I think I will use Geometer's Sketchpad the most. In addition, I feel that I learned the most about Geometer's Sketchpad for two reasons: it was the most interesting of all the programs we learned and it was the program I was most unfamiliar with. I really enjoyed creating the guided explorations using the program. This was the first time I created a guided exploration document.
I think this course will benefit me in the future. I especially enjoyed learning how to created PROFESSIONAL documents related to the field of education. Also, the course expanded my knowledge of building documents and how to use technology in the room effectively.
My view of technology has not changed after this class. I still believe technological devices should be incorporated into the mathematics classroom. This class made me believe so even more.
Monday, April 28, 2008
The Role of the Graphing Calculators
“The Role of Graphing Calculators in Mathematics Reform” is an essay written by Waits and Demana regarding the positive impact of graphing calculators in mathematics curriculum. Waits and Demana believe that the role of graphing calculators will not eliminate paper-and-pencil techniques; yet, the two methods will compliment each other.
The authors begin their essay revealing the history of graphing calculators in mathematics education. Prior to graphing calculators, teachers would have to schedule a time to use a PC and then provide a demonstration of the software program to the students. Thus, the computer software was not hands on for the students. This was a major benefit of the induction of the personal hand held graphing calculators.
According to Waits and Demana, the first graphing calculator arrived in 1986 by Casio. The graphing calculator became a huge success. Within three years, “the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards released in 1989 for grades 9-12 includes the assumption that graphing calculators will be available to all students at appropriate times because they are personal computers that fit in a pocket or purse” (Waits, 1998). The graphing calculators were relatively inexpensive compared to the PC software, making the availability to students much more convenient.
The accessibility of the graphing calculators to all students significantly reformed the society viewed mathematics educations. Waits, Demana, and many others favored the implementation of graphing calculators in the classroom. Waits and Demana conducted two computer graphing projects one in pre-calculus and the other in calculus, both producing text books that incorporate the graphing calculator into the classroom. Those who opposed the reform feared that graphing calculators may replace the traditional curriculum and abolish pencil-and-paper practices.
However, Waits and Demana believe they have “balanced approach” that combines the positive elements of the traditional curriculum with the graphing calculator. Their approach of learning mathematics allows the students to solve algebraically using the tradition method and then check their solution by using the graphing technology and solve using the graphing calculator and validate their answer with the pencil-and-paper technique (Waits, 1998). Waits and Demana deem that learning by rote memory does not imply the students have a conceptual understanding of mathematics, and the use of graphing calculators may allow for better understanding of various applications.
Lastly, Waits and Demana feel that professional development is a key factor is applying technology in the classroom. As the world of technology is constantly changing, teachers need to keep their knowledge up to date and be a valuable asset in their students learning experience.
The most interesting part of this article is that it was written almost ten years ago. In Waits and Deamana’s closing paragraph they state “it is clear to us that ten or fifteen years in the future the mathematics curriculum of today will have changed considerably to take full advantage of just the technology that exists today.” In my opinion, the authors’ prediction of the mathematics curriculum was correct. It today’s classroom, graphing calculators are used almost everyday and readily available to the students. For example in my placement where I attend everyday, each student owns their own calculator and in addition each classroom has a set of roughly ten calculators that the students’ may borrow. There is a television screen in each of the mathematics classroom that displays the screen of the teachers’ calculator. Thus, students are actively learning how to use the calculator correct. Additionally, there are large posters of the calculators with the buttons labeled so that the educator can teach the students the navigation of the graphing technology. Waits and Demana were also correct when they considered professional development a key factor in implementing technology in a classroom. In another example referring to my placement, staff development day at the start of the school year a workshop on the latest Texas Instrument graphing calculator called TI-Nspire was held.
In conclusion, I think Waits and Demana approach to integrating the graphing calculator into the traditional mathematics curriculum is beneficial to the students’ learning and a similar approach can be seen in the various classrooms today. Waits and Demana were correct in their thought process, just a little ahead of the rest of society.
References
Waits, Bert & Demana, Franklin. (1998). “The Role of Graphing Calculators in Mathematics Reform.”
The authors begin their essay revealing the history of graphing calculators in mathematics education. Prior to graphing calculators, teachers would have to schedule a time to use a PC and then provide a demonstration of the software program to the students. Thus, the computer software was not hands on for the students. This was a major benefit of the induction of the personal hand held graphing calculators.
According to Waits and Demana, the first graphing calculator arrived in 1986 by Casio. The graphing calculator became a huge success. Within three years, “the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards released in 1989 for grades 9-12 includes the assumption that graphing calculators will be available to all students at appropriate times because they are personal computers that fit in a pocket or purse” (Waits, 1998). The graphing calculators were relatively inexpensive compared to the PC software, making the availability to students much more convenient.
The accessibility of the graphing calculators to all students significantly reformed the society viewed mathematics educations. Waits, Demana, and many others favored the implementation of graphing calculators in the classroom. Waits and Demana conducted two computer graphing projects one in pre-calculus and the other in calculus, both producing text books that incorporate the graphing calculator into the classroom. Those who opposed the reform feared that graphing calculators may replace the traditional curriculum and abolish pencil-and-paper practices.
However, Waits and Demana believe they have “balanced approach” that combines the positive elements of the traditional curriculum with the graphing calculator. Their approach of learning mathematics allows the students to solve algebraically using the tradition method and then check their solution by using the graphing technology and solve using the graphing calculator and validate their answer with the pencil-and-paper technique (Waits, 1998). Waits and Demana deem that learning by rote memory does not imply the students have a conceptual understanding of mathematics, and the use of graphing calculators may allow for better understanding of various applications.
Lastly, Waits and Demana feel that professional development is a key factor is applying technology in the classroom. As the world of technology is constantly changing, teachers need to keep their knowledge up to date and be a valuable asset in their students learning experience.
The most interesting part of this article is that it was written almost ten years ago. In Waits and Deamana’s closing paragraph they state “it is clear to us that ten or fifteen years in the future the mathematics curriculum of today will have changed considerably to take full advantage of just the technology that exists today.” In my opinion, the authors’ prediction of the mathematics curriculum was correct. It today’s classroom, graphing calculators are used almost everyday and readily available to the students. For example in my placement where I attend everyday, each student owns their own calculator and in addition each classroom has a set of roughly ten calculators that the students’ may borrow. There is a television screen in each of the mathematics classroom that displays the screen of the teachers’ calculator. Thus, students are actively learning how to use the calculator correct. Additionally, there are large posters of the calculators with the buttons labeled so that the educator can teach the students the navigation of the graphing technology. Waits and Demana were also correct when they considered professional development a key factor in implementing technology in a classroom. In another example referring to my placement, staff development day at the start of the school year a workshop on the latest Texas Instrument graphing calculator called TI-Nspire was held.
In conclusion, I think Waits and Demana approach to integrating the graphing calculator into the traditional mathematics curriculum is beneficial to the students’ learning and a similar approach can be seen in the various classrooms today. Waits and Demana were correct in their thought process, just a little ahead of the rest of society.
References
Waits, Bert & Demana, Franklin. (1998). “The Role of Graphing Calculators in Mathematics Reform.”
Monday, April 14, 2008
Using Statistics in Everyday
During my student teaching experience, I found many students asking when we are going to use certain topics. For example, the 10th grade students thought it was a joke when I began to introduce the imaginary numbers system and did not know when they would use them again! My suggestion for teachers is to make a PowerPoint presentation at the beginning of each topic to introduce the topic and discuss real life applications!
Tuesday, April 8, 2008
Monday, March 17, 2008
Pitfalls to Teaching Geometry
Michael de Villiers reviews the pitfalls in teaching geometry. One pitfall that he decribes is the no change pitfall, which states that new geometry techonology requires change within the curriculum and classroom teaching strategies. In addition, teachers are required to learn the new software and adjust to the classroom changes. As a first year teacher, this is something that I do not want to worry about, unless the district made the process as easy as possible. For example, providing on-site training would be beneficial.
While reading the "painless learning" pitfall, I was discouraged because I don't see a way to avoid this downfall using technology only. Since much of the geometry software is not hands on for the students, then it is difficult to assess how much they are understand. Thus, a mixture of technology and paper-pencil learning is best.
While reading the "painless learning" pitfall, I was discouraged because I don't see a way to avoid this downfall using technology only. Since much of the geometry software is not hands on for the students, then it is difficult to assess how much they are understand. Thus, a mixture of technology and paper-pencil learning is best.
Monday, February 25, 2008
Will Technology Create Job Cuts?
I couldn't help but think of myself as a highschool student, sitting in a classroom watching a video recording. And my next thought was me SLEEPING in class.
I thought checking homework while playing a video was a great idea. However, if the whole class was presented this way it would be impractical. I firmly believe that in addition to teaching mathematics, my role as a teacher is to inspire my students. Students need to be encouraged. I don't see how a video can provide prompt encouragement to the students.
Also, I believe that social interaction is key to learning and this can not be demonstrated through a video.
I thought checking homework while playing a video was a great idea. However, if the whole class was presented this way it would be impractical. I firmly believe that in addition to teaching mathematics, my role as a teacher is to inspire my students. Students need to be encouraged. I don't see how a video can provide prompt encouragement to the students.
Also, I believe that social interaction is key to learning and this can not be demonstrated through a video.
Monday, February 11, 2008
Integrating the Graphing Calculator in the Classroom
The teacher who influeced my teaching the most, regarding technology, was my cooperating teacher at my first placement. She continuously stressed the importance of the graphing calculator. Solving quadratic equations was a topic I covered during my solo teaching. While in the past, I knew I should set the equation equal to zero and solve. I could do this process with my eyes closed. However, it was not until Mrs. Morgan showed me the graph on the graphing calculater that I fully understood the process. I learned the critical values were the points where y=0; therefore, these are the points where the graph crossed the x-axis.
This event allowed me to see that the students need to make connections between solving algebraically and graphically. It is difficult for students to make the connection on their own. In my experience, integrating technology is most beneficial to the students when it is combined with algebraic solutions. Also, many students like to use the graphing calculator as a means of a check. Thus, the students can do the work algebraically and check graphically. This is always a good compromise.
This event allowed me to see that the students need to make connections between solving algebraically and graphically. It is difficult for students to make the connection on their own. In my experience, integrating technology is most beneficial to the students when it is combined with algebraic solutions. Also, many students like to use the graphing calculator as a means of a check. Thus, the students can do the work algebraically and check graphically. This is always a good compromise.
Saturday, February 2, 2008
Blogging in Math
Contrary to popular belief, there is more to mathematics than numbers. Learning how to read and write mathematics is far different than memorizing formulas and procedures to get a solution. In current mathematics, conceptual understanding is being pushed more than basic skills. Many educators including myself feel that literacy in mathematics is a part of conceptual understanding. Once a student can defend his or her knowledge, the student can have ownership of their knowledge. This is where blogging comes into teaching mathematics.
As an inspiring mathematics teacher, I think blogging is a great tool to allow students to integrate journal writing and technology. If students can put into writing their knowledge of mathematics, I believe they will understand the material and perform better on assessments. Some examples of students' blogs might include: the steps to solving radical equations, word problem procedures and tips, explanations of formulas, derivations, and definitions of vocabulary terms. These blogs could also become a means of a study guide since the students will have access to the blogs outside of school.
In addition, the blogs are a means of communicating. As a future teacher, I will have the ability to comment on my students' post. Also, communication between parents is a possibility.
As an inspiring mathematics teacher, I think blogging is a great tool to allow students to integrate journal writing and technology. If students can put into writing their knowledge of mathematics, I believe they will understand the material and perform better on assessments. Some examples of students' blogs might include: the steps to solving radical equations, word problem procedures and tips, explanations of formulas, derivations, and definitions of vocabulary terms. These blogs could also become a means of a study guide since the students will have access to the blogs outside of school.
In addition, the blogs are a means of communicating. As a future teacher, I will have the ability to comment on my students' post. Also, communication between parents is a possibility.
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