Reflections

After completion of the final project for this class I can say without doubt that I learned a lot about technology integration. I found it rather difficult to integrate technology for math because a lot of math is usually completed with a pencil and paper. At least, I find that to be the most effective way to learn mathematics. It is good to incorporate the technologies since this is still a world where computers are taking over our lives...for the better of course. Even looking past math, technology is useful in all subjects areas, it just need to be used in the right places and for the right reasons. It is one thing to use technology in the class to merely use technology in the class, but it is another thing to use the technologies effectively.

Although an effective and exciting tool, it will never replace good old pencil and paper

Final Project

            A lesson plan for a high school geometry class that I felt would be an excellent example for technology integration is called “Hands-On Geometry: Using Manipulatives in Math 10: Lines and Line Segments Angles and Polygons,” written up by Kathleen Bracken. The idea of the lesson is to increase student understanding in the area of lines, line segments, angles, and polygons. For this particular assignment, I chose to stick with sections one and two, “Mira Constructions: Lines and Line Segments” and “Pythagorean Puzzles.” The total completion time of this unit plan is four hours or approximately one week of lecture, modeling, and practice, given the length of a class is approximately forty-five minutes.

Sessions 1 and 2: Access/Analysis

            The first mathematics standard I found based on this lesson plan is one about rotation, reflection, and translation of lines and line segments using physical technologies and virtual geometry software. Students will be using a tool called a Mira, a transparent device that creates a reflection of a written line or shape which acts as a mirror, for constructing reflections of given lines or line segments. Students would be actively participating in discussion based on their findings and constructions using this tool. There is also a basic mirror tool online which acts similarly to the Mira which can be used for simple simulation and modeling. As an alternative, students can use Geometer’s Sketchpad, computer geometry software, to construct lines and shapes in order to perform reflections, rotations, and transformations. This is a tool I am very familiar with and would be used for any and all geometry plans. It is useful for giving students a more accurate representation of geometric ideas and can help with understanding.

            The second standard which corresponds to the lesson is about explaining the criterion for two triangles being congruent. As a teacher I would lecture about the criterion for triangles to be considered congruent. Then, in order to better students understanding of triangle congruency, students will be asked to work in groups using rulers and protractors to collaboratively construct congruent triangles based on the criterion for triangle congruency. They can also use Geometer’s Sketchpad to construct congruent triangles as well as add the correct markings which could be used to show congruency when triangles are not drawn to scale. After students complete their work they will be asked to use the Smartboard to interactively display their findings to the rest of the class. The Smartboard will allow for manipulations of their work in case there needs to be correction.

            The third standard is about students knowing how to make constructions using a variety of tools. They will use tools such as a straightedge and a protractor to construct shapes such as triangles, squares, and other shapes with larger numbers of sides and angles. They will also use a compass and string to construct circles. For more complicated constructions such as using circles to construct an equilateral triangle, students can use the geometry software which can create more perfect circles which would lead to more accurate constructions of more complicated figures. As a teacher I would model for the students, using these technologies, how to perform these constructions and from there, students will work either at their desks or at computers to individually complete the work. After completion there would be a group discussion about how the constructions were completes as well as sharing the difficulties some students may have experienced.

Sessions 3 and 4: Communication/Evaluation

            The final standards covered in this lesson plan are proving theorems about triangles and using the Pythagorean theorem to solve right triangles. Essentially this is leading into the basic understanding of the Pythagorean theorem. What students will do is use Geometer’s Sketchpad to use the congruency of triangles to show relationships between them, more importantly, those for right triangles. There is an online tool known as NOVA which gives a clear demonstration of a proof of the Pythagorean theorem by breaking down squares which have side lengths of that of the triangles and fit the leg’s squares  into the hypotenuse square. As a teacher I would lecture about the proofs of triangles and about the basic of the Pythagorean theorem. Students would then individually use NOVA or Geometer’s Sketchpad to practice basic proofs of triangles and solve problems using the Pythagorean theorem. After they practice I would check for understanding by administering a brief examination about their understanding of triangle congruence and the Pythagorean theorem.

            It is clear that technology can be easily and effectively integrated into this lesson plan and using them, along with specific teaching strategies, would make mathematics more interesting and enjoyable.

Link to Speadsheet

Link to Lesson Plan

Math Using Technology

I have tried to write mathematics on a computer and all i can say is that it was a failure. If we want to bring math into the computer world, we need to find more effective ways of doing it. In this short clip, you will understand what I mean.

Less Ink, More Power

TI - Technology ... Does Not Compute

One of my favorite tools to use for math is my calculator. More specifically, the TI-89 Titanium. I first came across this calculator in my calculus class in high school. I asked my teacher about it and he said that it is a very advanced calculator that can do pretty much any mathematical calculation including finding limits, deriving, and integration equations. Of course, these are skills that I learned in the classroom, but imagine a world where learning these skills didn't matter and that we could use machines to do everything for us. Let me rewind just a bit.

I'm back in high school in this new world where learning skills was not practical and instead, technology was the only thing we needed to learn. Let's refer back to my calculus class. "Today class, we will be learning about  the "finding limits" function on our TI-89 calculators. You may be thinking, 'shouldn't we learn how to do this on paper first?'. The answer is (in this alternate world) of course not. Why would we need to learn the skills when we can obtain the answers using this pocket sized computer".

Perhaps we should look at history. "Ok class, we will be taking a test today on the civil war. Since we have our wonderful technology at our disposal, you may use your Ipads during the test. You don't need to have this information memorized because in the real world, you will always have a computer (such as the Ipad) to look up the information."

Hmm, something about this universe doesn't seem right. It appears that technology has taken over and people are not learning. Sure, we have the information already, so why bother learning it? Makes you think, huh?

Really, Why Would I Want To Be Here?

One of the biggest issues with education today, which has been shown to make a huge difference in students grades, attendance records, and behavior in the classroom, is the lack of motivation. If I have to sit in 6 to 8 different classes for 45 minutes, each and every day, it is obvious that at some point during the day I am going to not want to be in school anymore for that day... or even that week. Although it is crucial for students to attend lessons in various subjects, some students feel that after three of four hours of learning, they can't handle retaining anymore information and that each class attended decreases their motivation to pay attention. I remember back in high school I knew it was essential that I listened to the teacher in all of my classes, but during the later hour class and the subjects I did not care very much about, I was done listening and would shift my attention to doodling or thinking about the weekend coming up. Granted, I did try my best to stay focused and some of my teachers did try their hardest to keep the class interested. So what do we do to motivate our students?

Entertaining, yet sophisticated

Let's be real. In the secondary school level, using charts with students' names and gold stars will not motivate students; though I would be rather satisfied myself. We have to look into more mainstream ways of keeping students on task. Perhaps if we can relate pop culture into the classroom they will react positively. Maybe if we use more entertaining means of teaching we could keep more kids in school and provide them with the passion to learn. What other ideas might there be?

Interactivity #5

            For this interactivity, I interviewed a mathematics teacher of high school grade levels, who also happens to be a mathematics department supervisor of the Mahwah School District. I began by asking him whether or not he is familiar with the NETS for Students 2007. To quote him, he writes, “As I understand, the basic goals and objectives for these standards, to better prepare students for the digital age, by giving them access to various technological tools for critical thinking, real-world problem solving, global communication, project-based learning, 21st century goals and objectives as required by the NJCCS Tech Standard. It is clear to me that he has a clear understanding of the goals of NETS.

            I next prompted him about whether or not his particular school and/or district have begun to implement NETS. He responded with the fact that the school has not yet implemented these new standards, but are fully aware of them and are committed to NJCCS Tech Standard, which he believes mirrors NETS. He is unaware of any plans to adopt NETS since their primary focus is to pay closer attention to the NJCC Standards. He does not know how the state plans to implement the new NETS.

            This school district has had an increase in the amount of technology used in the classroom. For one, he explains that they use the, “TI-Inspire in both the middle school and high school as a formative, diagnostic tool.” He also stated that the district continually provides local funding to purchase digital tools for the classroom as well as budgets money within each of the teachers contracts specifically for professional development whether for tech training or other related resources.

            After inquiring about the Mahwah school district I was surprised about some of the information provided to me. Although NETS is a relatively new group of standards to be implemented within schools, I am surprised that further action has not been taken in order to become more up-to-date. NETS seems to be very useful and I believe every school district should begin implementing it as soon as possible. I was not surprised by the fact that although NETS has not yet been implemented, the district has other means of integrating technology into the classroom, such as the NJCCS Tech Standard as mentioned previously.

            As a future educator, I want to ensure that NETS-S and NETS-T are implemented within the school district. I want to be as diligent as possible towards making these standards one of the priorities, especially if I end up teaching in a school district that has not implemented these standards. If the district is unaware of NETS, I will make it my goal to inform the higher ups of the district about these standards and help to further integrate them throughout the curricula for math and other subject areas. We are living in a world where technology is becoming a primary resource and I believe it is important to teach our students using these tools.

Link to Spreadsheet:

https://docs.google.com/spreadsheet/ccc?key=0AmFRlBCmbnbUdHJTM1R3N0x0c2JHRkpEZ1ZqUU51S2c

CURR/READ Combined

           I did not believe I could do it, I have actually been able to relate this class to READ 411. My original thoughts on READ 411 were that I would be learning about teaching language and literacy to my students in some way, shape, or form. I was rather confused though, since I did not think that I could relate literacy to mathematics. My other thought was, if I believe I won't be able to relate literacy to math, I definitely won't be able to relate it to technology. 

           Now, hear I am with this revelation of the relationship between these two classes. I'll tell you where it began. For READ 411 I was given a rather large assignment of finding a student, preferably of high school age, and somehow teach them better literacy. I first though, "OK, I'll find a bunch of books and teacher my student to read better." What I did not discover until partway into the assignment was that I would be using technology to my advantage. 

   

           There was a session with my student that I realized that I did not have a book on me for her to look at. I was almost in a panic when I realized, "Of course, I have my laptop on me." I pulled out my laptop and found a piece of literature for my student to read and I implemented my literacy techniques that I learned in class. At this time, technology saved the day. From then on I figured that I would use technology at each of  the sessions with my student.