Module Five

Generating Meaning

This article addresses how students need to understand the real meaning of range, mean, median, and mode before they are really able to understand how to find the average. It talks about how students need to understand the concept of how to find the average and not just know the procedure. The article then goes on to explain how they need to look, determine, develop, recognize, and understand  to fully get how to understand the average. The article then goes to talk about different activities to do with the students to get them to be able to really understand the concept. I really don't remember that much about my elementary school math but I do remember that when my teacher would talk about mean she would just talk about how it was the average amount of a data set. I remember the teacher asking us questions like "how many siblings do you have?" or "how many pets do you have?" and then using that data we needed to calculate what the mean or average was. I think allowing us to find the average of things that were familiar to us helped us to understand how to do it. I remember having to add up all the numbers and then divide by the number of students we had in the class. 

Did you have a hard time understanding how to figure out the mean when you were younger?

Working with the Mean

Numbers of Peanuts in each bag: 5,7,7,8,8,9,12,

I used the cubes to find out the answer by first dividing the cubes into 7 groups. I then put the cubes into the groups that I already knew the amount of. After that I added up that amount of peanuts and got 41. I then took the number of total groups and multiplied it by the mean answer: 7 x 8 = 56, I then took 56-41= 15. After getting this answer I divided the 15 peanuts I had left over into the 2 groups I had left and got 7 and 8. 

The model helps me better see what the mean is because it makes it easier to picture in the separate groups. 

I honestly didnt use the line plot to help me figure out the mean, I felt using the blocks was easy for me and didnt need to use the line plot. Did you prefer one method over another? If so, which one and why?

The model helps to show what the mean represents because it helps to see how many are in each group. 

The average tells us about how many should be a fair amount of peanuts to be in one bag. 

How much Taller?

1. Grady uses the median to explain his answer when the teacher asks him how tall a typical 1st grader is. He says that he takes the shortest and makes a list going up to tallest, and uses the number in the middle. Since there is an even amount of heights in the data he chose the two numbers (51 and 52) in the middle. 
2. Dede uses the range to try and figure out the difference between the 1st and 4th grader. She states that the tallest 1st grader is 10 inches shorter than the tallest 4th grader. 
3. Tess found the median of the 4th graders and then found the median of the 1st graders. After doing that she compared the two
4. Jason uses the mode as he describes the number with the most amount of answers. 
5. Samantha takes the mean of the 1st graders and compares it to the mean of the 4th graders. 

In Lydia's case I think Erin has a good idea of the mean as an average because she uses the middle number between two values. She isn't quite able to explain what the answer would be but she knows that it is the middle number. 

In Phoebe's case Trudy shows she has a good idea about finding the average even though her group only found the average of their 4 people in their own group. She says that they would just had a few inches more a couple times to make up for the taller students in their class. 

In Phoebe's case Javier says that his group got the answer by using a calculator, this can be problematic because he doesn't know really how to find the mean and is relying on the calculator to find it for him. 

In Nadia's case Laurel knows how to find the average but when the average isn't a whole number she changes it to one. This could be an issue as sometimes the average needs to be a decimal. 

What are some major issues you think students have when learning about mean?

Further Questions

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

I remember when I was in high school and it was softball season I was ALWAYS looking in the sports page to see my batting average, compared to my teammates and opponents. What that meant was how often I actually got a hit and on base compared to the other players in the county. Only the top 30 were listed in the paper so it was always my goal to stay above it and for the most part I did. What the average meant in this case was how well I was hitting the ball or how bad I was doing. Seeing these stats either made me want to continue what I was doing at the plate or make me want to focus more and practice before my next game. 

Did you play sports in high school? If so, did you do something like this?

Annual salary is often a touchy subject for teacher whose low pay and high workloads are axiomatic. Search for 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?

For this I choose to look at both my home state of Ohio and where I currently live in North Carolina. 

In Ohio the average starting salary is $33,096. The average teachers overall salary is $58,092.

In North Carolina the average starting salary is $30,778. The average teachers salary overall is $58,092. 

I don't really want to move back to the cold, snowy Ohio that I'm from but looking at these numbers kind of makes me want to. These numbers just tell you what you get paid. It doesnt tell you all the extra time teachers spend outside of the classroom working. How much money teachers put into supplies for their classroom. 

If you could move and teach anywhere where would you go and why?