Thursday, May 26, 2011

P/T Conference Article

Monday's (May 23) Teacher2Teacher, a blog I highly recommend, featured an article regarding Parent/Teacher Conferences - something many teachers and parents face with anxiety.  It is entitled The Parent Teacher Conference: The View from the Other Side of the Table by John Blake.  It is a worthwhile, practical article with information any teacher can easily put into practice. To read this article, click on Teacher2Teacher Blog on the right hand side of this posting under Teacher Created Products.  John also has many products for sale at his Teachers Pay Teachers store.  

Listed under his article are several resources created by teacher for teachers.  I am fortunate to have one of my products included - Conference Checklists Based on Characteristics, not Grades.  I hope you will check it out.  Just click on the link below.

Parent Teacher Conferences

Wednesday, May 18, 2011

Much Ado About Nothing

I have decided to post some questions about zero that my college students have asked me in class.  I will say this, "Zero can surely give you a severe headache unless one knows its properties."  

Question #1 - Do you know why zero is an even number?    All mathematics is based on patterns.  Because of this, I know that an even plus an even number will always give me an even answer; an odd number added to an odd also gives me an even answer, and an odd number plus an even gives me an odd answer. In other words:    E + E = E     O + O = E     O + E = O

The numbers 4 and -4 are both even numbers. If we add them together, their sum is zero.  Based on the math pattern of  E + E = E,  then zero has to be even as well.  If we substitute zero in other problems such as 1 + 0 = 1, it fits the O + E = O  rule just as 2 + 0 = 2 fits the E + E = E  rule.

In Algebra, even numbers can be written as 2 x n where n is an integer.  Odd numbers can be written in the form of  2 x n + 1.  If we have n represent 0, then  2 x n = 0 (even) and  2 x n + 1 = 1. (odd)

I say all of this to relate an actual incident that occurred in my classroom.  I wrote the number 934 on the white board, and commented that since it was even it was divisible by 2.  One of my students was perplexed because he did not understand how 934 could be even when it contained two odd numbers and only one even number.  He actually thought that all the digits of a number had to be even for the number to be even.  Funny?  Not really!  Amazingly, he had made it through 12 years of school without understanding Place value as it relates to even numbers. Unfortunately, I had assumed that everyone (especially my college students) knew what an even number was.  I no longer make assumptions about students and their math knowledge!

Question #2 - Is zero positive or negative?    The definition for positive numbers is all numbers greater than zero, and the definition for negative numbers is all numbers less than zero.  Therefore zero can be neither positive or negative.

Question #3 - Is zero a prime or composite number?    To be a prime number, a number must have only two positive divisors, itself and one.  Zero has an infinite number of divisors so it is not prime.  A composite number can be written as a product of two factors, neither of which is itself.  Since zero cannot be written as a product of two factors without including itself, zero, it is not composite.

Question #4 - Why can't you divide by zero?    I love this question.  Back in the dark ages when I asked it, I was always told, "Because I said so."  Being an inquisitive student was not a blessing when I was growing up.  Math teachers who knew all did not want to be questioned!!!!  Anyway, I don't mind the question, and here is my practical answer.
 First, we must understand division.  Division means putting or separating a number of items into a number of specific groups or sets. When you divide, such as in the problem 12 divided by 2, you are really putting 12 things into two groups or two sets. Therefore, if you have the problem 8 divided by 0, it is impossible to put eight things into no groups. You cannot put something into nothing!

 Hopefully, this clears up a few things about zero.
 I leave you with this math cheer. 
(I always wanted to be a cheerleader!)

Zero, two, four, six, eight,
                               Who do we appreciate?

Even numbers!     Even Numbers!     Even Numbers!            

Tuesday, May 10, 2011

Can't Memorize Those Dreaded Math Facts!

Many of my college students come to me without knowing their math facts. Some do, but most do not. Since we use calculators in the class, it really isn't an issue.  It just takes those students longer to do a test or their homework. One day, the students in my Basic Algebra Concepts class (a remedial math class) were playing a math game to practice adding and subtracting positive and negative numbers. We were using double die (see picture) where a small dice is located inside a larger dice. (I have to keep an eye on these because they tend to "disappear". The students love them!)  I noticed one of my students continually counting the dots on the die. He was unable to see the group of dots and know how many were in the set.  It was then that I realized he could not conserve sets.

Conserving sets means that a person can look at a grouping or a set and identify how many there are without individually counting them.  (i.e. three fingers that are held up)  When a child is unable to do this, they cannot memorize math facts since memorizing is associating an abstract number with a concrete set.  Many teachers as well as parents fail to recognize the root cause of this memorization problem.  AND no amount of practicing, bribing, yelling, or pulling out your hair will change the situation.  So what can you do?

First of all, the problem must be identified.  Use a dice and see if the child must count each dot on each face. Try holding up fingers or laying out sets of candy (M&M's - yummy!) or using dominoes. Put five beans in a container, and ask the child how many are in the box. (They may count them the first few times.)  Take them out, and put them back in.  Ask the child again how many there are.  If, after several times, s/he is unable to recognize the set as a whole, then s/he cannot conserve sets.

How do you help such a child?  If you have small children at home, begin the conservation of sets by holding up various combinations of fingers.  My granddaughter just turned four; so, we worked on holding up two fingers on one hand and two fingers on the other; then one and three fingers, and of course, four fingers. I also like to use dominoes. They already have set groupings which can be identified, added, subtracted, and even multiplied. A dice is great because the child thinks you are playing a game, not doing math.  Roll one dice, and ask the child to identify the set of dots. Try the bean idea, but continue to change the number of beans in the box.  My granddaughters love the candy idea because they are allowed to eat them when we are done.  (All children need a little sugar now and then even though their parents try to control the intake.  I love being a Grandma!)

Gregory Tang has written two wonderful books for older children, The Grapes of Math and Math for All Seasons, which emphasize conserving sets. At times, I even use them in my college classes!  I was fortunate to attend two of his workshops presented by Creative Mathematics. He not only has a sense of humor, but his books can be read again and again without a child becoming bored. Check them out! 

Monday, May 9, 2011

My "Handle"

"Cookie", the nickname for my daughter, took a brief look at this new blog. She was commenting about my "handle" and thought "Skippy" was a clever name. Okay, I can see where scipi might be pronounced that way, but no matter how you say it, I thought you should know how and why I selected that name. My husband teaches science so I took the first three letters of that word and put them with pi since I teach math. I thought scipi would be pronounced as "sigh pie", but if you prefer to call me Skippy, I'm okay with that - as long as you don't compare me to the peanut butter!

Friday, May 6, 2011

New to Blogging

My daughter is an avid blogger.  She has always been good with words which means she loved centers and socializing when she was in school.  This is the first time I have ventured into such a new territory as a blog.  I ask myself, "Why would anyone want to read my blog?  I'm not an outstanding writer, but I do love math." 
Now there's the rub.  Who wants to read about math?  Who even likes it?  Many, many times I have heard a parent of one of my students say, "I understand why my child cannot do math.  I was never very good at math, either."  Right!  So you weren't good at reading; so, your child should be illiterate?  So you don't like to play sports; so, PE should be optional?  I don't think so. 

 My goal in life is to make people, students, adults, children, comfortable with math; to see its value; to learn to at least like it.  After all, there isn't a day that goes by that you don't use math in some form.  Did you read a clock today?  Did you buy something with money?  Did you go to the home improvement store to buy paint?  Did you cook or keep score while you played a game?  That is all math.  Useful - right?

 Ask yourself or your students, "What would happen if suddenly there were no numbers?"  To find out, read A Day with No Math by Marilyn Kaye, published by Harcourt Brace Jaovanovich, Inc. in 1992.  It is a great read aloud book.  In the mean time, I will post some helpful ideas about teaching/learning math, AND, if you continue to check back, you, too, might start to like the subject.