This  article just shows the importance of having a firm mathematical foundation by linking basic skills to algebra. If, we can get individuals to think outside the box and stop using the tradional ways of solving problems. By the time that person is in an algebra class things will beginning to connect smoothly and there is a pattern that will help in relationship to old concepts learnt and new ones being bridged together to the old ones. I can see a pattern in the Alpha letter system learned from last semester to this infornation that we learning in this new semester. Now, we are using squares.
 
One of my goals in life is to work with students who are from different countries and cultures. You may ask why? Well, in our family gatherings you can hear English, Arabic, and Spanish because some of us can speak all three of those languages or only two or only one of the three languages.I can gaurantee that the first thing a person from another country learns first before they learn the language of math. (I do not totally agree with the book on this subject matter but not ruling it out). Why? Everyone needs to make a living and it is very important to learn the monetary system of that country that you are calling home. By no means am I saying not to learn the language but $$$ signs speak louder than words. This does not only apply to  immigrants but right here in America we do not understand each other because of other diverse issues.Bridging the gap between cultures, neighborhoods, races, and languages can be challenge. There are times were it can cause serious problems amongst those individuals involved. The best way to intergrate is to show some similiarities and some things that are not the same between the languages, cultures, etc. It is imperative way these things are the way they are. There will be always be something the same and different.
My oldest child experienced ELLS from K-5 through 4th grade. He was learning both English and Arabic in the home but he was immersed in the Arabic more than English. He still takes notebook paper with the holes on the left and flips the paper to be on the right side (in Arabic you write right to left). Simple things such as this can be very challenging for those involved.
 
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Diversity and equality in the classroom and the home are very imperative in regards to the person being taught. I have two children and I have compared them against each other. One child needs constant step-by-step assists and is easily distracted. And the other child does not have these challenges. I have realized what worked for one child does not work for the other. And this is the case in many classrooms also. I have to be very innovative in helping my one child in learning the basics. He is a visual learner and I have to relate everyting to Star Wars to make a connection. I was wondering, if, he has some mild learing disability, a visual problem, or he is simply overwhelmed. I know that I am overwhelmed at times. Here are the steps that I am taking to help in guiding his learning process:
1. Do not bit off more than we both can handle
2. Gear learning to his needs and interest- build from there
3.Seek help on the areas of concern just to make sure that he does not have those challenges
It is not easy excepting somethings about your students but it is more taxing when it is in regards to your children. But in the end you are helpping them out in the long run. And we should never compare anyone against another person because we are all wonderful and beautiful INDIVIDUALS. We are learn differently and need certain things in order for us to move forward.


 
In chapter 12, there are many examples how someone can obtain the correct answer to a math problem. The new math strategies shows a student place value and also allows them the she the provess step by step in obtaining answers with a math problem whereas the compressed way does not. I also observed this in the Flint Community Schools which implemented this strategies possible in 2008 or 2009. I had the opportunity to work with one of the younger students who knows only this method of math strategies. And I also worked with one student who was from the academy that knew how to use the old and new strategies and could give account of what he learned and did from both. Then one student was from another public school district and could do the math; but did not know how to explain place value well in regards to addition and subtraction. But there are many ways in learning math and getting the answer. This does not make this particular student less than the other two; but they were older and use to doing things the old way. Teaching math on all levels for everyone to learn I believe is imparative because what I saw on videos and on my interviews. 
 
In reading chapter 23 it has a section on integers. The use of couters to represent positive and negative numbers. It makes it clear to see how to add a negative and positive numbers together and also adding the number line as another visual to teach integers. In the video that was observed in class showed how using different things to figure out math was very interesting. I have learned to love manipulatives.
 
My 5 year old was given his monthly homework packet. One of the assignments was to have your child to count backwards starting with the number ten. In the EMM (Elementary and Middle School Mathematics, Teaching Developmentally) book by Walle, Karp, and Bay-Williams had given advice in how to help children to aquire this skill such having a rhythmic fashion (page 128). Well, I taught my son the cool song that they use to sing on Sesame Street 1,2,3,4,5 and... Catchy tune, right? But, we are Starwars fans and we traveled through the Galaxy. We used the Millineum Falcon to travel and varies charaters to go to places such as Tatowine, Mustafaha,Naboo, and the planet of the Kaminoans. We started the space ship and counted down to zero. It was fun and my son had something to connect to what he is learning to something that he loves-STAR WARS!

Now, I am slowly coming on board in regards to using calculators. I used the microwave to teach my five year old to recognize his numbers. We are up to 2:00 minutes but for him it i"2-0-0". He has been fixing his pancake corndogs by himself! And I was visiting my eldest son's math teacher and she had calculators available and hung up on the wall for easy access for each student.
Technology is really cool once you try it because pen paper can be tedious but it is still necessary. Since I have been taking this math coarse;it is has allowed me to put into action some of the things in the book with my sons. Trust me they both learn differently. The youngest wants total technology and the other is likes pen/pad and technology.
It is possible that I will see how one can use fractions on a calculator. I am sure that it is possible.

 
Every person learns differently; and my job as a teacher is to be willing to listen, and be open to the needs, concerns, statements, questions, and thought processes of my students. This means that it is mandatory that I find ways to reinvent the "wheel" so to speak. Keeping in mind that I am teaching and learning new things by engaging in coversation and activities with my students. Bringing things full circle by building up knowledge already obtain and making a connection with new material. This means allowing the brain to rearrange itself inorder to grasp understanding of the new concepts presented in the classroom. Most importantly building a relationship of trust and confidence.
 
I am taking this Math for Educators and I have mixed feelings about it. It is not that I do not know how to do math. I can not really say that I do not like math, because over the years I have learned to love it. With that been said, I changed my mentality towards math. This really helped when I was taking math classes at Mott Community College and most of those classes were online coarses which I may add I did good in. Well, my oldest child loves math and all these years it was believed that I loved the subject, too. This was a big surprise, I did not. I wanted to make sure that my oldest child had a different outlook when it came to math and science. Reason being my attitude was negative like the rest of those in the world who had/have a bad attitude towards those subjects. I have actually learned more by helping my children and attending parent meetings on various subjects. (I can thank the staff at Neithercut specifically, Debra Ramsey, parent facilitator at Flint Community Schools). I loved the math and science nights because this information made it easy for me to help my child. Also, it gave me great ideas to do at home and outside of the home. Math and science are everywhere. For example, cooking is a great way to teach fractions! But with all that said I have a positive outlook concerning this coarse that I am currently taking...