Teacher Resources

Looking back on this semester I started wondering where on earth I was going to find all the materials I needed in order to teach math. We had to do a project as well that involved making an interactive map that would teach a chapter we had learned. I decided to do my map on the basics of whole numbers, but what I learned was in no way basic.

There are so many resources right at the touch of a button available for us today. I now realize that many great worksheets were already created and could save a teacher valuable time. One site in particular carried great information, http://www.proteacher.net. This website is a collaboration of teachers who have questions, information, papers, games, and more to share with each other. To give you an example, I was looking for information on working with number sets. I could not find this information anywhere on the internet- but then remembered this site. I typed in basic wording and came up with 3 forums. One includes a great worksheet from a teacher who used it in her own classroom (Here is a similar link to the one I found http://amazingworksheets.blogspot.com/2009/02/count-and-match-ladybug-1.html).

I am so impressed with all the wealth of information out there for teachers that I am now feeling quite confident I will have all the materials needed, plus some! Additionally, using an interactive map gave me an area to link all of this information to without overwhelming my computer. This map saves the information directly onto it and allows the user to easily access it anywhere with internet availability and a computer. The specific map we used was by http://www.mindomo.com/#editor, but there are many out there for use. I can't wait to get my teaching career going, and now I have confidence in knowing that I have access not only to great materials, but great people as well.

Applicable Integers

What are integers? Why are they even important? Words like integer can often times be confusing and frustrating. I have found, especially with this last semester in math class, that it is important to carry a dictionary on hand or be able to research words to learn their definition. Often times when we learn the definition of a word, we realize we already knew what it meant- we just didn't know the "official" name.

Granted, Integer is a basic term- but many people don't know it or don't remember it anymore. So, to make sure we are all on the same page I am going to use Merriam-Webster's definition:

Definition of INTEGER

1: any of the natural numbers, the negatives of these numbers, or zero

2: a complete entity 

(http://www.merriam-webster.com/dictionary/integer)

So, as we can see here... an integer is basically a whole number or zero (ex. 0,1,2,3, etc). But this also means that integers can be negative as well... -3,-2,-1. If we put these numbers all together we could represent them using a number line.

By using number lines we can quickly visualize the total number of items we have. Say we have 3 dollars. We want to put exactly $3.00 of gas into our car. We put the pump into the car and pull the trigger and two or three seconds later the pump suddenly shows we owe $6.00- we went from one full end of the scale to the other. This is revealed in the following number line.

When you study this number line you can see that a positive $3.00 is shown on one side of the number line and a negative on the opposite. If we were to count all the numbers on this scale we would come up with our absolute value of 6, or in this specific case $6.00 of total gas cost.  We can also see that we had $3.00, but now we are negative $3.00- in other words, we better start digging for change or use a card! 

So, although the words we learned today were very mathematical (integer, absolute value, number line, etc.) there's a good chance most of us knew the basic concept behind these terms. Also we likely  use these concepts repeatedly throughout each day whether consciously or unconsciously, pretty amazing! I will end this post with a cartoon I made for my other math class, I hope you enjoy it!

Multiplication Meltdown

In this post we are going to discuss multiplication. I'd like to start out by discussing how confusing multiplication can be for many of us. I will use my husband as an example (again!)... he uses math daily at his work- but hates trying to multiply in his head. He gets so confused... all the numbers get jumbled up inside his head. There are reasons for this... possibly, he never learned the basics of multiplication (times tables, etc.)- even more likely... he never really learned how we can group things out. The below video shows this conflict in a somewhat humorous- but rather realistic manner... the age of the video let's us know that this has been a problem throughout the years.

To look at multiplication... we must first learn to break apart what we are multiplying. We are going to observe this in one more video- one you may be familiar with! It's going "old school" but it is a great video to show how we break multiplication problems apart and group the numbers we are working with.

From this video you can see that multiplication isn't just about memorization... 5 x 5 = 25, it's about breaking apart the problem. Imagine 5 kids who each own 5 toys... if those kids had a party and brought their 5 toys each... how many would there be total? You can visualize each kid owning 5 toys, you can visualize them bringing their toys to the party... and then you can see the 5 separate groups of 5... then you could even count by 5's.... 5, 10, 15, 20, 25- our answer is 25.

By visualizing the problem we can work at solving it in a way we are going to fully understand- a way that will set the foundation for other similar (and even different) problems. We will learn the skills to break things apart and look at them in a way we will really be able to understand- and just as important, we will see that there is more than one way to solve a problem... and still get to the correct answer.

Useful Tools in the Form of Technology

Why does it seem like it's hard to connect with the younger generation? Many adults even find the younger generation intimidating. The truth is that we are not connecting with these younger generations like we used to. For many of us it's a mystery as to why this is happening, but I am going to try to solve one small part of that mystery that I have personally been experiencing.

It often seems like kids are bored with school, homework, or even family time. This is huge to me because often it seems like kids just don't care. The problem I think we are actually having is truly boredom. If we look at the lives of our kids or students, they are constantly active and moving- they are texting, talking, or emailing. They play interactive video games, computer games, or watch high action movies. After all of this happens, we then expect kids to sit still for hours on end while being lectured to on multiplication and division. It's no wonder students lose interest.

How do we solve this problem? By incorporating the interactive tools available to us. Many schools are now equipped with Smart Boards and at minimum, computers with projector or Dot cam screens. We can use this information to look up exciting games like at http://www.funbrain.com/kidscenter.html, or http://www.coolmath-games.com/. So many kids know what apps are on phones now, why not give them a fun math app- instead of games like "Angry Birds," etc. (don't get me wrong, "Angry Birds" does teach distance and other skills). This way they can play math at home and sharpen their skills.

By using the tools students use and spend much of their time using, we will be able to connect with them in a way they are comfortable with and excited about. I think connection is such a huge key here in shaping their future. How many people remember their parents not connecting with them? Parents who hated disco, the Beatles, Rap, or even Sesame Street. What if your parents would have used those things you were interested in to help your learning process and connect with your interests? How would that have changed your life today?

Equivalent, but not equal.

Math 1510... BLOG 2:
It's fascinating to see how students in younger grades learn how things have values. This is something most of us take for granted... but can you imagine what life would be like if we were never taught that 1 equals one thing (whether it is an apple or a dog... we know there is only one if we say 1 dog). I have included a video below to give an idea of what is meant by equivalency.

So it is pretty clear to see how important it is to learn at a young age relationships of items and numbers. This relationship can be explained through the use of equivalency. Most of us use equivalent relationships on a daily basis without even knowing it! When we compare lists of things, picking the cheapest or the best item out of a group of items (whether cost related or quality related), comparing a collection of books, dvd's, cd's, etc. to our friends to see what we or they are missing from the collection, even just looking at a calendar and associating what day it is with what number.

If anyone is out there checking out this blog- I would love it if you would write a little note about what you think the world would be like if your teacher would have never taught you values and equivalencies... what if you would have never learned that an apple could be represented by the number 1 or more than one apple with the numbers 2 or more? There is also a little survey on the right side of this blog to go with this topic.

Let's begin at the beginning, a very good place to start.

Math 1510 Blog:
So, maybe you aren't like me- and you did great in math, and it was never a problem for you. The fact is that even if you are a math pro. you still may be able to pick up some good tidbits through this site. First off, I would like you to answer a question on the right side of the page about 8 friends.

This question really got the ball rolling for me- it made me realize how robotic my former education shaped me to be when it comes to math and problem solving. Granted, I'm not a rocket scientist- or a mathematician... but I am going to be an Elementary teacher- and after this question, I realized just how easy it is for teachers to just teach methods and techniques without revealing the reasoning or real life that goes with the problems.

After working at question #1, you may have found your brain trying to solve the problem by reverting back to methods that may have been impressed upon it. Did you try to multiply? Did you break the problem apart? These are important steps to working towards a correct answer... in fact, it is said that we must all go through a process before we can actually solve a problem.

The process is described below:
A problem is a situation for which the following conditions exist:
1) It involves a question that represents a challenge for the individual
2) The question cannot be answered immediately by some routine procedures known to the individual.
3) The individual accepts the challenge.

To associate this with the problem posed on the right we can say that a question (8 people, how many handshakes?) was asked and perhaps represented a challenge to you. Perhaps you already knew the answer or perhaps you have learned the proper methods of solving it through a math class- but you still had to read the question that was represented. Next, you may have needed to use a procedure to solve it. I did as follows:
I know that 8 people shook hands, and the first person shook 7 people's hands (they don't shake their own hand so we can't count 8). Each time decreases by 1 since the person previously shook the next person's hand. I then add up all the shakes, getting 28 total. The chart below reflects this:
People           Shakes
1                       7
2                       6
3                       5
4                       4
5                       3
6                       2
7                       1
8                       0

Now I know there are other methods I could have used (equations with "n" representing an unknown number or "s" representing shakes... and for larger problems I would have done this... but for me this is how I had to break it down at first before learning the equations). So, lastly- we see that the individual accepts the challenge and tries to solve the problem... Kudos to you guys out there who tried to solve this problem- great attempts!! If you answered 64... do you think this could possibly be from the methods that were impressed upon us as young people? Use multiplication, use division, use formulas, etc.- but now we can see that there is more to it, we can't look at it initially and plot in a formula. We need to break apart problems and study them, and when our brain gets all jumbled up (like mine often does!)... we need to look for help and research how others have solved problems. By doing this we will gain the skills needed to figure out things we never knew we could before!

So, I suggest we all look at math from a new light... instead of seeing it as something that was imposed upon us at a young age- let's see it as a mighty tool that we can use to solve everyday challenges. We must take the challenge, solve the problem- and triumph! It's like a computer game or Wii game, we love them because they challenge us- we try to beat the game. Let's use math in a similar way- take the challenge, beat the problem... and you will feel a great sense of accomplishment.