Section 6.4

In section 6.4 we had an introduction to geometry. In the workbook we used the geoboard method of finding the area of a region. They were easy at first but, were more complex as we went along. We had to learn how to visually break units down to figure out the total area. I will need more practice with this as well as many other concepts in this unit, but the geoboard method was helpful. I think it has some to do with perspective and breaking units down into simpler parts.

In class we also had a reminder of square and cubed roots. I really thought the concept of using the factor trees and then putting the prime numbers from the factor trees under the root was a simple way to learn the concept of roots. We paired up the numbers for square root and matched the triples for the cubed roots. I wish I would have learned this method before I learned the algebraic method. I think I may have understood it better and I can see how this method would be a great way to teach students roots for the first time.

Section 6.3

In section 6.3 we talked about percentages. I think this concept is naturally difficult for many people but, is an important part of everyday life. I know how to calculate percentages but in class I realized I need more practice. If I have more practice I will be better at recognizing percentages and in everyday situations better understand how percentages are beneficial. For example, if I am shopping I can recognize if something is a good deal or a bad deal that I should just ignore.

The worksheet that we did in class with percent was helpful. One thing I learned was to find the "easy 10%" of the total amount first. Then it is easier to find the total amount. This is a good concept for figuring percents in a lot of situations. I will be using this method in the future.

This website is good for recognizing percent, it's fraction and an example of what it visually represents. I thought it was a little more difficult so it would probably be more appropriate for older ages.

In section 6.3 we also talked about scientific notation. We learned scientific notation is based on using powers of ten. We learned that positive powers of 10 are really big and negative powers of 10 are really small. This was a good reminder of the things I have already learned in my algebra classes, a new way of understanding scientific notation, how powers work and reinforcement of place value.

Section 6.2

In section 6.2 we covered operations with decimals. We worked a lot with decimal squares and shaded in areas that represent numbers. I learned the visual way for decimal representation and have a different understanding of how decimals work. Especially in the area of multiplication. We used our index cards to represent the multiplication of decimals using area diagrams. This was a helpful exercise and as we went around the room to see the different area diagrams. It helped me have more practice in figuring out which decimals were being multiplied.

The area diagrams are a great tool for teaching students. It would be cool to have some sort of colored transparency paper or something with the grids of the decimal representation. If you used primary colors (for example yellow and blue) you could put the yellow transparent paper down to represent a decimal (.6), and then lay down the blue transparent paper down over the blue to represent the other decimal you are representing (1.3). The shaded area of yellow and blue that makes green would show your answer (.78). This would be a great way visually to separate the decimal representation and to show the overall answer. This is also a great way for students to use manipulatives (kind of like how we do).

I also found this game for kids on this website. It is a way to show addition with decimals and is a good resource.

More on 6.1

The workbook pages for section 6.1 were really helpful. I have known about place value for a long time now, but seeing how the unit is broken down into smaller pieces that make decimals is a great tool. It was a new and simple way of explaining how decials work and why they make sense. It also makes sense that the smaller the boxes get in the unit the larger the place value. For example, the thousandths place is more accurate than the hundredths or the tenths. You can shade more exact in the broken up unit in the thousandths and can visually see how it is more accurate because of how much more precise the shading is. I liked these examples.

Even though Cory's bingo game today was fun and a great learning tool, it showed me I will have to practice and study the relationship with decimals and fractions. I will have to pay attention to the placement, for example .7 is 7/10, and how some fractions break down or simplify even if they are the smaller numbers that are more defined. An example of this would be 0.250 is 250/1000 which can be simplified to 25/100, and 1/4. The more I practice the better I will understand these concepts and eventually be able to teach to students more effectively. I also had trouble with finding the fraction between two fractions. I remember having trouble with that on the homework so I will have to do some studying to figure that out. For some reason it seems hard for me.

I also found this game that kids can play to practice place value and numbers with decimals. The students are put in pairs and have a secret number the other student has to guess. I thought this was a cool game to play, and is a non-threatening way to learn. .Click here.

Sections 5.3 and 6.1

The sections we covered in class were 5.3 and 6.1. The information covered in these sections is very complex. Children have a hard time learning the concepts of fractions and decimals and it can carry on in their adulthood. I had a conversation with Mrs. Andersen close to the end of class about how I realize I have been doing the process of math my whole life without understanding why I do it. I didn't have a good grasp on math when multiplication, division, fractions and decimals where introduced to me, and of course that is why I struggle with math. Even though I am a good student, the concepts are difficult for me to understand. This is probably because it's one of the first times I have tried to really understand it.

I guess it's true that the math world is changing. Now that I am taking Math 105, I am noticing more and more how math educators are trying to change the way we learn math. Even in one of my other classes we had a guest come in to talk about math because it was in the chapter we were discussing. The guest speaker mentioned several times that we need to change math to the understanding of the process instead of the achievement of the answer. She even had manipulatives and activities that reinforced things we have talked about in Math 105. It actually made me feel good because I recognized terms she used like the identity, commutative and associative properties and she talked about patterns and things we have already covered in Math 105. I thought to myself "maybe I am learning some things!" That is a good feeling.

I do agree that maybe my "turning point" will be when I am a teacher and can see that same excitement I had when I realized I really was retaining something in my students. That will give me the motivation to teach and love some (maybe not all) math concepts. I thought some of the examples we used in class were really helpful in learning fractions. I really liked the example of folding the piece of paper in to parts (3/4 x 1/2=3/8). I wished I could have learned some things this way. I think it is a great way for kids to see how one thing (in this case the piece of paper) into smaller parts or when it is no longer a whole piece. I think this is a better way to describe fractions than the pie charts. In the article Mrs. Andersen wanted us to read What's Sophisticated about Elementary Mathematics? by Hung-Hsi Wu, it is stated that "children lose their natural reference point when working with fractions from a circular perspective" (pg. 7). I can see where the number line would be more effective. I also like how the visual aids being used in the manipulatives kit and the examples we used in class are a way of seeing which fractions are bigger. Because this concept is so difficult to understand, students can actually see which fraction is bigger or smaller because of it's shaded area. I wish I would have had that when I was a student being introduced to fractions for the first time. I am glad however, that I can use these examples when I am a teacher to help students understand these concepts on a deeper level.

In the area of decimals from section 6.1, I also found it helpful that we went over the placement of base 10 again and had the visual of the shaded boxes and how they break down. It also re-affirmed some of the base 5 concepts for me that we have recently covered. In a way I wish I would have had a class like this in 6th or 7th grade. I was in pre-algebra in 7th grade and I think if I would have understood some of these concepts better, I would have been a better math student overall. It's pretty interesting.

For now I am going to keep trying through Math 105 to do my best to understand and focus on these processes for myself instead of doing what I have always done to just get through another math class. I will look forward to my "turning point" while congratulating Mrs. Andersen. Even though it's really annoying sometimes that it seems so easy for her to love and understand math, she really knows her stuff and gets people thinking. She's turned on a light on in me when it comes to a subject that is difficult for me.

A day of study tools.

Today was an interesting day for Math 105.  I have never been a math lover.  While Mrs. Andersen was talking about her valuable trip away from us she mentioned a conversation she had with a famous math genius.  He said he used to hate math until he had a "turning point" in which he had to learn it in order to learn what he wanted to learn in physics.  I know this is taking a long time to say but, the point I am trying to make is that I don't think I will ever have the "turning point" Mrs. Andersen was talking about in class today.  Let's face it, math is not one of my strengths nor one of my passions.  Although this is a fact I know I have to be a good student and always try to do my best.  I have to do this for myself and for my future students.  Today Mrs. Andersen was a good example of a great teacher and proved she is willing to help students be successful, but it's up to the student to take advantage of that help.  That's where I come in.

Today we learned some tools about how tests are written, and how to study for the upcoming units.  I learned some valuable tools such as what to study from the virtual classroom and making index cards of things to study from each unit.   I also learned how to prioritize my time a little better and be able to hold myself accountable to study the areas I need to study instead of what I want to study.  I have room to improve in Math 105 and with the tools I learned today I am going to try to better my grade and my understanding of this crazy thing called math.  The best to all of you out there who may never have that "turning point" like me.  Let's just keep trying.

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