Information Visualization Tools

            Information visualization tools are very important to incorporate into our lessons.  An information visualization tool is a visual tool that allows a student to view, analyze and understand challenging information.  My area of concentration is mathematics.  Some examples of information visualization tools in math are graphs, pictures and using manipulative tools.  All of these visual aids help students think about and understand crucial and complicated topics such as sine and cosine functions and the Pythagorean Theorem. 

            Some things that we should consider before we incorporate these information visualization tools into our lessons are our learning objectives, the way our students learn, constraints you have and the context in which the tools are used.  The learning objective will state what the goal of the lesson is and if a specific information visualization tool is appropriate or not.  To use an information visualization tool appropriately you need to know who your students are and how they learn most effectively.  We need to know if our students have the ability to use the information visualization tools in the time given.  Some specific constraints that we need to consider are time and if you will have the resources.  Resources can be computer lab time to see interactive graphs or software to draw pictures.  The last thing to consider is the context in which the information visualization tool is used.  An example would be if you already were using a visual aid then would it be appropriate to use another one.  As teachers we need to figure out how we could incorporate both. 

            Once we know how to successfully incorporate these information visualization tools into our lessons we need to figure out the best way to assess our students.  Assessing the way our students use these information visualization tools is not very different than the way we normally assess them.  We need to make sure they know how to analyze and understand the information they are presented in the information visualization tools.  An example of this would be drawing a picture to represent distances from three points of a right triangle.  Then the students would have to identify why they drew the picture the way they did and how the Pythagorean Theorem is applied.   

Technology & Pedagogy

My goal was to find a lesson that was engaging and allowed the students to think critically.  I chose this lesson because it was student oriented and it integrated technology effectively, but at the same time there were parts that I believed I could add and edit to make it a more complete lesson.  I truly believe there is no such thing as a perfect lesson because there is always a small hiccup that we do not account for. 

              There were certain parts of the lesson in which the curriculum, teaching strategies and technologies used were not completely connected.  In the first step the lesson describes how the circumference of a circle depends on the diameter of it.  The lesson then gives the students a procedure to follow integrating MIRA, which is a transparent geometric tool that reflects like a mirror to help understand characteristics of a circle.  In this example the technology and curriculum goals align very nicely, but I think the teaching strategies relied too much on the students to do all the work.  I would have liked to see the lesson reflect the teacher/student combination of work.  It would have made it more complete, although it is a great lesson.  I would have liked to see this second standard covered in the lesson because they could be so easily implemented so I added a standard and example.  In the part I added I had the learning more teacher centered because of the fact that most of the other parts were student centered and I wanted to see an even mixture.

            I believe the technology used in this lesson was perfect for the information that was trying to be taught.  Without this technology the lesson would have been a complete failure because it relied on it to create the learning materials and implement them.  A compass was necessary for drawing a circle that the students needed to examine.  Then MIRA and the geometer sketchpad program helped see ratios which led to the students understanding the formula for circumference.  This was one of the common core content standards.
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How the Document Camera Changed the Way We Teach Math

Every additional piece of technology can be an asset in a math class.  As teachers we just need to figure out how to incorporate these pieces of technology into our lessons.  I think the document camera is one of those pieces of technology that really helped advance the way that we teach mathematics.  Learning is becoming more of an active process every year.  Teachers are supposed to be engaging and involving students in their learning.  This piece of technology allows students to be more involved in the way they learn.  The document camera is an easy way to show students work on the screen or board. 

            It is so important to show and analyze student work because the chances are if one student made a mistake on a problem he/she is not the only one who did.  We can use the document camera in math class to show how our students are thinking.  This will help our students learn by exposing them to different ways of doing certain problems and showing them different mistakes that people make.  Making students analyze and critique work will allow them to be an active learner.  A document camera is one tool that can provide our students a way to be an active learner. 

            The document camera can become a destructive tool to our learning when a teacher starts to use it as a personal chalk board.  The document camera will not be helpful in this situation because it takes time to set up, use, and it would eliminate seeing the student work.  Being able to engage students in their learning is the most important aspect of using this piece of equipment or any learning aide for that matter.  My main focus when incorporating pieces of technology into my lesson is going to be how this technology is going to help my students learn more effectively.          

The Pencil in Mathematics

The first thing that comes to mind when we think about technology is computers, the internet or calculators, but I believe the pencil was one of the if not the most important pieces of technology to be integrated into the math classroom.  This has given our educational society an easy and cheap way to write.  Today this seems like a given.  If you ask students how they would learn without a writing utensil they would think you are crazy.  The pencil was so important to the evolution of the classroom and specifically math class because practicing exercises is so important in learning mathematics.  Students are much more likely to succeed if they are able to do practice problems on their own as opposed to watching the teacher do work on a blackboard. 

Pencils allow students to be assessed, practice on their own, and explore different ways of solving problems.  Imagine how difficult and time consuming it would be to test student’s knowledge and comprehension if they did not have pencils and paper.  Each student would have to be interviewed by the teacher to get a simple understanding of the student’s knowledge.  It is clear that this process would be nearly impossible with the growing number of students in schools.  Sure this process may have worked hundreds of years ago when a school house consisted of five to ten students, but today there would need to be a one to one ratio to assess students. 

Today, students rely so heavily on writing utensils.  It really is important to put your ideas on paper or somewhere that you can see and reflect them.  This is certainly true in a math class because you need to write your work down.  Also, you sometimes need to erase your work which the pencil allows you to do.  People have been doing this since the beginning of time.  We have proof of marks from the ancient Egyptians which were on this earth thousands of years ago.  Now with the invention of the pencil we have made it easier to write our ideas down.  The best technologies are the ones that make an aspect of life easier.  This is why so many of us listed our most important technology as our smart phones.  They have made reading email, accessing the internet, and talking to others a two minute process.  This is really what the pencil has done for our society.  When the pencil was created we no longer needed to use feathers and ink.  The pencil gave us an affordable way to advance the ways in which we learn. 

     

History of Technology in Mathematics

The Graphing Calculator has made reviewing and exploring concepts in math fun again.