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.

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?  

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