Case Studies 18-22

On your blog, respond to the following questions:

• Follow the thinking of Susannah throughout Andrea's case 19. What does she understand about triangles? What is she grappling with? What ideas or questions does she contribute to the class discussion? What does she figure out by the end of the case? -Susannah is basing her idea of what a triangle is on what the standard idea of a triangle. When students are first taught shapes the standard triangle shape are the ones that she is saying are triangles. She is not seeing that triangle can have different angles and side lengths. She contributes that they are part of the triangle family but that they are too stretched out to be real triangles. 

• Now go back and follow the thinking of Evan throughout Andrea's case 19. What does he understand about triangles? What is he grappling with? What ideas or questions does he contribute to the class discussions? What does he figure out by the end of the case?-Evan understands that Triangles have angles (points) he is trying to understand that triangles being stretched out can still be triangles. He tells the class that even if he were stretched out he would still be Evan, which was a good visual to give his classmates. 

• Consider Natalie’s case 20. What are the students learning about squares and rectangles? What do they still need to figure out? Refer to specific examples from the case to illustrate your ideas. - They are trying to figure out how to define a rectangle and a square. What makes a rectangle and what makes a square? Ms. Rivera gets the students to draw shapes that fit into their definitions and the shapes end up not being just squares and rectangles.
  
• Also in Natalie’s case 20, after line 250, the students are working to define the term square. Their conversation is as much about what a definition should be as it is about the particular term square. What does their discussion make clear about definitions? In particular, consider Roberto’s definition (“four sides, four corners, four angles, and it’s a square”) and the other children’s responses in the lines that follow.- Their definitions need to be clear on what shape they are defining, otherwise it could be defining multiple different shapes. 

• In Dolores's case 18 (lines 25-43) and in Andrea's case 19 (lines 162-168), students are talking about what it feels like to make sense of a new idea. Describe their conversations. Refer to specific portions of the text in your discussion. What is your reaction to their comments?
  
• Reread the questions posed at the beginning of this task. Discuss your answers to those questions, taking into account all the cases you were asked to read.

Entry 2 "I Scream, You Scream: Data analysis with kindergarteners"

What is the value of having students pose and investigate their own questions?

-This allows students to make it a question that excites them and is something that interest them. Instead of the teacher assigning a standard class wide question. It also teaches the students how to work together to make a decision. Once they decide on a question as a class and start investigating it allows them to talk to classmates that they might not usually talk to or find out that they have something in common with a fellow classmate. Along with forming great data collecting skills it is over all a great lesson for students of all ages. 

—How could this lesson be modified for use with older students?

- I could be modified to older students by making the graphing part more advanced depending on the grade level. You could also do what we are doing in class if it is fifth grade and make it for each individual student and make it into a project a poster type of lesson. 

If you were implementing this lesson with students, what would you change?  Why?-

-I honestly would not change anything, I think this teacher did a great job of making it grade level appropriate with the pictures and the coloring of blocks for the graph. 

Case studies

1. Look through Alexandra's and Beverly's cases. Identify, by line number, statements made by at least five different children that you think bring up important ideas or issues about collecting, representing, or describing data.

       1. 16-20

       2. 25-28

       3. 215-216

       4. 245-246

       5. 340-341

2. In Olivia's case 3, consider the data about family size:

Write down a few statement that describe the data. What do you notice as the most important features of this data set?

The number of people in the family, there are gaps in the numbers. There are a lot of students with 6 family members. 

3. Now consider the students' work in Olivia's case.

1. Lauren, Tyrone, and Jacob wrote two statements on their graph (Figure 2, p. 15, and lines 262-263). What do you think they meant? There are multiple students that have 5 and 6 family members and not as many students that have the other numbers of family members. 
2. Look at Inez, Isaac, and Samuel's representation and the discussion about their work (begins at line 276). What important issues about data come up in this part of the discussion? They were more clear and used the words range and typical 
3. What do Lacey's comments about gaps (line 327) add to an understanding of the data? There are some students that h
4. The data in the first two cases can be put into categories (bag lunch, school lunch; yes, no, sometimes). How do the data considered in Olivia's case differ from the data in the first two cases? What kinds of statements that students make about this data set couldn't be made about the data in the other two cases?

Introduction

    I have lived in Wilmington, Nc my entire life and so has my family! I will be the first to move away after I graduate and will be moving to West Virginia to live with my soon to be husband! In my spare time I like to spend time with my friends, have some down time catching up on my favorite Tv shows, shopping, spend time with my family (they are a very big part of my life) or hanging out with my furrbaby (cat) Audrey! My Fiance has my other furrbaby (puppy) Harley with him in West Virginia. Something unique hmmm well I'm not sure if this counts as unique, but a few years ago I stepped on a sewing needle after making a pair of shorts and didn't realize it was stuck in my foot, so I continued to walk on it and it continued to move farther up into my foot and eventually I started to feel it and had to have it surgically removed! Let's just say that was not a fun summer and I was stuck on crutches for a good two months. Never again will I sew a pair of shorts on the floor again. A little more about myself, I just got engaged actually the week before classes started and the wedding date is June 9th, so this semester I will be balancing a long distance relationship, school, and a job! Here is my story in pictures.....

 

Tell us about how you feel about mathematics

• Math is… Sometimes fun!
• When it comes to learning mathematics, I feel…. pretty confidant 
• When it comes to teaching mathematics, I feel… pretty scared that I won't teach it correctly 
• Elementary school mathematics should be…..fun and interactivr
• Name one thing you remember from your math classes in elementary school... 100 math facts sheets 
• It is most important that elementary math students learn...how they got the answer and make sense of math 
• Being good at mathematics means…. understanding what you are doing
• What do “good” mathematics teachers do to help their students learn mathematics? showing that there is more than one way to get the correct answer 
• What was the single greatest challenge that you have faced in mathematics? Understanding that there is more than one way to get the correct answer
• Growing up, what kinds of mathematical experiences did you engage in with your family or others outside of school? Honestly none that I can really think of, math has never really been a big part of my life outside of school. 
• Describe the best class you’ve taken in your recent past (any content area). When responding to this statement, please consider the following questions: What made it positive? What was the teacher like? What was the atmosphere of the class? What were the grading procedures? The teacher made the class interesting, hands on, and engaging. She was very supportive and understanding and provided help if we needed it. She also created a safe classroom environment so I felt safe asking questions and asking for help. She was also very fair with her grading and always gave partial credit.