Tracygillespie's Blog
Just another WordPress.com weblogArchive for October, 2009
Translating Pattern Narrative into Formal Language
Pascal’s triangle can be described as an quilateral triangle. It is bordered by 1′s going down the right and left sides of the triangle. The second row of diagonals are counting numbers 1,2,3,…. The interior triangles are created by the sum of the two numbers above. Each row starts and ends with the number 1. If you folded the triangle symmetrically, every odd row would match. Looking at the apex and down, the numbers are increasing.
“Working with the definition of linear patterns”
“Working with the definition of linear patterns”
Formal Definition: Non-traditional patterns – patterns that do not follow a repetitive format
Kid’s Language: Non-traditional patterns – a group of numbers or objects that do not follow a specific order
Formal Definition: Linear patterns – repeating indefinitely in either direction along a line/ exists when points form a straight line
My Definition: Linear patterns – a set of objects repeating in a line
The difference between the formal definition and my own is the word usage. Students can relate to a concept by examples. In order to have students learn definitions, you need to have them be a part of creating the definition. Before students are given formal definitions show them examples of number patterns and object patterns. Ask them what they see. Have students work in small groups to create patterns of their own. Then ask the students to come up with a class definition. After, give them the formal definition. Students can then perfect their class definition. They will remember what they created.
“My Reflection on Math Myths”
After reading “Math Myths”, there were two myths that I encountered when I was a student. Myth #1 for me was “Math requires a good memory, and memorizing formulas and rules is the best way to learn it.” Throughout my math education, I only remember memorizing. If there was a rule, the way to succeed was to memorize. Understanding what I was doing rarely happened. Since I have been in education, I have learned the importance of understanding what you are doing in math. I do believe that there is also an importance to memorizing after you understand. There are some rules that will never leave me, for example adding, subtracting, multiplying and dividing integers. Students should be taught to understand what they are learning, the meaning. When the understand, memorizing rules and formulas will not be difficult.
Myth #2 that I encountered as a student was “There is a “math mind” some people have it and some people don’t”. I remember being told this by family members. Not that I didn’t have the math mind but that it was in the family and that I should have one. The problem with this was when I wasn’t successful in math, I felt worse. I eventually realized some concepts I got quickly while others just took some time. There are always students who say, ” I just can’t do math!” It is important to take time with these students to find success in math. Giving them a little confidence could dispel the “math mind” myth.
Having the students make connections, engaging them and having the patience to find a way to make them understand will create “math minds”.
http://pumas.jpl.nasa.gov/
This is an interesting resource for math and science teachers. There are many examples of actvities on various levels. After reading through many examples, I thought that “Grandpa’s Social Security” was a great way of using real life experiences. The problem is to detemine whether Grandpa should start collecting at age 62 or 65. The students need to figure out how long a retiree has to live until the total benefits are the same whether he retires at 62 or 65. This activity teaches the students hoe Social Security works. There is a follow up activity that has the students interview people on social security and how much they make each month. This website should be checked out by math and science teachers!
Inverse Properties
Inverse Properties
When a number is combined with its inverse it is equal to its identity.
There are two types: Additive Inverse and the Multiplicative Inverse
Additive Inverse Examples:
The inverse of 67 is -67 > 67 + -67 = 0
The inverse of -54 is 54 > -54 + 54 = 0
Multiplicative Inverse Examples:
The inverse of 7 is 1/7 > 7 × 1/7 = 1
The inverse of 3/5 is 5/3 > 3/5 × 5/3 = 1
The inverse of 1/6.8 is 6.8/1 > 1/6.8 × 6.8/1 = 1
My Mathography
What I remember most from my early grades in math is memorizing times tables, doing drills and doing even or odd numbers for homework. I loved doing repetitive homework. I felt successful knowing what I was doing over and over again. I did not like percents at all. Now knowing how easy it is, I think back and wonder what I thought was so hard. I did not get the meaning that the number was out of 100.
The first thing I remember learning to do in math is adding. I specifically remember adding double digit numbers and the process of carrying over into the tens column. I also remember doing problems over and over again.
There aren’t any math teachers from elementary school that stand out as a favorite. If I had to choose my favorite math teacher, it was my 9th grade Algebra teacher. She spoke very softly which made me pay attention. She taught the lessons making sure we all understood what we were doing. There is nothing that stands out about the way she taught. I just remember that I did well and I enjoyed Algebra.
Math (except 10th grade-geometry) was always my favorite subject. I think the reason I liked math was that I was never bored. My mind didn’t wonder. If I practiced and did my homework, I understood what I learned. I didn’t always understand but I wanted to learn. Sometimes I thought I could get away with not doing my homework, I learned fast that that would hurt me. A reoccurring theme with me and math is the doing problems over and over again.
I am very active in my boys’ school and volunteer to do things a lot. Last year I was the parent teacher group’s president. I am trying to not do as much, but I did manage to get involved in a very cool idea for a fundraiser. It is a school cookbook. Parents and teachers send in their favorite recipes and then it gets sent to a company to pretty it up and bound them.
We sent the recipe sheets out and have 150 recipes returned. In order to get the cookbooks in before Christmas we have to pay a $200.00 rush charge. The company is really good at telling you how much it will cost to make the cookbooks. It depends on the number of recipes. They also tell you about how many cookbooks will be ordered based on the number of people who turn in recipes. They say for every person who turns in a recipe, they will order at least 2 books. According to the company, 150 recipes will cost $2.95 to make. They even tell you how much to sell them for, $7.00 each. You would make approximately $4.00 on each book sold.
Our dilemma is how much to sell the books for to cover the cost of the rush charge. We haven’t sent out the order forms yet because we aren’t sure what to charge. Some families turned in 1 and some turned in 3. My partner and I think we should charge $9.00. And this will surely cover the Rush charge and have us make $4.00 if not more on every book.
Math Vocabulary
Absolute Value
My defintion: the distance a number is from zero
Official definition: the numerical value of a number without regard to its sign
Links: www.purplemath.com/modules/absolute.htm
Tracy G’s Blog
Hello Everyone,
My name is Tracy Gillespie. I am the mom to 8 year old twin boys. They are very active boys who keep me very busy. They are on a travel soccer team together. Right now it is a little easier but one day they may not do the same activities.
I am a special ed teacher who co-taught on an 8th grade team for 11 years. When the boys were 3, I became a stay at home mom. I have been a substitute in our district for 1 1/2 years and I am currently pursuing a long term sub position. I am also studying for the Middle School Math Praxis. The test is November 14th!
I hope to develop my computer skills by taking this class. I also hope to learn ways to help students with learning disabilities learn Algebra!
