PUT YOUR BEARD IN MY MOUTH
#extradirty
Cosimo Galluzzi
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"I'm Dorothy Gale from Kansas"
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Today's Document
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taylor price
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One Nice Bug Per Day
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@adaraede339
I know that my apology won’t fix you or undo the hurt. Doesn’t mean I don’t want more than anything to apologize. Keeping this in my mind as the days lead up to the high holidays and I prepare to reach out to people I have hurt over the past year.
I think it’s interesting that so many teachers don’t understand proportional reasoning, yet are teaching it to their students. The clock problem mentioned in the article was challenging to the teachers, and I remember when we did that same problem in 118 and many people did not understand it.
I don’t think that I was really taught proportional reasoning in a way that made me understand the topic— it was all about shortcuts and numbers, and lacked application of the topic.
When teachers aren’t really good at a topic, their students can’t be either—so I think it is good that the teachers who attended the workshop mentioned in the article improved their proportional reasoning. And, unsurprisingly, the article says that students enjoyed working with proportional reasoning more, because it was no longer about just getting the right answer—there were meaningful steps to how they got there that the students truly understood.
The article says that teachers who just use the cross-products, a strategy that is only focused on getting the right answer, do not help students to develop their proportional reasoning skills. This leaves a gap in their math learning that negatively impacts their understanding and comprehension of other topics in mathematics as well.
7x7:
Even though it is kind of pretty obvious that 4x7 is going to be twice as much as 2x14, for some reason I didn't really make the connection until I saw this video. I also thought it was interesting how the students divided up problems with small numbers such as when a student divided 3x7 into 2x7 and 1x7, even though 3x7 isn't really a complex problem---although maybe it is to a third grader.
I also thought it was interesting that with 7x7, a problem that many of us probably think of as 'well, you just square it and you have the answer', the students divided up the problem into 3x7 and 4x7---I never thought about breaking it down.
I wonder if the class knows about squaring, and if the way that they solved this problem will affect how they think about squares.
Doubling and Halving:
Something that I noticed was when one of the students pointed out that the rows and columns were in a different order than everyone else, so it wasn't the same size. The teacher explained that they could easily look at it sideways or turn their head to the side and that it was the right size, regardless of which direction it was in. I think that the student hasn't fully developed a sense of conservation, so he saw the box a little differently than someone who has a fully developed sense of conservation
Even though many of the videos we have watched show doubling and halving and we have talked about it here and in M118, I wonder if students actually like using doubling and halvling.
MRI videos response
Sergio seems to have a really hard time with mental math even though he is working with multiples of ten, especially with the first problem. He gave up on the first one and on the second one wanted paper, but figured out the answer mentally after going over it step by step with the help of his teacher. The third one seemed to me like the least clear cut question,but for him was surprisingly the easiest. I think that Sergio needs to do a lot of work on his tens multiplication, and would benefit from a lot of extra practice.
Video 3.1 Response
This number talk is in a third grade classroom, and the problem addressed in it is 38+37.
I really liked how while the students were thinking about answers, the teacher reminded them to let others think and not raise their hands until she asked to (implying that she didn't want people to be distracted by other people having their hands up)---which is definitely one of my favorite aspects of a number talk. When she said this, she initially said don't raise your hands until I tell you to, but then she quickly said until I ask you to, reminding herself and the students that she is asking them, not telling them. This shows me that she really believes in being an asking teacher, not a telling one, which we learned in class is a better way to teach and for students to understand and retain the information, because they have to figure it out themselves instead of simply regurgitating something the teacher already said or showed.
In math while we were growing up, many of us didn't really realize the real value of the tens place--- if a problem was 44+53, we would add the 4 and the 5 without really thinking about the fact that the 4 was really 40 and the 5 was really 50. When one of the students started saying he was going to add 1 and 6, the teacher asked him if he was really adding 6 and 1, which helped the student reinforce and remember the concept of place value.
Video 5.6 Response
This number talk was about 1000-674
I liked the strategy that one of the boys used: if you add 400 to 674, you'd be over 1000, so an answer above 400 wouldn't be possible. (to determine that 426 wouldn't be a feasible answer).
I noticed that the students had a lot of different strategies, and the teacher wrote all of them, and asked who else had used each of those strategies. I also thought the look of horror on the face of one of the girls sitting in the front when Jackson originally said 324 was hilarious. The way that all the students started ooh-ing when he said 324 and they all wanted to correct him/ give the correct answer was interesting. I remember being in math class growing up, and one person would give an answer, and no one else would really give another answer, even if it was wrong. My teachers also never asked us to explain HOW we got our answer, so that is one part of number talks that I really like.
I liked how, like in most of the other number talks we've watched, the students were able to have a conversation with each other, not just with the teacher, but I did think that in this particular number talk, they were having their conversation more through the teacher rather than them talking to each other.
I liked how patient the teacher was when one of the boys was taking a while to articulate what he was trying to say, and didn't cut him off even though he was stuttering a bit. She could have (and the teachers I had growing up would have) just told him to "spit it out" or called on someone else instead, but she waited for him to give his answer in his own time.
Video 2.1 Reflection
This number talk was about 8+6. It was similar to the number talks that we participated in during M 118, but it was different to see young children, who are the target audience for number talks, participating in them.
I noticed that the students were all very respectful of each other The teacher asked students to explain other students’ answers. I also noticed that the students weren’t afraid to be in front of the class. The teacher also wanted as many students as possible to share their answers, even though she probably could have gotten through the lesson faster with one student’s strategy.
I wonder how she was able to get the students to be so respectful of each other and how quietly they motioned that they agreed with each other.
