Variations about the mean
Surprising this Annenberg
assignment was quite easy to understand and I went through the problem
quickly. The one part that I did
struggle with was the very last set questions f - h.
f.
What would happen to the MAD of a data set if you doubled every number in it?
g.
What would happen to the variance of a data set if you doubled every number in
it?
h.
What would happen to the standard deviation of a data set if you doubled every
number in it?
I wish they had
provided an interactive area where you could plot out the change. It was hard to wrap my head around these
three. Em, did you figure these out?
Generating meaning together
I really enjoyed this article. I liked how the teacher did not just come out
and tell her students what the terms range, mode, median and mean meant. Instead, she let them investigate. She let them search the data for their own
answers. By doing this, I believe she
allowed her students to develop a deeper understanding of each concept and her
students walked away feeling accomplished.
I feel like this is a pattern that happened way too many times. What do you think Em?
Working with the Mean – Activity
In this activity, we
were asked to use our interlocking cubes to help demonstrate the problem and
our solution. Once I figured out the
first problem with the cubes, I was able to see the answer more clearly on the
line plot.
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Now use your representations to figure out how many peanuts could be in the other two bags so that the mean number of peanuts in all seven bags is 8. Try to figure this out without adding up the peanuts in the five bags. Find at least two different sets of numbers for the two bags that will work to solve this problem.
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What is the least number of peanuts there could be in one of
the additional bags? What is the
greatest number?
The least number there could be is 1 and the greatest number would be
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I
approached this problem the same way.
Counted the overage in bags 3,4,5 which was 8. ( that is one over my
mean) I then counted the missing peanuts in bag 1, which is 2, added that to 7,
which gave me 9. Remembering that I was
over 7 in my initial count of overages by 1 and the 1 that I placed in bag 6 I subtracted
them from the 9, which left me 7 in bag 7.
What if the mean number was 10?
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Again, the approach was the same. I counted the overage in bag 5, which was 2. Subtracted that number from 10, which gave me
8. I put that number in bag 6. I then counted the missing peanuts in bag 1, 2,
3, and 4, which was 11. Add 11 to the
10. And put that in bag 7.
This was fairly easy for me to do but sometimes when things seem easy its because I missed the concept all together. Did you get similar outcomes?
Video - How Much Taller
While watching this
video I noticed that the students were confusing two separate concepts average
or mean and mode. I did not like the way the teacher cut
every child off while they were explaining their thinking and gave her interpretation
of what they were going to say or trying to say. I do not know what she was trying to do, help
them or guide them to the wrong answers.
Em, did this bother you at all? What do
you think she was trying to do? Do you think it helped their understanding or
hurt it?
In my opinion, the
children did not understand the definition of mean. Jason’s answer of “53 because that’s the
average” At first I was impressed that he knew to look for the average until me
gave his explanation of what the average was “most common height.” Jason knew he wanted to find the average but
gave the definition of finding the mode.
It is hard to tell what the teacher was teaching in this
clip or what her intentions were for her students to take away. Nevertheless, from this clip alone I feel she
only confirmed in her students misconceptions about what the mean means and how
to find it.
Choose at least two questions:
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?
Interesting data…
Teacher w/ bachelor’s
degree with 0-2 year experience $2,566.67 a month. I will not be eligible for a raise until my
6th year working and then the raise is minuscule $35.oo extra a month. Looks
like I will be eligible for a raise every year after that. I thought about trying to be an assistant for
one to two years just to become more comfortable with being in the school
system but a teacher’s aid makes $1,935.51 -$3,087.64 a month. I am sure this depends on experience, time in
position and schooling. I am sure I would be hired at the lowest pay.
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 found a story related to the first question I answered in
this weeks State Port Pilot entitled
This article tells about the possibilities of a pay increase
for beginning teachers from $30,800 to $35,000 over the next two years. Here is
an excerpt from the article:
“According to data collected by the National Association of
Educators, the national average starting salary is $36,141.” This means that of all the starting salaries
in all the states the average pay is $36,141. We will still be underpaid based
on average but we would no longer be the least paid teachers in America. What is doesn't say is will this pay increase travel up the line or will teachers that have been working for years still be underpaid for their qualifications. Nothing is official as of yet so I wouldn’t
hold my breath!
Hi partner, it seems that you and I had the same difficulties when trying to answer problem E10. I believe this is because we are not familiar with using this method. To be honest I learn about the variance and MAD about a year ago and did not use it once the class ended. As you pointed out if there was an interactive area where we could have plotted the changes with the numbers that were given that would have made a world of difference.
ReplyDeleteWe shared the same insight about the TCM article. Students used hand-on activity where they were able to use manipulate the data to come up with the correct definitions. Like I have already stated in my blog my learning about this concept was the complete opposite. I was given the definitions which was followed by a few examples. I would memorize the formula and use it on a test. This is why so many students have difficulties when working with mathematical ideas.
We use different methods to come up with our answers for the peanut question. I wasn’t able answer the second half of the question. However, I was able to understand your thought process and clarify my thinking…good job btw…
I was definitely bothered while watching the How Much Taller. It seemed that some of the students had a difficult time articulating their words. Instead of giving them the time to process what was being asked she would ask the question and once the first words came out of their mouths chimed right in. I hope that I am able to exercise enough wait time in the classroom.
For one you will not be hired at the lowest pay!!! As you already know my intentions of starting of as TA mirrors yours. However, after seeing the differences in pay the though makes me cringe! I guess at this point only time will and opportunity will dictate how and when I enter into the school system once graduated.