Blog 4

Blog 4 invented strategies

I have not been able to really think of beside some mental computation going on in my student teaching. I have seen one student work out a subtraction problem where they broke up the problem by a fact that they knew. The problem was 700-549. What the student did was subtract 700-550 to get 150 and then add one more to 150 to get 151. The only way I knew what the student worked out the problem like this was because I asked if they could explain what they did. I have seen this strategy before but I wouldn’t of known the student used this strategy if I didn’t ask. I was glad the student worked the problem out that way and encouraged the student to continue to use the strategy and to show what they thought that way I could see it when I looked at their work.

Based on the Student’s explanation the student solved the problem 700-549 like this:

700-549

Step 1) 700-550=150

Step 2) The student knows that 550 is 1 more than 549 so the student knows they need to add one more to 151.

Two other ways to solve the problem:

700-549=

Different Method

Step 1) 700-500= 200

Step 2) 200-49= 151

Math Talks Moves

1.1 Revoicing
I have a really good example of revoicing a student's response this past week. I wish I would of taken a picture of the students work and how I wrote down his explanation. The students were working on a scavenger hunt where they moved around the classroom and work on various fractoin problems.  One student was working on 4/8+2/4 and he work out the problem and got the correct answer. He had completed the problem quickly so I wanted to keep him busy so I asked about how he solved the problem. The student explained to me the he multiplied 2/4 by 2 to find the answer. On the students paper he wrote 2x2/4x2. I went to the white board and said so you are telling me 2/4x2 is equal to 4/8. The student agreed and then I wrote is 2/2 equal to 2. The student took sometime to reply and the he said no 2/2 is one whole. We then started to talk about how he worked out the problem correctly but his explaination was different. I wrote out on the board and ask if 2/2 and 8/8 and 1 are any different. The student said that 8/8 is bigger and then we talked about part of a whole. The student then realized that he was simply multiplying the problem by 1. I didn't really think much about our conversation that day but looking back at it I see how the conversation the student and I had was much more than simply saying yes the student wrote the problem down right. Restating the student work can really bring out more from students and how they deal with math.

1.2 Asking students to restate someone else's reasoning
 I think this can be an effective strategy to reinforce others students strategy and alllow the student to examine his explanation when someone else states it. It makes me think about how something might make sense when they say it but everyone else does not get it. I think this strategy may be ineffective if other students are not grasping what the student is saying or if anyone understands. I think it might guide discussion but I'm not to sure if I would want to leave students feeling like they are right when they might be misintepreting a concept. I think using other strategy works well for asking students to restate someone's reasoning but on it's own I don't think it can really stand on it's own.

1.3  Asking Students to apply their own reasoing to someone else's reasoning
I think this is what should be combined with asking students to restate someone else's reasoning. I think this type of questioning is good for allowing students to look at how they understand a concept. I like how it is the why that is important and not if the student disagrees or agrees.

1.4 Prompting students for further participation
Participation is very important for effective discussion. I think I as a math teacher need to create an environment where student can be open to discussion. It takes a lot for someone to put their thoughts out in the open. There is a certain vunerability when anyone talks about what they know. Especially when they are not confident in a certain subject or topic. I would want discussion to be as equal as possible because I have seen that it is often the ones that don't need help are the ones who talk the most.

1.5 Using wait time
I think I'm improving in this area but there are times when I can't help but jump in. Ten seconds does feel like a long time but it is needed. I think that I sometimes I want to go over something the moment a student might make a mistake. I am able to wait when I'm thinking about letting the student process the information but I do admit I often don't give a student enought time when they make a misstep. I definitely is a skill that I would like to work on.

2. Thinking about the revoicing from this past week, I think the discussion was really effective. I think it was a really good teaching moment for me as well as the student. I think I will be more aware of how to lead a discussion and how it could take off into deeper understanding of a topic. I don't have any photographs from this discussion. I took a photograph of a student's paper but nothing is clear on the photo.

3. I think about the conversation the student and I had and I feel like I could work on allowing the discussion to be more flexible and for me to be aware of it. I went into the discussion thinking about how 2/2=1 and how is it different from the number 2. I think the conversation went really well but I think I might of only of let it go off in one direction. I think I could of explored how 2/4 times 2 is different from 2/4 times 2/2. I think these type of discussions really help a students' understanding because they are analyzing not only a problem but their understanding of math.