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/