Module 3

Textbook Reading

Tally Sheet- Students add a tally to help keep track and record their data.

Pictograph- Students can record their data using images. The images can equal various amounts

Bar Graph- Students use rectangular bars to represent their data

Line graph- Students will use to show change over a period of time.

Pie Graph- Compare their data in a circle with percentages.

Stem and Leaf- Students split their data into parts (stem and leaf). The first digit is for the first number, then the leaves are the second. For example in the chart stem 2 and leaves 035. For this chart the students threw the baseball 2.0ft, 2.3ft, 2.5ft.

Median as a Tool

Kindergarten:

• Mean: 1.2
• Median: 0
• Mode: 0
• Range: 0-6

Grade 1:

• Mean: 5.2
• Median:5.5
• Mode:7
• Range:0-12

Grade 2:

• Mean: 8.8
• Median: 8
• Mode: 8
• Range:3-13

Grade 3:

• Mean: 9.6
• Median: 9
• Mode: 9
• Range: 2-19

Did you have trouble with Mean, Median, Mode and range? If so, how?

The four grade I believe are different. It seems like the younger you are the less teeth you may have lost. In the two higher grades majority had lost a lot more than the younger grades. Kindergarten had the highest number of students in one category. They had 10 students have had 0 teeth fallen out.
If we were strictly working with the mode, then it would be able to tell me the largest category of each grade that had the most students. For example if we knew just the mode for kindergarten (0). Then we know that 0 was the most selected number among the students. A great number of the students had lost 0 teeth. We wouldn't be able to determine the distribution of the students if we just stayed with mode. We wouldn't know the majority without comparing all the numbers.

If the median for each grade was reported, than we would be able to compare the grade through a spectrum. If the median is a low number, then those students in that class had stated smaller numbers. If the median was higher, then we know they selected higher numbers.

Designing Data Investigations

Using Sally’s case 4, talk through the discussion that starts with Chad’s observation that “something’s not right” (line 93). What are the students noticing? What are the teacher’s and Sally’s roles in this conversation? 

The students noticed that two of the students were placed in the wrong group when trying to record their data. They noticed that the boys sudden change in his decision could alter their drawings of their data. The teacher never told the students what to do, she simply asked more questions to help them figure out their own questions and thoughts. The other students also helped the two boys figure out that if they changed their initial selection, they much change their clip on the board, so everyone has the correct data.

• A. What important mathematical ideas are coming up in this discussion? 

The students are learning how to properly ask questions, collect data, and analyze the data based of off a survey.

• B. What emotional issues are coming up? How are these interconnected? 

I think that the only emotion really coming out is that the students are very passionate about their data collection. They narrowed down their question the second time themselves, they pointed out flaws to each other, and they helped correct their data. I think it is great that they are so enthusiastic about data collection. This helps encourage the students to critically. 

In Nadia’s case 5, what are the students learning about the relationship between defining the question and the results of their data collection? You will need to point to specific examples to support your ideas about this. 

The students are learning that you must define a question properly to get the correct answers for your data collection. When the students were discussing the number of languages one can speak, I think Nicole had the best explanation how to write a question properly for more accurate answers. On lines 190-194, Nicole mentioned how when asking about languages, you need to ask how many languages do you speak fluently and define fluently for the person so you can have more accurate answers for your data.

Using Andrea’s case 6, think about the connection between the intention or purpose of data collection and how a data investigation is designed. 

• A. Consider the first two questions that students came up with in Andrea’s class: How many people in your family? And how many houses are on your street? How could what you want to find out influence how you define each of these questions? 

You would have to make the proper adjustments and make the questions more specific. The question How many houses are on your street could not work for everyone. Like they said, not everyone lives in a house. I would redirect the question and ask the students what kind of building do they live in (house, apartment, camper, trailer, etc). 

• B. Now review the last part of the episode, about Natasha and Keith (lines 331-362). Natasha seems to have a clear idea of what kind of information she wants. Look carefully at the paragraph about Natasha’s ideas about their question. What does she want to find out from this survey? Why do you think she was unhappy about the question they eventually used? 

She wants to find out the number of states your purposefully visited. Not just the airport or driving through to get somewhere else. She is unhappy with the question they went with because it is not what she specifically wanted. It is a lot more broad than she had hoped. Instead of finding out the states people visited purposefully, to make it simpler on everyone, they just stuck with state you set foot in. This would frustrate me too if you couldn't put the right words together to ask what you think is a simple question.

I Scream, You Scream

That students should be able to pose questions, gather data, and represent that data in graphs seems reasonable enough – until you consider that these are the stated expectations for children just four to eight years old!”

I think the word "should" is not the right word to use. Using that word makes it seem as though they should have all that knowledge mastered. It would be better to phrase the statement students should begin posing questions, gathering data, and so forth. I think students should begin practicing these concepts. You may have some students understand what is happening, but others may not grasp the concept as well as the other. I liked how the teacher helped the students with their data collection. She helped them narrow down the questions, she helped them begin the data starting process, and reviewed their data they collected. Of course, not all the charts were correct, but they were close. I think the students will need some help, before they are ready to grasp this concept so soon. At least for children that are four to eight years old. 

Do you remember doing any similar data collecting like in the article?

Explain the importance of recording data in meaningful ways.

I think that if we were to collect data just to collect data, what would be the purpose? We ask questions and gather data for the purpose of finding our new information. Data collection is used everywhere and used to answer needed information. 

Can you think of places data collection is important?

The purpose of data analysis or statistics is to answer questions. Give some examples of questions that children in the lower elementary grades might want to answer by collecting data. Also give some examples for the upper elementary grades. 

Lower Elementary Grades:

• What is your favorite color?
• What is your favorite animal?
• How many siblings do you have?
• What is your favorite TV show?

Upper Elementary Grades:

• What is your dream place to travel
• How many presidents can you name?
• How many elements on the periodic table can you name?

Would you assign students a question or let them decide?

Module 2

Categorical Data Sort and Analysis

Before beginning the sorting activity, I thought that it was going to be interesting. I was excited to see all the different people my peers' would like to have conversations with. I thought that many of us would have the same people I was very surprised to see that only one name was repeated. 
In this activity I created 6 categories.

Creators/ Inventors

• Antoni Gaudi
• Bill Gates
• Aaron Swartz
• Mark Zuckerberg

Novelists

• Jane Austen
• Paulo Coelho

Change Promoters

• Rosa Parks
• Malala Yousafzai
• Haregewoin Teferra

Religious Figures

• Jesus Christ
• Jesus Christ

Celebrities

• Drake
• Oprah Winfrey
• Lauren Graham

Leaders/ Political Figures

• Queen Elizabeth I
• Queen Victoria
• Barack Obama
• John F Kennedy
• Michelle Obama
• Nelson Mandela
• King Leonidas
• Maxine Waters

After this activity,I think that this showed a lot about my peers. Many of them chose very influential people; people that made a difference whether to the world, a small community, or to that peer. It was difficult when sorting names into categories. My change promoters category was initially called rights activists, but I was left with Haregewoin Teferra. She may not have been fighting for rights, but she was trying to promote a change just like Rosa Parks and Malala. 

I think a question I would have also asked would be to describe the person with three words. I think this would have also helped sort the choices. My peers may have chosen these people for different reasons that I may not have thought of when I sorted them into categories. 

I would used a similar activity in my classroom for the first few days of school. If I asked the students who their hero is, or someone who inspires them, I could use their answers to put the students into groups (group seating).

Did you also have trouble making the categories?
Were you unfamiliar with any of the people listed?
What changes did you have to make as well to make sure everyone fit in a category?

Statistics in the Elementary Grades

I enjoyed reading this article. It gave great examples of how to use categorical and numerical data in a classroom. This article also informed us of the difference between the two. For categorical, they used shoes that their focus. They prepared questions, data, and results based off of the types of shoes worn. They also gave different examples how to make a categorical shoe problem (type of shoe, color, how it ties, etc). 
For numerical data, they used sports as a problem. They compared the number of goals made in different soccer games. This allowed students to compare all the games and learn about fair share value (the mean). 
Both categorical and numerical data expose the students to statistical problem solving. The students learn how to make questions, collect data, review data, and be able to interpret the data with representation. After reading the article, I was able to recall having to do similar statistical problem solving in my younger elementary school years.  I remember building a chart about our favorite colors. Each student wrote down their favorite color and we created a bar graph. Not even realizing it, but I was working with data and statistics way before middle school. I guess you really are never too young to learn about data and statistics.

How Many Pockets

What are some important features of what’s happening in this classroom?

• Students in the circle with the teacher
• The chart on the board
• The teacher using statistical terms

What did you notice?

• The teacher points out data change.
• The students helped each other count their pockets

What stood out for you in regards to the students’ thinking?
the students had a hard time determining Denise's thinking "5 has a lot". It took a discussion for the students to come to the  conclusion that a lot of people have five pockets in the classroom.

What stood out for you in terms of the teacher's moves?
The teacher continues to build off of the students statements and encouraged others to join in. This helped other students to make and understand explanations.
Do you agree with the teacher's methods?

As you think about each of these, what’s the idea the students are working on?
The students are working with categorical data. They were comparing the different amounts of pockets students have.

List the questions that you are focusing on for last Subheading.
Describe the four components of the statistical process and a possible statistical question that could be used for a data project.

1. Formulate a question: Students think and compare various questions to use in a statistical process.
2. Collect data: Based off of the question, the students begin to collect all their answers.
3. Analyze data: The students can create a visual representation and review what they have gathered.
4. Interpret the results: The students discuss what their final finding were from the answers of the questions.

Possible Question: How many students have brown as their eye color?

Do you find coming up with statistical questions for youth challenging.

Observe a group of people (such as people waiting in line at the movies, grocery store, etc…). Explore the different ways you might collect data and categorize them (eye or hair color, type of shoe, left handed or right handed, color of backpack or book bag, color or style of clothing, etc…). Discuss which ways yield the most interesting information and best fit the group.

I chose to observe my husband's friends at our weekend cookout. There were many different ways I could categorize them. I could use shirt colors (there was yellow, red, green, and white shirt colors), hand use (1 was left handed, the other 5 were right handed),  and I also could have used food choice (3 ate burgers and the other 3 ate strictly hot dogs).
I think it was interesting to see which hand most people dominantly use. I did not ever notice that one of my husband's friends was left handed. It was very fun to watch and find out new things.

Introduction Module

About Me:

I live in Jacksonville, North Carolina. I am from Fort Worth, Texas.

I have an amazing husband, a beautiful almost 4 month old daughter, and three dogs.

In my spare time I like to read, craft, and play with my daughter.

Something unique: I was captain of the wrestling team in high school and wrestled a little in my first year at UTA.

Feelings about Mathematics:

Math is challenging.

When it comes to learning mathematics, I feel determined to understand.

When it comes to teaching mathematics, I feel very nervous.

Elementary school mathematics should be fun.

Being good at mathematics means you may understand math differently than others.

What do "good" mathematics teachers do to help their students learn mathematics? Show the students there is different ways to find the answer.

I would like to have a conversation with Malala Yousafzai. She almost died defending what she believed in. She is a big advocate for women's rights and education.