Online Gradebooks

With technology becoming more and more dominating in our society, online gradebooks is becoming very popular.  There are many benefits to using the online gradebook, especially for the parents.  Teachers are able to use these online gradebook for many things, including posting grades and notifying of due dates.  If a student was absent when the assessment was given, and needs to make up the test it cannot be handed back to the rest of the class until this student takes the test. Which is a benefit of the online grading towards the students, the students that took the test can see online if the grades were posted. 

When using online gradebooks students and their parents are also informed of the progress, or decline in grades, throughout the marking period.  The students’ grade at the marking period would be less of a discrepancy of a false grade because all of the grades have been posted for the course.  I also believe that the online grading allows students to be held a little more responsible for the grades they are earning.  By having a student’s grades posted, which can be frequently checked, the student will know at all times how they are doing.  If a student looks at their grades and notices that they are not doing well, they are responsible to do what is necessary to raise their grade.  Simply, I think the excuse of “I didn’t know I was doing bad” will be eliminated.

Online Math Games!

It seems to be that many students think that if anything involves math, it is not going to be fun, especially, how can a math game be fun?  I think it is important to realize that the way we, as teachers, are presenting the content area to our students really affects their outlook on the subject.  Playing a game intrigues a student’s interest because it is not a method that is used to teach them often.  Games are a great way for students to actively participate in a review of material.  Online there are many games that students can play that require using their math skills.  One of the websites that I particularly like is www.math-play.com.  There is a huge variety of games to select from and very well organized.  I also like that this website provides games that are more than one player which will incorporate the students having peer interaction while using the technology in class and reviewing the content being taught.  I wish when I was being taught math throughout school, I was able to use online games as an interesting way to review instead of a lecture.  

Khan Academy

After many years of explaining math problems to my close friends and family, I came across a great study tool when I was personally challenged while studying, Khan Academy.  Khan Academy is a free website that provides instructional videos in a variety of subjects.  I found this to be especially helpful however with mathematics.  While learning new math content that is difficult to understand for the first time, using Khan Academy to reinforce the content could clarify one’s confusion. A teacher could incorporate Khan Academy into the classroom for students to use while doing homework or studying outside of school.  This website can be very beneficial if a student is experiencing confusion on a concept while trying to complete the assignment.  By introducing this tool to students they will be able to be held responsible for their own learning.  Not only can this website be introduced to students, but also to the parents and guardians of the students.  This tool can be useful for parents that are assisting their children with assignments, but do not have the best understanding of the topic.  It is essential for someone to be educated if they are helping educate others.  Over all I think Khan Academy is a great online source for learners to use.  The website provides the videos that explain subject content in different ways.  The only requirement in order to watch these videos is to sign up for a free membership.  This subscription cannot be beat!

Technology Integration Plan

The smart board was the first technology that came to mind when thinking about popular uses of technology in the classroom.  The smart board raises the potential of the classroom transforming into an interactive community.  While teaching an introductory lesson on probability to 9^thgraders, I would use the smart board along with other technology to transform the lesson plan.  I used this lesson in Educating English Language Learners and made adaptations to support and English Language Learner.  At the end of the entry you will find a link to the matrix that identifies the standards, strategies, and technologies incorporated with this lesson. 

To begin the lesson, the teacher will introduce an activity with a demonstration of the game ‘Rock, Paper, Scissors’.  The students will then, with a partner, play 18 rounds of the game.  They are to record the results of each game on a distributed worksheet that will keep their results organized.  The information they are acquiring will be used later on in the activity when comparing the results of each pair.  For this portion of the lesson, the students will be using the smart board as a visual representation while the teacher is introducing the activity.  The worksheet that will be handed out to the students will be a table where the students will record the moves that were made in each game and the winner.  This will familiarizing the students with the possible outcomes of the game and keeping the results well organized.  These results will be used in the next part of the activity.

To analyze the information found during the experiment every student will graph the number of wins out of the 18 games they had.  If the student was Player A, they will use red, if the student was Player B, they will use blue.  By using the smart board, the students are able to work as a class and interactively create the graph displaying the outcomes of the pairs.  The class will also participate in a discussion regarding the relationship of their results and the rest of the class.  If overall was everyone was similar or were there any noticeable patterns. 

The students will work in pairs to determine the mean, mode, and range for the set of data the class came up with.  In order to do so they will use calculators to complete the required math after plugging in necessary information into the related equation.  After a few minutes, of working with a partner, the entire class will go over the problems that were completed on the smart board.  The students will go over the steps of solving for each value and then relating it back to the graph of the plotted data.  It is important for the students to be able to see the visual of the relationship between what they are discovering and their original data.

In order to take the students’ learning to the next level, the students will be creating and using manipulatives to represent the possible outcomes of the game.  The students will create manipulatives that will be rearranged to represent the possible options of playing the game.  Working with a partner, but having their own manipulatives will allow for the students to personally create their own tree diagrams, but still have the support of their peer.  After making the tree diagram representing the possible outcomes, everyone is also required to copy it into their notebooks.  A list of guide questions will be displayed on the smart board to remind the students what they should be thinking about while trying to answer the question of if the game would be considered fair.  Working with a think, pair, share strategy here will force each student to analyze the question and information given, but also use their peer to communicate their individual ideas to agree on and then represent them to the class. 

Finally the students will be using the manipulatives once again to relate probability to the world, and tying all the newly taught information together.  After discussing the results of the mathematical model as a class, the students will be asked to think about a different game, and to with their manipulatives, create another tree diagram representing the possible outcomes of the new game.  The smart board is continuously being used to encourage peer participation, interaction, and cooperation.  Working as a pair then comparing the results as a class will help students being comfortable in taking risks as learners because they are using results that they came up with as a team rather than by themselves. 

https://docs.google.com/spreadsheet/ccc?key=0AgbQGzgMTUO_dHVqSk9tczJ4UExyRFM4WERMUlRyekE&usp=sharing

Geometry with Technology

Teaching geometry has progressed greatly with the advancements in technology.  The presence of technology in a geometry classroom has many benefits.  Teaching geometry without the use of technology would not be effective for many students mostly because geometry is a very visual and hands-on topic in math.  While taking geometry, many students feel overwhelmed and they are required to memorize what seems like an endless amount of properties, definitions, shapes, and formulas.  If all of this new information that geometry students have to learn is not presented in ways that are easily understood, the students will be faced with even more difficulty.  By using different forms of technology, a teacher is able to visually present information and concepts to students rather than lecturing the content.  A very useful tool while teaching geometry is a computer program called The Geometer’s Sketchpad.  There are many things that this program can be used for in the classroom.  Students can use this program to create accurate and precise points, lines, and/or shapes that can be used in homework assignments, projects, or presentations. Exploration activities can also be assigned where students are using Sketchpad.  Sketchpad helps students visualize and manipulate many different shapes, theorems, properties, and relationships in geometry.  While learning a new topic, it is beneficial to many students to be able to complete activities that are hands-on.  The students will be physically completing tasks that will lead them to the understanding of certain content.  Online there are many activities students would benefit from because of the personal exploration of the content as well as the manipulating and visual presentation.  Presenting the information where the students are using technology will help them understand content as well as critically think about the content being taught.  The growth of technology has enhanced the way we are able to present information to students, and has become such an important part of the curriculum.

Class Website

In order to provide students with necessary information at home, many school districts provide teachers with websites that are linked to the school’s homepage.  Depending on the teacher’s preference they are able to create attached links for each class use them to however they think they will benefit the students best.  As a math teacher, there would be many different purposes that I would use a website for.  Having a calendar on the website that provides your students with what information was covered in class, the homework for the night, project due dates, and test and quizzes would be very helpful for students and parents to remain organized and on track with the class.  If a student was absent and is able to make up the work, it will be posted on the calendar and will prevent them from being behind the rest of the class.  The class website can also have the link to the online textbook, if one is being used, as well as links to helpful sources related to the topic being studied.  Documents can also be uploaded to the website to be downloaded and accessed outside of school.  Overall, I believe that a class website is very beneficial for students’ learning.  They are able to easily access the information they need about the class in an organized way in one location.  The website also forms a responsibility over the students for their work; the calendar is provided to eliminate the potential of confusion of important dates and daily assignments.  Parents are also able to access the information published on the website which will help them understand what is going on in the classroom each day and be involved in their child’s education.  The website is an efficient form of communication between the teacher and students that is always accessible.

Online Textbooks

As technology is becoming such a large part of the classroom, versions of textbooks are becoming available as online editions.  Through what I have experienced, there are both positive and negative aspects to using an online math textbook.  In order to get the most out of using an online textbook, the user must be familiar with all of the components provided.  A student’s confusion or misunderstanding with these different functions throughout the website can prevent the student from being able to use the resource to learn.  My first experience using an online textbook was in Calculus II, during college.  In the beginning of the course, I was not familiar with this online source and I tried to avoid using it because it only caused me confusion.  I finally realized how necessary this resource was in passing the course, so I began to educate myself on the different aspects of the online text.  There were so many different things that I was then able to do and use to enhance my learning.  In many online math textbooks, especially for younger audiences, the layout is easy to follow and understand.  There is usually a side menu bar that organizes the website into the different tasks that you can complete.  This usually consists of a search bar, a link for each chapter of the book, chapter quizzes, chapter tests, practice games, vocabulary reviews, and more.  The benefit of these extra programs being available to students is limitless, but also depends on the particular student’s motivation and study habits.  Online textbooks provide students with the newest available editions of the text at a much more efficient method.  Students no longer have to transport textbooks between home and school to complete assignments.  The school district is also saving money by using online textbooks because the cost is much cheaper than purchasing hundreds of hard copies.  In order to prevent student confusion and avoidance of using the textbook, teachers should educate students on how to properly use the functions of the textbook at the beginning of the school year.  By doing so the students will understand what is available to them just by using their online textbook.   Using online textbooks will continue to expand and will especially benefit the students using online math textbooks because they will be provided with so many more examples, tutorials, and activities to help them understand the content.

Remixed Canvas

While beginning the process of remixing a canvas I was a bit concerned with what subject I was going to do.  In my mind I was set on finding a science canvas that I could relate to math, but when I came across “The Changing Ideologies of Race, Culture, and Demographics” I instantly thought about statistics and statistical analysis.  When I was familiarizing myself with this unit, I realized that so much information would be so useful while teaching statistics; specifically analyzing data and inferencing.  There are so many numbers and relationships that can be created with the topics of Race and Culture that I think it would be very interesting and beneficial for the students to learn about.  They can analyze trends of certain characteristics in an area throughout time that could even have significance in their life.  Race, Culture, and Demographics are all things that everyone can relate to yet they are so frequently misunderstood.  I think that this unit together would really educate students on such important topics and then analyzing them statistically to create even more importance and relevance.

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2758&mode=view#network6 

Mathematics Unit Plan

While first using the PLAY website I found myself a little confused how to complete each task.  As I continued to familiarize myself with the different functions and as I got more comfortable with the website creating my canvas was not as difficult as I originally expected it to be.  When trying to summarize my unit I found it hard to narrow the standards down to which ones would be in this unit.  Throughout this unit the students will be introduced to two algebraic expressions and solving for when they are equal.  This also introduces a new idea of solving an equation for the value of a variable that makes the statement true.  The students will also be introduced to using variables as a representation and writing expressions in order to solve a problem. The idea of a balance scale is used throughout the unit for the students to visual equality throughout both sides of an equation.  Graphs are also used to show the intersection of two expressions represents where the expressions are equal. 

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2478&mode=view#network6 

Technology and Pedagogy

While researching the NCTM illuminations provided on the website, I came across a lesson plan called Algebra in Balance.  This intrigued me most because in my fieldwork, two of the Algebra classes are learning how to solve equations.  My Cooperating Teacher also presented the idea of an equation as a balance for the students but I thought these online activities could have been useful.  The lesson is using a balance online where students can enter algebraic expressions on each side.  There is a red and a blue side of the balance which corresponds to the color line on the graph so the students are able to identify which line relates to which equation.  The activities are helpful for the students to explore equations and how to solve them.  The questions that are facilitating the learning and thinking throughout the activities are very helpful in leading the students to think more critically.  The lesson plan had a lot of student based learning which is very beneficial and effective, however it does take a lot of time and may not need to use all of that time.  I think more teacher interaction and class discussion during each activity would benefit the students while they are exploring this new topic.   The interaction would could provide support and clarify any confusing before moving onto the next activity. I would have however changed the order in which the activities were assigned.  I believe that the Balancing Equations activity would have been much more beneficial in the beginning, rather than the end, and the Pop Balloon activity would have been understood better in the end after exploring the Pan Balance a little.  I believe the technology used in this lesson compliments the students learning and is a good way to introduce the topic.

https://docs.google.com/spreadsheet/ccc?key=0AgbQGzgMTUO_dHRRbUk3MVJnU1NnZENOOGtKdS1mLXc&usp=sharing

Technology & Pedagogy

Throughout my experience of writing lesson plans I have found it hard to incorporate certain online activities in a math class.  However I have come across some that seem they would have a positive impact on the students’ learning.  The lesson I chose was called Exploring Equations and I got it from the National Council of Teachers of Mathematics website.  The lesson plan used a web based activity that showed the balancing of an equation and the different affects each coefficient and variable can have on the entire equality of the equation.  Overall, I believe that the lesson is well planned and designed for the maximum comprehension of the material by the students.  It is very helpful that the students are exploring the topic of solving a system of equations with a familiar item, a balance, to represent that both sides of the equation need to be equal.  I do believe that it is necessary for some commentary throughout the students’ researching because it will encourage them to think more critically about the overall relationships they are trying to find.  The standards that were listed on the lesson plan online were from the National Council of Teachers of Mathematics standards, but also do apply to the Common Core Standards of Mathematics as well.  The technology that is being used is the web based activity that represents the equation balance of an equation.  It is very useful in picturing a mathematical equation as a balance and the operations and numbers as objects that need to equal out on each side.  I do not think a different type of technology would be necessary in supporting this lesson because it seems that the online activity would be very beneficial.  

https://docs.google.com/spreadsheet/ccc?key=0AgbQGzgMTUO_dFRmLXQ1M2RfSWM3bnRNYW44enYwQnc&usp=sharing

Pencils are Important

The pencil is a writing utensil where you can erase the marks you made with the provided eraser.  Math is a subject where trial and error is necessary in mastering the information.  In order to fully understand a topic, it is necessary to experience mistakes throughout your learning process.  Mistakes help teach you the correct way of going about a certain situation.  While solving a math problem, it is easiest to fix your mistakes, which can occur frequently, while using a pencil.  When I reflect on when I was growing up and the progression of learning math the first thing that comes to my mind is making many mistakes.  However, I also remember always being told to use a pencil by my math teachers.  Looking back I can realize that this was for my own convenience.  It would have been much more frustrating learning new material if I was not able to erase something on my paper if I made a mistake.  Throughout my lifetime, I realize that there has been an evolution of writing utensils which makes learning easier.  There were times when pencils did not exist and ink was the only way of writing something down. When I think about this, I first try to recall my experience of learning how to graph functions, and then try to image doing so without using a pencil but rather ink.  The technology that was used to create pencils, whether they are wooden or mechanical has helped teaching mathematics.  The pencil is a very important tool while learning math and I do not think anything will be able to replace it.  There are many things that a computer is able to teach a student, but there are also things that need to be written down, with pencil and paper, in order to be fully understood.    

History of Technology in Mathematics

Holding hands with the answers.

Calculators

Technology has provided us with many different learning tools that assist in presenting new information to students.  The calculator is one of the pieces of technology that assist in the students’ learning and education in mathematics.  Not only is this important and used during school, but many people rely on a calculator in their everyday lives.  The tasks a calculator can perform vary depending on the type of calculator.  There are some that only operate simple algebraic expressions where others can find the derivative of a function.  The calculator plays a very important role in learning mathematics and can assist in completing a task that is too difficult, tedious, or complex for someone to do on their own.  A calculator is also a good way for students to check if their work done without a calculator was completed correctly.  The simplest form of a calculator is one that is capable of calculating the addition, subtraction, multiplication, and division of numbers.  This is also the foundation of our mathematical knowledge.  When we first learned math we started by learning these four operations that were then expanded into more complex concepts and topics.  As our mathematical knowledge expands, there are calculators that are also capable of doing more complex math.  For example, a graphing calculator is able to graph a function on an x-y coordinate plane.  For a student that is just learning about functions and how to graph them, a visual of a graph will be helpful in the initial lesson of graphing functions.  Another benefit of using a calculator is the time that is being conserved during a class.  By using a calculator, a result is given to you almost instantaneously, which could have taken ten minutes if it was done by a person.  Time is restricted in a classroom each day by the length of the period, and calculators are able to help speed the process of understanding a lesson.   

Not only is a calculator helpful in a classroom, but calculators are used every day outside of the classroom. There are many tasks that are understood how to be completed but take too long or too much effort to complete them so many people rely on a calculator.  While paying a bill at a restaurant many people use their calculators on their phones to find the amount of tip and then the total bill they will be paying.  Calculators are also used very frequently while shopping.  If there is a discount on a certain item it is more convenient for some people to calculate the new price through calculations on a calculator rather than in their head or on paper.  Finally, many jobs, such as accountants and architects, require a calculator to perform tasks in their work assignments. 

The main purpose of technology is to make a situation be more convenient for the user.  Math is everywhere and used for so many different everyday activities.  Such a small form of technology that is used to teach mathematics in schools is also used throughout almost everyone’s lives daily.  There is some kind of impact a calculator has on each person and without it there would have been a different route taken to arrive at an answer.  The calculator is very convenient for the user when trying to reach the solution. 

Technology Autobiography

The three technologies that I decided had the most impact on my life are the smart phone, social media, and email.  All three of these technologies have had affected my life in many ways.  These three technologies are continuously used throughout each day of my life.  My smart phone is the main social connection between myself and friends and family.  My phone has most of the capabilities of a computer and can retrieve information or preform many tasks.  The communication through my phone, whether it is text messaging or calling, is the most used form of communication I use.  My phone is also capable of updating and alerting the user about information through different apps which informs many people of the current events going on in the world.  Social Media is another form of technology that has impacted many people’s lives.  Social media profiles allow individuals to create a profile that describes how they portray themselves.  These profiles are also forms of communication. The ability to share information and opinions on one’s profile is encouraged.  This is a different way you will be able to learn knew information because of the publicizing of a story on a social media site rather than a data website. Finally email is another form of communication and has become much more popular over my lifetime has become increasingly popular.  With the popularity of communicating through email growing, its effectiveness on society has also increased.  I do not, however think that email has an impact on the ways I learn new information. 

Throughout the video I noticed many different uses of technology while amongst the young participants; although I think the main purpose was continuously based from personal enjoyment and entertainment.  For example, a lot of the young people were able to express them through the usage of technology, whether it be having a social media profile, create music, or read and write.  These personal hobbies that are supported or created from technology are also forms of communicating and exposing yourself to information that you may not have come across another way.  However, another portion of the participants from the video were also using the technology for an academic purpose.  Some of these students were using technology to learn languages, write, read, and take pictures.  Technology can be used in many different ways and is a very helpful aid when learning new information.  People in society today have however become dependent on certain forms of technology which can be a very large downside to the usage and importance of technology.