Module 2

Lost Tooth

I generated the line plots below in the blog so spacing may be off some but the numbers should be correct.  I could not find a program that would actually form a line plot.

KINDERGARTEN

X
X
X
X
X
X
X
X
X            X     X    
X     X    X     X     X          X  
0     1     2      3      4     5     6

FIRST GRADE
                                           X
                                                    X
X          X     X     X     X            X                    X
X          X     X     X     X     X    X     X     X    X             X
0     1     2     3     4      5      6     7      8       9    10   11    12   

SECOND GRADE
                                         
                                                         X
                                                         X
                                                         X
                                                         X
                                                         X
                                                         X    X
                                                 X     X    X     X              X
              X                                X     X    X     X     X       X     X
0     1     2     3     4     5     6     7     8     9     10     11     12     13

THIRD GRADE


                                                   X
                                           X     X
                                           X     X
                       X                 X     X     X                 X                                            X
          X          X    X          X     X     X          X     X    X         X                 X     X
0   1   2   3   4  5    6     7    8     9     10     11  12  13    14   15  16   17  18  19    Don't Know

Questions:
1. In reviewing the data I noticed that the grades were all different because in kindergarten many of the students had not matured much so the majority lost 0 teeth.  If I had to find a similarity I would say that First-Third grades were the most similar because more students were beginning to lose teeth and they numbers were pretty balanced for those grades across the line plot.

2.  If just the mode was given to you then you would know what the most common number of teeth lost for each grade would be but that would be all.  You would not be able to determine how many students were in the classroom, what the highest and lowest number of teeth lost were, and you would only have that one set of numbers from each grade level to base information off of. 

3.  Median Number of Teeth Lost For Each Grade:
 Kindergarten:    0
 First Grade:       5.5
 Second Grade:   8
 Third Grade:      9

In knowing the median that would allow me to know that was the middle number in the collection of the data.  That would also give me a good idea of what the average number of teeth lost for each grade was because when working towards the median it is usually very close to the average number.

4.  If just the median and range were given to me it would give me an idea of what group of numbers were used as well as what the middle number is.  I would know what the middle number was and the range could help me to know how far out in each direction I could go. 

If the lowest, highest, and median numbers were given to me I would know the numbers we were working with from each grade level across the x-axis and in having the median number I would know what the middle number was and where the majority of the data would fall.

I think the statistics would help to form an adequate picture of the data because you would be able to find a mean, median, mode, range, and form graphs from the data that was given.  It would give the person doing the study a general idea of what the amount of teeth lost at each grade level would look like.


 Case Studies

Case Study number 4 with Sally was very interesting to me because it was the first time I have actually noticed that you need to be clear cut and direct with asking questions.  This study showed how the question that I would think so simple as "Did you have milk with breakfast?" could be twisted into a big confusion and lead students to finding other questions outside of that one question.  This case study helped me to build an understanding that in order to collect the data you are looking for that your question needs to be in a direct fashion.  Also, this case study taught me how checking behind yourself on data is important.  The students in this lesson had clothes pins to show how many students had milk with breakfast and then formed groups of who did and who did not.  When the groups were formed the students noticed that the groups were off.  The teacher and Sally had to show students how to compare the clothes pins with the actual number in the groups as well as had to help them work through why the groups were off as well as how they could fix the groups.

Case Study number 5 with Nadia was another one that showed me how when asking a question you need to be direct.  The question that was trying to be reached here ultimately was "How many times have you moved from house to house with all of your belongings" but when asked the general question of "how many times have you moved?" students were finding themselves confused as to what moving meant.  When doing research and wanting to find an exact result you must make sure your question is clear, direct, and to the point even if you have to explain it further to make sure you get the appropriate results you are looking for.

Case Study number 6 with Andrea shows how forming a question in a clear and direct way can prove difficult for the person asking the question.  The person asking the question knows in their mind what kind of information they are looking to obtain from their study but when asking the question to others they might not see it so clearly and will have to question further.  This study showed me that when forming a question for a study although it may take a lot of thinking time you need to take the time to build a question so that you get the information you are looking for without confusing the people you are actually asking the question to. 

Textbook Questions: Writing to Learn
1. Statistics is different from mathematics because one key difference is focus on variability of data in statistical reasoning.  Mathematics works more with numbers and procedures where statistics is more about working with numbers to collect data about a certain population.
A mathematical question would be: how did you go about finding the mean and what does the mean represent?
A statistical question would be: Given the mean of the data, what can you determine about the data that was collected?

2. The shape of data is "a sense of how data are spread out or grouped, what characteristics about the data set as a whole can be described, and what the data tell us in a global way about the population from which they are taken." (page 72)   This to me means that the shape of the data tells us everything we need to know about it.  It lets us know the groupings, the characteristics of the data, and would allow for us to graph the data collected.

3. Attribute activities are important because they allow for students to sort data and teaches them ways to categorize and group data to use in their studies.

4. Data questions that could be asked to students at the K-2 level could be ones such as:

• What is your favorite day of the week?
• What is your favorite food?
• What is your favorite color?
• What is your favorite part about school?

Data questions that could be asked to students in the higher elementary grades could be ones such as:

• Who is your favorite historical figure?
• Who is your favorite author?
• How many miles do you live from school?

(**Also Other Question to Consider**)

5. When putting data into categories the graphs that can be used are bar graphs, circle graphs, picture graphs, and tally charts.  All of these graphs help to organize data into their different categories in order to look at the data as a whole.

6. A histogram is a type of a bar graph that the categories' are consecutive equal intervals along a scale(pg.81) and are used for grouping data by a specific interval.  "The height and length of each bar is determined by the number of data elements falling into that particular interval" (pg.81)

7. To form a circle graph teachers can use the human circle graph techniques where students get in a circle and stretch string among them in order to show their separation of differences.  Another way students can form a circle graph is through drawing the circle by hand on a piece of paper, a board, or whatever materials they have and dividing up the circle into parts according to their data.  The third way students can form a circle graph is by starting off having students to make a bar graph and then having the students to cut out the bars and tape them from end to end.  This will form a circle where students can determine a center and well as draw lines from the different points.

Circle graphs displays ratios rather than quantities which allows for a large set of data to be compared to a smalls set of data.

8. An example in where you could use median over mean would be in a situation where someone was talking about real estate.  If you had houses at the prices of: $20,000, $200,000, $1 million, $1.5 million, $2 million, $2 million, and $3 million you would want to give people the median number that the houses were worth you were selling because if you were to average the low $20,000 house into your prices then it would give a very swayed result and mislead the buyers.

A reason someone one choose mean over median could be in a case of owning a restaurant that prided their selves on having an affordable $5 menu.  In that case you would want to use the mean to prove to customers that the average price of a meal is only $5.

Other Questions to Consider:
Recording data in a meaningful way is important because it gives the person collecting the data as well as other people that the data is shared with accurate information on what was collected.  Data needs to be recorded in a meaningful way to that it can be understood as well as interpreted and set forth on the usage that it was collected for.