Patterns and Problem Solving

Fibonacci Numbers
In the first chapter we covered in Math for Elementary Teachers, included Patterns and Problem Solving.  Something that was a reoccurring theme that the teacher Amy DelMedico went over was the patterns in our daily life or living things in nature.  When when we saw a picture of a  a Nautilis shell, or a sunflower, I would have never thought math.. or even patterns.  These patterns that occur naturally in nature are interrelated to Fibonacci numbers. Fibonacci numbers traditionally start with 1 and 1, each successive number can be obtained by adding the two previous numbers. 1,1,2,3,5,8,13,21..and so on. Amy Del Medico showed us a very cool video on Fibonacci numbers in class, the link will be listed below.

http://www.etereaestudios.com/movies/nbyn_movies/nbyn_mov_youtube.htm
(This movie was made by Cristobal Vila)

Some examples of the Fibonacci sequence in nature is a sunflower or a pine cone 

Example of Fibonacci Numbers in nature (Below)

Image: Brewbrooks Found At: http://www.google.com/imgres?imgurl=http://amazingdata.com


>A good Blog About Fibonacci Numbers is: Geometry and Nature
>Fun Game for Fibonacci Numbers (its a little tricky at first) http://www.yourdiscovery.com/games/play/fibonacci/




Pascal's Triangle
Another topic we reviewed in Math for Elementary Teachers is Pascal's Triangle. Pascals Triangle is very interesting and has a lot of different patterns. Pascal's Triangle is a triangular pattern of numbers that starts with 1 (in Row 0) and continues to row 1 with 1 and 1 (example below)

1

1              1

1              2              1

1              3              3              1

1              4              6              4              1

The top Row is 0

The second row is 1 

The third row is 2

and so on

the yellow highlight shows 1+1=2 and that is how that line is formed

the second line has 1 and two listed in blue and in the fourth line 3 listen in blue because 1+2=3.

I have highlighted a few just to show how the numbers in in the next line down are developed.

I never really looked at math in patterns, but when I do it seems to come a lot easier.  If you would have told me to try to figure out the next line in Pascals triangle in the beginning I would never have been able to.  But when breaking a big problem down into a smaller one it is much easier to understand it. It is crazy to think that nature and math is related at all.  

>A couple games to help finding patterns are :
Pattern Cracker
Preschool- Crazy Patterns
What Comes Next

I have found on YouTube a video to help finding sequences


I have learned that making connections with math and the real world make it a lot easier to understand and when you break big problems down in to smaller ones it is much simpler. With Fibonacci numbers and Pascals triangle when broken down you can find the next numbers  or sequence with simple addition.

Problem Solving

Something that we have just recently learned in Math for Elementary Teachers is a technique for problem solving. 

Polya's Four Steps to problem solving. (This can apply to more then just math)

Step One - Understanding the Problem

Ask yourself do you understand what is being asked?

If you do not know what a word means look it up, or ask your teacher to clarify further.

Step Two- Devise a Plan

In step two this is where you choose your strategy to solve the problem.

Step Three- Carry Out the Plan

This is the step in what you are doing.

Step Four- Looking Back

In this step of the process you review or evaluate your outcome.  This part involves more then just finding the answer, and this may take more then one time.

I have found that this process is very important in some problems I have encountered in math.  By making sure I understand what is being asked then I know that I am going to answer correctly (or I am at least on track).  When devising a plan I found it important to break the problem down into smaller parts and working from there (carrying out the plan). By looking back on what I have done I can see what I have and have not done correctly and what little mistakes I have made.  

Another important thing I learned from our teacher Amy Del Medico is, Never erase your work.  For example if you have a very long math problem with many steps and you get to the end of it and you do not get the right answer, if you do not erase your work you can look back at your work and see if you made a simple mistake. If you erase your work and you made a simple mistake you may be doing a lot more work then you need.

Me

Hi, My name is Brianna Harvey and I am taking Math for Elementary Teachers at Waubonsee Community College.  I am taking this course because it is a required course to both transfer and to get my associates degree in Special Education.  I love working with children and can not wait to start teaching.

To be completely honest I was really worried about taking this course because I am not the best at math.  As it turns out I am enjoying class so far, it is very hands on, which is different from any math class I have ever taken. When learning new concepts each step is broken down in the problem, and you are told why you are doing it- which helps me better understand a problem and better explain to others what should be done.

One of the assignments for this course is to make a blog, and another is a Inquiry Based Learning Project.

(I have never done a blog before this is my first one, so this is going to be an adventure on its own.)