Module 4

How Much Taller Video:

This video was very interesting for me to watch and I was very surprised to hear the responses that the students came up with.  When the teacher asked the question: "How tall is the typical first grader?", everyone's answer was very interesting to me.  Samantha talked about how she thought that the typical first grader would be 1 to 2 inches smaller than her because a lot of the students heights were close to her but she still felt like most first graders would be smaller.  She never really explained why which confused me but it was neat to hear her explain in that way instead of trying to use the mean, median, mode, or range.  Llyod's response talking about the middle number of the data was the closest to the average was very smart to me.  In doing data collections I have noticed that a lot of the times that the mean is most of the time close to the average.  The question of "How much taller is a fourth grader than a first grader?", was also a very interesting conversation for me to listen to.  Llyod was the most impressive student to me in this part of the video because he wanted to use the range as his tool of finding out how much taller the fourth graders were than the first graders.  I was also surprised to hear that he did not think an adequate number could be taken from this study and that a larger sample would need to be taken in order to have an accurate response.  One thing that stood out to me throughout this video was the when talking about average(mean) students related it's definition with mode's definition of "most common".  I am not quite sure if that should have been addressed by the teacher and clarified or not...any suggestions?

Case Studies:

My confusion of mean and mode as "most common" continued when reading through the case studies and completing the assignment.  I felt like students were closely relating the two and may have almost had them confused at times.  In Lydia's Case study Erin intrigued me when talking about finding the middle number (median) to help determine Robbie's numbers.  This lead to a class discussion of how to find median as well as mean.  I also must say I agreed with Robbie in this case study that using his mean may not give an accurate data point on the line because he never actually blew the distance they were wanting to use.  In Phoebe's case study I enjoyed Trudy and Javier's usage of mean and the way that they explained it.  Although they only used their group of four members to determine the mean for the average height for the grade they still showed they understood mean and knew how to get it.  The students did ask questions that were valid points about them only using four members to determine and expressed their concerns that those four members could have been really short or really tall which would not have been accurate.  I think those are all great concerns but the fact that the group used mean versus adding up all numbers like some of the other groups was impressive.  In Maura's case study I liked reading the students responses because they used ideas such as median, range, shape of data, and are using numerical statements.  I enjoyed the numerical statements because it showed the students thinking about different concepts such as how since 5 fourth graders were taller than any first graders that the fourth graders must be taller.  Although we know that may not be accurate I still found it to be a good way of thinking.  Nadia's case study surprised me in when talking about the mean students did not want to use 13.2 but instead wanted to use 13 because it was a whole number and because it "came up the most".  This is another time where I felt like mode was being confused with mean because you can have a remainder in an average.

Other Questions to Consider:

Find examples of averages in a daily newspaper, from the sports page, or any page.  then describe what these averages "mean"--their significance, implications within the context of the story, and so forth.

***I had to use a website because my parents have gotten rid of their newspaper before I could get to it but I did find a website showing important averages related to something I am interested in.***

I looked at the website: http://www.usa.com/public-school/kenansville-elementary-kenansville-nc-370120000499.html?nv=duplin-county-nc-public-schools that showed the average scores for Kenansville Elementary School, the school district, and the state average for scores on the EOG tests.  These averages allowed for the person viewing them to be able to see how Kenansville Elementary students scored on their EOG’s by grade level as a whole in comparison to the average for the school district and the state.  This website does a good job with using averages because they have it organized using percent and has other information to compare it to.  I like being able to see how students perform at different grade levels on tests and I really like seeing how each school compares to their school district as well as the state.  This would be a helpful website when explaining averages to a class because you could explain to the students that the number (in percent form) is how all the students in that grade performed and that adding the scores up and dividing by the number of test taken would give them an “idea” of what the average score was in that grade for each part of the test. 

Annual Salary is often a touchy subject for teachers whose low pay and high workloads are axiomatic.  Search the virtual archives of a newspaper in an area where you would like to teach.  Look for data about averages and entry-level salaries as well as information about pay scales and increases.  Evaluate the data.  What does it tell you?  What doesn't it tell you?

School teacher salary has always been a hot topic due to the fact that it is considerably low for the amount of work that the teachers put into their job.  In doing my research online about salary I found the average pay for an elementary school teacher in Duplin County to be $38,656.  I must say I was shocked when I saw this because it was considerably higher that what I had seen in past years where the average elementary school teacher was making $34,000.  I was shocked to see that the 10^th percentile pay was $31,180.  This surprised me because in looking through websites and articles I noticed beginning teacher salary to be $32,300.  I am however confused as to how some people are making less when first year teachers start out with a higher pay.  The different data I have researched have shown me that there is a pay increase for earning your masters and well as being national board certified.  I did learn that you must be teaching three years before becoming national board certified but I was not able to find the information as to how much the pay increase would be.  I was able to find information about how two of the schools in Duplin County that were under revision from the state had a $5,000 sign on bonus incentive for teachers who were to start teaching there.  I was not able to find out if it was an automatic $5,000 or if it was over a course of contracted years.  Teacher’s salary is always going to be something in question but I believe that to be a good thing because it needs to be.  Teacher’s need to get paid reasonably for the amount of work they have to put in not only in the school day but as well as work they are having to do when they get home.  Needless to say I believe a teacher’s job is never fully finished

Do some reading and thinking about the concept of the average or mean and its application in schools through the bell curve.  What does the mean suggest in terms of grade and achievement?  Why is the concept represented with a bell curve?  What are the implications for grading on the curve?  Is it fair?  Why or Why not?

 

The bell curve is something that I was familiar with in relation to my statistics class but after researching it I now feel like I better understand its relation in education.  The bell curve is shaped like a bell and has a middle section that would be for the “average” score on something and then the outside two areas; the one on the left would be for low grades and the one to the right would be for higher grades.  I also learned that standard deviation is connected with bell curves.  Once the teacher has found the mean scores for the test they can then use standard deviation and determine how far out in each direction they want to go in order for the score to be considered “average”.  The bell curve is designed as a tool that shows where the majority of the students are scoring and to show that there are some students who are not performing as well or are performing better.  The bell curve could be considered unfair because when the teacher decides what the standard deviation in both directions will be they already have an idea of how many students they need to fit within the “average” portion.  Bell curves are a neat tool to see how the students are performing as a whole but I do not personally think they should be something dwelled on by the teacher. 

 

 

Working with the Mean Activity:

How did you use the cubes to figure out the problems?

I first got my cubes out and divided them up into the five groups that were already listed for me.  I removed the extra blocks from the 9 and 12 bags and used them to form groups of 8 in the cubes I already had laid out.  I then counted up how many cubes I would need to form the other bags and to make the mean 8 for all of the total bags.  I knew I needed to work with 56 blocks because when (I understand that there are actually no bags of 8 in this group but the average is still 8)  I did the same thing by adding the numbers up and again I was able to get 56 and when divided by the number of bags (7) I was able to get a mean of 8 again.
divided by the total number of bags (7) I knew I would get a mean of 8.   I was able to make 4 bags with 8 peanuts, 2 bags with 7 peanuts, and 1 bag with 10 peanuts.  This gave me a total of 56 which when divided by the total number of bag (7) gave me a mean of 8 for the 7 bags.  Another set of numbers I was able to come with was 2 bags of 10, 2 bags of 9, and 3 bags of 6. 

How does this model help demonstrate what the mean represents?

The model helped to demonstrate mean because it allowed for me to use manipulative to guide me to finding it.  This model let me know that I had to have 7 bags and that the mean of those bags needed to be 8 peanuts.  I was then able to determine that I was going to need 56 peanuts to work with so that I could make the average for each bag 8 peanuts.  This model showed me how you need to work with the number and figure out the total number your going to be working with to allow you to work through the problem and to use the manipulative to your advantage.

How did you use the line plot to figure out the problem?

When working with the line plot I first used the numbers that were given to me and put them on there as a way to see how many more I would need and a way to see how far I would be away from the actual mean of 8 when forming my bags.  I used the line plot hand in hand with my actual groups of cubes to give me a visual as well as a graph on paper.

How does this model help demonstrate what mean represents?

This model helps us to understand what mean represents because it gives you a visual of how close the bags are to being 8 and how you need to alter them to keep the bags as close to 8 as possible when only having 7 bags. 

What does the average tell us about the whole data set?

The average in this data set tells us that the majority of the bags that we get should have 8 peanuts in them.  It allows for people to know that they can expect for their bags to be around 8 peanuts because that is what they are averaging as a whole group.