Math for Elementary Teachers II 1512

Fundamental Counting Principle

When two events occur sequentially, and you want to know how many ways for these events to occur together, you can use fundamental counting principle. And it's something that is very easy to visualize and figure out! Two things I love when doing math.

For example if you have event X that has 2 different outcomes and event Y that has 5 different outcomes, then there are 2*5 different ways for events X and Y to occur together. It doesn't get much easier than that!

You can also use fundamental counting principle when you have more than just two events as well. You just continue the multiplication process. An example would Be event A has 3 outcomes, event B has 6 and event C has 3. The total different ways for outcomes to occur would be 3*6*3.

I think this process is so easy to use and follow. It is very quick too!

Math for Elementary Teachers II 1512

Tim Bedley and His Teaching Techniques

So Tim Bedley likes to use a process of teaching by letting students figure out the answer without being told the answer, even when they have questions. Instead of giving them the answer, he turns there question into another question that they can understand and are able to figure out the answer. I think this is awesome. What better way to teach than to actually show students how to figure things out, on the own.

Without a doubt I think this process not only teaches students things, but teaches them in a way that they will remember and feel confident in using. They can actually think of how they previously solved the problem and how it can be used to solve other problems! Brilliant!

In his video he uses different outfits to engage his classroom and how many possible outfits they could make with 3 shirts and 3 pants. Here is the link if you would like to check out the video https://clc.ims.mnscu.edu
/d2l/lms/content/viewer/main_frame.d2l?ou=1389676&tId=11007266.

An example I think that would work great with students would be using healthy snacks, how many different healthy snacks could the students make with 2 fruit choices, a choice of milk or juice, and a choice of yogurt or nuts. I think the children will like seeing what is possible and they always love food so if they could eat some of their results I think it would help the process stick even better!

Here is a short video of a student talking about how much she enjoyed Tim Bedley's teaching style and how she had fun and learned more!

Math for Elementary Teachers I 1510

Estimation

Where would we be in this world without estimation? About this much, about this far, almost, close to and so on. I would be lost! And I think that students would also be missing something if they are not taught estimation and how or when to use it and how it helps.

There are so many different benefits of estimation. Lets start with the simple ability to quickly add up or subtract a group of numbers for fast results; an example would be at the grocery store and trying to figure out your total, or how much change you will have.

I cannot imagine not having this skill, I'm pretty sure it is something I use on a daily basis. It isn't only helpful when I am grocery shopping, or giving directions but also when trying to figure out an array of other things. When students are learning to add it can help them come up with the answer faster than figuring out exact figures. They can estimate, then if needed go back and figure out the exact answer and see how close their results were. It is a great learning process and tool.

If you have difficulties estimating here is a helpful site: http://www.aaamath.com/est.htm 

Math for Elementary Teachers I 1510

Reaching a Consensus

After viewing a video watching a classroom figure out an answer to a problem, without too much help fromt he teacher was an eye opener. There is a teacher in the classroom who is there to help the students, but not give away the answer, after seeing how well it worked and how much the students helped each other solve the problem when one was wrong, showed me a new way of teaching. This is the video that I watched demonstrating this technique.



I think reaching a consensus is a great way of teaching, instead of just asking for the answer right away when they don't know it. This way they are hearing several different ways other students have found the answer and seeing different ways of the thinking process. Although, I can see how it might be a little confusing if they are getting the wrong answers for themselves and other students, this is where the teachers presence and leading them in the right direction without giving away the answer is so much more beneficial.

The students in this video had so many different ideas on how to  figure out how many dogs each person had, almost every student had a different way of thinking and showing a different way to come up with their answer, whether it was or wrong it was how they thought. Then when talking with other students they were able to see the correct way to solve the problem and agree on one set answer.

Math for Elementary Teachers II 1512

Mean, Median, Mode and Mid Range.

Sounds like a bunch of words that have nothing to do with math to me, well at first they do anyways. When I think of figuring out the Mean of a group of numbers I usually call it the average. It is the same procedure and gives you the same answer yet it has another name, why? To try and confuse me? Or is there a real reason that has logic behind it?

Median to me automatically makes me think of middle, which helps me remember what step this is; the middle number in a list of numbers. Nice and easy, especially if the list of numbers is an odd amount!

Mode, why not just say most? That would be easier for me to think of when I am trying to find a mode in a group of numbers. No mode, would mean there are no numbers that repeat themselves, so again most would still make sense (to me anyhow) because if there are no numbers that appear MORE than any other number then the answer is no.

Finally, the word Mid-Range, which for some odd reason makes me think of home on the range every time I see it. Kind of makes me chuckle, but of all the terms listed in this blog I would say this one is closet to what you are actually trying to figure out. So whomever made up these terms for these procedures gets a thumbs up on mid-range :)

Here is a catchy little tune for remembering these procedures: http://www.youtube.com/watch?v=oNdVynH6hcY

Math for Elementary Teachers I 1510

How fun are Egyptian numerals, Babylonian numerals Mayan numerals. I can only imagine how long it would take to actually work with these graphics, but they do look cool. I've never actually worked with numerals other than numbers and I found this part of the chapter pretty interesting.

When using Babylonian numerals, for example, I did first have to learn how to multiply by the base number which at first was a little challenging. but after doing a few problems I caught on pretty quickly. It also took me a few minutes to see where the position of a digit is in relation to its value. It does take a little longer and a somewhat drawn out process of finding what each graphic equals then multiplying then adding, but none the less it looks cool so I like it!

I wonder what it might have been like to live in a time where I would have actually used these graphics for math problems. I also wonder if what I am think about them is what an ancient Egyptian might be thinking about our numbers and how we do math. A question I will never have the answer to, such is life!

Here is a short YouTube video that talks about Babylonian numerals. http://www.youtube.com/watch?v=fPHBeYtp1Tw&NR=1

Math for Elementary Teachers I 1510

So it is the second week of class and I am already starting to feel lost. Numbers can be very overwhelming sometimes. I usually enjoy math and find it fun to solve a problem and get the right answer. But somethings in math I don't think I will every fully understand.

For example, this week we have been learning about sets, subsets, intersections, unions and a lot of other stuff I one minute I think I am understanding things and the next I find myself at a loss and very confused. Does anyone else seem to have this problem? If so what or how do you figure things out? Or if you understand these mathematical words and procedures that go with them can you please explain them to me in a light that I will possible understand! Please :)

A website that I sometimes use to help me through some questions I have is http://www.onlinemathtutor.org/help/math/sets-intersection-union-subsets-disjoints/ it gives a few definitions of things, and shows what symbols mean, and even has a spot where you can do math problems.

Math for Elementary Teachers II 1512

Analyzing data, where to begin right? After going over this weeks topics I feel like I am seeing things for the very first time. Ways of graphing and plotting and the what have you's on how to put information into a readable and usable form.

But if it's supposed to be so readable why am I some what if not more confused by the data shown in a certain ways than I am just looking at the numbers? For example a back to back stem  graph; am I the only person who has never seen or heard of this before? When or why would anyone use this or how would  this be an easier way to look at numbers?  When I see a list of numbers all missing the first digit which I then have to reference back to to the stem I am like what? To me it just seems more difficult or easier to misread a line and have a wrong number.

However, a way to show data that I do like is in a graphical way. Like a dot plot or a circle graph. It seems so much simpler to just look and see what you are looking for. Now I know not everything can be put into a graphical display for but wouldn't that be nice? It would be for me anyways :)

Here is a fun little website that you can make all sorts of graphs in easily, it's actually kinda fun too!
http://nces.ed.gov/nceskids/createagraph/

My First Blog, EVER!

Hello! This is my first blog and I am very excited to be learning something new! My future blogs are going to be math and teaching related and I hope to learn new things and even teach you a few new things with these future blogs!