Final Project

In my Google spreadsheet, I have supplied the strategies and technologies that will achieve the curriculum goals of the NJCCCS and the NETS-S. Together, this equation of strategies and technologies aid in the visual and cognitive understanding of these ninth grade Algebra students on the topic of Graphing Linear Equations and Functions.

Each lesson of the unit plan is introduced with a collaborative classroom discussion and/or group practice time. As the teacher, the discussions and all modeling will be done with a projector. I prefer to use the projector over a chalk board because copies of graph paper and various colors of markers benefit with accuracy and visual understanding—some students need several colors to differentiate between lines and “see” the process step by step.  

In the first two days, we use strategies that allow students to learn individually and cooperatively while accessing/reinforcing their understanding through the visuals provided by the Smart Board. In these two days, the students will investigate trends of coordinate points by using the Smart Board, which will help with accuracy, and Google Spreadsheets or Microsoft Excel, to easily and quickly compute the values of the x or y intercepts. Students need to have skills of applying background knowledge of the topic and usage of technology to create their matrix.

On the third day, the goal of the lesson is to create linear functions and find the slopes of them. After starting off with a group discussion, there is an independent practice that will act as a form of assessment to identify the skill and knowledge each student has. The independent practice is lead using the SmartPal where the teacher writes an equation or function on the board and asks each student to use the intercepts to make a quick sketch of the graph. The SmartPal allows for self-assessment by comparing results from peers. It also allows the teacher to quickly see which students are lagging behind and are in need of better instruction. The graphing calculator is then used to check responses for the more difficult functions.

On the fourth day, students will have enough practice to be able to analyze/identify characteristics of certain functions. With analysis comes critical thinking that will be produced by collaborative groups of students. Using the graphing calculator, students will be able to classify lines based on the direction of their slope and interpret these slopes as the rate of change in a real life situation. They are able to define purpose and gain an understanding of where linear functions are used. The lesson is ended with a summative assessment that is a quiz of all the topics covered in the lesson.

Day five compresses all previous knowledge and allows the class to make connections of all topics covered in the lesson previously. Students should be able to know the characteristics of linear functions, be able to put them in y-intercept form, and understand how to identify the slope by looking at the graph. Students are put into groups for cooperative learning where they are to interpret graphs visually to assess their visual understanding of graphs and to do so, they play a game called Algebra vs. Cockroaches. The game tests their understanding of the concepts but is also a fun motivation device that assesses speed and accuracy. This and the homework assignments count as a formative assessment.

The sixth day of the unit plan is reserved to solve systems of linear equations graphically and relate the solutions to real life problems. This makes the lesson authentic because students can relate prevalent world issues to the behavior of graphs. They are encouraged to think critically, make predictions, and interpret the behaviors through an interactivate exercise from shodor.org, and again study the behaviors from a KhanAcademy Graphing exercise. The seventh day of the unit plan was not included in my spreadsheet because it is a summative assessment—unit test where students are allowed to use their knowledge and calculators.

The formula, “Technologies ₊ Strategies = Standards” was very helpful when breaking down the unit plan. It allowed me to see the direct connection between the standards and technologies and visually understand that they are to act as a supporting factor to the unit plan and not as a forced add-on. It is important to keep that in mind because often times, forcing technologies into instruction causes a distraction where the teacher becomes the subordinate of the technology and the curriculum is jeopardized. By properly incorporating the technologies and associated strategies, both the student and teacher are able to achieve the core curriculum standards and NETS and smoothly sail through the unit. 

Learning New Things

I have to admit, this course has introduced me to many new technologies that will amplify my lessons when I become a teacher. I have found sources that offer online tutorials of new technologies and files for me to use in the classroom.

The best technology is definitely Google Documents. I had no idea about it before I took the course and now I use it for all my papers. I even wrote an academic math paper on it for my Advanced Calculus II class. It is quite amazing and I find it easier and more accessible than Microsoft Word. All the Greek symbols are conveniently placed so there is no searching for them, unlike in Microsoft Word where one needs to use codes to find the proper symbol.

And it is free! We all know how costly it is when buying a new computer to also have to purchase programs. Google Documents saves every file so one does not need to worry about losing them.

However, I found a flaw. When I finished my academic paper for math, I tried to print it but encountered a problem where Google Docs had to convert the file to a PDF before printing. It did, but all the symbols were converted into question marks and the format of the paper was changed.

So, maybe there are still bugs in the programming but I am sure it will be fixed soon. This is just a minor setback. Google Documents has many other tools and I am glad I got the chance to explore with it.

I will definitely find use of it in my classroom and ask my students to use it for projects and assignments.

Another technology I recently explored was in my Selected Topics for Modern Mathematics class where we used socrative.com. This program is specifically designed for a classroom where all students have iPhones or iTouches. The teacher is able to create assessments and have students work through the assessments individually through their device. It was interesting using it in class and it had benefits such as providing the teacher with accurate feedback as to each student’s response. The student can even communicate with the teacher and tell him that he does not understand the material well—this is important because many students are too shy to blurt out that they need help from the teacher. It is a subtle way of communicating.

But with the good, there comes a bad. I honestly have to criticize this use of technology for a simple assessment. We cannot guarantee every student has an up-to-date iPhone that they can use in class. Also, there was a tremendous amount to time that was wasted for everyone to log on and set up the program. Then we needed everyone to complete one question then move to the other, some students could not connect to the internet, we had to follow a certain format to inputting the correct answers, etc.

So it is important that we pick and choose the technology we bring into our classroom to support the lesson and methods of learning. We cannot put technology into the plan only because we are told we have to. 

Technology and Teacher-Student Interaction

With students being able to use the computer or any other technological invention in the classroom, is the time between teacher and student interaction decreasing? What potential problems will this cause?

Some administrators and parents are concerned that “teaching across computers might decrease the frequency of one-to-one student-teacher communication or increase the amount of time that teachers spend on their workstation.”

However, this fear has been decreased by research that says that the technology enhances the interaction with students and teachers. There was an increase in the amount of factual information that was given to the students who were able to remember it easier through visuals.

“Beyond the widely expected benefits of computer-based education-increased student-to-student collaboration, learning of computer-specific skills, expended research avenues, and enhanced critical thinking opportunities-the utilization of technology can lead to improved interactivity and create more student-centered environments.”

I personally believe that the teacher and student interaction will be enhanced with new technologies because there would be a clearer focus on what the goals of the lesson are. There will be better organization and class time will not be wasted on off track topics. If we are worried about students being distracted when using the technology, we have software to monitor the students and make sure they are on track.

For example, Vision is a classroom management technology that allows the teacher to spend more time on the lesson and eliminate distractions.

“Vision classroom computer management lets you make the most of your time when integrating technology in the classroom. it gives you the tools you need to control sources of distraction, monitor student computers, get started without lost transition time and notice as soon as someone needs your help.”

The best thing that I like about it is that Vision enables teachers to have direct communication with their students and allow more one-to-one attention.

My Sources:

http://www.netop.com/fileadmin/netop/resources/products/education/vision/whitepapers/Vision6_Whitepaper_Classroom%20Management_EN_Print_NRB.pdf

http://www.netop.com/classroom-management-software/products/netop-vision

Mathematics Toolchest

I have been following this blogger for a few weeks now. He is a Mathematics professor at the University of Washington. 

He defends the use of technology in school and in the mathematics classroom and makes some very intelligent points. 

This stood out to me the most: 

“To me, mathematics is about solving problems by understanding them more deeply, finding ways to explore them, finding elegant proofs, looking for ways to visualize and compute with deep structure, etc. Math software is simply another tool or technique that one can use to massively enhance one’s ability to solve mathematical problems. Asking whether or not to use computer technology in mathematics is no different than asking whether or not to use “logical reasoning” or “linear algebra” or any other major tool in the mathematician’s tool chest.” 


And he is correct! Technology is used as a way of enhancing learning, not cutting corners to find the answers. It is used to visualize, to understand, and to explore. 

His next great point brought up Carl Gauss, who is known as a mathematical genius since he was a child. 



“Gauss spent years counting the 216816 primes up to 3 million…and wrote in a letter in 1849 that there are 216745 such primes. Any undergrad can type ‘pi(3*10^6)’ into Sage and get the right answer instantly.” 


Why must we waste time on what is already proven? Using technology accelerates the time spent on problems and simultaneously provokes new ideas. In mathematics, there are things that are impossible (because it takes too much time or is just too straining on the mind to solve.) If we are provided the technology, why not use it? We are not here to re-do what too years for many amazing mathematicians to do, our purpose is to expand on what they did and create more. 



Check out his blog! 

http://sagemath.blogspot.com/2009/04/technology-in-mathematics-education.html

Interactivity #5

I contacted a tenured High School Mathematics teacher from North Bergen High School, an urban school in North Bergen, New Jersey. He teaches Algebra and Geometry classes (9-12 Grades).

He was not familiar with NETS-S and NETS-T so I told him it constructs a pathway for the future digital age by implementing technology and digital resources in classrooms. Hearing this he said, “Technology is important to be integrated into a high school mathematics classroom--it’s used at least 75% of the time and I often encourage students to use graphing calculators and software in lessons and projects. The school receives some government funding so we are able to provide calculators to only higher level classes (Calculus, Pre-Calculus, Algebra II).”
However, after reading the standards from NETS-S, he was unsure if his usage of technology fulfills the standards and his curiosity led him to ask fellow colleagues if they were implementing NETS-S in their classroom.

According to him, the district of North Bergen has begun to implement the NETS-S but not all teachers have been informed about the standards that correlate with them. He mentioned that it is a slow process where there is a plan to create a team of teachers who will be responsible for working with subject-area teachers to coordinate the lesson plans with supporting technologies. His assumption as to why the process is slow is that it is difficult to provide equal technology use to all classrooms because of funding and infrastructure design--the classrooms are ill-equipped with modern capabilities.

I was not surprised by the teacher’s lack of exposure to the NET-S standards. It would be hard for the district to notify teachers about new standards when it takes years and infrastructure changes to implement. In his mathematics classroom, the usage of technology increases student productivity and accelerates the lesson but he finds that there is a lack of application exercises that will spur the logical growth of students as a community, what the NETS-S wants to promote. He suggested what is needed is a guide to teachers and administrators as to how they can properly support lessons by adding technology to the plan. These guidelines should include the entire school community, administrators and teachers, so they can provide the correct funding and training seminars.

I’ve learnt the main idea of the revised, 2007 NETS-S, is not the use of technology, but the action of using it as a tool to learn and develop. This is a big difference in what we have in most schools where technology is used as a source to provide visualizations and supplemental exercises but not promoted as a tool to help improve skills and understanding. I will promote the usage of NETS-s in my school and speak to others about it because it focuses on the individual responsibilities of teachers and students. In my mathematics classroom, technology will be used as a fun and innovative tool that will aid in student’s motivation and understanding individually and as a community.

https://docs.google.com/spreadsheet/ccc?key=0Alw0ASiqVJO_dDJpNzNLdS12Q2c3cC1vajVXZXEzWnc#gid=0 

Private Investigator

I want to start off with a quote: 

"... technology is a valuable tool in the teaching and learning of mathematics, for it has the ability to empower mathematics students as well as mathematics instructors. What better way to empower students than to provide them with their own private investigator, one which will work day and night at the request of the mathematics student who holds power over it, willing to perform tasks repeatedly, however mundane!"

I chose this quote because technology can be seen as a personal private investigator where students are able to explore mathematical concepts and develop a purpose in solving problems and finding new methods to do so.

This website provides an analysis of what and how technology is used as an aid in mathematics skill development, problem solving, reasoning, and communication. As simple as it seems, the website illuminates the beauty of technology to young explorers who yearn for a better understanding of mathematics. It allows them to visualize and apply knowledge to grow new ones.

http://frank.mtsu.edu/~itconf/papers96/kimmins.html

It truly is "Powerful"

I know many people who grow up hating math simply because think they do not understand it—they have given up and because they gave up at such a young age, it is ingrained in their head that math is difficult and that they will never understand it. We know that there is a need to express math in a more concrete manner where students can visualize and connect the steps of problems one at a time. They need help retaining the steps and understanding the concepts to move on. I strive to become a mathematics teacher to change the way mathematics is taught and perceived. 

It has become easier to teach and learn with new technologies like the Smartboard, online programs, and Geometer’s Sketchpad, where students get a clear-cut visual of the processes they must take to accurately work out these math problems. According to the article, "The students have better and sounder knowledge of the concepts of mathematics. The animations are so powerful; bisecting an angle becomes a really visual experience." Math has become more fun and innovative because student’s are able to experiment and explore with these technologies.

Teachers are given power. This power will open the mind of our students and change their “math is hard” mindset to “math is fun.” We must make good use of what is available to us and our students.

Article: "Technology adds to students' math comprehension"

http://www.eschoolnews.com/2010/03/17/technology-adds-to-students-math-comprehension/

Interactivity #4

The construction of Box-Plots is an important topic in higher level High School mathematics. I chose this lesson because it fulfilled some common core standards for Statistics and made use of online technology. However, I feel that there are some technologies that are more beneficial to teachers and students that could have been implemented into this lesson plan. 

The original curriculum goal is to introduce the topic of graphically representing data through box-plots and using quartiles. Yet, it seemed to focus more on the study of pre-constructed box-plots rather than emphasizing student interaction with them, creating a gap in the curriculum goal itself, teaching strategy implemented, and need for technology. Although there was a project where the students would gather data and eventually construct their own boxplot, student’s ability to recognize one and construct one would be flawed; the students must be able to notice the purpose and effects of different types of data on the box-plot before they are able to construct their own. 

Therefore, they can accomplish this better understanding with the new introduction of interactive technology I provided. The students are able to organize and preserve their data more efficiently through a Google Spreadsheet and input their data in a TI-83 calculator, which is easier to use and more accessible that a computer-generated activity page. To improve the teacher’s method of providing or modeling examples (instead of giving the students online pictures of pre-constructed box-plots) I will use a Smartboard to allow the students to see how manipulating data can skew the box-plot. By interacting with data, students will be able to retain the knowledge and purpose they discovered. 

Lesson Plan:

https://docs.google.com/spreadsheet/ccc?key=0Alw0ASiqVJO_dDJpNzNLdS12Q2c3cC1vajVXZXEzWnc#gid=0 

Computerized Standardized Tests..Will Make Successful Students?

Testing methods and systems are continuously changing and now we await the major change of computerized standardized testing. The article states, “the tests should be more connected to the kinds of classroom activities teachers find valuable, rather than requiring so much separate test-prep time.” Maybe this will promote a more hands-on education that I believe is well needed in classrooms of today (I also find this statement contradictory to previous “suggested methods of teaching” that emphasized rote memorization and repetition for success in these standardized tests). But having the opportunity to enable students to learn real world applications of mathematics and other subjects is golden and will be a major benefit to the American education system. In these new computerized standardized tests, there is a plan to implement, other than multiple choice questions, student’s skills in media, technology, speaking, and math to real-world problems.  For example, “Students might be asked, for instance, to design a park on a plot of land, using geometry to fit in the playing fields and financial literacy to create a budget.” It is a great concept to gear students up for future and independent and advanced learning.

However, some students just aren’t good test takers as it is. It is different working off of a computer—the constant typing and clicking noise is sure to continuously breaking one’s concentration. It’s just my opinion and there are tons of questions we can bring up along with positive and negative consequences that come to mind. I am sure that not all students in America are able to use a computer and become educated in using it. One needs a lot of experience to manipulate software well. What about bugs and glitches? How can we compensate if the software fails and old computers break down? I really hope the switch to computerized testing works out well because the future of our children is at stake.

Try reading the article here: 

http://www.csmonitor.com/USA/Education/2010/0902/Race-to-the-Top-promises-new-era-of-standardized-testing

I find it interesting. Even the Praxis II Tests are becoming computerized. I can say from experience, I have taken a few computerized tests and I cannot immediately pinpoint the reason why, but I find myself doing poorly. The environment is difficult to get adjusted to and concentrate. Looking at the computer screen makes my eyes hurt and tired, especially when it is too bright or the color patterns and contrast do not coordinate well. 

Do any of you have similar feelings when taking computerized tests? Or, what are your opinions of the changes? 

Technology Integration, Personal Experiences, and Cats!

Well, maybe just a picture of a cartoon cat, but I just found this website that I think will be very beneficial to us as future teachers. It provides hundreds of types of technology we can integrate in the classroom with details on how they can be used and what grade levels it will benefit most. Everything is here--software reviews, games for our students, projects, tutorials, etc. It is also beneficial to the older generation of teachers who must integrate technology into their classroom but first need to learn how to. It provides a purpose to using the technology and step by step directions on how to use it. You cannot go wrong. I wish I found this site to add to interactivity #3, but I am sure I'll be referring back to it later.

The tab that I found most beneficial is the "New Teachers" tab that provides articles and advice for new teachers, diaries of other first year teachers, and many opportunities to virtually experience a classroom.

Check it out and I hope you will also use it in the future.

http://www.educationworld.com/a_tech/gadget/gadget035.shtml

Personal Reflection: Interactivity #3

This collaborative project was a great exploration exercise of the many technologies available to teachers. I started my search and was overwhelmed at the amount of information I was able to find that kept pouring out at me one after the other. The group was able to generate an authentic list of many beneficial technologies but it is nowhere near complete as there are thousands left out there that we need to bring notice to. It was also great for us to collaborate because we are able to put our own view on what we thought was most beneficial to the classroom and our students.

More than just finding links and fancy names, I was able to understand how accessible and easy to use these technologies are. As a teacher, we are provided with step by step instructions and lesson plans to support our teaching along with additional resources so the students can explore on their own. There are fun games and software students can interact with and learn while building up their curiosity through modeling—a change from continuous direct instruction. I can see how some of these technologies can be used in the CURR 314 class as we are discussing different types of assessments and what will constitute a balanced assessment. For example, many of the virtual activities such as using software to create and learn can be used as a formative assessment.

Seeing all the great technologies available and easily accessible to teachers, I will definitely save the spreadsheet and refer back to it when I am ready to teach. As I learned from my Read 411 professor, teaching must be cognizant with the changing nature of technology along with other factors of the environment. This way, both teachers and students will continue to be effective.

Are Students Mastering Skill or Technology?

Technology in a math classroom can be fun, innovative, and helpful to students because it allows them to merge their creativity with topics that are usually categorized as “tricky” or “difficult” and requires a lot of skill. So we provide this technology hoping it will bridge the gap for the majority of students. Sometimes we hope it will help them visualize and analyze problems better than direct instruction and teacher modeling. The students along with the teacher are learners when it comes to the new technology where they are both learning to master it at the same time and depending on the knowledge of the teacher with the technology, learning how to use is can become an easy routine or a struggle. Either way, there are a lot of benefits. But here is an interesting situation I found while conducting some research.

Quote from a paper by E. Paul Goldenberg:

“But empowerment requires control. If students were not

masters of the old tools, it is no favor to give them new

tools that they also do not master. Sometimes students

do know enough algebra to solve a problem but still fail

to use that knowledge because they lack the fluency or

    experience to use it effectively and confidently in problem 

    solving. The same applies to electronic tools. Learning just 

 enough about a spreadsheet to solve a particular class of 

        problems and then moving on or learning a few construction 

         tools on geometry software to illustrate a particular collection 

  of geometrical facts, and then moving on leaves students 

   limping users of the tools, not experts who could whip out 

        the tool as needed to help reason about and solve a problem.”

I find this rather interesting and it might just hold a lot of truth. Yes, the child is getting a different perspective on how to problem solve or visualize shapes, but does mastering the technology mean he is mastering the material?

I guess it is another two-sided argument that can easily go either way. This is just something to consider when in a classroom and debating whether you, as a teacher, should spend 3 days teaching students how to use technology and mastering it instead of giving supplemental modeling and formalized assessments to teach them from the textbook.

If you want to read the whole article, it is here:

http://www2.edc.org/mcc/pdf/iss_tech.pdf

Free Online Lectures

This is a great website where lecturers are able to post course videos for anyone to view! These professors are from Harvard, MIT, Yale, and many more big names. This is another great example of communication technology that is very helpful to High School and University students. It is always nice to have additional resources when going through these difficult courses. Being a Math major, I searched through the math section where most topics are listed with at least ten videos per topic. The videos are separated by topic so it is easy for a student to find a video relating to the topic he seeks. Searching Google or YouTube are also helpful but I find it to be time consuming since everything on the internet is not always directed towards education. Often I find myself browsing through over 10 websites and still not being able to get the extra help I want.

This is convenient to provide students in a higher level classroom because supplemental thoughts and notes are always helpful. Everything is made easily accessible so it only takes a few steps to find what you want.

But here is the link. 

http://academicearth.org/subjects/

Check it out whenever you are in need of additional help in whatever topic you want. 

Interactivity # 2

"Competition+Struggle=Innovation

The cause for America's jolt in math education"

Scribner, Campbell. "Sputnik Mania! ." History and America's Schools. Wordpress, 06 02 2011. Web. 12 Feb. 2012. 

http://misterscribner.wordpress.com/2011/02/06/sputnik-mania/ 

The Hierarchy of Digital Distractions

I just found this and it is pretty interesting. Take a moment and digest this. (You might need to go to the link to see it better).

It shows how distracting technology is and at the top of the pyramid, is "Device Failure" while "Any kind of actual work" lays at the bottom of the pyramid. It is evident, at least in my life, that if any physical technology I own breaks down, I devote all my time to fixing it and this problem becomes most important to me. Now thinking about my problems with technology made me reflect on the numerous classrooms I have entered and the teacher had to postpone or delay a lesson because he could not get the technology to work correctly. Introducing so much technology in the classroom is bound to cause more delays if people misuse them or it just simply does not work. 

http://www.informationisbeautiful.net/visualizations/the-hierarchy-of-digital-distractions/

Interactivity 1

            The introduction of technology in my life had a slow start when I first came to the country. However, with this recent wave of new technology popping up here and there—iPhone/iPad, e-reader, laptop, game consul, how can I not get in on it? We are the generation that relies most on technology, it has become a way of life and the way of the future—it is a necessity in schools and in the workforce as everything is now computerized. Regardless of what initiative one has with this technology, it serves as an opportunity for self-improvement by being a way to express thoughts quicker and more efficiently, exploration of a new and developing world, and improvement of self-image.

The internet is the best form of communication even if it is not used in direct contact with another physical being. It is a transfer of knowledge—a place to learn and develop one’s self. Development starts with a desire and curiosity to know. The internet is an endless pool of thoughts and knowledge where one is able to explore and receive a response almost instantly.

My top three communication technologies are the iPhone, Youtube, and, Social Networks. Forget about texting, the iPhone puts the world at your fingertips. Everything is easily accessible through a few touches of the screen. It has become essential in my life where I use it for alarms, music, research, games, blogging—just about anything you can think of. Youtube allows users from almost anywhere in the planet to upload videos for the world to see. It provides a chance to learn and explore other countries and cultures without stepping outside. It is a medium for education as a student can easily search instructional videos and lectures. In my classroom, I would recommend students to seek the help of YouTube as a source of supplemental explanations for even I, as a student, am currently using it to assist my understanding of math problems. I don’t socialize much on the internet but Social Networks (like Facebook and MySpace) are a good place to meet with other people. I remember when I was Olivia’s age, I also had a Myspace. I customized my page every few weeks, I would learn how to search for images I wanted, and tweak codes to get specific font colors. These minor things added up when I was put into a computer science classroom and was able to recognize symbols of basic coding and formats.

            All these benefits sound amazing and will help a student explore and work on his creativity. However, these sources produce potential dangers and massive sources of distraction. Going back to the video with Olivia, she spends about five hours a day online customizing her Myspace account or chatting with friends. How is there time to do homework or recreational activities? It is fun to be creative customizing MySpace pages, but can they be as creative with writing assignments? Children no longer know how to put their creativity on paper because it is made easy to take an idea off another website. She, along with some of the other students from High Tech High said texting was very important to them and they could not put the phone down.

            Because of texting, students do not need to physically speak to each other and as Olivia’s Big Sister says, “I have learned to shorten about every word in the English language to three letters and/or numbers.” This way of writing is sticking with students who can longer produce complete sentences or fully spell a word.  

            Technology is the way of the future so taking one step forward, we must find a way to include more educational material into the world of discovery our students revolve around.