Blog Post 6

This week I chose another task out of the CGI book to do with a student (pictured above) The question was--John has 11 cars. Josh has 6 more cars than John. How many cars does Josh have? The student I chose is the one I have done both of my students interviews with as well. She immediately gravitated towards the beads that I bring with me to do the interview. Then she put them into two piles, one of 11 and one of 6. She counted silently when she piled them. Then, she counted all the beads on the paper (silently, though moving her finger over each one) and told me that Josh has 17 cars. I can clearly see her thinking here. She put the 11 cars in one pile, then knew she had to add 6 more to that pile to get the "total." This task showed me, and extended on the knowledge of the student I already have, that she can count using 1:1 correspondence past 10 and close to twenty. It also shows me that she grasps the concept of addition, even when the question is posed in different ways.
Questions I have :
1. How can I have more accurate measurements/assessment of my students' math skill level?
2. It seems as though the student has grasped the "procedure" of the tasks I bring in. How can I extend the tasks to challenge her?
3. How can I get a more accurate understanding of the class as a whole and what they are learning?

I think to get a more accurate understanding of the student's math skill level I need to do two things: branch into other areas of mathematics, and choose more open-ended tasks. I feel as though lately I've been getting quick, procedural responses from the student which makes me think she is either accustomed to the routune, or the tasks are below here level. By varying the tasks (how they are worded, the topics they cover, etc) I may gain a more accurate understanding of her overall mathematical knowledge. For example, next week I might do something with shapes or number recognition. Lastly, I might try to talk to their second teacher and see if I can look at some of the thinks they have been working on. They'll be written in Chinese, but perhaps the teacher can explain to me the concepts that have been doing so I can more accurately plan my tasks and upcoming lesson.