Online Homework

Online homework has its positives and negatives to it. One positive is that it saves time for the teacher when grading homework. Online homework programs grade the students homework electronically and the teachers can put the results directly into their grade book. The teachers will have the ability to see who truly completed the homework before the class starts. This will allow the teacher to know who completing their work at home before school starts. Online homework also saves the teacher time in the classroom because she does not have to walk around and check who did their homework and then collect it if she pleases. 

Online homework can also be bad, this is because it is very easy for students to guess the correct answer or cheat on it to get a good grade. One way this can be done is looking at the examples that are given with the question and the students just plugging in their numbers instead of the numbers in the example. This is not good because the students are not truly trying to solve the problems on their own for practice. Another way you can cheat on the online homework is by putting the wrong answer in on purpose so that the computer gives you the correct answer. Lastly many of the web-assign questions can be found on google, where students can easily look up the correct answer. Unlike written homework there is no work to prove that the child did the correct computations to solve the problem on their own. 

Another negative of online homework is input issues. Many times the student will have the correct answer but type it in differently than the computer wanted and it will be wrong. This will give that student the idea that he is solving the problem wrong when he may be right. 

I am not 100% against online homework but if I was to use it in my classroom I would ask my students to bring in their work on a separate piece of paper to hand into me so that I can make sure my students are really doing the work and that they are doing it correctly. 

Unit Plan Canvas

At first, when I looked at this assignment I was a little nervous because I had never used PLAYground before and I was unsure what to expect. Once I started this assignment I quickly saw that this site was easy to use, since everything that was needed was right there. Creating this canvas was very fun for me. I liked how it is set up and I think that students would really benefit from it. They can use it to see an overview of the unit, and use it as a reference if they need some extra help. On my canvas I tried to include examples of each topic weather it was through video, pictures, or links to websites. This canvas is also a great way to share ideas with other teachers, they will be able to go to your canvas and see what you are doing for certain topics and you can easily go to other canvas yourself to get more ideas for teaching. 

I choose this topic of congruence because it is often a difficult topic for many students. For IA #3 I choose a high school geometry problem that is similar to my canvas. I wanted to do more on congruence and proofs because many students find this difficult and I wanted to create a canvas for my students to reference to get the extra help they may need. I posted many examples and a video for my students to view if they are having difficultly on this topic. 

http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2446&mode=view#network6

Technology Workshops

                        Schools are starting to really push technology in the classroom. Technology is something that the students can relate to and it is something that they are interested in.  Technology is a great way to gain your students interest in learning new concepts in math. You can use many different kinds of technology in math, such as a calculator, document camera, smartboard, computers with excel, graphing programs, online homework websites, and much more. Although not all teachers are familiar with new technologies that can be used in the classroom. This may cause teachers to stress out and become over whelmed if they are expected to incorporate technology into their lessons but are unsure of how to do so. 

                   To fix this problem I think that schools should hold technology workshops separated by subject area for teachers to go. These workshops can be used to introduce new technologies to teachers and show them all they can do with technology to enhance their lessons. This is a great way to better a schools ability to use technology and is also a great way for teachers to get the most out of the technology they are given. For example a simple graphing calculator can do so much more than many people think, by attending the workshop teachers will have the opportunity to learn all of this. 

                   Also, the smartboard can do so much to better a mathematics lesson. Many teachers including myself do not know all the functions of a smartboard. With these workshops teachers will have the opportunity to ask questions and practice with their own smartboard after the meeting. This is a great way to better teachers in a school, and it will benefit the students too. By teachers understanding and using technology students will be more engaged and eager to learn new things, since technology is something that grabs their attention instantly. 

Technology & Pedagogy

I choose this lesson because I am very interested in teaching geometry and this lesson was on a geometry topic. This topic went over a way that students can experiment with quadrilaterals and diagonals.

This lesson was all group work and discovery based. They used diagonals to prove different theorems on their own. They also used a computer program to help them do this. The curriculum goals, teaching strategies, and technologies used were mainly in alignment with the curriculum goals. The programs and worksheets that were used stated and explained exactly what the students should be discovering on their own. The students knew where this lesson was going and the group work was a great way to do this. 

The diagonal tools program is essential to achieving the curriculum goals because this program allows students to see and move around the diagonal lines and the endpoints of the quadrilaterals to see how it affects the properties. From this they can make conclusions to help them prove and derive theorems from what they see. Using a document camera would of only made the lesson better so that each group could better see what each group came up with, rather than just holding it in the air and talking about it.    

URL:https://docs.google.com/spreadsheet/ccc?key=0AqXZhRFVVYr-dG8weVl2anIyNlBkT2pTVXlEOGkzMXc#gid=0

Smartboards

Smartboards are a great tool in the Mathematics classroom. They allowed teachers to graph equations accurately, show videos, move objects around with their hand, and much more. Smartboards have many features that will benefit a teachers lesson.  Graphing is a perfect example, when a teacher wants to graph an equation, they can open up the graph paper and graph the equation right on the board. Unlike a chalk board where the lines will not be perfectly straight, and the points will not have perfect spacing.

Smartboards also work as a regular board if teachers want to open up a blank sheet and show examples step by step. They can do this by opening up a blank page and then use the smart markers to write. They have the option of many different colors to show different steps in a problem. They can also easily erase and start over if they have to. The great thing about writing examples on a smartboard verses a chalkboard or a white board is that your writing can be saved and printed or posted on a class website. This is a great tool for teachers incase a students is absent or so that they can go back and see exactly what they did on a certain day. Using a chalk board or white board this cannot be done.

Smartboards are not only useful in math. For example in a history class, a teacher may want to show students where something on a map is that they are learning about. Instead of just pulling down the old fashioned maps that hung from the walls, the teacher can open up a map and project it on the smart board. This is more beneficial because teachers can write on this map to highlight and show students exactly what they are talking about. Then they can erase if for their next class. 

Smartboards do have some glitches. If the calibrator gets messed up what the teachers are trying to write will not be accurate. Their writing will come up in the wrong spot. Also if a teacher has a whole lesson planned using the smartboard and for some reason the projector is not working they will not be able to do the lesson. Teachers should always have a backup plan just incase the smartboard is not working one day. 

   

Calculators in a Math Classroom

          Many people agree with the use of calculators in the mathematics classroom. I cannot say that I am one of them. Calculators cause many students who are not strong in math to become dependent on them. This causes students to forget, or never fully learn multiplication and division, and many other mathematical concepts that the calculator can compute for you. I am not fully against calculators because they can calculate things faster and more conveniently than a person can, but I do think that there needs to be full understanding of a concept before they are introduced.  

          Since calculators are being allowed in middle school, students are entering high school not knowing how to do long division, add/subtract/multiply/divide fractions, multiply, and other basic mathematical concepts that should be known. I can say this because I have seen it first hand from substituting and talking with my cooperating teacher. She told me that each year since calculators were introduced in the local middle school, her math students remembered less and less of their basic skills. Therefore, she has to spend more time on the basics rather than moving on to what is actually in that years curriculum.

          Another downfall of calculators in middle schools is that many students do not yet fully understand the meaning of certain concepts and they enter the calculation incorrectly in the calculator. For example, I was substituting this past week and a sixth grade student wanted to calculate 125/4 and he entered it into his calculator as 4/125, giving him the completely wrong answer. He did not know that this was wrong until I showed him the correct way to do it. Calculators will give young students misconceptions about mathematics because they have not yet mastered all the skills they need. If this student was more skilled in division he would have realized on his own that that answer could not possibly be correct.   

          Although, I do not think that calculators should be eliminated all together. Calculators should be introduced in high school, only after students fully understand the methods of a problem on paper. Graphing calculators can show students what graphs of  different functions may look like that you can not accurately graph on paper. They can also speed up the process of calculating basic solutions to a long problem. Teachers should not allow their students to become dependent on calculators and they should monitor their use in the classroom. 

History of Technology in Mathematics

Were teaching machines really helpful, or was it a way for students to speedup their learning process without guidance from a teacher?