTunes U has been hosting educational podcasts for seven years for the iPhone and iPod Touch.

Apple iTunes U has been the main site, playing host to educational podcasts since fall 2005. Educators from more than 1,000 institutions worldwide have provided their instructional materials in the form of video or audio lectures and/or lecture notes in pdf format on the iTunes U site. Users from more than 124 countries have access to the podcasts and can download them for free.(Pauline Chow)

The significance of such technology for the math classroom is the availability of quality instructional materials. Harrisburg Area Community College (HACC), an iTunes U provider since 2007, has developed six complete math and science courses which are now available for download as Apps for the iPad, iPhone, and iPod Touch on the new iTunes U. The courses, selected for their broad appeal to students and the public, are Differential Equations¹, Intermediate Algebra², Principles of Mathematics³, Trigonometry⁴, Statistics⁵, and Astronomy⁶.

Endnotes

¹   a sophomore-level math course required in engineering, mathematics and science.

²   a developmental math course.

³   a college math course for non-science/math students.

⁴   a math course required for calculus.

⁵   a math course required in many disciplines such as psychology, business and computer science.

⁶   a core requirements science course