Generating Meaning
This article is about teaching the students the how to understand the true meaning of the mean, mode, and median without giving them the terminology at the very beginning. They are being asked to look for patterns, develop their meaning of the mean, mode, and median, and then understand the representation of the data set. They focus on finding the meanings of the words and then how to find them. I don't remember learning these specifically in elementary school, so I cannot truly recall how it was taught. I know when I took MAT-143 at Coastal Carolina Community College over the summer these were introduced and the teacher more so explained it. Because it was an online class it was up to us to learn and understand it, which I did from the textbook readings.
Working with the Mean
I got the following possible answers: The first set would be
5, 7, 7, 8, 8, 9, 12
The second set would be 5, 6, 7, 8, 9, 9, 12
~Honestly at first when you messaged me I hadn’t even looked
at the assignment yet….then I did and I was like ummmm what?!?
But as I played around with the cubes I knew I had to have
the average number of 8 “peanuts” per bag. I made the 5 bags I had into 8 “peanuts”
as much as I could and then added pieces until I reached 8 “peanuts” per bag. Then
I separated the original “peanuts” back out to each bag and played with the
remaining “peanuts”. The remaining number of “peanuts” I had to place on the
representation was 15, so I could have selected any combination of numbers that
totaled 15. 1 and 14, 2 and 13, 3 and 12, 4 and 11, 5 and 10, and the chosen
ones 6 and 9 and 7 and 8.
Because the mean is the average, using the cubes helped me average
out what I had and then allowed me too visually see the numbers and what I
could create with them.
The line plot….well first I think I made it incorrectly so I
went back and tried again. After watching the video on the Annenberg site it
made this whole process a little clearer. I made the bottom represent the bags
and then color coordinated the marks, as I moved them around I crossed them off
and placed the color in the new row. This again allows us to visually see the
numbers on the paper to create the answer of the numbered pair for the
remaining 2 bags.
The average tells us the equal shares in the distribution, which
can then tell us the total number of items we have.
What do you think
Aubrey? Do the pictures help, sorry it is sideways?
How Much Taller
In the video Dede answers the question of “how much taller
is a fourth grader”. She says 10 inches because that is the difference between
the tallest 4th grader and the tallest 1st grader.
Grady answers “how tall the typical 1st grader is”
by organizing the data collected in order from smallest to largest and finding
the median.
While Jason uses the mode to answer the question because he
selected 53 inches as the most common height.
In Case 27, Zia is using the range to decide “if one group
is taller than the other”, she recognized that the 4th grade range
is 52 to 62, while the 3rd grade range is 51 to 54.
Abby also mentions
her use of the line plot, she states that the 4th grade line plot
starts an inch after the 3rd grades plot. There are 5 students in 3rd
grade that are 51 inches, but no 4th graders are that height.
In Lydia’s case, Erin has the idea of the mean, she wants to
use the number in the middle and is trying to explain it to her partner. Erin
seems to know that she needs the middle value but is at the beginning stage of
explaining why. She is understanding that the 2 numbers are important but not
sure how to use that information yet.
In Phoebe’s case, Trudy and Javier are both very close to
understanding the average, but at first they only see it as a number between
the calculations. They took the height of everyone in their group and divided
which gave them their own group average. Though the teacher has to “pull” the
information out of Trudy at the end she is able to understand that they essentially
took numbers off the taller members and put them on the shorter members. This
is important to grasp because to me it is the foundation of understanding what
it means to find the average. The total number stays the same but the
individual numbers inside can change. Does
that make sense to you Aubrey?
In Nadia’s case, the first group with James, Jordan and
Laurel all decided that the average was 13 not 13.2 because you can’t have .2
of something. This is problematic because while you can’t have a fraction of a
letter you can still have a fraction. In the Annenberg video is shows to
represent it in a fraction so it would be better understood if the answer was
13 3/20.
Another problematic student idea I found was Linnea in
Phoebe’s case, she is misunderstanding the definition of the word average.
Average is not the most common and this will cause her to have errors in her
data set. Learning and understanding the difference between mode, median, and
range is very important.
Aubrey, did you find
other problematic areas or do you agree with mine?
I think the children for the most part understand how to reach
the answer of the mean but not really what it means, or how to explain mean in
words. I can relate, I have to stop and think about the difference between them
when working with these concepts.
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 grades
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?
Ahh, the bell curve. I can remember never liking this
method, as a student who prides herself on studying and getting good grades, I
found it unfair that a teacher would give a better grade to another student
because some did better than others. Those extreme outliers either way could
potential hurt the grades of all the students. But while reading an article on
grading on a curve I have come to realize that if the teacher uses the results
in different ways it would be beneficial to all students, like for example if
most students got certain questions right more points could be rewarded but I
think my favorite way would be to round up to 100% and then add the same
percentage to each students grade. The biggest downfall I see is that if a
student does badly on a test and the teacher grades on a curve they are still
being rewarded for not knowing the answers…but I also understand that some
people, like me, have severe test anxiety and the curve could help ease the
stress. Aubrey did you ever have a teacher use a curve? I had a college professor who did, but I don't think he did a curve a certain way.
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?
I want to teach with DODEA so I decided to look at the pay
scale for them. They have all of the pay charts available online so you can see
the past few years as well.
This allowed for me to see the pay increase percentage over
the years. For example the starting pay for 2016-2007 for a Bachelor’s Degree
and Step 0 was $46,981 the same starting level for this year has a pay rate of
$48,390. The information provided shows a 3% increase per year. However, these
charts do not take into account the taxes for the state that you work in or the
cost-of-living in the area. The data I found does also show me the increase for
each step, but I don’t know where that comes into play, and the amount if I
have different times of service and degrees.
I decided to look at the pay rate for North Carolina and
there is a significant pay difference between DODEA and North Carolina
teachers, I hope I can get back into the DODEA system.
Aubrey, are you planning on teaching on or off base? Are you staying here in North Carolina?
This module was very rough for me. I understand it a little bit better after your explanation. Thank you Tracie for being able to explain it the way you did. Once you did that it was easy to see where I went wrong. I agree with what you said about the video and see how the kids who had a greater understanding of the concepts had clear answers. I have had teachers use a curve in high school but no other time. I would like to teach on base, but I've heard it is near to impossible to get on base. I have worked at the CDC on base so I know pay is so much better on base. I am staying in NC. My main concern is that once I accept a job that means my kids will have to change schools and that may not be a bad thing but they have already switched schools once when we moved on base.
ReplyDeleteTracie I apologize for this week. I have not had the time I usually do to complete the module with adding in field experience. I am hoping to get internet back at my house this week so I can work better on the next module. Thank you for being an awesome blog partner in helping me understand more of what we are learning.
Hi Aubrey!
DeleteFor the article, I agree I found them working the data/problem out interesting. They were able to learn and understand what the words meant instead of learning the definition and then just doing the math. I tried to remember learning these concepts in grade school, but I can't recall. I guess I have blocked that part out, I know I was a good student, just cannot remember specifics.
For the "Working with Mean" part, I am glad I helped you some, I am more than happy to meet up this week and dive into it more if you'd like. But honestly once I watched the video on the Anneberg site (down on the bottom) it clicked for me.
How did you do with the case studies? We came up with different responses and some similar.
With the curve, I might have had teachers use a curve but I remember Mr. Barnes with Coastal did. When I think about it I think I was happy to hear this, but after reading about it I wasn't so sure anymore. The benefit for some is greater then for others...do you think you'd grade with a curve if you had higher grade level?
I've looked into pay in a lot of different places, like Pennsylvania. They had a decent starting pay, but the retirement benefits are great. Why would the kids have to change schools, for the convenience?
Don't worry about the module, we got it done and we will continue to strive for completion. I'll keep you on your toes :)