Week 6: Reflection

I was able to be in the class four days this week: every day but Wednesday (because they had a field trip that afternoon).

Much of what students worked on this week continued to be review of multiplicative comparison, and on Friday they moved on to “multiplying by 10s, 100s, and 1000s.

On Tuesday, I led the Teacher Time center, based on a multiplicative comparison worksheet. My teacher mentioned she would like it if we had a chance to use “n” in place of the unknown number. The first two questions on the worksheet gave students a multiplicative comparison situation, that ended with students doing an additive comparison. This shift seemed to be difficult for many students! It was interesting to see that many students “got” that the first two questions were multiplication – but most also struggled to flexibly move between multiplicative comparison and additive comparison.

The first question asked something along the lines of: A fire dragon burned 8 times as many huts as a fire beetle. The fire beetle only burned 3 huts. How many more huts did the fire dragon burn than the fire beetle?

First Thought. A few struggled with understanding that the first question started with 9 groups of 3. These students struggled to set the model up correctly and so I tried to give them opportunities to use tiles as physical manipulatives to understand the situation. Some students interchanged 9 groups of 3 with 3 groups of 9, which makes sense because multiplication is commutative. However, in the situation, (1 group of 3 + 8 groups of 3) will result in a different final answer (24 huts – 3 huts = 21 huts) than (1 group of 9 + 2 groups of 9) which results in (18 huts – 9 huts = 9 huts).
Second Thought. Most students found their answer by multiplying 9×3 = 27 huts. Only a few students really noticed or understood that 27 huts was not the answer, but that, instead, “how many more huts did the dragon burn than the beetle” meant to subtract. It seemed that shifting from multiplicative comparison to additive comparison was difficult. I tried to support the students by focusing their attention on the final question and asking them what they thought it meant, but many students seemed to really be mentally blocked from using subtraction.
Third Thought. I tried to work in the “n” with the first two groups, but I think even in a small group there is a wide range of understanding of what the tiles meant or what the squares in the model meant, so moving to calling the number “n” seemed to be just one other thing at the moment. Only one student among the twelve in those first two groups really seemed to respond to that.
Fourth Thought. I will keep working to communicate manipulative expectations. The groups really varied in their reactions to the availability of physical tiles. Some students immediately began grabbing tiles without using them as mathematical tools, but instead began creating patterns with them. I tried to communicate clearly, but again this communication is something I will have to continue working on.
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Week 5: Reflection

Because of my schedule, a reassessment (of ideas from the first exam), and a Professional Day at the school on Friday, I only was able to go to school on Wednesday this week.

On Wednesday, I led the Task: Multiplicative Comparison that I had prepared. I worked with small groups of 3, rather than full groups of 5 or 6. Unfortunately, I saw them during the Hands-On center rather than during Teacher Time (which is normally when I will do a task). Hands-On center time is usually when students choose (or are given) a math game to play with each other, so the students I chose to work with were anxious to finish and play a game. Paradoxically, that made it difficult to focus on the questions and we took 15 minutes each time. In the future for a task like this one, I would try to make the task more like a game, only work with one or two students, or request to work with only two groups of two students each across the whole centers time.

Something that I noticed, about which I can sympathize with undergraduate student teachers, is that I see how busy the class always is and how my teacher has organized it to run smoothly and I don’t want to disrupt that. I could have asked for the extra time with one group of students (as I wrote above) – I was aware I would need it – but I chickened out because I wanted the task to support the teacher and students in their current context. It was difficult to ask even for half of a group rather than a whole group.

Another, somewhat unrelated observation, is that some students have asked me to call them by nicknames (e.g., “Peanut Butter Sandwich,” “Pretty, pretty princess,” “J.J.,” and “Renaldo” or “The Great Renaldo”). Partly, they suggested the nicknames because I was learning their names, and partly because I think they feel special. I think it’s fun, but I have noticed some students ask me, “Why do they have nicknames?” I try to answer: “They asked me if I would use that name.” But I can see that it privileges some students over others – even though each student could ask, there are only some students that will ask. Some students would like to have a nickname, but will not ask for it. Some students would like to have a nickname, but will not ask for it. Other students don’t care one way or the other. I’m not sure how to make that “fair” other than to let them know I’m happy to call them nicknames if they’d like one!