Math Interview

Monica Beland March 30, 2008 TE 910A Interview Assignment Student: Amber Grade: 1 School: Dingeman Elementary School Information I used throughout the interview: She listed her friends as Joanne, Rachel, and Savannah. She told me that she had an older brother who’s name is Raymond and that he is 9 years old. Her favorite thing to do is cheerlead on her cheerleading team. Interview Questions: 1. Can you count by 3s? 10s? Show me on paper. 2. Can you show me 24 with the cubes. Please explain this to me. (Add 10: How many do I have now?). 3. Raymond has 5 apples. His mom gave him 7 more apples. How many does he have altogether. 4. Amber has 21 toy cars. You give 5 toy cars to Joanne. How many toy cars to do you have left? 5. Rachel has 19 marbles. How many more marbles does she need to have 32 altogether. 6. Amber has 9 marbles and Savannah has 4 marbles. How many more marbles does Amber have than Savannah? 7. Rachel has 3 packages of gum. There are 5 sticks of gum in each package. How many pieces of gum does Rachel have. (3 pack with 12 sticks of gum in each package.) 8. At a party there were 18 M&Ms left to be shared among 3 children. How many M&Ms should each child get? 9. 20 children are to be driven to the park. If each car had seat belts for only 4 children, how many cars would be needed to drive all 20 children to the park? 10. Can you write a problem with a bigger number that you can solve? 11. 19 children are taking a mini-bus to the zoo. They will have to sit either 2 or 3 to a seat. The bus has 7 seats. How many children will have to sit three to a seat, and how many can sit two to a seat? 12. Imagine that this is a brownie (draw a rectangle). Could you show me how you might share this with two other people so that each person gets the same amount? Do the same for 3 people; 4 people; 5 people. Strategy: 11. In question 11, Amber first drew out 19 lines and 7 lines. She was drawing a line from one of the 19 to one of the 7. In the middle, she

stopped all of a sudden. She erased everything and drew 7 seats. Then she placed 2 lines in each seat. She said that these were the 2 people that sat in each seat. She then counted all of the people in the seats to get 14. After that, she put a third person in every seat until she got to 19. She concluded that 5 seats have 3 people and 2 seats have 2 people. When I asked her to explain why she erased everything, she told me that she figured out a better way to do it on her own. Then she told me that she put 2 people in every seat because she knew at least 2 people had to be in the seat. She put the 5 remainding into seats of 3. This was an example of direct modeling. She showed me how she got the answer through a visual representation. She also figured the answer out using counting. She went from counting by 2s to counting by 3s. 8. This was one of the only times that Amber really utilized the cubes. She took 18 cubes. One by one, she put each cube into a different pile until all of her cubes were in 3 piles. After she put them in three piles, she counted to see how many were in each pile. This is also a type of counting and direct modeling. 7. When I first asked Amber this question, she quickly got the answer without using any cubes or writing. She said that all she had to do was count by 5s for 3 times. She said, “5, 10, 15.” When asked if she could show me 3 packages with 12 pieces of gum, she took out her paper and used tally marks. She put the 12 tally marks in 3 groups. Then she added all of the tally marks to get 36. At first this is an example of counting and recall (because she knows that 5 added 3 times equals 15. 12. When I drew a picture of a square brownie, Amber was quickly able to divide the brownie into equal halves. When I asked her to divide it into thirds, she drew three lines in the center of the square (creating 4 pieces). She then explained that the fourth piece at the end did not count. It was extra brownie that they did not use. I asked her to draw the brownie into fourths. She drew 4 vertical lines in the box (creating 5 pieces). Again she said that the last piece was extra and did not count. This was a part of the derived facts. She took what she already learned about fractions and tried to apply it to the parts of a whole. Her derived facts were mostly incorrect about fractions. What I learned from this experience: This was an incredible learning experience because there are not many times when a teacher can sit down alone with a student and ask the student how the student got the answer that they got. It helps to get in their head for a moment and think about how the student is thinking about math. If a teacher can do this, they can understand what the

students are struggling with. This experience has also taught me to question why students are doing math the way they are doing it. Many of the brief questions are easier for the children. The children seem to struggle the most with word problems. How I felt during the Interview: I was excited to see how Amber would do during the interview. I knew that Amber is incredibly bright and has a strong desire to learn and explore. I was expecting her to do well. I was very at ease with Amber before and during the interview. I felt more comfortable as we started getting into the questions. At times I was very shocked with how fast she came up with the answers. I thought that she would want to use the cubes more. I was also very shocked with how many questions she got right. I was going to stop at the multiplication and division questions but I kept on going since she was getting the answers so quickly. She was happy for the extra challenge. This was a very positive interview because she felt so confident in her answers. I felt like I empowered her to believe that she is great at math. Anything that Surprised Me: I was most surprised by the amount of answers she was able to consider and solve! I thought that we could have to stop at multiplication and division. One of the most shocking times was when she counted the five packs of gum by 5s. She did not need to count on her fingers or draw me a picture to represent this. She knew this so quickly. Even when I changed the number to 12 pieces of gum she quickly drew the answer out with tally marks. Then she counted the tally marks by 5. She was very fast and efficient with a high accuracy rate. Any Implications this interview has for instructions: I think the student has a strong foundation in addition and subtraction. She knows how to use both in word problems. She is able to differentiate between addition and subtraction in word problems. I think she also has a very good foundation in multiplication and division. She was able to count by groups just like multiplication. She was also able to separate into groups just as division does so. The next area I would like to teach Amber is fractions. She understands that fractions are part of a whole and that all parts should be equal but she does not understand why there can only be a certain amount of pieces. I think she would pick up on fractions very quickly.