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My aha moment was seeing first hand (with the adults as the students) that talking it out really is the key to solving math problems. It was so interesting to see how we were able to work through the problem orally to discover our own mistakes and misconceptions.
I noticed this with the 4th grade students we worked with as well. When they talked about the problem and explained their thinking, they were able to be reflective and see that they had made a mistake. However, they did not often explain their rationale to each other. They explained it to the adults in the group. This tends to be the case with my class as well.
I am looking forward to developing my students ability to consciously question one another and learn from each others mathematical thinking.
Kathy and I worked together with one student and it was very much a challenge to only ask her questions. The student read the passage once by herself and we read it many times throughout the course of trying to solve the problem.
She immediately picked up the numbers two, two, and 10 and determined that the answer was 14. When I asked her if there was any more information in the text that may change her answer she quickly responded with a no. I suggested that we reread the passage just to make sure. Our student said that she was confused by the words split and divide. We had to explain to her that "divide the rest of the cookies into two even piles" and "split the remaining cookies into two equal piles" meant the same thing.
With some prodding, we got to the idea of working backwards to get to our total. We discovered that our student is very much a CONCRETE thinker and we had to draw a circle and divide it in half to give her a place to put her cookies (i.e. her beans) because she kept taking away from the pile that she just created. She even had to draw a person to store the cookies that were eaten because "you can't spit the cookies back out!" I think our questions may have been more leading than they would have been for a more abstract thinker, but in this case it was necessary for our student to help her begin to understand the concepts within the passage. For example, after putting ten beans in one half of the circle, we would ask her specifically, "If there are ten beans in this half and this other half needs the SAME amount because they are equal parts, how many beans would go in this half?"
At first glance it would appear that this problem was too difficult for our student, but when I listened to what she was saying I noticed that she had a bit of understanding of the passage, especially after an explanation of what certain words meant. For example, she said, "Jen did the same thing as Maria." We were able to meet her where she was and help her apply what she understood.
Working with the student at class was very difficult for my partner and I. I realized that when I thought I was asking only questions to my class at times, I clearly wasn't. It was a lot more difficult than I thought, even though we could see the misconceptions. I've been practicing in my class with small group conversations, but it still seems a bit awkward at times. The change has clearly been good, but definitely difficult.
I found the experience of working with 3 fourth grade boys to be quite challenging when trying to get them to figure out the problem just by asking them questions. Tom and I both worked at moving them towards a solution, but were not successful. The only question that seemed to move their thinking was, "Where are the cookies?" Once the boys began to account for the cookies, they seemed to have some sense of how to keep track of them. But it never steered them in the direction of considering "working backwards". Neither of us really knew how to get the boys to think of doing that. It was frustrating. Luckily, the students enjoyed the process and didn't get too wrapped up in it, even though they never figured out the answer.
As I recognize, this is an ongoing, learning process.
Working with fourth grade students was a challenge but worthwhile. I learned just how prepared the teacher must be in terms of understanding the problem, anticipating multiple misconceptions, knowing students’ strengths and challenges upon having previously established strong bonds.
Furthermore, I understood the value of math discourse and visual aids when utilized with probing questions at most opportune time to allow students to adjust their thinking and offer explanations.
I think we would had been more successful if the lesson plan template was offered at the beginning of class to jot down notes and questions to ask fourth graders during larger group discussion to better facilitate the task in order not to offer too many clues.
As usual, I found the class to be very valuable.
Although I must admit that working with the 4th grade students was quite a challenge. It took great self-control to not make sure they came up with the correct answer.
Through it all, however, I can clearly see the value in asking guiding questions rather than telling them how to solve it.
As well, I once again found working with my grade level team to help me guide my next steps.
I loved being able to work with the 4th grade students! They really bettered my understanding of what this whole class is about. I came away realizing that I still have a lot of work to do as a teacher to better my understanding and skills with math discourse. Working in Kinder is a whole different world then working with 4th graders. It was a lot of fun to work with students who are more detailed and accelerated in their thinking. I appreciated when Eileen came over to help Erika and I with some questions for our students. They were stuck on one idea of the problem and Erika and I had some trouble getting them away from this misconception. I would enjoy working with students again at the end of this class and seeing if I would be able to help them differently. :)
Working with the 4th grade students was a good way to put problem-solving in action, especially when we had the luxury to be with one teacher and one group. Still, the problem was very challenging and the reasoning may well change, given another day…or maybe we asked too many questions, or not the questions that should lead to the ah ha! So a valuable learning experience for us teachers and one to refine and try in our class.
It really felt great when I had my aha moment explaining my work on the cookie problem to the class. Talking through my thinking and explaining along the way really made my mistake obvious to me as I was working on the board. It was so powerful to me that I have revisited using the white board to show work instead of projecting student work already done. I see my students taking more pride in showing and explaining their work on a math problem. They actually smile and say, "I see where I made my mistake." They have been supportive and patient with each other as they work through problems.
Boy, what a challenge working with the two fourth graders. Robin and I worked on asking guiding questions, but we could only get them so far with the time we had. It was a lesson on leaving the problem and coming back to it later.
It was great to work with students under the guidance of eileen and other teachers.
I worked with Danelle and Michelle and we had two fourth grade students. One student held back and the other was outspoken. It was hard to get the quiet student to participate when the other student just kind of took over.
I was glad I had partners to remind me not to go to far with my explanations. Our students ended up solving the problems. It was with a final question from eileen that the students finally got it.
It was eye opening working with the fourth grade student. I was really glad that I was working with Mo. First of all, the problem was challenging. I was able to solve it, but not immediately.
The student we worked with was quiet and unsure of how to approach the problem. I had trouble thinking of questions to guide her. It is definitely much easier to just show them how to do it. Mo was really good at asking questions, but our student was just positive that she had solved it and was done. Asking guiding questions is definitely something that I need practice with.
I really enjoyed watching the fourth graders solve this very challenging problem. It was hard to keep quiet and let them talk it through. I'm going to need to work on asking those guiding questions. Our two students were so close but we just couldn't manage to come up with the right question. Eileen, however, stepped in, asked the right question and suddenly the students had their ah-ha moment. So much fun to watch!
Working one on one with a student only asking questions was really hard for me. First, the level of the problem seemed very high for this student and also because she was EL. The language likely played a part in the complexity of the task. I was struggling to find the right questioning to guide, yet not tell the student how to think about it or even do it for her. It gave me a better appreciation for how difficult it might be a student with no experience to do this.
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