Technology Integration Plan

               The lesson I choose to use for my matrix was a lesson on fractions that I taught in my methods class last semester. I choose this lesson because it was mainly student based and I wanted to accommodate the lesson to contain more technology. The first time I taught the lesson it did not contain any technology besides the use of calculators and a projector. I wanted to recreate this lesson to teach the same topic, but this time using technology. This was a challenge for me but I was successful at doing so.

                The first row in my matrix contains a do-now activity, teacher directions, and small group work. First the students will complete a do now activity individually to review the idea of equivalent fractions. This will take five minutes and then I will go over the answers with them as a class on my smartboard. I will then explain to the students the activity that they will be completing in groups, which will be discovering how to add and subtract fractions with unlike denominators. I will split the class into groups of 4 and they will begin working collaboratively. In their groups they will be first working with fraction circles that they can write on with expo markers and erase. With these circles they will be trying to figure out how to represent equivalent fractions with these circles by coloring in sections of different circles. This is a visual process that will help them for the next step, on coming up with a procedure to add and subtract fractions with unlike denominators. 

                The second row in my matrix contains small group work, me helping each group one on one, experiments, and student collaboration. The students will now be working on an online activity to start the process on discovering how to add and subtract fractions with different denominators. They will go on a site call illuminations and open an activity that allows them to create fractions with unlike denominators. The fractions in this site will be represented in circles or squares, which ever they choose. I will tell them that once they created a set of fractions to add or subtract them. I will tell them to try many different ways of doing this. I will have my students add or subtract these fractions by hand on their white boards and then check their answers in the calculator. They will see if their process was correct or incorrect by using the calculator to check their answer. If they were wrong they will have to try a different way until they get it right, and if they were correct I will have them create a new set of fractions on the computer to try. The students should take multiple tries until they start to discover a method on how to do this process. As students are working I will be walking around to answer questions without giving away the process and to check for understanding. 

                 The third row of my matrix relates to small group work, student collaboration, one-on-one help, student explanation, written procedure, and peer-evaluation. In this step students will be coming up with a step by step process on how to add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions. They will discuss their results to the online activity and collaborate on a method that works. I will ask them to write the process on their white boards in steps. To do this they will have to evaluate what their peers are saying and decide if they all agree or not. This will take cooperation and critical thinking from all the group members. I will be walking around to each group to see what they came up with. 

                 The fourth row of my matrix includes a large group discussion, Q&A, teacher assessment, teacher participation, and direct teaching. In this part of the activity the students will have came up with a process on their task. Once every group is done I will ask each group one at a time to share their results with the class through the document camera. They will tell the class what they came up with and the class and I will discuss our opinion on their process. We will then decide as a whole if they are correct or incorrect. Each group will get a chance to share their results. Then as a class we will come up with a master process. I will then go over examples on the smartboard to clarify any misunderstandings on this process. 

                The fifth row of my matrix it involves individual/small group work, student collaboration, and self-assessment. In this last step students will work on the computer and solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Here students will master the process and get more practice on solving problems of this type. They will use white boards to record their work and use calculators to check their answers. 

Matrix

Video Chatting for Extra Help

     Some professor offer to their students that they can receive extra help for a course through video chatting. Professors do this by setting an hour a week or night that they will be online to chat through video to help on homework, or review for an exam. They make this video chat open to a group so that many people can join the chat at once and so she can help everyone. Do you guys think this is a good thing to offer for high school students?

    I think that this would be a conservational topic. This is because of the issue teachers getting to close to their students in the wrong way. By opening up a video chat students may accuse a teacher of saying something that they did not. It also might give students the wrong idea. High School students are in the process of growing into young adults and they may get the wrong idea when video chatting from home with their teachers.

    On the other hand this would open up many chances for students to get help on their homework if they get stuck at home or help them review for a test. Receiving extra help from their teachers one on one can help students bring up their grades and receive it from their own home. Teachers would pick an hour everyday to be available to their students and students would have the ability to reach out to them for educational help on a topic. 

    I do not know if this idea is realistic because not all teachers would be willing to do this without extra pay, but I think that is defiantly something that can be considered with much discussion for the future. This would have to be carefully thought out because of all the problems that can occur, but many positives can come from this too. 

Electronic Attendance

     I am currently doing my fieldwork at Kearny High School and the high school takes attendance of the students electronically. They do this by having the students scan into school with their student ids. The teachers also have to take attendance in each of their classes and submit it through a program called Genesis. Doing this keeps track of the students who cut class. They can check this because if a student is signed into school but not in class means they cut class. Online attendance cuts down on the amount of class cutting because the students know they will easily get caught through the online attendance program. It also helps monitor who is in the building at all times in case of an emergency.  

             I think that this system works well and it should be implemented in more schools because it is quick and effective. No longer does someone have to walk around and collect the attendance from each room in the morning and manually record the absences in a computer. It is also beneficial because it automatically keeps track of how many days a student is absent or tardy to school. They can keep track of this and try to stop to many absences if it becomes an issue for a student. 

     Having students scan into school also reinforces that they need to be on time. No longer can students sneak in after the bell rings and get away with it. Since they have to scan in everyday the scanner clocks what time they got to school. They cannot come to school late and get away with it because the scanner will point it out right away. In the past a students first period teacher might let them get away with being late to school, but the scanner will not. 

     I have never seen another school using an attendance system like this. All the schools that I have been to and substituted in still use paper attendance. Has anyone else seen an attendance system like this? I would love to hear your comments and if you agree or disagree with taking attendance in this fashion. 

Online Grade Books

     Online grade books are becoming much more common in schools today. Some teachers like to use online grade books because it easily calculates grades, class averages, and much more. Using paper grade books requires you to calculate manually every average which can allow for error. Teachers who do not like using online grade books say it’s because they are not good with technology or they do not trust that it will properly save. They are nervous about the risk of losing all the grades. 

     I think that online grade books are a positive piece of technology in schools because it saves teachers a lot of time because they no longer have to calculate grades by hand. The system does it all for you, all you have to do it input the grades that you want to be averages with the corresponding percentage. This system also is always correct, and makes no mathematical errors, which can easily happen when teachers make the calculations by hands. 

     Online grade books also can make graphs of the class averages to show students where they stand compared to the average of the class. They will be able to observe if they are doing above average, average, or below average. This will allow students to assess their work so far and improve if needed. If they are below the class average they will know to work harder and get extra help if they feel they need it. Paper grade books do not do any of these things for the teacher. If a teacher wanted to show this from her paper grade book she would have to create the graph by hand. Online grade books are also beneficial because once a grade is entered the guidance counselor can pull up a student and see all the grades. This is a good thing because if there is a problem with that student they can call the student down and ask what is going on. Overall, I think that online grade books are a great thing that a school can offer. 

Learning through Power Point

          I was never a huge fan of power point presentations. I felt like they were boring and many teachers just read off the slides. I do not feel like power points are a good use of technology in a math class, because math is interactive and you need to do many examples on paper. This is something that you cannot do with a powerpoint. A powerpoint presentation is used more for factual lessons, not interactive lessons. I do not feel that power point is appropriate in math. 

I do not think powerpoint can never be used in other subjects such as english or history. In english and history there are many more facts and opinions being presented where power points can do the job. Teachers can use power points to organize there lesson into different slides and teach one or two facts at a time. This allows students to focus on one slide at a time and not become overwhelmed of a whole page of information at once. 

In math classes teachers can use interactive websites, typed up outlines of text and examples where they can write in the work on the board, or they can use handed out worksheets for the students to work in groups with any tools they need to figure out a problem. To me these are better options to get learning to take place in a math class than using power point presentations. When I was a student and I had to learn from power point presentations I was always bored and usually did not pay attenuation because the teachers always scrolled throughout the slides to fast and I couldn’t get all the notes down, and they were lecture based not student based. 

Learning Through Video

There are many mathematical videos on the internet that teach various mathematics concepts. Do you think videos should be used in the math classroom to teach or reenforce a concept or skill?

I think that using videos in a math setting is a good way to show students different examples of how to solve or do something. For some reason as soon as you say you are going to show a video it grabs the students attention right away. This is a good way to teach a concept or introduce a new concept and have all your students paying attention. You can also show a video to help your students learn a long formula like the quadratic equation through a song. My high school math teacher showed us a video of the quadratic equation when I was a freshman in high school and to this day I still remember it. So as you can see videos are very effective in a math classroom because they help the students to remember formulas or learn concepts in a way that relates to them. 

Students love the use of technology because that is their life style so anyway you can incorporate technology into a lesson such as video is a good thing. Not all teaching should be done through video but if there is a video that you think would be useful to your students learning, showing it in class would be a good idea. 

Another way to incorporate video into your students learning is by giving them a list of videos to watch on their own time, if they need more examples of a concept. They will be able to watch these videos at home when they are working on their homework if they forget how to do something. I do not see any negatives to incorporating videos into your lessons.   

Collaboration Canvas

Remixing another classmates canvas was very fun and creative. I had a hard time finding a canvas to remix that would go well with my original unit. I used an art canvas to remix and I was creative with what I choose to do. I am having my students create a piece of art only containing congruent triangles. The art also must be of trees in nature and it has to show the effect trees play in art. 

I added videos and pictures to show students how to contract congruent triangles by hand using a compass. I also added pictured and videos to show students how to contrast a basic tree out of triangles. Those videos were just a simple tree, their art works will be more complex.  

I had some difficultly finding art pieces that also contained math, but I did my best to make it work. I had a fun time with this project and I think that it is a great way to show us how to use different subjects in one class. Mixing more than one subject into the same class will be beneficial to the students because they will be able to see how math can be used in other areas of their study as well

Canvas:
http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2755&mode=view#network6

Online Homework

Online homework has its positives and negatives to it. One positive is that it saves time for the teacher when grading homework. Online homework programs grade the students homework electronically and the teachers can put the results directly into their grade book. The teachers will have the ability to see who truly completed the homework before the class starts. This will allow the teacher to know who completing their work at home before school starts. Online homework also saves the teacher time in the classroom because she does not have to walk around and check who did their homework and then collect it if she pleases. 

Online homework can also be bad, this is because it is very easy for students to guess the correct answer or cheat on it to get a good grade. One way this can be done is looking at the examples that are given with the question and the students just plugging in their numbers instead of the numbers in the example. This is not good because the students are not truly trying to solve the problems on their own for practice. Another way you can cheat on the online homework is by putting the wrong answer in on purpose so that the computer gives you the correct answer. Lastly many of the web-assign questions can be found on google, where students can easily look up the correct answer. Unlike written homework there is no work to prove that the child did the correct computations to solve the problem on their own. 

Another negative of online homework is input issues. Many times the student will have the correct answer but type it in differently than the computer wanted and it will be wrong. This will give that student the idea that he is solving the problem wrong when he may be right. 

I am not 100% against online homework but if I was to use it in my classroom I would ask my students to bring in their work on a separate piece of paper to hand into me so that I can make sure my students are really doing the work and that they are doing it correctly. 

Unit Plan Canvas

At first, when I looked at this assignment I was a little nervous because I had never used PLAYground before and I was unsure what to expect. Once I started this assignment I quickly saw that this site was easy to use, since everything that was needed was right there. Creating this canvas was very fun for me. I liked how it is set up and I think that students would really benefit from it. They can use it to see an overview of the unit, and use it as a reference if they need some extra help. On my canvas I tried to include examples of each topic weather it was through video, pictures, or links to websites. This canvas is also a great way to share ideas with other teachers, they will be able to go to your canvas and see what you are doing for certain topics and you can easily go to other canvas yourself to get more ideas for teaching. 

I choose this topic of congruence because it is often a difficult topic for many students. For IA #3 I choose a high school geometry problem that is similar to my canvas. I wanted to do more on congruence and proofs because many students find this difficult and I wanted to create a canvas for my students to reference to get the extra help they may need. I posted many examples and a video for my students to view if they are having difficultly on this topic. 

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2446&mode=view#network6

Technology Workshops

                        Schools are starting to really push technology in the classroom. Technology is something that the students can relate to and it is something that they are interested in.  Technology is a great way to gain your students interest in learning new concepts in math. You can use many different kinds of technology in math, such as a calculator, document camera, smartboard, computers with excel, graphing programs, online homework websites, and much more. Although not all teachers are familiar with new technologies that can be used in the classroom. This may cause teachers to stress out and become over whelmed if they are expected to incorporate technology into their lessons but are unsure of how to do so. 

                   To fix this problem I think that schools should hold technology workshops separated by subject area for teachers to go. These workshops can be used to introduce new technologies to teachers and show them all they can do with technology to enhance their lessons. This is a great way to better a schools ability to use technology and is also a great way for teachers to get the most out of the technology they are given. For example a simple graphing calculator can do so much more than many people think, by attending the workshop teachers will have the opportunity to learn all of this. 

                   Also, the smartboard can do so much to better a mathematics lesson. Many teachers including myself do not know all the functions of a smartboard. With these workshops teachers will have the opportunity to ask questions and practice with their own smartboard after the meeting. This is a great way to better teachers in a school, and it will benefit the students too. By teachers understanding and using technology students will be more engaged and eager to learn new things, since technology is something that grabs their attention instantly. 

Technology & Pedagogy

I choose this lesson because I am very interested in teaching geometry and this lesson was on a geometry topic. This topic went over a way that students can experiment with quadrilaterals and diagonals.

This lesson was all group work and discovery based. They used diagonals to prove different theorems on their own. They also used a computer program to help them do this. The curriculum goals, teaching strategies, and technologies used were mainly in alignment with the curriculum goals. The programs and worksheets that were used stated and explained exactly what the students should be discovering on their own. The students knew where this lesson was going and the group work was a great way to do this. 

The diagonal tools program is essential to achieving the curriculum goals because this program allows students to see and move around the diagonal lines and the endpoints of the quadrilaterals to see how it affects the properties. From this they can make conclusions to help them prove and derive theorems from what they see. Using a document camera would of only made the lesson better so that each group could better see what each group came up with, rather than just holding it in the air and talking about it.    

URL:https://docs.google.com/spreadsheet/ccc?key=0AqXZhRFVVYr-dG8weVl2anIyNlBkT2pTVXlEOGkzMXc#gid=0

Smartboards

Smartboards are a great tool in the Mathematics classroom. They allowed teachers to graph equations accurately, show videos, move objects around with their hand, and much more. Smartboards have many features that will benefit a teachers lesson.  Graphing is a perfect example, when a teacher wants to graph an equation, they can open up the graph paper and graph the equation right on the board. Unlike a chalk board where the lines will not be perfectly straight, and the points will not have perfect spacing.

Smartboards also work as a regular board if teachers want to open up a blank sheet and show examples step by step. They can do this by opening up a blank page and then use the smart markers to write. They have the option of many different colors to show different steps in a problem. They can also easily erase and start over if they have to. The great thing about writing examples on a smartboard verses a chalkboard or a white board is that your writing can be saved and printed or posted on a class website. This is a great tool for teachers incase a students is absent or so that they can go back and see exactly what they did on a certain day. Using a chalk board or white board this cannot be done.

Smartboards are not only useful in math. For example in a history class, a teacher may want to show students where something on a map is that they are learning about. Instead of just pulling down the old fashioned maps that hung from the walls, the teacher can open up a map and project it on the smart board. This is more beneficial because teachers can write on this map to highlight and show students exactly what they are talking about. Then they can erase if for their next class. 

Smartboards do have some glitches. If the calibrator gets messed up what the teachers are trying to write will not be accurate. Their writing will come up in the wrong spot. Also if a teacher has a whole lesson planned using the smartboard and for some reason the projector is not working they will not be able to do the lesson. Teachers should always have a backup plan just incase the smartboard is not working one day. 

   

Calculators in a Math Classroom

          Many people agree with the use of calculators in the mathematics classroom. I cannot say that I am one of them. Calculators cause many students who are not strong in math to become dependent on them. This causes students to forget, or never fully learn multiplication and division, and many other mathematical concepts that the calculator can compute for you. I am not fully against calculators because they can calculate things faster and more conveniently than a person can, but I do think that there needs to be full understanding of a concept before they are introduced.  

          Since calculators are being allowed in middle school, students are entering high school not knowing how to do long division, add/subtract/multiply/divide fractions, multiply, and other basic mathematical concepts that should be known. I can say this because I have seen it first hand from substituting and talking with my cooperating teacher. She told me that each year since calculators were introduced in the local middle school, her math students remembered less and less of their basic skills. Therefore, she has to spend more time on the basics rather than moving on to what is actually in that years curriculum.

          Another downfall of calculators in middle schools is that many students do not yet fully understand the meaning of certain concepts and they enter the calculation incorrectly in the calculator. For example, I was substituting this past week and a sixth grade student wanted to calculate 125/4 and he entered it into his calculator as 4/125, giving him the completely wrong answer. He did not know that this was wrong until I showed him the correct way to do it. Calculators will give young students misconceptions about mathematics because they have not yet mastered all the skills they need. If this student was more skilled in division he would have realized on his own that that answer could not possibly be correct.   

          Although, I do not think that calculators should be eliminated all together. Calculators should be introduced in high school, only after students fully understand the methods of a problem on paper. Graphing calculators can show students what graphs of  different functions may look like that you can not accurately graph on paper. They can also speed up the process of calculating basic solutions to a long problem. Teachers should not allow their students to become dependent on calculators and they should monitor their use in the classroom. 

History of Technology in Mathematics

Were teaching machines really helpful, or was it a way for students to speedup their learning process without guidance from a teacher?

The Geometer's Sketchpad

Today technology is a huge part of every students life, so why not use it in the classroom? Using technology in a classroom can enhance a students learning on a weekly basis. As a future mathematics teacher I think that technology can further help a student’s understanding on a topic, when used correctly.   

One example of a piece of technology that can be used in a Geometry classroom is The Geometer's Sketchpad. The Geometer's Sketchpad is a computer program that allows you to do many things relating to geometrical ideas. For example you can find areas, perimeters, angles measures, and much more. With this program you can allow students to experiment with different geometry theorems and they can see what happens when you change one aspect of it. This program can also help students try and prove theorems. 

Using this program in a classroom will help students who learn from visual settings because it allows you to physically see how theorems work. It will prove to students that the theorems written in their textbooks are actually true. This program can also be used for students to create figures and practice solving for area. They can do this by creating a figure on the sketchpad and then solve it on paper. Once they solve this they can use the program to solve for the area and the student will be able to see if their answer matches what the program gave as the answer. 

I like this program because it does not automatically find answers for you. Students need to first know how to set up a problem that they are trying to solve by creating it on the sketchpad. Then they need to figure out what the problem is looking for before they ask the program to solve for it. This program helps students think critically about problems because instead of the teacher giving a picture along with a problem the students can use the sketchpad to experiment with different approaches to a problem. Students can then pick the method that works best for them and use that method in the future. This program makes it easy for students to start over and try many methods because things can be undone and redone if a mistake was made. 

When using technology in a classroom teachers need to make sure that their students do not become dependent on these technologies to solve problems for them. I think that students should first understand a concept completely on paper before they are given a calculator or other piece of technology to further their understanding. Students should first know the basics before they move further. For example if a student is given a calculator before they memorized their multiplication facts they may never learn them on their own because the calculator will always be there to compute the problems for them. 

Technology Autobiography

The three most important influential communications technologies in my life up to this point are my cell phone, laptop, and the ability to video chat. These devices play a huge role in my daily life, so much that I cannot imagine myself functioning without them. My cell phone is the most influential piece of technology in my life, it is there for me to always stay in contact with family and friends on the spot. My cell phone also allows me to easily access the web to search a piece of information when I do not have access to my laptop or computer. Another thing that I use my cell phone almost every day is its ability to turn into a GPS. Besides the three things I listed my cell phone does much more, from helping me stay organized to allowing me to stay up to date with current news events. My laptop is also a major technology in my everyday life. I use my laptop for mainly academic purposes, such as writing papers, blogging, checking my email, and much more in the academic world. If I did not have my personal laptop it would be much harder for me to get my work done since I would not have access to the internet or word documents at my home. Video chatting is the third most influential piece of communications technology in my life. I video chat with my brother ofter since he is away at school six hours from us. I like to video chat with him so that we can see each other and it feels more real than just talking on the phone. 

These three technologies help me learn new information everyday right on the spot. For example with my cell phone I can search the web, call or text someone, and read books or magazines. My laptop takes finding out new information even further because I have access to everything I can possibly think of. I can search the web and read detailed journals or documents. I can check my email to find out if there is any changes to a course. I can also video chat from both my laptop or my phone.   

These three technologies are not always as good as they seem. I think as a young adult in this world full of new technologies we become quite reliant on them. For example during Hurricane Sandy, my house lost power for 10 days. Durning those 10 days I did not have any form of communications technology available to me. I felt lost in some way almost as if I did not know how to function. I need to learn how to function incase the technology I plan to use that day fails on me. I need to always have a back up plan to allow me to learn new information.   

In the video, Alan made a great point. He said that “Being able to experiment with technology is what makes it technology. If people did not experiment with test tubes back in the days of Newton nothing would have happened. Its paving the way for us to move forward as a species and a civilization.” (2:33) I agree with his statement completely because in order for us to move forward in the world we constantly have to experiment with new technologies to learn what works and what doesn’t work. Throughout the video there were many similarities between the students and I. Some similarities consist of always having my cell phone with me even if I do not bring a purse. I also agreed with the girl who said she did not like abbreviations, when I text I do not use short words I always try my best to text how I would type a paper or talk to someone in face to face situations. Some differences with me and the students in the video include using technology to make music or videos, I do not do those things with technology because I do not have a great interest in music or video making, although I do like to take a lot of pictures with my cell phone. All of these students used technology to improve their lives in meaningful ways and to help them learn new information.