First Video Segment: Why might the teacher ask students to think about differences in the range at each grade level? What insight do you get into children's thinking as they talked about why the ranges would be different?
I feel like the teacher asked the students about the differences in the range at different grade levels to get the children's minds working and to show them that the range is going to change as the grade levels do. The children are all talking about how they think the range would be for the different grade levels to inquire about the research before they form their graphs and do their research. When listening to the students thinking about why the range was changing I must say I chuckled a little bit. Children have such elaborate ideas at young ages of what they believe. The last little boy who spoke was talking about how he thought that the number of teeth lost was because some peoples bodies just want new teeth. Although we know that is not exactly how it works, that child showed me how students are all going to have their different ideals as to why things happen and how to conduct their research.
Second Video Segment: Did the children notice what you consider to be important features of the data? Are there features that they didn't notice?
The children in this video segment noticed quite a few important features of the data. The two girls pointed out one thing that I did not expect them to. When they mentioned that the boy who had only lost 2 teeth in comparison to the girl who had lost 12 in the first grade was probably due to the fact that he was young for his grade. The students were able to point out the mode, the minimum number, the maximum number. They also had the total number of teeth that were lost in the classroom. I did not notice in the video where the average and median were talked about. I feel like mean, median, mode, and range are all things that need to be discussed together especially when working with different data.
Third Video Segment: Did the children notice what you consider to be important features of the data? Are there features that they didn't notice?
The children noticed what I thought they would. They were surprised that a student had lost 6 teeth in kindergarten because in their second grade class a few people had lost 7 teeth. During the part talking about the third grade class the students made good points on the "I don't know category" because they talked about how it may be due to the fact that they had lost so many teeth over the years they could not keep count anymore. The group discussing the kindergarten surprised me because they didn't mention much about the highest numbered category or lowest. They did talk about range but I feel like they should have elaborated more on their findings.
Stem and Leaf Plots Article:
I found this article to be very informative and interesting but the majority of things that I read I already knew about stem and leaf plots. I have always enjoyed doing stem and leaf plots for some reason and the usage of displaying birthdays through a stem and leaf plot is actually a very neat idea. Instead of starting off in kindergarten teaching stem and leaf plots in the form of ones and tens the teacher could introduce the stem and leaf chart in the form of the birthday one shown in the article. The idea of displaying numbers on a stem and leaf chart made more sense to me when reading about forty-five in that kids could mistake that with 405 instead of 45. If we were to teach students to say things such as "forty zero" to help students to not get confused in writing their numbers.
I plan to use stem and leaf plots in my classroom as I mentioned earlier as a way of organizing information for the students whether it is with using place values with numbers or in seeing something like the birthdays. Stem and leaf plots I feel like really help students to grasp the ideas of the ones, tens, hundreds, etc. places because they get to see the numbers broken down by their place values.
Other Questions to Consider:
Find an example of a line graph and share on your blog. Describe the data used in the graph and why the line graph is an appropriate representation.
This line graph shows the students scores on their 10 math test. The dot is located at where their grade was for each test and then the dots are connected with a line as the grades are collected. It allows for the students to see the change in their grades by looking at the line changing. The numeric values of the test number and the grades are correlated that's why using a line graph for this collection of data works well.
What is the difference between a bar graph and a histogram?
Bar graphs generally represent categorical data and histograms represent continuous data. Another different between the two of them is the way they are drawn. Both graphs use bars but in a bar graph the bars are generally separated and in a histogram the bars are drawn together.
Bar Graph:
Histogram:
I think it is funny you chuckled at some of the students' responses. Students come up with such elaborate answers when we ask them to think about things. I feel like this is a good thing because it means our students are thinking and using their imagination. Do you think we should correct students when they say things like "some people's bodies just want new teeth?" or do you think we should let the student think that is completely correct?
ReplyDeleteI also kind of forgot that the two girls said that maybe the boy who had only lost 2 teeth was young for his age. That was a very smart hypothesis from the girls. What do you think about the teacher asking the girls how they could find out the answer to this hypothesis to further their data collection?
I liked that you made a comment about the "forty-five" "405" thing. What do you think about teaching students to say one number wrong so they get another number right?
I also always liked stem and leaf plots. I thought they were fun to do, but I always got annoyed with myself when I missed a number and had to erase and go back to fix it to have the numbers in the correct order. I really like math though. I enjoy solving problems and working out graphs.
Would you rather use a bar graph or a histogram? Personally I would prefer to use a bar graph.
I think instead of really correcting the student immediately we could keep getting answers from other students and then say "all of these are good answers but what do you think about "this" (giving a more exact answer). I think the teacher asking the students about how to prove their hypothesis is a valid question to ask and it would help to elaborate on their findings. I really don't know exactly how I feel about teaching students to say numbers in a wrong way so that they get them correct but it may could be beneficial. I prefer to use bar graphs vs. histograms because they are what I am used to using and I feel like they look neater in form!
ReplyDeleteI think I agree. I think we should say something like, "well what do other people think about losing teeth?" and then if the correct answer does not come out, correct the answer.
ReplyDeleteI also think teaching to say the wrong thing could be a good thing but I am still not sure how I feel about it. It makes me think that students are going to always say forty-zero or thirty-zero and not ever get it right. It is proven that once a student is taught one thing, it takes a really long time to reteach them the correct thing, so I think the only way I would do this is to teach them to say the correct thing as well as the incorrect thing.
I am glad to know that my idea of letting students ramble off ideas without correcting them right away is a good idea. I was kind of worried about me saying that but now that you agree I feel much more comfortable. I also must say I believe we should just teach the students to say the numbers in their correct form because from experience re-teaching students takes a long bit of time like you said. I am the same way though I must say. Once I know how to do something one way it is really hard for me to change my ways of thinking.
ReplyDeleteI do agree students should be able to ramble off ideas to an extent. If they are completely off, I do not think we should let them ramble unless we have set up our class to where we always allow other students to agree or disagree and add on. If this is the case, I think we should see if anyone else has an idea that might be closer to right answer and then say "hey, I think Johnny has a better idea but good thinking Susie."
ReplyDeleteGreat discussion you two. Children will ramble as something will catch his or her eye and it will spark a memory and then you'll get to hear the entire story if you let it go. It always reminds me of the "If you Give a Mouse a Cookie" book. It is a delicate balance of knowing when it's appropriate to cut off a child and when it isn't.
ReplyDelete