Technology Integration Plan

            The lesson I used for this matrix is one I have used in my unit plan for my methods course. It is a unit on transformational geometry and this lesson focuses on translations. The standards I chose are from the 8^th grade geometry section. The standards state that students should be able to describe the effect of translations on two-dimensional figures and be able to describe a sequence that shows the similarities between two figures.

            The first row of the matrix relates to the Do-Now activity in the lesson. Students will see a picture of two triangles on a coordinate plane, reflected on the overhead projector. Students will take a couple of minutes to describe the translation occurring in the picture. They use the Smart Pals to record their responses and share with a partner. After everyone has finished, the entire class engages in a classroom discussion. In this part, there are a lot of student pedagogical strategies, such as student participation and group discussion among partners. The large group discussion involves an interaction between me, the teacher, and all of the students. The overhead projector and Smart Pals are the two technologies used for this part. In this section students are critically thinking, solving problems, making decisions, and communicating with each other.

            The second row of the matrix represents the group activity of the lesson. Students will be given directions to an activity, as well as a worksheet that explains their task. They will explore translations using tangram shapes and the graph paper that is given to them. They will also analyze what is occurring in their graphs and answer specific questions, related to the standards. The tangram shapes serve as a visual representation for the students. The large group discussion at the conclusion of the activity and the Q & A portion of the lesson are a couple of the pedagogical strategies used in this section. Students will bring their completed graphs and worksheets to the document camera for the rest of the students to see. The document camera and the tangram shapes are the technologies that are used in this portion of the lesson.

            The third row of the matrix has the students use software on computers to complete their exit card. I have them interacting with another program, to have them visualize the lesson in multiple ways. The technology in this portion (computer and online software) enriches and transforms the ways in which the students are learning the material. Instead of lecturing the students, the computer software and interactive activity lets the students explore the topic of the lesson in their own way. They are also using what they have learned in the lesson, as well as the online activity to help them explain, in words, the translation that is occurring. For this part of the lesson, I would provide a lot of guided practice into making sure the students stay on task when on the computers and to assist them with the online software, if needed.

            The fourth row of the matrix has students communicate to their partner their understanding that the two figures are similar. They can do this in whatever way they want. They can persuade their partners in words or they can use the online software to enhance their explanation. This gives students another opportunity to use the materials that work for them. If the online software helped them understand the material better they can use it to help their explanation. If the activity with the tangram shapes helped them better they can reflect on that in their explanation. Whichever option they choose it is their choice and I, as the teacher, will only be there as a helping hand to assure they understand the content.

            The fifth and final row of the matrix explains the homework assignment. Students will demonstrate their creativity and innovation by creating their own real life problem/situation where translations occur. They will have specific questions to answer and criteria to meet for this assignment. Students will be thinking critically, solving the problems, and making decisions during this process. Students can use the computer and internet to generate pictures to explain their problem. Again, students have the option of doing this if they choose.

            This matrix helped me lay the lesson out step-by-step with the appropriate strategies and technologies. One can look at each row and clearly see what technologies and pedagogical strategies are used. The layout is a good way to make sure that nothing is left out. It is also a good way to organize lessons.

URL: https://docs.google.com/spreadsheet/ccc?key=0Agvr5L6t2qQGdHlNZ3hUb08xaVF2d0Z2RUo0UmUwOVE&usp=drive_web#gid=0

Illuminations

Illuminations is a site for teachers to use as a resource. It provides more than 100 activities that are aligned with the common core standards. It also has more than 600 hands-on lesson plans, a review of standards, and numerous online links and resources for further information. Teachers can use this site as a resource to assist them with their lesson plans. For teachers who have been teaching for a while and are not familiar with the technologies available for them, this site can be very useful for them. It also has numerous activities for teachers to assign their students. The activities and lesson plans are split up into specific grade levels. Teachers can pick and choose specific activities based on their students’ grade level and/or level of understanding. The site also provides free apps for mobile devices. For our students who are in the higher grade levels, these mobile apps can be very effective in providing students another resource to use when preparing for an assessment. It also has a section called calculation nation. This section provides different games for students to challenge themselves or their peers.

This site provides various tools for both teachers and students to use. Different content in mathematics can be hard to teach and even more difficult for students to understand. As teachers, it is important to provide students numerous explanations and examples of the specific content. Today we have been hearing that is important to incorporate pictures and manipulatives into our math lessons. Students have to have a lot of visuals to learn math. The Illuminations site is one resource that can help with this aspect. Teachers are able to use the site if they are having trouble representing and/or explaining a certain topic or lesson.

URL:  http://illuminations.nctm.org/

Google Sketch Up

            Google Sketch Up is a software that creates 3D models. This is a technology that can develop a student’s higher-order thinking skills and creativity. Sketch Up provides its users great tools for drawing 3D figures. This program can be used to explore different mathematical concepts involving 3D images. It is difficult to draw a 3D object on a sheet of paper. With Sketch Up teachers can show students a 3D image and explore the mathematical concept right on the program itself. If there is a Smart Board in the classroom, teachers can have students come up to the board and explore the 3D image. The software can be very useful in a math classroom for that main reason. In the past, teachers struggled with explaining 3D figures to their students. As a student, it was very hard for me to imagine a 3D image in my head and then having to figure out different mathematical operations on that figure. It would have been very useful to have a software, like Sketch Up, to help me visualize this better. If schools would incorporate the use of Sketch Up in their classrooms, higher-level math classes would benefit from it the most. I would not suggest having the software installed in elementary classrooms and even middle school classrooms. It would be more useful in a high school classroom. 

            Would Google Sketch Up be beneficial in any of your classrooms?

Using Technology to Instruct

            In the content area of mathematics it is important to grab the students’ attention the moment they walk into class. It is essential to start the class off with an engaging activity for them to work on or view. For example, the Khan Academy offers video tutorials for different math topics. Teachers can present these videos in the beginning of their class and then facilitate a discussion after the students have viewed it. These videos can grab the students’ attention and formulate a discussion for the lesson. Students can also ask questions about the video and use it as a resource to look back on if they are confused with the lesson at any point. If I use these videos as an attention grabber for my students daily, they will become accustomed to it and be prepared for my class every day. It will become a routine for them when learning new topics. The students can also have access to the videos at home by simply going to the URL site for the specific video. I can also give them the URL link in class so that they have it and have no reason not to use it as a resource. Students need to have as many resources and aids as possible, especially with math, because some concepts are difficult to understand by learning it one way. It is important to teach math lessons in different ways. The traditional way of teaching is by having the teacher lecture and writing notes on the board. However, nowadays the Khan Academy can serve as reinforcement to the lesson and can teach students differently.

            If something similar to the Khan Academy were available for your content area, would you use it in your classroom? I would love to hear your feedback!

Should iPads be allowed in Math classes??

            I have heard, recently, that some schools are providing iPads for their students in the classroom. Students are able to take notes on the iPads and use special software to enhance the lesson they are learning. Personally, I believe incorporating technology in the classroom is great because it keeps the students engaged in the lesson and it can be beneficial and helpful to some students who may need reinforcement of the lesson. With math, technology plays a big part in lesson planning, because we want to keep our students engaged as much as possible. In recent times, I have found that the easiest way to do this is to incorporate some form of technology into the lesson, or to use some form of manipulative.

            However, I would not necessarily choose the iPad as my first technology choice. Any form of computer will get students to be off track and they might explore other things that do not pertain to the lesson. Students in today’s society are very “tech-savvy” and can figure out how to get to certain websites that may be blocked. That is why I am against using iPads or computers in the classroom. On the other hand, if the teacher uses a program on his/her computer and projects it on the white board or smart board, then I believe that is appropriate. Students can still be involved in the lesson and be engaged in the activity, without having the accessibility to their own iPad or computer. They can go up to the smart board and play around with the program, again, without being tempted to search other things or get off task.

            I believe that the choice is ultimately up to the school district and its teachers on whether or not to bring iPads into their schools and classrooms. However, the teachers also have a choice on whether or not they wish to use that technology in their classroom. They need to trust their students to not tamper with the device and to use it according to the lesson. 

Collaboration Canvas

When I first read the task for the interactivity I thought it would be easy to remix the canvas, since I had already created my own. However, once I began working on the remix it became a little difficult. I could not understand some of the formatting things on the canvas itself. I also found it a little difficult to collaborate math with another content area’s unit plan. Once I reviewed a few of the canvases I was able to decide on one to remix and had a plan on how I would incorporate math into it.

The canvas I chose was the Earthquake unit plan. I first looked at the grade level it was aimed for so I knew what math standards I needed to incorporate. In this case, it was 8^th grade. I reviewed the standards and designed my remix canvas according to that. For my content area I added the idea of creating scatter plots and analyzing those graphs to determine slope and intercept. In my gallery I included photos of scatter plots so students can see examples. The video serves as another tool for students to refer to when creating their own scatter plot. I did not remove anything from the original content, because it all seemed valuable to keep with my content.

URL: http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2535&mode=view#network6

Virtual Math Class?

                I am sure you are all aware that some math classes are being taught online now. There are a few 100 level math classes here at Montclair State University that are taught completely online. I have researched some other schools to see if they do the same thing and one professor actually taught a discrete math course designed for secondary math teachers online. She was a little nervous at first, because she had never taught this class before, let alone online. She had to decide on a textbook to use, how to collect/grade homework assignments, organizing class time, and technical preparation. She also learned that online classes are taught in two different ways. Synchronous technology allows the students and teacher to be online at the same time and interact with each other. Asynchronous technology allows the students and teacher to interact at other times. She decided that her class would have two hours a week of synchronous class time and the rest would be asynchronous. What she did for the synchronous class time was send her students a PowerPoint presentation so they could write on the slides during the class time. At the end of her journal she gives advice to teachers who are about to teach an online class for the first time. The most important thing to remember is that an online class is different than a traditional class. Teachers should get some training with the software and hardware and they should get to know their technical support. Finally, she reminds teachers to have fun with it.  

            Personally, I would not like to take a math class online. I need face-to-face interaction with my teacher to fully understand the material. However, I think that online classes might work for lower level/basic math classes, where face-to-face interaction is not necessarily important. Students should have the option of taking their math class online or in a traditional classroom. Every student is different and learns differently, so by having this option it gives them an opportunity to learn the material in a way they feel comfortable with and that will be beneficial to them. What do you think? 

Unit Plan Canvas

Creating the canvas was a little challenging for me as I have never used the “play” website before. However, creating the canvas is very self-explanatory after looking around the different widgets on the side bar. It is a great way to lay out a unit plan, because it identifies each section well. Students and other colleagues would be able to understand how the unit is going to be planned out by looking at each widget and noticing what is going to be taught and how it will be taught. 

The unit I chose for this assignment is 8^th grade statistics and probability. The lesson I had used in Interactivity #3 touched base on functions as well as statistics and probability. However, for this unit I decided to focus on statistics and probability. I find this topic interesting because students can relate it to their own lives. There are many examples that we, as math teachers, can bring into the classroom and use as a resource to explain this unit. Students are not only learning the different concepts of finding probability but can use it in their own lives outside of the classroom.

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2183&mode=view#network6

Different Forms of Technology Used in a Math Classroom

                When teachers hear that they have to use technology in their classroom they sometimes begin to worry if they are unfamiliar with technology, or simply not technology savvy. I, for one, would be classified as one of those people. However, using technology in a math classroom does not have to go into such great detail. There are a variety of computer software programs that can help students learn math and also help them present their information better with representations such as graphs and charts. Students nowadays are knowledgeable of the software that is available to them on the computers. It takes them less time to figure software out then it would take me, for example.

            There are geometry drawing programs available on computers that can be used to make and verify the relationship between the number of sides of a polygon and the sum of the interior angles. Students can also use the program to verify their own arguments or relationships of different geometric topics. Spreadsheets can also be used to generate patterns from formulas. Students can use them to verify or disprove their predications. Students can also use the spreadsheets to learn how to write formulas in different forms. Word processing and presentation programs, such as PowerPoint, can be helpful tools that students can use for presentations. They can use the word processing document to write reports and present their results from their mathematical investigations. Teachers can also have students imbed spreadsheets, graphs, and equations in their documents to further explain their findings. Students can use PowerPoint to make presentations to their peers in the class.

            Overall, using technology in a math classroom does not have to involve intricate tools, such as a smart board or other advanced tools. These computer software programs are tools that provide concrete ways for students to explore abstract concepts, enhance success for visual learners, promote higher-order thinking skills, and deepens understanding.

The Use of YouTube in Math Class

            Many people may think that YouTube is only used for entertainment purposes or for people to post funny videos on. However, that is not the case. In an article that I recently read, a teacher used YouTube videos in her classroom to enhance her lessons or to simply engage her students in the lesson of the day. For example, she used a video on YouTube to introduce a lesson on the Pythagorean Theorem, which helped her hook the students’ attention. She found that not all the videos she showed interested her students. In fact, the student found some videos to be boring. In turn, she took their complaints as an opportunity to challenge her students to create their own video. The assignment was for the students to make their own video illustrating the math they found boring from the YouTube video. She believed this would allow the students to show their creativity and use technology in an appropriate manner. As a result of this assignment she was able to assess her students’ understanding of the topics they chose and determine what areas they may have a weakness.

            I never thought about using this form of technology in my classroom. As a college student I have used YouTube videos to study for exams when I was unfamiliar with the math topic or needed a further explanation. However, I did not realize how many mathematical videos there are on YouTube that can reinforce a lesson for students or help teachers engage their students in the lesson. After reading this article I will definitely take this idea into consideration for my future classroom. I think that this is a great way to get students excited about math and have them express their creativity and reasoning behind their concept of the topic. This is also a good way to encourage group work and have students explore a different form of education. 

"Technology & Pedagogy"

I chose this particular lesson plan because I wanted to learn how to incorporate real life situations into lessons that I will be teaching, which is sometimes difficult to do in mathematics.

The curriculum goals, teaching strategies, and technologies used in this lesson, for the most part, are in complete alignment. The Activity Packet provided outlines the curriculum goals perfectly. Each step provides specific directions that students need to do in order to move on to the next step. The only thing I would say that is not in alignment is the teaching strategies used. For the most part, all of them are efficient in explaining the lesson and providing a demonstration to show an example of part of the experiment. To create the scatterplot all the students have to do is enter the data and then the excel program can create a graph. In order for teachers to determine if the students understand the concept of graphing a scatterplot, it might have been a good idea to give another set of data (already completed) and have them create a scatterplot themselves on graph paper.

The excel spreadsheet is essential to achieving the curriculum goals, because the software can create a scatterplot based on the data that the students input. I would have liked to read that students present their group work via the smart board or a document camera. Allowing group presentations would incorporate the use of the smart board and/or document camera which would have given students the opportunity to express their reasoning behind their thought process during the experiment.  

URL: https://docs.google.com/spreadsheet/ccc?key=0Agvr5L6t2qQGdGJGYzUwQk52R2Vad2lxS09JNlptN1E&usp=sharing

Smartboards in Mathematics

            What really is a smart board? Why did they give it such a name? What is meant by the term “smart”? These are questions that cross my mind when someone mentions a smart board. During elementary and middle school all we had in math class was a chalkboard that later on was replaced by a white board. It was not until high school that smart boards were coming into the classroom and teachers were beginning to use it. At first, I thought it was a replacement for a projector. However, once the teacher began using it daily I understood what purpose it served. For one, I think that smart boards save valuable lesson time, especially in math class, because teachers do not have to write notes on the board, necessarily, and can use that time using the smart board. It is an alternative way to giving notes, for example, because we can just have the notes already up on the projector for students when they walk into class. It also serves as an interactive way of learning for the students. As teachers, I think that we have to give students more of an opportunity to explain their reasoning and understanding rather than giving them all of the information. One way for this to happen is to have students come up and use the smart board to show their peers their method of doing a particular problem.

            However, are smart boards really that effective? Are students engaging more today with the smart boards then they did ten years ago with the chalkboard or white board? As Michael Staton says in an article titled “Why Smartboards are a Dumb Initiative”, “They [smartboards] are just the least cost-effective way to improve learning” (http://theinnovativeeducator.blogspot.com/2010/05/why-smartboards-are-dumb-initiative.html). He also points out that teachers believe it is the only way to save time from writing notes on the board. However, you can do this in numerous ways that do not include a smart board. He mentions they can use a projector, screen shot something, or use Microsoft OneNote. He does not mention any information on whether students were engaged more with the smart boards or with regular chalkboard/white board. However, after reading his argument he raises some good points that I wish to explore and gather more information about. 

Techniques to Teaching Math Using Technology

            As I was deciding on what my topic would be for this blog-post I was researching different techniques of teaching math to students using technology. I came across an article that had different ways of teaching math lessons using different forms of technology. The first tip it gave was to send weekly extensions of the math curriculum via text messages to students. When I initially read this sentence it alarmed me, because it meant that I would have all my students’ cell phone numbers and they would have mine as well. I did not know how comfortable I would feel doing that, since nowadays you hear so much about inappropriate student-teacher relationships. However, when I continued reading it gave an alternative to the text messages, which was to do it through emails. I do not see this as being a big issue, since emails are so common and it does not involve having everyone’s cell phone numbers.

            The article then began to mention how to teach certain lessons using technology. The first lesson was teaching angles. A fun way to teach this would be to set up a scavenger hunt for the students and give them disposable cameras to take pictures of their answers. I thought this was a fun idea, because it is a different approach to the standard form of teaching and it gets the students engaged in a fun activity. It then mentioned teaching multiplication tables using an interactive whiteboard. It stated that students would have the opportunity to come up and group different shapes to show a multiplication problem. Again, this seems like a good idea because it takes away from having the teacher do all the teaching, and gives students the opportunity to explore new concepts and help their fellow peers. This also gets younger kids interested in math, and it can make it more fun for them because they are able to interact with their math problems. The students will see the concept not as a new math technique, but rather a game. 

"History of Technology in Mathematics"

The invention of the Scantron eliminated the hassle of grading multiple choice exams.

Teaching Style

            I am currently taking Teaching for Learning 1 course, which I am sure most, if not all of you, are taking as well. As part of our assignment for this week we had to read a chapter in our textbook entitled, “A Resource Guide for Teaching K-12”. In that chapter the author talked about the two main teaching styles and how they are different. The two contrasting styles are the traditional style and the facilitating style. The text went on to say that in today’s schools teachers must use aspects from each, but with a stronger inclination toward the facilitating style. I found this interesting and wanted to share my views on this, as well as get your opinions on what teaching style you might want to incorporate in your future classrooms.

            I personally, agree with the text, in that it is important to teach more in the facilitating style with a little emphasis on the traditional. Students in our classroom may have been taught the traditional way by other teachers and may not be familiar with the facilitating style. The text also says that a teaching style is determined on the teacher’s personal characteristics, experiences, and knowledge of research findings on how people learn. This is a very valid point, because most traditional teachers are not familiar with the new findings on how students learn nowadays. For example, a lot of classrooms have smart boards and teachers are incorporating technology into their lesson plans. In the traditional classroom you would not find that. You would see a teacher at the front of class lecturing and instructing the students to take notes and memorize things for tests. However, today, teachers are encouraging group work, peer learning/teaching, and are less the instructor and more of a guide to the students. I find that this is more effective for students to better understand the material and engage more in the classroom.

            In my future classroom I intend on incorporating both teaching styles in my lesson plans. I think it is important to try new ways of teaching and see what works and what does not work for the students. It is also a good way to get feedback from students on what works for them and what difficulties they might have with others. The traditional teaching style will always serve as that “crutch” for us teachers, in that we always have it to fall back on if our new style does not work. However, as we continue to learn new things each day I believe the traditional teaching style will become a thing in the past.

I would enjoy hearing what your thoughts are on the contrasting teaching styles and how you plan on incorporating technology in your classroom, if you intend to do so.

"Technology Autobiography"

            The three most influential communications technologies in my life are my cell phone, social networking, and emails. These have shaped my life for the better and worse. By having my cell phone always with me makes it easier to get in contact with someone, especially in the case of an emergency. It is also a very fast way of communication, because it is quick and easy to pick up the phone and text someone or give someone a call. I look to social networking when I am trying to find things out right away, because I know the information provided is always fast and up-to-date information. Emails also serve as another way to communicate with people quickly. I find that if a person does not feel comfortable dealing with conflict face-to-face they can simply deal with the problem via email. It has also played a major role in communication between professors and students. In the past, the only way students were able to get their questions answered was either in class or during their professor’s office hours. Now that email has come into play students are getting their questions answered quicker because they can now simply send their professor an email and get a response within 24 hours, typically.

            These communications have also shaped my life for the worse. I tend to notice that my cell phone causes me to be distracted. In classes I can tell that students are distracted or lose focus because they are paying more attention to the text message they just received. Social networking is not necessarily always exciting and a great thing to look at. People do not realize that employers, professors, etc. can see their profiles and they might have inappropriate pictures or posts that may get them in trouble. Recently, social networking has caused bullying to occur which has led to people committing suicide. People may not be aware of how strongly their posts, pictures, etc. can affect someone’s life until it is too late. Emails can be interpreted the wrong way, depending on the situation. I find that it is better to approach a conflict face-to-face so no one’s words are taken the wrong way.

            The technologies have impacted the ways in which I learn new information. The easiest and fastest way I tend to find up-to-date information is with social media. If I need or want to see how one of my friends is doing I will look at their Facebook page or Twitter before I text or call them. With that being said, I rely on text messages to “check in” with family and friends instead of picking up the phone and having a conversation the “old fashioned way”. Nowadays, people do not even communicate verbally over the phone. They rather find out how they are doing by texting them. Even if the information on social media may be wrong or misleading, I still find myself believing the information because it is my first source of knowledge. Later on, if I read something else and I find out that the original information was wrong then I will agree with the second source.

            There are some similarities and differences between my uses of the three technologies compared to those among the young people in the video. We both agreed that we use technology mainly for social purposes, such as cell phones and social media. We both said that the main reason why people are connected to their phones is because they are constantly texting friends to find out different information. We both also agreed that we could not live without our laptops and/or phones. We would not know what to do if we lost our phone or could not connect to the internet.

            There were also some differences between my uses of technologies and those mentioned in the video. The people in the video expressed that they use technology for school projects, such as using there camera phone to take better pictures or making websites for their school. I, on the other hand, have never learned how to create a website or even explored different applications on a computer. The young people also said they experiment with technology, because experimenting with it is what makes it technology. Again, I am not tech-savvy and would not even be interested in experimenting with computers or any other technologies, because I would be afraid of messing things up or breaking things.