Tweeting in Math

After having watched the Grey’s Anatomy Twitter Episode again and then blogging about it, I became inspired to research different ways in which I could actually use twitter in a classroom setting.  Then I found this website that gives 50 great ways to use twitter in the classroom.  Many of the ideas listed were great for English or History classrooms as I had expected, but there were so many great ideas to incorporate into a math classroom as well. I was very pleasantly surprised.  The very first thing the website says is “Tweet about upcoming due dates or assignments.” Yes! How many times do students hand in assignments late and their excuse is “I didn’t know it was due”.  Other suggestions include coordinating assignments and sharing notes, which are also great suggestions especially if anyone was out sick that day, they can still get the notes and assignments they missed so they do not fall behind in class. (In a math classroom it is easy to fall behind because most mathematical formulas and concepts build off each other and work together in order to do more complicated problems.)  Some thing that I didn’t know is that you can also post sample questions, videos and math games for additional practice.  The final thing that I also thought would be very useful is to post summaries of lessons.  In a math classroom this could mean posting the important rules, concepts and formulas we covered in the chapter so the students will know exactly what to study for the test.  I can’t wait to start teaching and try out this form of technology and see how it works for me.

http://www.teachhub.com/50-ways-use-twitter-classroom 

Math Apps

The website I found is more of an ad for IPads and IPhones; however it does describe the usefulness of these two forms of technology in the classroom. The website discusses the top 5 Math apps for the IPad and IPhone and how they are very useful for every math student from basic algebra and geometry to advanced calculus. They even have an app that has math games for children to practice addition, subtraction multiplication and division.  The apps that I thought would be the most useful in my classroom are WolframAlpha (Universal), Apollonius (iPhone), and Math Ref (Universal).  WolframAlpha is able to do computation and calculate complicated integrals, but it also gives the student step by step instructions on how to get the answers on their own so they can apply the steps on future problems and exams. WolframAlpha also allows students to look up different mathematical theorems, rules and axioms which is extremely helpful is classes such as geometry, modern algebra, and advanced calculus.  The Apollonius app also seemed really helpful because the description reminded me of Geometers Sketchpad which is something that we were required to use in my geometry class which I found extremely useful.  Unfortunately it says that this app is only available for the IPhone and not the IPad because I feel it would be more useful on the IPad given that the screen is bigger which would make it easier to draw different shapes and angles.  Math Ref also seems like an amazing app for any math class because it provides so many different formulas, tips and examples; it’s like having a giant math textbook at your fingertips, and the best part is you don’t have to look through the text book to find the formula your looking for, just type it into the search bar.  These apps are a great way to get all students involved and with the fact that so many students have IPads and IPhones it’s would be something that would be pretty easy to bring into the classroom.

 http://www.imore.com/2011/05/18/top-5-math-apps/

Twitter as a Learning Tool

May I start by saying you will love this video! I love Grey’s anatomy, and this episode made me a believer in twitter when I was more against twitter than anyone I know.  In this Episode Dr. Bailey tweets about her surgeries in order to teach many different doctors at different hospitals about the different techniques she uses.  The Chief of surgery was strongly against Bailey tweeting her surgeries because he felt it was in appropriate, but he becomes a believer too when the all the tweeting leads to saving a life! Watch to find out how… In my math classes I may not save a life by tweeting about mathematical formulas and giving study hints, but I may e able to help students with their homework and studying for tests by perhaps tweeting practice problems and solutions to study.

http://www.youtube.com/watch?v=P2F5w4hsouw 

Youtube as a Study Tool!

The link I attached to this post is a youtube video about finding the derivative of trigonometric functions.  It shows step-by-step instructions of how to find the derivative of the tan function.  What I really like is that the teacher reviews the derivatives of sin and cos because as we already know tan = sin/cos.  This is great because it helps the students better understand the concept behind why the derivative is what it is instead of just memorizing the answer. I used youtube a great deal when I was taking calculus because the great thing about youtube that you can get in the classroom is you can pause and rewind the video when you need clarification.  When I was taking calculus I would watch youtube while doing my homework so I could get step-by-step instructions of how to do the problems.  After doing a few problems I was able to understand the different steps need to solve the problems and this made me very successful in the class.  I highly recommend youtube to anyone struggling in math because they have videos for everything I can think of and it really does help a great deal when it comes to understanding the different steps of computation.

http://www.youtube.com/watch?v=dOOlmwIltZ8 

Website for Math Articles

This is an interesting website because it provides access to many articles from teachers who have found many different ways of implementing technology into their classrooms.  This article also describes the different tools that can be used such as Excel and the TI-Nspire in order to introduce new mathematical topics.  Many of the articles are about the different technologies they can use to model and graph many different functions and geometric shapes.  The best part about the website is that even though you have to subscribe to the website, the subscription is free!  There is even an article that talks about aids for building proofs, which I feel, is an area that students usually struggle with in math.  Beyond building proofs there are articles that discuss how to discover theorems.  Mathematical theorems are often hard for students to understand, but if they are working to discover them on their own they will have a better grasp on the concepts.  Theorems are important because with the use of different theorems we can prove new mathematical concepts and have our students becoming real mathematicians. 

https://php.radford.edu/~ejmt/ContentIndex.php 

Tackling problems facing technology in math education

This article is important because it is very objective and provides both the positive and negative aspects of trying to incorporate technology in the classroom.  One of the biggest problems in a math classroom is calculator dependency.  The newest graphing calculators have a wide range of functions and graphs that they can perform, solve and draw. Because of this, many teachers fear that their students will depend solely on the calculator instead of sharpening their mathematical knowledge and skills.  The key is figuring out the proper method of teaching in order for students to learn how to use the calculator as a mathematical tool in order to perform higher levels of thinking and work more efficiently instead of just using the calculator as a crutch.

            Another big problem with incorporating technologies into classrooms is the lack of access to different types of technologies.  Most schools cannot afford to provide every student with a laptop or graphing calculator. Therefore students are often required to provide their own forms of technology, which is very difficult in lower income areas.  With these different forms of technology becoming imperative tools in the classroom, schools should be required to have a these technologies available if the students are unable to provide them for themselves.  Because these technologies have to ability to get students more engaged in lessons and learn more efficiently, we as teacher have to be able to come up with different solutions to these problems that could prevent technology from being used in the classroom.

http://schoolcomputing.wikia.com/wiki/Technology_in_Mathematics 

Evolution of Technology

This article was interesting because it was about how much technology in the classroom has evolved thought the years.  There was obviously not always digital technology in classrooms but the technology they did have seemed to work for them and continue to progress rapidly much like it does today.  Many of the technologies we use today date back to as early as the 1890s!  Just as the chalkboard was important back then, it is still often used today especially in math classrooms for writing new formulas and showing step-by-step solutions to problems.  The pencil has been around in the classroom since as early as 1900 and is still one of the most important tools of any math class.

            Videotapes have been around since 1951 and we still use this type of visual technology, but of course now we are able to look up any needed videos on youtube.  Educational television has also been around since 1958 and I feel it is a great way to get students interested in a subject.  There are so many educational programs geared toward children to get them interested in learning such as Bill Nye the Science Guy or Sesame Street for younger children.  Teachers should take advantage of these television programs because they would be a great way to start a lesson and get the students interested.  The article goes on to describe other technologies that we know to be important in classrooms today such as graphing calculators and smart boards. There are of course other technologies such as IPads which are not used too often in classrooms currently but hopefully in the future they will be incorporated more.

http://edudemic.com/2011/04/classroom-technology/ 

Technology Benefits Article

This is a great article that I found about incorporating technology into the classroom. Many teachers or future teachers such as myself are hesitant to bring technology into the classroom because we are afraid we don’t know how to use it well enough and the students will know more than we do.  This is a very strong possibility, however as this article points out, the students can also be great teachers of technology as well.  The students and teacher will not only gain a better understanding of technology, but it puts the student in a more active role to be learning more about the subject as well.  Teachers have reported an increase in self-esteem and motivation.  Many students even work on technology based projects during their free periods due to the fact that the use of technology is fun and more appealing to them. This was not just at a high school level; students at the elementary level were able to gain a great deal of knowledge about computer programs.  They can easily do this in a school computer lab and accomplish more complex tasks than they could in a regular classroom.  Or given only a few computers in a classroom, the students can be broken up into groups to work on projects where the more technology savvy students can be helping and coaching the others.  This allows for more cooperation and group learning which is an important part of any classroom and society as a whole.  By teaching technology and group learning and cooperation at such a young age we will be able to create more effective citizens which should be everyone’s goal as future teachers.

Here's a link to the article, enjoy!

http://www2.ed.gov/pubs/EdReformStudies/EdTech/effectsstudents.html

Great Word Problems

http://algebra-word-problems.blogspot.com

Hello everyone, I'm sure you are all busy with finals right now but I found I great link that I think will help you if you are a math education major. It certainly helped me. Its a link that gives a bunch of different algebra word problems and the answers.  It even has different levels of algebra depending on what type of lesson you might be planning.  I love word problems because they teach students a lot about how to use and apply different formulas to everyday life, but it also teaches them critical thinking skills as well because they must first come up with a plan to solve the problem.  This link that I found is really great because it will be a huge help to me in my future lesson plans.  Not only does it have word problems but it has word problem videos and contains links to other fun brain games to challenge students while keeping them interested and engaged.  The problems on this site are great because they are challenging but on level.  They often have more than one step and require a great deal of critical thinking but require a mathematical background that is on level and appropriate.  I also like that the problems do get more difficult as they go on and require the students to perhaps draw a picture in order to plan out how to solve the problem.  This is an amazing site and if you get a chance you should definitely look at it because I believe it will help you plan lessons and allow your future students more opportunities for critical thinking.

Final Project Area of Triangles Lesson

My lesson plan is about teaching students how to calculate the area of a triangle.  I believe that I could complete the lesson within two days but we may need a third day to really understand all of the concepts.  The first day consists of reviewing how to find the area of a rectangle. I would start by putting a few examples on the smart board and asking for student participation.  They should already have an understanding of how to calculate the area of a rectangle but if they have forgotten anything it is always important to have a quick review. We start with calculating length multiplied by width, which hopefully the students themselves will be able to explain.  I will show students that this is the same as saying base times the height.  It will now be easier to explain to the students how to get the formula for area of a triangle.  I will start the explanation by drawing another rectangle on the smart board and drawing a diagonal line across the center. if By drawing this diagonal line across the rectangle the students will be able to see that we would get two triangles.  I will ask the students to use their critical thinking skills to see if they can tell me what area of one of the triangles is given the area of the whole rectangle. Hopefully through this visualization the students will be able to tell me that to find the area of one of those triangles we would simply divide the number we have for the rectangle by two. This now gives us the formula one half times base times height.  At first it is easier to work with only right triangles because they are easier to draw and measure.  When using right triangles the students can draw two equal triangles and make a rectangle, which also helps them better understand the formula we just came up with.  After allowing the students to explore these concepts and formulas using graph paper, pencils, rulers and protractors, we will discuss acute and obtuse triangles.  The students must first understand the difference between these two triangles and how to draw them.  After practicing drawing these two new types of triangles, I will explain to the students that the same formula we used for finding the area of a right triangle also works for finding the area of an obtuse or acute triangle.  The only difficult part about this of course is finding the height of the triangle.  I will of course have to explain that the height or altitude of a triangle is the line segment from one vertex (or angle) of a triangle to the opposite side so that the line segment is perpendicular (or forms right angle) to the side.  The students will work in groups to draw and label the sides and heights of different triangles.  Using The Geometer Sketchpad the students will have to create three examples of each different type of triangle (right, obtuse and acute).  The students will then record the data (lengths of sides and altitude) that they themselves have created on the computer and use that data to calculate the area of each triangle.  In this activity the geometer’s sketchpad is extremely useful because it will allow the students to explore many different types of triangles as well as better understand the relationship between base and altitude and the opposite vertex.  On top of all this, it gives the students accurate measurements of angles and sides so that they can have more accurate data and more accurately calculate the areas of their created triangles.  The final assignment of the lesson will to be to calculate the area of different shapes that I give them using their new information about triangles.  I will give the students a few different shapes such as octagons and stars, which they will have to break up into different size and shaped triangles in order to find their areas.  The students will use the geometer’s sketchpad to draw the triangles inside the given shapes. They will then label the measurements for each side and calculate the area of each small triangle that they have created.  Adding the areas of the triangles together they will be able to calculate the area of each of the given shapes.  They will have to submit their work and drawings online as well as show how they calculated each area on paper so I can feel confident that they have understood the lesson.

 The following is the link to my lesson plans:

 https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndENsSDF0YzVBUFdnSVFwUU16M250Mmc

Edutopia Video

I love the most recent edutopia video! it seemed like the students were having a lot of fun, and they were learning so much! not only in the classroom but in their athletic activities; however in the sports they were competing in such as cheer leading, they are learning not only about their health but about velocity and other aspects of sports that work into different ares of study such as science and mathematics.

Interactivity #5

The teacher I interviewed is an Algebra I and Algebra II teacher in Newton Public Schools.  When asked about the use of technology in the classroom the teacher did not seem extremely thrilled about the idea, but admits that the smart board has been a nice addition to the classroom because it is very useful when proving and working out problems on the board.  The teacher also admitted that NETS-S and NETS-T standards are a new concept because though the school does encourage the use of technology in the classroom, the NETS standards are not stressed.  He agrees that the first standard is important in mathematics because using graphic visuals to visualize a function can be very beneficial and help the students to better understand the curves and slopes of functions.  If the students can visualize these functions at a young age, they will have an easier time with more advanced levels of mathematics such as calculus when they will need to find the areas under these curves.  On the other hand, he like most math teachers feels that if the students use calculators too often they will become dependant on the calculators and not be able to the math on their own.

He also agrees that the other standards are important because they deal with analyzing data and being able to effectively collect that data, graph the data, and then analyze what the data tells us and report results.  Graphing is an important tool in a mathematical classroom, and he agrees is something that he could incorporate more into the lesson.  I tell him that there are a lot of different technological tools that make graphing easy, and remind him that graphing using these technological tools will allow the students to make more accurate graphs and be able to much more accurately analyze the data they are working with.  Practice using these tools will also help students in the future if they take any statistic or data analysis classes.   These skills are extremely important in today’s society and will make these students better citizens in the future, which is of course one of the main points of education.

Something important that I believe came from our conversation is that these technological tools are not always a crutch to students, but they can be used as important educational tools on which the students can build and gain a better understanding of mathematics.

You can view the changed to my Lesson Plan in Google Docs at 

https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndFRqVnRBamV4aXVXOFJwLUxlbHFzalE

Interactivity #4

 

https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndFRqVnRBamV4aXVXOFJwLUxlbHFzalE

I chose this lesson plan because is well written and clearly laid out.  It also satisfies some of the important NJ standards.  I saw that the teacher used technology but she was not taking advantage of all the technology available.  I felt I would be able to incorporate different technologies that would help the students better understand the lesson and aid them with homework.  I did feel that the curriculum goals and the teacher strategies were very well aligned.  She had clear goals and strategies for explaining the lesson and assessing student understanding.  Unfortunately as I mentioned before, she did not take advantage of the technologies available.  The only material she listed was an overhead projector which is a great tool to use every once in a while, but students have a tendency to loose interest if the teacher is only putting different slides on the projector instead of using different interactive technologies.  The technologies that I listed, such as the in class math game, I feel are essential to achieving the curriculum goals because it gets students involved during the class.   The other technologies such as cramster and youtube are also extremely important because they can help the students during their homework by giving them examples and step-by-step instruction. Through seeing additional examples on these sites the students may be able to better understand the steps and formulas needed to solve the given homework problems.  Also though using these additional resources the students will have a better understanding of the lesson and be able to apply their knowledge to future tests.

#3 Useful Classroom Technologies

I thought this was a great group activity because we had to work together and be sure to read each other’s technology choices so we did not repeat them.  I liked reading my group members ideas because they were often things I had either never though of or had forgotten about, many of which we have used in many of our math classes already.  This activity definitely makes you realize how important and how helpful technology is in a math classroom.  At first it seemed like a lot of work to find 10 different technologies used in the math classroom, but once I started researching the topic there were so many, it was almost hard to narrow it down to what I thought were the ten most effective teaching technologies. 

As we learn in our other classes, two important aspects of teaching are teaching literacy and assessing understanding.  Many of the technologies on or list are visual aid because in math is so important to connect terms and formulas to graphs to gain literacy and understanding.  A few of the technologies are also tools for assessment such as “Math Teacher Tools” which helps teachers create worksheets which can then be graded, “Math Pad Plus” which allows the students to do the worksheets online, or my personal favorite “Dream Box Learning” which assesses the student’s progress, identifies the area which the student is struggling in, and provides further practice and instruction.  “Dream Box Learning” has games and animations that make learning fun for the students and assessment easy for the teacher.

#2 Calculators: A Helpful Tool

Calculators are an important technological tool in a math class because they aid in calculations as well as allow the student to better visualize the equation through graphs; however, the picture illistrates how important it is to still know and understand how to do the calculations by hand.

Top 3 Influential Technologies

The three most influential technologies in my life are cell phones/texting, Facebook, and YouTube.  Texting allows me to stay in contact with loved ones throughout the day as well as quickly exchange small bits of information with friends, class mates and coworkers.  Because I do not always have my computer with me, I consider texting the most efficient way of communication.  Facebook is also very important because it allows you to get in contact with everyone even though you may not have their phone number or know them extremely well.  It is easy to find a classmate on Facebook and send them a message asking a question about class or homework or a project you may be working on together.  YouTube has been very helpful to me in many of my math classes because many times there are teachers that post videos on YouTube on how to use a specific formula in math and it has made doing my homework so much easier because even though I have the book for the class it is easier to understand when someone is doing an example in front of me.  Like the students from the two videos, I can not picture my life without my phone or my laptop; however I do not let technology consume my life.  Olivia listens to music constantly and spends hours on the computer in the basement of her apartment complex. This is why technology can be harmful because she is not getting any exercise, nor is she spending quality time with her family.  The children in the second video seem to be using technology in a more constructive way but one boy admits to not being able to go to class without tweeting about it because he considers twitter such a big part of his life.  I'll admit that I am biased because I see no need for twitter, but I consider it unsafe to be posting your every move on the internet.  I see no educational purpose for twitter, but if anyone can give a valid argument for tweeting i would like to hear your opinion.

Hey everyone I'm excited to get blogging, so I'm making this post to make sure everything works correctly. Hope to hear from you soon!