This course has introduced me to some unfamiliar technologies. Sad to say, but I had no idea what a blog was before I started this course. (How? I have no idea). Although I am not an expert I learned the most about Microsoft Office 2007. Changing from 2003 to 2007 presented a large obstacle, which this course helped me overcome in my other classes. I am particularly fond of PowerPoint and the endless amount of possibilities creating one. I wish I could say I will use the Smart Board the most, but we all know that’s a lie. While teaching, I believe the use of the graphing calculator will be relied on the most and because of this, utilized the most.
As a whole, my view of technology has opened up a lot of doors for me. Knowing there exists technologies which can make sketching and data tables easier to create will help me in various lessons, not just mathematics. I think technology is a wonderful tool and when executed the right way can completely contribute to learning. I feel more confident incorporating different technologies in classrooms and feel utilizing technologies in lessons will be a growing strength of mine!
5.01.2008
4.21.2008
Effects of Graphing Calculators in the Classroom
Effectiveness of Graphing Calculators in K–12 Mathematics Achievement:A Systematic Review by Empirical Education is a research report about the use of graphing calculators in the classroom. The research includes grades K-12 in mathematics. I enjoyed reviewing this article because I hope to be certified 1-12 by the end of next May (with a concentration in mathematics, of course). This article includes research from various studies: girls vs. boys, calculators vs. non-calculators, studies in China, a comparison of mathematical topics (i.e. Algebra vs Statistics using a calculator). Included in the twenty one page article are charts, graphs, multiple studies and the results. After each case study the article explains each test performed and what the outcomes were. It turns out that calculators, especially graphing calculators in the higher grades, show an increased level of confidence when performing mathematical computations. Mentioned are the positive results from the use of calculators by students with disabilities. It also shows that there is no difference between the performance of boys and girls!
After reading this article, I found myself agreeing to most of the research. I was, however, surprised when I read certain studies, not by the results, but the different studies. I believe calculators, when used appropriately definitely enhance mathematical learning. To go through elementary school, middle school and high school without the use of a calculator is restricting on not just mathematics, but sciences and technology.
Link to site: http://education.ti.com/sites/US/downloads/pdf/eei_graphingcalcreviewreport_2006.pdf
After reading this article, I found myself agreeing to most of the research. I was, however, surprised when I read certain studies, not by the results, but the different studies. I believe calculators, when used appropriately definitely enhance mathematical learning. To go through elementary school, middle school and high school without the use of a calculator is restricting on not just mathematics, but sciences and technology.
Link to site: http://education.ti.com/sites/US/downloads/pdf/eei_graphingcalcreviewreport_2006.pdf
4.10.2008
Why Statistics?
I recall in high school asking the question “When will I ever use this?” Now in college, I can see applications of the mathematics we were forced to learn in high school. If one of my students asks me “when will I use this?” I will emphasize the importance of statistics. Companies must know public opinion on foods and clothing, music and television shows. Statistics is an important factor in basing decisions on whether to continue with a product or take the product off the market. Polling the public is a good way to see opinions on certain topics, but how will you calculate results if you don’t know statistics?
Statistics play a very important role for students in school, as well. Teachers may calculate the mean and see how everyone compares. Students can use this information to see where they fall among the class. Analyzing other statistical data from an exam or project assignment may actually help students. Discussing this information with students will help them see how decisions are based off the facts. We have to be able to calculate the facts and we do this with statistics.
Statistics play a very important role for students in school, as well. Teachers may calculate the mean and see how everyone compares. Students can use this information to see where they fall among the class. Analyzing other statistical data from an exam or project assignment may actually help students. Discussing this information with students will help them see how decisions are based off the facts. We have to be able to calculate the facts and we do this with statistics.
3.16.2008
Pitfalls in Geometry Software
Reading the provided article about pitfalls of dynamic geometry brought up great points. I am witness to the great things geometry programs provide but am also affected by some of its pitfalls. The sections ‘“Makes Practical Obsolete” Pitfalls’ and ‘“Painless Learning” Pitfalls’ mentions the use of these geometry software programs as being used alongside the hands-on activities. I completely see the need for hands-on activities no matter how terrific a software program may be. Without the use of multiple means of teaching, using geometry software is teaching students how to execute the program and not necessarily teaching geometry skills and knowledge. In my classroom I will always remember using multiple ways to teach a concept or theorem.
Another point the article mentions that sticks out in my mind is that teachers don’t have to know the material inside and out before they teach it. I know I tend to shy away from material or information I have not mastered. I fear I may approach a question I may not know the answer to. The horse/car metaphor used throughout the article was appropriate and helped me understand that I don’t need to know everything about a topic. (I also know it’s okay to tell students I just don’t know!) In my future classroom, I don’t plan on ‘diving in’ new material or programs, but teaching with programs that may be unfamiliar.
Another point the article mentions that sticks out in my mind is that teachers don’t have to know the material inside and out before they teach it. I know I tend to shy away from material or information I have not mastered. I fear I may approach a question I may not know the answer to. The horse/car metaphor used throughout the article was appropriate and helped me understand that I don’t need to know everything about a topic. (I also know it’s okay to tell students I just don’t know!) In my future classroom, I don’t plan on ‘diving in’ new material or programs, but teaching with programs that may be unfamiliar.
2.12.2008
Teacher vs. Technology
I do not believe that mathematics teachers are in danger of being replaced by technology. The subject of mathematics is too complex to be watched, or listened to. Having a proctor sit-in on a recorded math lesson will not benefit the students as well as having accessibility to actual math teacher. Student questions may arise that a recording or proctor cannot answer. What if a student has trouble entering a function on his/her calculator? Having recordings played in place of teachers may lose the students who are not visual or audio learners. As teachers, we need to teach all learners, not just visual learners. In high school we had a distance learning program, where students had class over a television and our school provided a proctor. The students disliked the idea and had a negative learning experience.
Let’s assume video recordings do take the place of mathematics teachers. If technology takes the place of mathematics teachers, it should take the place of other content areas as well. Parents may argue their children do not need to attend school because they will have the recordings of lessons their children can watch at home. Without students attending classes, the idea of school becomes ineffective. If, by chance, technology does start to take over, I would stay up to date with new material and ideas that recordings cannot compete with to keep my job.
I agree technology works wonderfully alongside a teacher, but not well enough to replace a teacher.
Let’s assume video recordings do take the place of mathematics teachers. If technology takes the place of mathematics teachers, it should take the place of other content areas as well. Parents may argue their children do not need to attend school because they will have the recordings of lessons their children can watch at home. Without students attending classes, the idea of school becomes ineffective. If, by chance, technology does start to take over, I would stay up to date with new material and ideas that recordings cannot compete with to keep my job.
I agree technology works wonderfully alongside a teacher, but not well enough to replace a teacher.
2.06.2008
GSP to the Rescue
Although I do not remember an ‘A Ha’ moment in my mathematics experience in high school, I do recall one in geometry my freshman year of college. Our first journal assignment was to find five centers of triangles. With the help of Geometer Sketch Pad (GSP) this was possible. Typically when I think center a circle comes to mind. Trying to find one center of a triangle, to me, is doable – the centroid – the concurrence of the vertex and the midpoint of all three segments. Trying to find at least one other center by pencil and paper is not doable for me. I thought all centers would connect at the same point, all the time. Using GSP I was able to create altitudes, perpendiculars, angle bisectors and intersecting bisectors with two exterior angle bisectors to form four other centers of a triangle. Without the use of this program I do not think I would have been able to complete the assignment.
Having technology assist my understanding of triangular centers will contribute to various teaching approaches in my future mathematics career. Bringing up the theory of multiple intelligences is a perfect example. Being able to use technology, in my case GSP, serves as a visual image for mathematical concepts and will help visual learners (as well as other learners). When I saw how the altitudes connected and intersected, I could see the triangle’s orthocenter. There are many benefits of using technology: faster computations, being able to manipulate graphs, solve equations, find derivatives, the list goes on. Even though middle schools and high schools may not have GSP, I plan to incorporate other forms of technologies, such as graphing calculators. These calculators graphically show functions which help students visualize the math, similar to GSP. My hope, as a teacher, is to provide my students with the opportunity to make connections and ‘see’ the math, whether it be on a computer program or a graphing calculator or another form of technology.
Having technology assist my understanding of triangular centers will contribute to various teaching approaches in my future mathematics career. Bringing up the theory of multiple intelligences is a perfect example. Being able to use technology, in my case GSP, serves as a visual image for mathematical concepts and will help visual learners (as well as other learners). When I saw how the altitudes connected and intersected, I could see the triangle’s orthocenter. There are many benefits of using technology: faster computations, being able to manipulate graphs, solve equations, find derivatives, the list goes on. Even though middle schools and high schools may not have GSP, I plan to incorporate other forms of technologies, such as graphing calculators. These calculators graphically show functions which help students visualize the math, similar to GSP. My hope, as a teacher, is to provide my students with the opportunity to make connections and ‘see’ the math, whether it be on a computer program or a graphing calculator or another form of technology.
2.03.2008
"I'm a math teacher so why do I need to know how to blog?"
Keeping up with the rapid advances in technology can be challenging. Incorporating these advances in the classroom has benefits for both students and teachers: communication, accessibility, information and availability. Anticipating a career as a mathematics teacher I can see possible opportunities using a Weblog.
Blogging is a new technological idea which has many benefits for teachers. I believe in integration among the grade curriculum, and blogging could play a key role. Different content area teachers working together to create an interdisciplinary project and post it on their blog site could fulfill many district and state requirements. Research, writing, discussing and presenting a topic in which all subjects are included and individual information is posted, is an excellent way to integrate subjects. If students encountered questions specific to a specialized teacher, they could receive feedback and clarification from the specific teacher. After posting the question and answer, other students with the same question could access this information.
Blogging is an excellent opportunity for students and teachers to provide responses to assignments, pose questions and share ideas. In mathematics, students have the accessibility of the teacher for answers to questions on homework. Classmates being able to communicate with each other over homework problems, for example a proof, is a great way of open discussions in which a teacher can give guidance if he/she feels they are going in a wrong direction.
Posting higher-level math problems or focus problems (to introduce a topic for the following week) can be a great weekend assignment. Discussions online and/or in class the following Monday would provide background knowledge and thoughts for the upcoming week. In class on Mondays, we find many students who have not touched their notebooks since the class on the previous Friday. Having weekend assignments or discussion questions on Weblogs can provide an assurance students utilize their resources.
In order to provide these opportunities and ideas for students, teachers need to know how to use Weblogs. Providing as many opportunities for our students as we can, is a major goal for teachers. Blogging is one of these opportunities.
Blogging is a new technological idea which has many benefits for teachers. I believe in integration among the grade curriculum, and blogging could play a key role. Different content area teachers working together to create an interdisciplinary project and post it on their blog site could fulfill many district and state requirements. Research, writing, discussing and presenting a topic in which all subjects are included and individual information is posted, is an excellent way to integrate subjects. If students encountered questions specific to a specialized teacher, they could receive feedback and clarification from the specific teacher. After posting the question and answer, other students with the same question could access this information.
Blogging is an excellent opportunity for students and teachers to provide responses to assignments, pose questions and share ideas. In mathematics, students have the accessibility of the teacher for answers to questions on homework. Classmates being able to communicate with each other over homework problems, for example a proof, is a great way of open discussions in which a teacher can give guidance if he/she feels they are going in a wrong direction.
Posting higher-level math problems or focus problems (to introduce a topic for the following week) can be a great weekend assignment. Discussions online and/or in class the following Monday would provide background knowledge and thoughts for the upcoming week. In class on Mondays, we find many students who have not touched their notebooks since the class on the previous Friday. Having weekend assignments or discussion questions on Weblogs can provide an assurance students utilize their resources.
In order to provide these opportunities and ideas for students, teachers need to know how to use Weblogs. Providing as many opportunities for our students as we can, is a major goal for teachers. Blogging is one of these opportunities.
Subscribe to:
Posts (Atom)