Module 5

Generating Meaning

This article is about how to introduce mode, mean, median, and range through various lessons. Start with range, and work your way through the categories. Let the students identify these categories and allow them to create the definitions for each. This helps the students develop a basic understanding.

I don't recall the process of going through mode, median, mean, and range like this one. I do remember reading about them in a textbook and we had a worksheet with various number sets that we were told to complete. 

I was shown the procedure. My teacher stuck to textbooks and worksheets. We were told what it is, how to find it, and then we were sent to do it ourselves.

Did you have a similar experience, or did your teacher help you create your own understanding of each feature?

Working with the Mean

6 and 10
4 and 10

For the cubes, I lined up my cubes from smallest to largest and mad my cubes of 8 lie in the middle. I began plugging in numbers that were skipped and tried to keep 8 in the center.
Did you use your cubes differently?

For the line plot, I drew it out and plugged all my numbers. The line had a steady incline so I plugged in missing numbers on the line and numbers before and after the line.

For this data set, I believe that the average gave us the middle number. We had no reoccurring numbers and the average would be similar to the median.

How much Taller? Video and case studies 

1.
The students measured their own heights in inches (282). 
The students my have known that to compare data, they must be the same units.

The students used two line plots to compare data (292 and figure 41).
The students created two data plots to compare the grades. They are using critical thinking skills by visually comparing the two.

The students notice range on their plots (312-314).
The students at different points in the case mention range. They were using range as the deciding factor on which grade was actually taller. They were noticing which had a higher range, where the range started and an overlap in the two grades as well.

The students notice a clump (328).
Students notice a clump on the graph. They are slowly beginning to make notice of mode without realizing.

The students notice mode (367).
The students took into consideration that mode could be the factor to base their reasoning off of. "The clump" is higher on the fourth grade graph than the third grade graph.

Did you find different features? If so, what were they?
2. 
One thing mentioned in case 27 (Maura), on line 453-455, Leah mentions that they could add up all the numbers (heights) to determine which is largest. I think this is a great first step in helping the students determine mean. 

The student Ilsa (Nadia's case) wanted to find the middle number but wasn't sure how. Her thoughts were to add or subtract, but she couldn't quite figure out how. She had a great thought process that with the data that was collected, we needed the middle number.

3. 
In case 26 (Phoebe), a small group of students took the average of their small group to determine the average height of their class. One student mentioned how they need to measure everyone because "what if the people in your group were different sizes from everyone else in the class?" (151-155). he made the connection that this is not the proper way to find the mean, but they are off to  good start. The student student is headed in the right direction, but sometimes taking a small sample to determine the whole can be problematic and can cause misinformation.

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 had to go to several different places to find the salaries. 

The annual salary for Texas teachers starting pay is $28,080. If you look for pay by location, they give you the average made. In my hometown, the average salary is $53,640. They do not mention the starting pay, so this number is very misleading when you are beginning your teaching career. They do not list the range where the average was taken.

Where do you plan on teaching? Are the number what you expected?

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.

In a sport article about Dallas Mavericks Player Dirk Nowitzki, it mentions how he averages about 23.9 points per game. This means that when Dirk plays his games, he typically scores around 23-24 points per game. This is not a guarantee because the range may vary, he could score lower or higher than the average. However, comparing the numbers from all his games (which is a lot), he does however typically stay in the same range.