Module 3:

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Lost Teeth Video:

1st Video Segment- I believe that the teacher asked the students to think about the differences in the rage of each grade to get the students to realize the different information that will be projected on their data. I think she was doing this so that students can see that even if the range is high does not necessarily mean that grade has lost more teeth. I believe that the students thinking was very advanced when they were trying to hypothesize what the range would be. They were recalling the data they had collected and using life experiences to support their answers. Also, the students were remembering changes they had to make to their data and how that would affect the range. For example, in one of the classes the highest number of teeth lost was 12; however, a student that who had lost 12 teeth had lost another tooth that night. They had to move her to 13 because of this, which will affect the range.

2nd Video Segment- I think the students noticed important features in the data. At the very beginning of this segment, the two girls presenting their data comment on how they thought it was unusual that one first grader had not lost any teeth, but that we was younger than the other first grade students. I think this was very important because it almost appears to be an error in their work; however, it shows that they were aware of this and researched this to make sure it was correct. Also, the students took time to see if the range matched the predictions they had made before. The majority of the students were surprised that the range was so high when they had predicted it would be lower. The students also took time to compare were their class had lost the majority of teeth versus the majority of teeth lost in the first grade class.

Final Video Segment- The students did a very good job of presenting the information from the kindergarten class. They stated the range was 0-6 and how it was surprising that one student had lost six teeth since the majority of students in that class lost 0 teeth. Both students did a great job of noticing important features in the data and comparing the data to their own class.

I think that the teachers asks the students to think about differences in the range at each grade level so students can see that if one grade level has a higher range, that doesn’t necessarily mean that they have lost the most amount of teeth. I think by students looking for this they were able to physically see that the range just had to do with the lowest number of teeth lost and the highest number of teeth lost. The children impressed me when they stated their reasons they believed the range would be different. They began recalling information and changes they had collected in their data to create a hypothesis. Also, I believe that the children did notice important features of the data. They could name the total teeth lost, the highest amount and lowest amount of teeth lost, the range, and much more data. Even on the graph representing the 3rd grade class they had a category for students who could not remember how many teeth they had lost. I did not catch any features they did not notice.

Describing Distributions Module from Annenberg:

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I was unsure of problem A6 part a. I know that the mean is approximately 62.35, but I don’t understand how it compares to the correct response of 60 seconds? I’m honestly just really unsure what this is supposed to show us about our data? Any help on this would be appreciated! J

I also was a little unsure of problem C5. I understand cumulative frequencies, but was a little thrown off by what the relative cumulative frequency was. The instructions said that to find the relative cumulative frequencies you would divide the cumulative frequency by the total number of data values. So since there was 52 estimates for the example, would you just find the cumulative frequency then divide it by 52? I think I’m making this a little more complicated than it should be, I just want to make sure I am not doing everything completely wrong!

I did really enjoy going over the stem and leaf plots and histograms. It has been a really long time since I have used a stem and leaf plot and I don’t think I’ve ever used a histogram graph before. Most everything was explained really easy and I thought it was really neat to see how the histogram graph works.

Stem-and-Leaf Plots Article:

I believe the most interesting thing I learned from this article is that elementary aged students are not too young to start using stem-and-leaf plots. I was amazed that the students picked up on it so easily. I remember having trouble with these for some reason in high school. I would just look at all the numbers and become confused. For some reason it just never registered to me the number on the left represented the tens place. The examples from Annenberg and this article have made it so easy to understand. I would love to use a steam-and-leaf plot in my classroom for the same example as in the article. I think using the parents ages was a great example and the children were really interested because the information was related to them. I believe that another good example would be when using a larger amount of data.

Blog Questions:

1. What kinds of graphs can be used for data that can be put into categories?

-There are many different graphs that can be used to place data into categories. One of the easiest example that we have been working with is the line plot graph. Below is an example of a line plot graph. We can place X’s over each category to represent how many is in that category.

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Another example would be a pictograph. It has the same concept of a line plot graph. Below is an example.

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Probably one of the most common graphs we use to place information into categories is a bar graph.

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This bar graph is a great example that shows how to place 3rd and 4th graders favorite sports into categories. It also is a great example of how you can compare the two grades side by side to see a visual difference.

2. What is the difference between a bar graph and a histogram?

-A bar graph gives a single value for one category. It gives a specific answer.

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In the bar graph above, we can easily see that the number of black cars that drove by was 10.

-A histogram does not give a specific numerical answer. Take a look at the example below.

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We can see that there were 30 estimates made between 30 and 40, but we do not know a specific amount to make a definite answer.

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Module 2

Textbook Reading:

For the textbook reading I choose to describe the stages of graphing experiences that children should encounter and to give examples of each stage under Developing Your Math Teaching Skills on page 63. Children’s graphing experiences progress through four overlapping stages: concrete, concrete-pictorial, pictorial-abstract, and abstract.

The first stage is the concrete stage. During this stage students should actually use concrete materials and only compare two events or things. The book lists examples such as students wear glasses or do not wear glasses, walk to school or ride to school, and students who are left-handed or right handed. If students use the example of determining whether or not more students wear glasses, they should get up out of their desks to create a physical line. The teacher should explain to students to stay in a straight line and not to move around because if they do they might miscalculate the data. Once you have two lines (a line with students who wear glasses and a line with students who do not wear glasses) students should be able to determine whether more or less students wear glasses based on which line is longer.

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The second stage is the concrete-pictorial stage. During this stage, students will use picture representations of objects along with concrete materials. Students may also compare more than two events as well, however, they still need to maintain the one-to-one correspondence between objects. There are many different examples you could use for this stage. My favorite example was making a concrete-pictorial stage to determine which flavor of ice cream students liked best. To do this, the teacher can make a bulletin board with the heading “My favorite Ice Cream.” Across the bottom of the bulletin board place pictures of the different ice cream flavors. Each student will get a cut out of their favorite ice cream cone and pin it over the category. The teacher will encourage students to interpret the graph and have them be involved in a discussion.

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(Pictured above is an example of an elementary classroom that has completed this activity.)

The third stage is the pictorial-abstract stage. During this stage students start making the transition to abstract graphs, but still incorporate pictures. I found an example of a pictorial-abstract graph online that was used to find a class’s favorite book. The book logo was pictured along the bottom so students still had a pictured image. Above each picture the students placed colored blocks forming what is similar to a bar graph.

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The fourth and final stage is the abstract stage. In this stage, students begin to look at many different objects versus the one-to-one approach they have been focusing on in previous stages. Also, students will begin to place colored blocks or stickers with a bar or line graph. I really enjoyed the example of finding out what car passes by the school most often the text provided. I think it is a very good way to make a bar graph and to incorporate science (observing and making a hypothesis) into the lessons as well. Below is a third grade worksheet I found online that is similar to this process. The bar graph is of how students arrive to school and they are to answer questions based on the graph.

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Data Organization and Representation Module from Annenberg:

RAISINS

Problems B1-B4 were very interesting to me and very similar to an example our textbook provides. For problem B1, “How many raisins are in a half-ounce box of Brand X raisins?” we have to count all of the boxes. I came up with a range of 25-31 raisins in the 17 boxes. Because the boxes had different amounts of raisins, we cannot say there will definitely be X number of raisins in a box. Problem B2 asks if we had counted all 17 half-ounce boxes and all of the boxes included 28 raisins could we say how many raisins would be in another box of the same brand and we could strongly say there would probably be another 28 raisins, since each box has had the same amount of raisins and the data has not varied. However, problem B3 asks can we definitely say all of the boxes will have 28 raisins and the answer is no. We would have to look at many more boxes than just 17 to make that conclusion. Finally, problem B4 wants us to look more closely at how many raisins Brand X might have in each box. We definitely know that there should be around 25-31 raisins; however, we can say there will probably be around 27 or 28 raisins in each box since those numbers appeared more often.

I also thought it was very interesting looking at the frequency table in section C. At first I thought that a frequency table would make simple questions harder; however, I found that, for me, it actually made answering question C2 A-J much easier to answer. For example, question C2 part C asks “How many boxes have between 26 and 28 raisins?” Instead of having to go back and count all of the dots the numbers were already listed and you just had to add the numbers.

Median as a Tool in Data Description Activity:

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Each set of data does have similarities and differences. Grade 1 and Grade 3 are similar in that the number of students who lost teeth are more evenly spaced. Kindergarten and Grade 2 are similar in that the number of students who lost teeth are not evenly spaced and have a certain number much higher than the others.

If just the mode for each grade level was provided, it would be easy to calculate how many teeth most of the class lost. For example, the mode of Grade 2 is 8. We would easily be able to determine that most of the class has lost 8 teeth. However, we would not be able to determine how many more students have not lost 8 teeth because no other numbers are provided.

Median:

Kindergarten = 0

Grade 1 = 5.5

Grade 2 = 8

Grade 3 = 9

If just the median was provided for each grade level we could easily see what number of teeth most students lost for that grade. We could easily see that students in grade 3 loose more teeth than Kindergarten through second grade. We could also easily see that students in Kindergarten loose the least amount of teeth.

If the median and the range were provided for each grade level it would give you a better sense of the data. You would be able to know the least and most amount of teeth students have lost and the median would provide around the middle number so you could have a pretty good estimate of what you data looks like. If the lowest value, highest value, and median was provided, you would have a definite idea of what the lowest and highest number of teeth lost was, as well as, around the middle number of teeth lost. However, this would not give us an adequate picture of the data collected. We would be missing a lot of details from the class. For example, in the 3rd grade class we would not know that 2 students could not recall how many teeth they had lost. This could eventually effect our data and if we were not able to see all of the information we would not know this.

Designing Data Investigations Case Studies:

I really enjoyed reading over and answering the questions on the case studies. I think my favorite was Case 4 dealing with Sally, the teacher, and the 1st grade students. It was amazing to me to see how quickly they were able to define what counted as jeans and what did not. They also were very quick to pick up on when their line of students did not match their data collection. The students went through and rechecked everything. Once they discovered their problem they fixed the problem in their data and their line.

I Scream, You Scream article from TCM:

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When I first read the statement, “students should be able to pose questions, gather data, and represent that data in graphs,” I assumed this was aimed at upper level students. I was completely shocked that these were standards for students’ ages 4-8 years old! What I was even more shocked about was how well they were able to complete these standards. Each student was involved in picking a topic to collect data about and collected the data on their own using tally marks when most of the students could not even read yet! After collecting their data they were able to make graph and determine which flavor ice cream was the most and least favorite. Some students were even able to tell how many more or less certain flavors had than others. This article truly shows what students are capable of when the teacher helps and challenges them.

Blog Question:

It is very important to record data in a meaningful way. If we do not record data in a meaningful or correct way we can end up with incorrect information. Because of this, it can lead to serious problems. For example, say you are a scientist working on a project dealing with unclean water in another country. You want to raise awareness that this is becoming a large issue so others will help provide clean water. However, something goes wrong during you study and the data you recorded ends up being incorrect and saying that the unclean water is not really that bad. Because of this, people that need help will not get it. It is important that we take time to record our data correctly and double check that our recorded data matches our research so that we can help others with our data.

 

 

Module 1

Categorical Data Sort and Analysis:

Upon first looking at all the names supplied by my peers, I was unsure of how to categorize them. There were so many different names, from figures from history, to television actors, to world record holders. I finally decided to just cut apart the names and start stacking them when I saw names that were similar. Finally, I started combining the names until I had three different categories.

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Pictured above is my first sorted data. (I’m not exactly sure why it turned out blurry.) First, I created a category called historical figures. Underneath I placed the names: Nelson Mandela, Haregewoin Teferra, Sarah Palin, Albert Einstein, George Washington, Susan B. Anthony, Sheryl Sandberg, Thomas Jefferson, John F. Kennedy, Rosa Parks, and Andreas Vesalius. Placing the physician Andreas Vesalius and Sheryl Sandberg was really stretching it. However, I figured that since Sheryl Sandberg is the CEO of Facebook and Facebook is such a part of this generations lives, she will fit into history, as well as a physician that is doing good works for others. Next, I created a category for the names that had to do with religion. Underneath this category I placed the names: Jesus Christ, Joyce Meyer, and Pope Francis. Obviously, Jesus Christ is a religious figure, and Joyce Meyer and Pope Francis has made it their lives goals to spread the word of God. Lastly, I made a category headed figures associated with TV, books, and music. Underneath the category I placed the names: Etta James, Lila Diane Sawyer, Edgar Alan Poe, Oprah Winfrey, Judy Garland, Lucille Ball, Johnny Deep, Steve Irwin, Sherlock Holmes, Elaine Davidson, Lisa Delpit, and Professor Albus Dumbledore. Television, music, and books usually go hand in hand so I thought all of these names fit fairly well together.

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This next picture shows the second way of categorizing the class data. At first, I thought we had to place all of the names in three categories; however, this time I tried to make the categories more specific and left out some names. The first category I came up with was political females. Under this heading I placed the names: Rosa Parks, Haregewoin Teferra, Susan B. Anthony, and Sarah Palin. I was unsure of whether to place Sarah Palin under this category, but she does presently work with politics so I figured it would be the best category for her to fit into. The second category I made was those who appear on TV. Under this heading I placed the names: Sherlock Holmes, Professor Albus Dumbledore, Lila Diane Sawyer, Lucille Ball, Johnny Depp, Joyce Meyer, Steve Irwin, Oprah Winfrey, and Judy Garland. Even though not all of these people are actually actors, they do appear on television as characters, or have their own shows. Lastly, the third category I made was former presidents. Under this heading I placed the names: George Washington, Nelson Mandela, John F. Kennedy, and Thomas Jefferson. I thought about making a category to do with American presidents; however, Nelson Mandela was the president of South Africa so I thought I could just make the category include him as well.

Each name listed from my class members really shows me the unique interests each of us have. There was such a great mix of people. Only one name was repeated and I saw and researched some names I had never known before. I also think this data shows that even though the majority of the class thought of very different names and all probably have very different personalities, we can all relate and connect in different ways.

Some further questions I would like to pursue based on the data would be to talk to some of my classmates about the names they picked. For instance, some of the actors could have written quite a few books that I am not aware of. This would make the names easier to put into different categories.

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Further Discussion:

 To me, there were a few names that did not seem to fit anywhere no matter what I made the different categories. At first, I tried to include all of the names, and I did, but you could definitely tell that some names seemed a little off. Next, I made my three categories more specific and I left some names out. This made the categories easier to understand, in my opinion.

Article: Statistics in the Elementary Grades:

 I personally do not remember any experiences from elementary school on data collection and analysis, except for using M&Ms. I remember in almost every class having to separate the M&Ms by colors and creating different categorizes, then finding the mean. From what I remember, my experiences were quite different than the types of lessons that were used in the article.

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I was very surprised by the shoe lesson in the article. I really enjoyed that the students could actually get involved by using their physical shoes. Also, I never realized how many different categories that you could come up with just from observing shoes in the classroom.

How Many Pockets? Video:

Some important features I noticed in this video was that the teacher was really good with presenting and making the students see all of the data. If there were no students with only two pockets, she did not just skip over that number, she let the students realize that there were no students with two pockets. Also, another important feature I noticed was that the students were sitting on the floor near the teacher and were given the time to count their pockets and make corrections. I believe this made them feel more involved in the lesson.

At first, I noticed that it took the students a long time to figure out how many pockets they had. Also, I think some students did not fully understand what the teacher considered a pocket. I believe I would have had the students stand up and I would have demonstrated quickly what I considered a pocket and counted my own in front of them. I think the students would have had an easier time counting standing up as well and this could have cut out some of the extra time spent on changing the student’s answers because they counted their pockets incorrectly.

What really struck me about the student’s thinking was that they caught on to the point of the lesson very quickly. The automatically knew that most of the class had five pockets because it had the most number of X’s. You could tell that they understood this, but was having a difficult time at first verbalizing it. What struck me about the teacher’s moves was that she was really able to keep the students on task with one idea. Instead of venturing off on many different takes the students could have come up with from the data, she took the topic the first student said of the majority of the class having five pockets and she just kept expanding on the topic. She helped to keep the class in a very large and detailed discussion for a second grade class. The teacher was able to help the students see that collecting data can be easy and how to come to simple conclusions.

Statistics as Problem Solving Module from Annenberg:

When I think of statistics, my mind automatically goes to math class and sees a bunch of random numbers. However, after this module I have really been able to see that you can use statistics almost anywhere and with anything, not just numbers. A general question that deals with statistics is how many pets students in a class have. Here is how you would carry out each of the four steps …

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Step 1: Ask a Question- Make a line graph on the board in front of the class just as in the How Many Pockets video. Next gather the students around and briefly discuss the types of pets you can have in your home. Ask each student to determine how many pets do you think most students in the class have at home? Give them some time to think about an answer.

Step 2: Collect Appropriate Data- Have each student tell how many pets they have at home. Over the number of pets they have place an X over that number on the line graph on the board. Continue collecting this data until each student is recorded.

Step 3: Analyze the Data- Once all the data is recorded and organized, give the students time to look over the data and make some observations. During this time they should be able to see that a certain number of pets has more X’s than the other numbers and that a certain number of pets has less X’s than the other numbers.

Step 4: Interpret the Results- During this time the students should be able to conclude that most of the class has X number of pets based on their analysis of the data.

I am having some trouble working with the population problems. I understand how it is saying you can use a representative sample to figure out statistics for an entire population, but I’m not sure how else to set this problem up. I’m assuming maybe you could make a question where the representative sample was asking 20 people in a population whether they vote or not in a town population of 1,000 to determine the voting population of that town.

Blog Question:

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 I observed a group of students studying at the library. There were many different ways that I could collect data from their group, such as eye and hair color, their type or clothing and shoes, or even by gender. However, I categorized the group by their different laptops. Since I was in a college library, anyone can assume there were multiple laptops being used. I decided to break down and sort them by the brand of laptops they had or if they had any at all. To me this was very interesting because I could almost determine who was more determined to work on course work and who used more technology than other.

Introduction

About Me:

My name is Amy York and I an extension student majoring in elementary education at UNCW. I am originally from Patrick County, Virginia, but moved a couple of years ago to Jacksonville, North Carolina when I married my husband, David, who is an active duty marine.

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We do not have any children, we are waiting until I finish school and have had some time to work; however, we do have a fur-baby that we love very much! Pepper is about seven and we rescued her only a few days after our wedding.

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In my spare time, I really enjoy reading and writing. I have spent a lot of time this summer with a good book by the beach! My husband and I also love spending a lot of our spare time taking Pepper on walks and spending time in the park. I do also enjoy restoring old furniture. I will go to flea markets and find old stools mostly and sand them down and paint different designs on them to sell. I love being able to take something old and make it look brand new again. I also do spend a lot of time volunteering through my church and have been on a mission trip to Quyquyho, Paraguay in South America. I loved being able to work with the children there and I cannot wait until I have the opportunity to go back and volunteer again.

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Mathematics:

Math has never been my strong point. During my school years I always remember feeling like I was a step behind all of my other peers trying to keep up. I was able to go all the way through calculus and receive college credit while I was in high school; however, I do not remember one thing from the course and can remember struggling through.

Math, to me, is very important because now that I am older I can see where you can use math in almost everything you do. I believe it is very important to help work with students to really show them how to use math and how to make it fun. When it comes to learning mathematics, I have noticed that most everyone can benefit from using visuals. Even if students do not necessarily need the visuals, they can help you realize how you can actually use math in real life situations.

Because of this, I think when teaching mathematics, you should really strive to make it fun and use visuals, manipulatives, or other tools. Since math is a subject that a lot of students tend to have a difficult time with, we should spend some extra time coming up with ideas where students can use their hands to make something when going over measurements, or cook an item when working with fractions. It does take a bit more work on the teachers part; however, the students will really see how using math comes in handy everyday and they will have fun completing the tasks as well. I believe showing students that mathematics is used in everyday life and that it can be fun is very important in the elementary classroom. This lets students see that they can enjoy mathematics, instead of dreading it throughout their whole school career.

To me, being good at mathematics does not necessarily mean that you have straight A’s in your math class. Being good at mathematics means that you can relate the problems to real life situations and use creative ways to find the solution to a problem. Also, it is being able to break a math question apart and find a different approach to the problem if you are having difficulties seeing it one way. A good mathematics teacher will help a student relate the problems to real life situations and learn his or her students. The teacher will help each student learn the way he or she needs.

Conversation With A Well-Known Person:

If I could have a conversation with a well-known person I would pick our first president of the United States, George Washington. President Washington did so much to get our country running and truly believed in everything our country stands for. I am very passionate about helping less fortunate children and families, and my husband and I hope to adopt from Paraguay in South America. I have helped at two different children’s homes in Paraguay. Because of this, and my husband being an active duty marine, I notice many people now not realizing how good they have it and not realizing that so many people have died to give them this freedom. I would love to sit down with President Washington to see what he was thinking and feeling when he helped get this country up and running and how he thinks we could bring some American pride back. I also think it would give me a new sense of pride hearing him describe everything he went through.

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