Probability is the number idea representation of a chance. This could pertain to horse racing, dice rolling, and lottery games amongst other things that do not represent money. I most often correlate probability with gambling because that was how I was raised. "I bet you your dish duty next week that dad pushes his glasses up 4 times during dinner." Of course the other person was allowed to pick the higher or lower end of the spectrum and if the number was not right on or in the direction that was bet on, it was a push and we found something else to wager on. If I would have known more about odds at that time, I would not have these dish pan hands.
In high school we started to learn about probability and I just could not grasp the concept. It was very frustrating for me as a student to understand the idea and not be able to execute it correctly. I was a little anxious to start up again with probability as my track record with it has not been the best. I took the advice of a few classmates and decided to look up the content on youtube. I thought that if I could get a few differing perspectives on the matter, I might be able to see where I went wrong in the past.
This particular video is best for explaining probability to a crowd more advanced than a first grade classroom. The great thing about having the internet and sites like youtube is that you can find so many different ways to portray the same idea. A video that is more suited for a younger crowd of math learners is below.
I think that just learning in a way where I could pause, rewind, and work along with at my own pace has been very helpful to me. I feel like I can now stomp around probability and maybe even pick a winning horse. I think I'll even take a piece of the action the next time I have dinner with my sister and father.
Thursday, June 23, 2011
Tuesday, June 21, 2011
1512 Post #2: Same Difference
I really started to hit a rhythm with homework at the end of last week. I was cruising through my review of mean, median, and mode when I couldn't for the life of me identify what it was about math I did not understand in high school. Then it hit me. I should I say I hit it. Standard deviation. I had to put that in bold colors because that is how I saw it when I came to that section. I had totally forgotten all about this procedure for math.
Just today I was trying to think of a name for this post title. I wanted to get a clear cut definition of the word deviate. Mirriam Webster dictionary classifies deviant as the action of going against rules, principles, or standards. I immediately started to think about how much I hate it when people say "same difference". No it is not the same, there is a difference. Unless I have three apples and either you or Carl eats one (I don't care who really eats my apple) I still have two apples no matter who ate the third. In that case, sure I'll accept same difference, but often times people use it in situations that do not warrant that phrase.
Back to the idea of standard deviation in terms of math. I was cruising along working on homework problems figuring out the mean, subtracting the mean from each number on my list, squaring the result, adding those squares, dividing by the number of data elements on the list, and then finding the square root of that answer to get the standard deviation. It was then that I realized that I don't hate standard deviation as much as I hate my calculator. For some reason, it was rounding to the nearest hundredth place when I was trying to complete that last part of the problem. I now have a new calculator that I am sure will do the trick if I could figure out how to work it.
I was able to find a really cool website that has different avenues for student help dealing with standard deviation. Math is Fun does appear to be geared toward a middle/high school. There are games, puzzles, worksheets, lesson plan ideas, and differentiated explanations to concepts that all teachers could find useful. While it is a matter of memorizing the route to get to the desired location with standard deviation; we must also remember to explain the reasoning. This is not a time where we should use "same difference" between the students learning the meaning of the work or memorizing the steps without cognitive thought.
Just today I was trying to think of a name for this post title. I wanted to get a clear cut definition of the word deviate. Mirriam Webster dictionary classifies deviant as the action of going against rules, principles, or standards. I immediately started to think about how much I hate it when people say "same difference". No it is not the same, there is a difference. Unless I have three apples and either you or Carl eats one (I don't care who really eats my apple) I still have two apples no matter who ate the third. In that case, sure I'll accept same difference, but often times people use it in situations that do not warrant that phrase.
Back to the idea of standard deviation in terms of math. I was cruising along working on homework problems figuring out the mean, subtracting the mean from each number on my list, squaring the result, adding those squares, dividing by the number of data elements on the list, and then finding the square root of that answer to get the standard deviation. It was then that I realized that I don't hate standard deviation as much as I hate my calculator. For some reason, it was rounding to the nearest hundredth place when I was trying to complete that last part of the problem. I now have a new calculator that I am sure will do the trick if I could figure out how to work it.
I was able to find a really cool website that has different avenues for student help dealing with standard deviation. Math is Fun does appear to be geared toward a middle/high school. There are games, puzzles, worksheets, lesson plan ideas, and differentiated explanations to concepts that all teachers could find useful. While it is a matter of memorizing the route to get to the desired location with standard deviation; we must also remember to explain the reasoning. This is not a time where we should use "same difference" between the students learning the meaning of the work or memorizing the steps without cognitive thought.
Monday, June 20, 2011
1512: Post #1: Sure: I'll take some pie!
Analyzing data can be done in a variety of ways. There's the dot plot, the stem-and-leaf, pictographs, histographs, bar graphs, pie graphs, line graphs, scatterplots, and box-and-whisker plots; just to name a few. While I have always been a very visually receptive learner, I was having a hard time picking up the need for all of these different ways to show the same idea. I was also interested to see how all of these data analysis methods are introduced to students and at what age.
Upon further research into the benefits and limitations of each, I can now appreciate the multitude of options. The box-and-whisker plot is a good way to visually show a range of data that has been collected. They are relatively easy to produce when given the data and can be adjusted fairly easily with the addition of more data. The bar graph is good to use when trying to determine the difference between the information given. The same could be said with a pie graph. If I wanted to see which of our expenses cost the most money compared to the others; I would use one of these methods. Actually seeing how much of the "pie" is being eaten has a profound effect on budget crunching and the ability to let little luxuries go.
As for the grade level for when these different graphs are introduced to our students; it is all relative to the curriculum. Some states require a basic knowledge of it in elementary grades and others keep that same requirement for graduation of high school. Districts also vary from what they feel is important to introduce and what has worked for them in the past with success in regard to testing.
Some students will have never seen a box-and-whisker plot until they are in college taking a class on how to teach elementary students math (ie- me). Most younger students enjoy the graphs with pictures or with the answer written on it. I found this website BrainPop Jr., which has some great resources for teachers who are trying to come up with fun ways to present ideas of all kinds to their students. It is geared toward younger students, but the site overall is a good resource for most elementary school math skills.
Upon further research into the benefits and limitations of each, I can now appreciate the multitude of options. The box-and-whisker plot is a good way to visually show a range of data that has been collected. They are relatively easy to produce when given the data and can be adjusted fairly easily with the addition of more data. The bar graph is good to use when trying to determine the difference between the information given. The same could be said with a pie graph. If I wanted to see which of our expenses cost the most money compared to the others; I would use one of these methods. Actually seeing how much of the "pie" is being eaten has a profound effect on budget crunching and the ability to let little luxuries go.
As for the grade level for when these different graphs are introduced to our students; it is all relative to the curriculum. Some states require a basic knowledge of it in elementary grades and others keep that same requirement for graduation of high school. Districts also vary from what they feel is important to introduce and what has worked for them in the past with success in regard to testing.
Some students will have never seen a box-and-whisker plot until they are in college taking a class on how to teach elementary students math (ie- me). Most younger students enjoy the graphs with pictures or with the answer written on it. I found this website BrainPop Jr., which has some great resources for teachers who are trying to come up with fun ways to present ideas of all kinds to their students. It is geared toward younger students, but the site overall is a good resource for most elementary school math skills.
Sunday, June 19, 2011
1510 Post 2: What's your number?
Perhaps I am alone on this one, but I am having a hard time with the different numeration systems. I really thought I had struck a certain genius when in fourth grade I could finally understand the grandfather clock in our front foyer. It was of course in Roman numerals and up until that time, I had only used digital means for telling time or my Mickey Mouse clock that had the numbers written in Hindu-Arabic. By the way, I did not even know what Hindu-Arabic was until a few years ago.
When I started this chapter in our class and saw that I needed to figure out the method behind the characters and how they correlated to numbers I knew; I was a little confused to say the least. I wondered out loud why I needed to know how many bent reeds (Egyptian)and pointed fingers would represent the amount left on my car loan. I started slipping into 13 year old Sarah. The one that sulks, makes things more difficult, and tries to undermine the meaning behind the lesson.
That was when I had to take a break and slip into the role of an educator, not a student. I tried to think of the different ways I could look at the information that would make sense to me and also provide a correct response. Working with the math lab available to us in our classroom and using the help provided there was just what I needed. While taking a math class like this has been a little difficult to adjust to, having these resources available provides the differentiation from the text that I needed.
While I still do not particularly like working with Babylonian, Mayan, and Egyptian numerals; I have learned how I work best with these ideas. I have also come to respect the idea that math has a place in history and art. Just as it is important to learn what is relevant in our world today, it is just as much so to learn what was relevant when civilization was advancing.
By the way, I am happy to report that I have less than one pointed finger, one bent reed, and a couple of coiled ropes until I can call that Minivan mine.
When I started this chapter in our class and saw that I needed to figure out the method behind the characters and how they correlated to numbers I knew; I was a little confused to say the least. I wondered out loud why I needed to know how many bent reeds (Egyptian)and pointed fingers would represent the amount left on my car loan. I started slipping into 13 year old Sarah. The one that sulks, makes things more difficult, and tries to undermine the meaning behind the lesson.
That was when I had to take a break and slip into the role of an educator, not a student. I tried to think of the different ways I could look at the information that would make sense to me and also provide a correct response. Working with the math lab available to us in our classroom and using the help provided there was just what I needed. While taking a math class like this has been a little difficult to adjust to, having these resources available provides the differentiation from the text that I needed.
While I still do not particularly like working with Babylonian, Mayan, and Egyptian numerals; I have learned how I work best with these ideas. I have also come to respect the idea that math has a place in history and art. Just as it is important to learn what is relevant in our world today, it is just as much so to learn what was relevant when civilization was advancing.
By the way, I am happy to report that I have less than one pointed finger, one bent reed, and a couple of coiled ropes until I can call that Minivan mine.
1510 Post #1: Why are we doing this again?
As I desperately try to keep my head above the swirling numbers; I often question what it was that drew me to math and education in the first place. In elementary school I was the student who loved math but never really excelled at it. I had all the confidence and little skill set to match. Now as I get older, I am finally able to see the path that my teachers tried to lead me down so many (not going to say how many) years before.
This tied in well with the reading for this week regarding the way math is being taught to our children. Often times as youth we are told that x+y=z because it does. You follow this idea and this rule and you will get this outcome. This has been very little explanation to those of us who love the question "why?". The YouTube clip of a response to "An Inconvenient Truth" questioned if we just want them to follow the route and memorize the path, or do we want our children to have a deep cognitive base in the material which they can also explain?
Not only will having a base factual knowledge of the material we will teach our students increase their self-efficacy toward math; they will also understand why it is they will need it or apply it toward their life. As educators we need to remember that it is not always about the end result as much as it is about the journey and understanding that is picked up along the way. Math can be a very scary subject to students because there is little wiggle room for interpretation. Explaining the reason behind the madness will go far for many students who love the word why.
This tied in well with the reading for this week regarding the way math is being taught to our children. Often times as youth we are told that x+y=z because it does. You follow this idea and this rule and you will get this outcome. This has been very little explanation to those of us who love the question "why?". The YouTube clip of a response to "An Inconvenient Truth" questioned if we just want them to follow the route and memorize the path, or do we want our children to have a deep cognitive base in the material which they can also explain?
Not only will having a base factual knowledge of the material we will teach our students increase their self-efficacy toward math; they will also understand why it is they will need it or apply it toward their life. As educators we need to remember that it is not always about the end result as much as it is about the journey and understanding that is picked up along the way. Math can be a very scary subject to students because there is little wiggle room for interpretation. Explaining the reason behind the madness will go far for many students who love the word why.
Thursday, June 16, 2011
General Information
I found it very odd that we needed to keep a blog for this class. When I signed up for the required math classes, I assumed it was going to follow the role of traditional math classes I have taken in the past. I thought we would learn of the new methods and rules that have come into the classroom since I was last there. As I have started to read through my classmates, I have started to see this as more of an opportunity to catch ideas that might have initially grazed my focus. Reviewing what my classmates gained from the information in their own words is going to give me great perspective on the issues that are going to be facing us in the classroom both when it is full of eager learners and during those times when it is not.
Beyond diving into math for my summer; I have taken up golf recently with my husband and two young sons. I have also started running as a stress reliever and great workout. I am working toward certification for elementary education in Minnesota with the ultimate goal of teaching a college course similar to what is offered at Bemidji State through the DLiTE program. Here is to a safe tan, long summer, and good grades for all!
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