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The one moment that will stick with me from this last class was the saying, "We need to get the misconceptions out." What a simple and empowering statement. Although I hadn't put my finger on it until now, this simple concept has been guiding my instruction ever since we began our class. I have found that encouraging discussion around student's solutions, rather than focusing on the solution, has provided far deeper student understanding.
Although I wasn't able to make it to class on Monday, I have been thinking a lot about how my mathematical knowledge has increased. I think the biggest thing I have taken away from this class is that “math talks” can be worked into everyday teaching. My big a-ha is that it is OK to not come to a conjecture or a conclusion in 1 day. It’s OK to stop, reassess, and continue later. I have been guiding my instruction based on how my class is responding to the lessons. It's not worth it to force an entire lesson on them in one day if they need a few days to take-in what the concept is. I have been doing mini-math lessons and breaking things down into multi day lessons. My class seems to create a deeper understanding of the concepts being taught and have been able to actually discuss ideas more deeply.
I agree Tom, getting those misconceptions out stuck with me too. Listing them with my students helped this week. Also, since we're in the middle of fractions, really going over bar and number line models together is something I need to be better at.
I am understanding the great value of allowing the students to experience what perseverance feels like. They need the time to process their thoughts and work through their misconceptions.
I have noticed that when students are given the opportunity and time to prove their answer, particularly when it is an incorrect one, they often times can revise their thinking by simply catching their own mistake (e.g. I drew too many circles, I forgot to jump when I counted on).
I just love to hear the Oh! and the Ah! of a child who has an aha moment!
My aha moment was when I realized my "go to" for fractions (finding a common denominator) didn't work so well. My mathematical knowledge increased because through discussion and trial and error, I found that bar models and number lines were more convenient tools for solving the fractions problems than the common denominator strategy. I will take back the open sharing strategy. I will ask my students probing questions such as "how?," "why?" and "who did it different?" to understand deeper their mathematical thinking.
I would say that I have gained better insight on the value of letting a student sit with their frustration or struggle when working on problems. I felt I understood how to address the fraction problems from our class, but I wasn't able to succinctly come up with a conjecture based on this. I sat with it a while and was slightly perturbed that I couldn't come up with any standard conclusion. It was okay that I didn't eventually get it. Luckily, somebody stepped in for me. In my math teaching, I feel I am too quick to help my students solve their problems, and I don't let them sit with their struggle for a while. But I learned something from my students just yesterday when they (a small group of 8) were struggling with Problem #1. I was scrambling to help clarify for each of them, and then let them go on to #2 once finished with #1. I assumed they would still be confused when attempting #2. As it turned out, each of them successfully answered #2 as if it were never a challenge before. I was so impressed and pleased. I recognized that the fog they experienced in their confusion was beneficial. I need to get comfortable with it as a teacher and as a student in this class.
Thinking about the misconceptions that are in my class, and that I see regularly, I'm really starting to understand the full value in them. Celebrating the misconceptions as learning moments has really helped changed the culture of my room. It's hard for the students to trust. To trust me, and especially to trust each other to be brave enough to take risks and truly learn. Highlighting misconceptions and showing them to the class as an exciting opportunity has re-framed my teaching a lot, for the better.
Working together in a small group where strong relationship based on mutual trust and camaraderie has been built has allowed me to correct my own "misconception" regarding equal groups using hands-on manipulatives. The small and whole group discussions allowed me to feel safe without particular pressure to solve or speak when more time is necessary to process the information.
I wonder how my own class can be structured in order to facilitate the kind of dialogue that is assisting me to feel more confident regarding mathematics when students struggle to group items by ranging in numbers (2-10) and express strategies utilized to solving the problems. I would like to use “Number Rope” to increase number sense and explicitly teach different methods to adding before delving into “Open Sharing Strategies” so students believe they are mathematicians.
I am enjoying these classes because it reminds me how my students are feeling. You give us a math problem and at first I panic and think, "I can't do this" After a little thought I finally can try and solve. The thinking process for our students is so important and the discussion part for me in class helps me grasp concepts better so I know it is great for our students. Very powerful.
I am really enjoying these classes and it truly makes me work outside of my comfort zone. I loved doing the visual number line. I did it with my class of first graders and they jumped right in and amazed me. I am getting better at making kids persevere for their learning and really working on my math talks. There is lots of "Bird Walking" in my math talks and I am really enjoying the conversation. I could never put money on where our math talk will lead us.
I have looked over the intentional talk templates. I especially like the trouble shooting one. I do most of my daily teaching reflection in the car on the way home and this template has guided my self talk. This class is interesting and I always come away with something to implement.
I accidentally left the comment for this in another section of the blog.
I enjoy these classes cause it forces me to get out of my comfort zone. I found myself teaching math like I have been teaching it for the last ten years. This class is about students having a deeper understanding and being able to orally explain it to their peers using the proper terminology. What I've been able to walk away with is templates that focus my instruction, number talks, and an understanding how to look for assess math practices.
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