Why I Married Tyler

Most people see my sweet husband as a quiet, shy guy. More of a background kind of a person who's really good at keeping me balanced. This is all true but what no one else knows or sees is how hilarious and DRAMATIC he is. Here's a few of Ty's statements-

I walk into Ty's apartment... 45 minutes late...

Ty: {Eating peaches straight from the jar} I'm eating peaches. You know how angry I get when I eat peaches.

Walking to the car after school...

Ty: Sometimes when I'm at work {at Costco} people pull out their Sam's cards and it's like a shock to the heart.

As we're grocery shopping, picking out some hot cocoa mix...

Ty: Just for the record, I like my hot cocoa with milk. Not water. Milk. Am I making myself clear?

Watching a movie...

Ty: Oh girl. I love you. {Completely unprovoked}

Emily: I love you too.

Ty: I love the way you make the Mac N Cheese.... I love the way you pour the milk

So there are just a few but I'm looking forward to many many more.

So We're In Love

This is what happened in the last six months.

We met on a blind date doing this:

Neither of us wanted to go but we did. We were set up by the one and only, Jenny Bush, who is the reason for three eternal companionships.

And then I went here:

And Ty went here:

And I thought maybe we wouldn't work out because many a relationship has been murdered by EFY. But we talked almost every night and then finally we were able to spend my week off together.

And we went here (Lagoon):

And here (Idaho):

But then I went back to EFY and after 2 days of that we decided it was too hard without each other, mostly because we loved each other.

But then I went here:

And though I love my family, I really missed Ty. And I told him that I was getting back two days later than I actually was. I surprised him and he hugged me so tight I couldn't really breathe.

And for our last summer hurrah, we went here:

And the Disney Magic really got to us.

So then we decided that what we really wanted was to be together forever.

FOR-EV-ER.

And on September 27, 2010, this is what happened:

And on December 18, 2010, this is where we'll be going:

So we can live happily ever after.

Blog #7

Farren, L. H., Olson, J.C., & Davis, D. (2010). Shrinking your class. Mathematics Teaching In The Middle School, 16(7), 386-391.

This article describes how bringing in hands on activities help students grasp a relational understanding of the concepts being taught. The school brought in grad students to teach students about scaling and ratios. They started with different toys spread out across the room and had the students guess to what scale they were being represented in comparison with its real life counterpart. After they got comfortable with those concepts, students made models of themselves using a scale 20 times smaller than themselves. They used aluminum foil, floral foam, bendy straws and toothpicks to construct themselves and then they were allowed to construct accessories to go along with them.

The article spent a lot of time explaining the specifics of the activity rather than the purpose or outcome of the activity. They authors almost sounded surprised that come testing, students were able to remember scales and ratios better than other concepts that were being tested. Of course students will remember the hands on activities better! They have experiences that will be able to remind them of the things that they learned. So I agree with the main idea of the article, I think the activity would be very beneficial in a classroom, however, I think the teacher and author were a little bit dense if they were surprised at the outcome.

Blog 6

Guerrero, S. M. (2010). The Value of Guess & Check. Mathematics Teaching in the Middle School, 15(7), 392-398.

This article attempts to justify the importance of guess & check. Guerrero suggests that when students are taught how to make educated guesses, it's much easier for them to make more educated guesses with later situations. They are able to learn directly from the immediate problem they might be working on but they are also able to learn generalized techniques for other problems Guerrero specifically uses an example of a story problem where students have to find the individual lengths to each side of an enclosed fence.

I believe that guess and check is always a valuable tool, especially when you don't know at all what to do. In fact, I've never questioned the validity of the technique. I think it's a powerful learning tool, especially when students are wrong. They can see where they went wrong and what they can do to fix it. There's so much learning that can come from getting things wrong. I've noticed with my school work, when I get things wrong, it's more of a motivation for me to go back and figure out where I went wrong and how to fix it. After that, I usually have that knowledge forever because I took time to learn it.

Warrington Paper

There are a many advantages to Warrington's take on teaching division of fractions to her students. One is that it develops a relational understanding before it even introduces an instrumental understanding. The students never attempted to "flip and multiply" because that wouldn't have made sense to them yet. Another is that the students estimated before they actually tried to get the right answer so they new an approximate range that their real answer should be in. This also shows that they were developing a relational understanding. Another plus to this technique is that Warrington didn't tell her students if they were right or wrong and let them lead the discussion in class, whether it was in small groups or the whole class. This allows students to feel safe in the classroom and let them share their ideas without the fear of being wrong because no one actually knows if they're right or wrong.

There are disadvantages to this technique as well. One is the fact that it takes a lot of time to go through this kind of discovery process with every kind of mathematics that you come across. In some cases, it would be so much faster to slap an algorithm on the board and call it good. Another disadvantage is that if there's one student who understands right away, they kind of inhibit other students' learning because they are not given the time to figure it out completely on their own. I know if classes that I've been in that sometimes I just wait around for one of the "smart kids" to bust out an answer, sometimes because I have no clue what's going on but sometimes because I'm just lazy.

Constructivism

According to von Glasersfeld, constructivism is the way that we learn. He suggests that all of our learning and our ideas come from past experiences. Our reasoning is not questioned, regardless of what we are taught in lectures, until we have some real life experience that makes us change. Until our conclusions are questioned, they remain correct in our minds. Von Glasersfeld uses the word "construct" rather than "acquire" or "gain" knowledge because knowledge is not something that someone else can hand to us. Knowledge is something that we have to build and modify all on our own.

Similar to what we did in class with the fraction blocks, I think a way that I would bring constructivism into my classroom would be through visual explanations. Concepts and principles don't always make sense in lecture form. If I used hands on experiences, such as the blocks we used in class, the physical aspect of the exercise would shatter any ill-conceived principles or rules that a student might have constructed on their own.

Benny Article

In Erlanger's paper about Benny and the self taught math program, his main point was that it doesn't work and that teachers are necessary to guarantee a certain level of success. Benny was clearly a bright child since he managed to make up math rules that made sense to him and they worked for him about 80% of the time. His teachers didn't notice how much he was struggling because in comparison with the rest of the class, Benny was doing quite well with the program. His teachers had no reason to work individually with him unless he asked for help, and even he thought he was doing well so there was no reason to ask for help.

I think it's ridiculous to think that teaching mathematics principles can be done without the guidance of a real live teacher. If you don't know the correct math rules as a student, and you don't build upon those rules, you will not be able to progress very far. The high school student that I tutor had a very "hands off" math teacher last semester. Now she has a new teacher, and when I come to help her with her homework, most of it is finished ahead of time becomes she's gaining relational understanding at school just because her new teacher is involved with his students.

Skemp's Article

Skemp's article discusses the differences between relational understanding and instructional understanding. Relational understanding involves knowing the proper way to solve a problem, including how you would set it up, and why you would set it up in that manner. Instructional understanding is knowing which algorithm to apply without knowing the reasoning behind it. From these definitions, you can tell that instrumental understanding is included within relational understanding just like the diagram that we drew in class. Each of these has different advantages. While instrumental understanding is relatively simple and just takes memorization, relational understanding provides long term benefits because when you understand the "why" of a problem, you can easily replicate the "how". Instrumental learning can provide results fast, and when a student gets the right answer quickly it can give them confidence. However, when teaching new information, relational understanding can be applied more readily. A student wouldn't always see which numbers to plug into an equation without having a relational understanding. When a student understands relationally they are less likely to seek external rewards and they are also more likely to seek relational understanding in different areas of life.

First Post

1. Mathematics is the study of numbers and their practical application in our daily life.
2. I learn mathematical concepts best when they are explained to me and then I have time to try it by myself, make mistakes, try to fix my mistakes, and then ask for additional help. In high school, math came easily to me so I never had to branch out and try other methods of learning.
3. I think my students will learn best visually. I have found that it's easier for me to explain things when I have a picture or diagram or something to show.
4. Student have more tools and resources in the classroom than there used to be. Technology has played a huge roll in that. I know growing up that math based computer games not only helped me learn, but made it something that I enjoyed and wanted to spend my time doing.
5. I tutor a high school student. I asked her what the square root of 100 was and she pulled out her calculator. I was in shock. In her defense, her mother said that when my student was in the 4th grade, "they" (I don't know who "they" is, the people who make decisions I'm assuming) had decided that they were no longer teaching times tables and that mental math was a thing of the past. Just watching my student struggle through basic math shows me how detrimental that is.