Module 2

Textbook

The question I chose to answer was: Describe the stages of graphing experiences that children should encounter, and give an example of each stage.

A child should encounter four graphing stages. These stages are overlapping which means a child can use any combination of the four to display their results. They are listed in order of development as concrete, concrete-pictorial, pictorial-abstract and abstract.

The first level is the concrete stage. In this level, children use tangible items to construct graphs. These items should only represent on thing such as “cat or dog” or “yes or no”, any more choices can be confusing at this age. An example would be “Do you own a pet?” Students could record a yes or no answer.

The second level is the concrete-pictorial stage. In this stage, children use tangible items as well as pictures to construct their graphs. They can compare more than two events at a time. Our book gives a great example book on page 72-73 involving birthdays.

The third level is the pictorial-abstract stage. In this level, children can use any combination of the previous stages while also making the transition to the abstract. This means they will start using stickers, colored cards or a combination to represent their data.

The fourth and last level is the abstract stage. In this level, children take the one to one comparison they learned in the first level and expand it to on to many. “Rectangular bars replace the colored squares and line graphs are introduced.”(pg. 75) Children who have spent sufficient time in the other three stages should transition into this stage with little to no problems.

This seems like a normal progression to me. What do you think Emerlyn?

Annenberg

As of problem C3 I have had little problem with this series of question. I chose to answer this one because it asked us to compare the frequency table with the line plot

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Which questions in Problem C2 were easier to answer with a frequency table than with a line plot? Which were harder? I feel the only reason it was easier to answer the questions with the frequency table rather that the line plot is we did not have to count the dots repeatedly. It was faster to have the numbers listed.

Problem C6

Which of the questions in Problem C5 were easier to answer with a cumulative frequency table? Which were more difficult? I found it easy to use the cumulative frequency table when I was trying to find individual frequencies I could not just look to the chart to find the answer I had to subtract and it was just confusing. 

Did you have a similar problem with this question?

Median as a tool in Data Description Activity

Kindergarten   

17 Students                    21 Total teeth lost                1.24 average tooth lost per student                                               

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	IDK

                                                                               

 1st Grade

20 Students                   111 Total teeth lost                   5.55 average tooth lost per student

							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	IDK

2nd Grade

20 Students                  175 Total teeth lost                  8.75 average tooth lost per student

								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	IDK

3rd Grade

23 Students                      202 Total teeth lost                        9.62 tooth lost per student

 (2 students did not know the number of teeth they had lost so I omitted there data)

									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	IDK

The amount students in each grade were about the same. Students in 1^st grade lost 5 times more teeth than students in kindergarten. Again, there was a gain in tooth loss from 1^st grade to 2^nd with around 25% more teeth lost in the second grade than in the first. We start to taper off as we head into the 3^rd grade with only a slight increase in tooth loss. Students in 3^rd grade lost approximately 1 more tooth than the students in 2^nd. While I was compiling the data I was thinking, is this tooth loss per year or over all tooth loss? This would make difference in my interpretation of the data. What do you think about that Em?

If we look at the mode, you can see what I was explaining above.

·         K-0:  little loss

·         1^st – 7  : a big jump from 0

·         2^nd - 8  : slow increase (I showed a slightly larger increase)

·         3^rd  - 9  : slow increase

You do notice the increase of loss especially from K to 1^st.

Median: The median and the average of each group were very similar. Looking at all the data I could see how just the median could be helpful in estimating tooth loss in that grade but you would need more information to get an accurate number.

I really don’t see what information you can gather if just given the median and the range. In this case, it is not enough information and so of it could be misleading for example, the range for 1^st grade is 12 but the range for 2^nd is 11.   Am I missing something here?

Case Studies

From the case studies, I saw how important it is for your data to back up what your representation shows. You can’t have your data say one thing and you charts say another. In addition, I learned how important it is that you ask clear questions with defined meanings. If your population does not have a clear picture of what you are asking them, how can they give you the type of answer you are looking for?

I Scream, You Scream

The stamen was “Students should be able to pose questions, gather data, and represent data in graphs…[at a very young age].” I feel this is true. We are all born curious. As humans, we search our environment for the necessary data to answer questions every day.  Did mommy (or should I say Grammy) leave the room? Good I can climb the stairs! Children survey their surroundings, collect data and interrupt what they think they can do next. Ok…so maybe they can’t gather the information and process it the way we would like them too but that is where the teacher comes in. We can foster this hidden talent just like in Cook’s classroom.

How do you feel about this Em?

Explain the importance of recording data in meaningful ways.

I feel the more relevant you make the data to the students who are collecting it, the more meaning it will have to them. They are more likely to remember what they are studying, put more thought into the question being asked, and more effort into the collection and interpretation process. The more meaning the data has to the recorder the better the outcome.