Running Head: Interview Assignment1

Fraction and Decimal Interview6

Fractions and Decimals Interview Assignment

Gail Lindsay

KSU

ECE 7525

Types of Problems the Child Solved Successfully and Struggled With

The fourth grade student that I worked with got all the problems correct. Problems D-E were very easy for him. He was able to show me by using the provided worksheets how to cut up the different items into equal parts. Problems A-C were a little more challenging for him. Even though I provided him with scratch paper, he was able to solve them in his head. Problem F was the most challenging for him. He had to use the pizza worksheet 3 times before he was able to cut it into 7 equal parts.

Overall Judgment of the Child’s Understanding of Fractions

I think this student had a strong understanding of fractions that use equal sharing. When I returned him back to class, his teacher had told me that he was in our schools advanced math class. I think he had a strong intuitive understanding of equal shares. On problem A, he used repeated halving with coordination at the end. He visualized 12 cupcakes with ½ cup of sprinkles on each one. He said that he knew ½ and ½ equals 1, so he added the ones together to get 6. On problem C, this student was also able to divide up the 6 cookies. Then he took the remaining cookies and split them to divide them equally to get a total of 6 ½ cookies each.

Overall Judgment of the Child’s Number Sense

I think this child has good number sense. He was able to understand proper and mixed number solutions like in problem B and C. He was able to answer problems that the solution came to more than 1 like in problem A and C. Empson, S. and Levi, L. ( 2011) state “Equal Sharing problems where the answer is greater than 1 are easier for young children to solve and help bridge children’s understanding of whole numbers and fractions” (p. 10). More complex was his ability to solve problems that were less than 1 like in problems B and D. As stated earlier, the only difficulty the student showed was with F. Empson et al. (2011) explains “Older children tend to be able to partition more accurately. But there are still many partitions such as into sevenths or tenths in which it is impossible to achieve more than roughly equal areas, even for adults” (p. 27).

Next Steps for this Student

Amelia ordered a birthday cake that was shaped like a circle. She wanted to cut it into 10 equal shares for her and her 9 friends to share. Please show me how she should cut the cake. I think this is an appropriate next step since the student I worked with struggled with this on problem F. Empson et al. (2011) explains “Learning how to create fractional quantities on their own using part-whole and other kinds of representations contributes to children’s understanding of fractions in the long run…” (p.28).

I would tell the parents that their child has strong number sense and understanding of equal share fractions. He needs further development with drawing partitions especially with smaller fractions. He could practice at home using an online math game; such as, http://www.mathplayground.com/index_fractions.html. This would allow him to work at his level and differentiate as he gets stronger. As the teacher, I would set him up with a partner that was a little stronger than he is to work with and solve drawn partitioning problems, so they could talk through the problems together. I would tell the parents that they could work with him at home on this also. I would send home some printable fraction games for them to play as a family. After a couple of weeks, I would follow up with the parents to report the progress he has made and see if they have any questions or concerns. Aguirre, J., Mayfield-Ingram, K., and Martin, D. (2013) state “The ultimate goal is to have everyone walk away from such a meeting with an understanding of the child’s mathematical strengths and needs and a specific plan that shows how mathematics learning will be supported at school and home” (p. 102).

References

Aguirre, J. M., Mayfield-Ingram, K., & Martin, D. B. (2013). The impact of identity in K-8 mathematics learning and teaching: rethinking equity-based practices. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Empson, S. B., & Levi, L. (2011). Extending children's mathematics: fractions and decimals:. Portsmouth: Heinemann.