Monday, December 10, 2012

Math and calculators

So, for my last post I decided to take a poll on Facebook. It was "How many people hate doing math without a calculator?" I got a good response: 10 people said they hate it, 1 person said depends on the math, and 1 said they hate when you have to use a calculator. One response was from a math teacher she said "I'm a math teacher and i always double check my work with a calculator better safe than sorry" That is a very valid point. It's a shame no a days that so many people rely on technology for answers. I myself and victim to that, I always use a calculator to do, even the simplest, math. At work I am a head cashier and we have to what they call price accuracy.  We used to have to fix meat products which are by pound. I would always get the calculator because they idea of multiplying a problem such as 4.13pounds times 3.59, but since I started taking Math 107 I wanted to try and do it on my own. Ever since I started doing it I kept doing it. It was so much easier to be able to just walk over to the cash register do the math, and fix the problem, then trying to track down a calculator. I will admit there is some math that requires a calculator, but then again how did they do math back when there wasn't any technology. The idea of trying to divide 2.3786 into 3,000,500,900.87996 would be scary without a calculator. I wish that technology didn't provide such a crutch to people around the world. If you think about kids today would be outside all the time if it wasn't for technology. It is so much easier for a parent to put their child in front of a t.v. instead of taking them outside. I am glad that we got the chance to go through a math class without a calculator. In all my years of school I remember always having a calculator during class, math, and tests. I always have an IEP that says I can have access to a calculator. It was great seeing short cuts to understanding and completing math problems. When we were told we were doing decimals and fractions without a calculator I nearly had a panic attack. It actually wasn't that bad though, I never really gave it a chance. I must say that this class has been an eye opener for me and I look forward to continuing part 2 of this class.

Sunday, December 9, 2012

Montessori math at home?

It is amazing what technology can give the world today. For instance, Montessori math approach at the touch of y our hands on an i pad. Now children can us Montessori method at home without their parents having to spend big dollars for them to go to the school. But what is Montessori exactly? "Montessori education is characterized by an emphasis on independence, freedom within limits, and respect for a child’s natural psychological development, as well as technological advancements in society." Montessori.org Children in a Montessori program are more independent and can choose what they want to learn. So if a child wanted to spend most of their day playing with this Hundred board, they could. Typically a child in Montessori stays on a topic until they mastered the topic and move on. Montessori believed in Pascal's theory that the human has a mathematical mind. Montessori also said that the human mind, or mathematical mind, is “a sort of mind which is built up with exactity.” "The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error." http://www.infomontessori.com/mathematics/introduction.htm 
Since, infants learn the world through sensory skills Montessori believed in incorporating these skills into math. All of the ways children learn math in a Montessori program are hands on, like the sand paper numbers. Shown above. It is in early childhood research and theory's that children all start their learning with their senses. A child learn through touching and experimenting with objects. I think the Montessori approach to use this known fact of development in her math approach, and all of her approaches are great. I found this cool website that gives a break down of what Montessori math is all about, it's a bit lengthy but if your interested here is the link. Montessori math 
But, all together I think it's a cool idea to introduce some of the Montessori math approaches to children who can't afford to go to such schools. With kids so obsessed with technology these days, why not give them programs that have an educational value to them?  

Monday, December 3, 2012

Math and students with disabilities.

Is it possible for students with disabilities to learn math like children without disabilities? Yes, according to CEC, Council for Exceptional Children, children with disabilities can learn problem solving in math and grasp the concept as well. In the article it says: "New developments include mechanisms to identify children who will have difficulty with math in the early grades, techniques to help students problem solve, moving from computational math to a more conceptual framework, and ensuring that students with disabilities are prepared to tackle advanced subjects such as geometry and algebra - even if they haven't mastered all the computational elements of mathematics." This sounds amazing, it seems like people are always giving up on special needs children and it is such a shame. To know that it is possible for them to learn the same concepts in math as non-disabled children is very heart warming. It is also said however that teachers will have to change their approach to teaching math to children with disabilities. John Cawley of University of Connecticut states, "They will need to place more emphasis on understanding the basic principals of mathematics, as well as making the subject accessible and meaningful to students." Although it sounds silly that just by changing something so simple can make a difference, it is found that a lot of special education teachers are finding this change rewarding. It is found that students with disabilities are doing just as well as their counterparts and are becoming more confident in math. The teachers who are changing their methods are still staying in the guidelines  of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics.
     There are strategies to follow when you see a student with disabilities struggling with math. This is because students with disabilities, "....may have difficulty reading the problem and/or they may just take the numbers and add them up, disregarding what is to be solved." It is best to help the student first identify what time of problem they are trying to solve by concentrating on the specific information in the math problem, a good way to do so is have them draw a picture. Visuals can be a great way for students with disabilities to better understand a problem. This is actually true with anyone trying to understand a math problem.Another method would be to introduce the word problem on video, this would allow the child to visually see the problem and play it as many times as needed. John Woodward states : "we no longer live in a computational, paper and pencil world, we must base math instruction on conceptualization. He recommends using visualization, number lines, and other manipulatives to help students understand place value, fractions, and even algebra. That way, students can see what's really going on when we do division or positive and negative numbers." This is a very important aspect, I believe everyone, not only students with disabilities, need visual aides to best understand the concept that is being presented.  If you want to read more on the article I have been talking about click the following link: students with disabilities and math

Wednesday, November 28, 2012

Ma & Pa Kettle Math

It's amazing to think that someone could say 5 goes into 25 14 times. I know that Ma and Pa Kettle was just a old comedy show back in the day, but by watching this video on you tube I was amazed. It really makes you think. Pa Kettle argued that 5 goes into 25 14 times,because 5 doesn't go into 2 but it goes into 5 once and you bring down a zero and 5 goes into 20 4 times. Watch the video,  then Ma kettle proves it with multiplication and Pa goes to prove it by adding 14 5 times and gets 25. It's wild, it makes you really understand why math has rules, if math didn't have rules anyone could come up with what they believe is the correct answer to a solution, like Pa Kettle. It also makes you think why are the rules of equations the way they are? Some are proven some aren't, why are the one's that aren't proven followed? This is one of the reasons why math both confuses me and amazes me. I was always able to catch on to how to do and equation but I was also the one to be like why I am doing this? I would always over think it so I got turned off to math. But back to the video, not only does the way Ma and Pa Kettle perform the math work out but they are so convincing! If they were teaching a younger child who is new to math that child would believe them! But then again if your teaching a younger child who is new to math anything you want they may pick it up as being right.
                  So that brings me to my next topic that I was thinking about because of this video. If a teacher isn't properly teaching their students math then the students will be learning the wrong ways to do things. In grade school I had a lot of teachers who taught different methods to getting a solution, I didn't like that. This can confuse students who were taught one way by their previous teacher and are no being told to do it a totally different way.
                  But what it all comes down to is that if someone believes that math is done a certain way it is hard to steer them otherwise. You can't really prove to them that your way is the right way if their way makes sense to them. I think that the rules of equations should be integrated into anyone that is studying to become a math teacher. If the teachers are well educated in what they are teaching then the students will learn correctly, and not become ma and pa kettles.

Thursday, September 20, 2012

abc conjecture...what?




            The New York Times put an article out on September 17, 2012 about a mathematician, Dr. Mochizuki, who posted a 500 page paper on August 30. In this paper he claimed to solve the abc conjecture. This is the use of letters that represent mathematical variables in equations, where 3 integers share no common divisors other than 1. This means they will be all primes numbers since even numbers are divisible by 2. I.e. a+b=c.  This of course has many mathematicians in an uproar of excitement and doubt. Some are saying that if it’s true it would be a great break through while others are questioning it. Minhyong Kim, a mathematician at the University of Oxford in England and the Pohang University of Science and Technology in South Korea, said ““It would be a fantastic breakthrough.”    The ones questioning it say, how can you agree with it if you can’t say what the ingredients are.  It is said when someone first starts to read it, it looks like something from outer space, interesting. But none the less it should be taken into some seriousness because Dr. Mochizuki already has significant numbers of proofs under his belt. It is said that it will take months if not years to carefully review this new information and the information already gained from previous years. This is a new language basically that has to be carefully broke down and understood. How cool would it be if he did solve it though? I have a hard time as it is understanding math but to know that there is people out there that can actually break math down piece by piece and make sense and proof of it, wow. It’s easy to understand that if you have one apple and put it with another apple you get 2, but something of that complexity, to actually be able to prove it, is out of this world. There will definitely be a lot of people arguing this breakthrough and a lot going along with it, but to say which side I’m on is hard.  As I said before math is hard for me as it is and to be asked to agree with someone who claims to have proved a theory on math, forget it. But to also say I disagree with it is a lie, because I don’t know it. I think I will leave the solving of major math theories to the professionals and stick to my lectures and textbooks. To go any further I think would make me go insane. Does anyone else think they could try and understand proof to a major theory? 

Sunday, September 9, 2012

To be a math phobic or not to be?

    Is there such thing as having  a math phobia?  Yes! There are many people who when they see numbers start to panic and try to avoid it at all cost. I myself believes all math should be done with a calculator and avoiding. I work as a head cashier in my job and we have machine that counts the registers for us, the register tells us how much change to give, and I always have a calculator in my pocket for price adjustments. Anytime I have to figure out math with a piece of paper and writing utensil I blank. It can be the simplest math problem and I suddenly become dumbfounded. Why is it though that this happens to people all over the world? What causes this fear of numbers?  How can someone overcome the phobia?

    Well I did a search on the internet and came across a web site that gives explanations for most of these questions. The website is http://www.anxietyatoz.com/anxiety-types/math-anxiety.htm. According to them math phobia is created when someone is has a bad experience with my in the past. Such as a child in school who gets a question wrong and is embarrassed in front of other students. It can also come from teaching methods in which someone is taught. When a deadline is put on a student to learn way more than they are capable of they do poorly, causing them to think they can’t handle math and give up. When someone has a phobia to anything they always have symptoms. Someone who is math phobia may all of a sudden be confused, negative, have loss of memory and be hit with a sudden panic.  They may also have physical symptoms as well such as sweating, increased heart rate, headache, and nausea.  It kind of seems like being math phobic is a disease, but is it a curable disease or are people such like myself destined to be scared of math forever?

    According to the website, there are ways to try and overcome math phobia. First, support is a BIG one. With teachers, family, or colleges there helping you through your phobia it can make it easier. It will help show you that it is ok to be afraid but that if you keep working at it you can overcome it. People can also practice more, practice makes perfect. Ask someone to show different techniques on how to approach a math problem and hopefully one will come more easy and you can finally understand. The one I feel is most important, is to believe in yourself. You can have anyone telling you, “you can do it”, but unless you actually believe in it you can’t. You will always hold yourself back, instead be the voice inside saying, “it’s just math, try your best and see what happens.” And for those who are really math phobic, go see a psychologist. They can help you get down into your inner self and resolve your conflict.

    Well after all that, I am still math phobic. But I know I can only do the best I can and that’s good enough. I did a lot better on the  first 2 quizzes then I thought I would, so that’s a step! For everyone else who is math phobic, good luck! We can overcome!