Share and learn from each other by posting comments, photos, and videos.
I appreciated having time to dissect the "engaging" worksheet that I created and gave to my students concerning adding and subtracting fractions. I learned how to make the worksheet stronger, as well as, how to address the misconceptions some of the students have.
I like the concept of having a class discussion and see how students are or aren't willing to put themselves out there in order to share their thinking. While I haven't had much whole class discussions in general with creating conjectures, I think there is a lot of value in making that part of their learning process. My previous models have focused more on speed and accuracy, but doesn't allow time for creative thinking. Many students approach problem-solving from different angles, and if they can help another student with their own understanding, that will benefit all of us.
After the class I was excited to try out conjectures with my kinders, At first I was feeling challenged by what a conjecture would look like in kinder and how to go about it. I got some great tips in class and couldn't wait to try it out.
I love the idea of the students making conjectures. It is so true that you need to let them do it. I have tried to provide them with conjectures, but it doesn't register with them unless they have that "ahaa" moment.
The story problems that we have at the beginning of the class help to deepen my mathematical background in that it gives me the opportunity to see how others solve the same problem differently. In particular, it has been a challenge for me to use the Cuisenaire rods and I had to ask my self, "How is this deepening my understanding if I already know how to solve for x?"
I really have been thinking about this for a few days and this may be my "aha" moment: As the teacher, if I have a deep understanding of how to solve a problem in both concrete and abstract ways, I can easily toggle back and forth with both and help my students strengthen their mathematical practices, especially #2-5. I would also be able to anticipate any misconceptions the students may have and direct them accordingly.
I implement the use of conjectures casually during math centers on a more consistent basis. I would like to try it more often as a whole group using different methods to keep them engaged during the process. For example, maybe one week I would use number strings, another week, I would have a "juicy problem" for them to solve, etc.
Question: Is it necessary to always write down a student's conjecture? Sometimes, when we are in the moment, I feel that taking the time to write it down would disrupt the flow, excitement, thought process of my first graders.
I was unsure of what a conjecture would be like in Kindergarten. It seemed advanced. I was nervous about the conjecture WE were doing in our class let alone bring it back to Kinder. I also love to hear what Eileen has to say about worksheets. I have done less worksheets this year than ever before and I am finding my students are still understanding addition. It makes me feel great that I can get out the fun manipulatives and recycle half the worksheets.
I would like to continue to pose open ended story problems so my students can practice asking questions and be motivated to solving them using method of choice. Afterward, I want to lead my class to use “Open Strategy Sharing” and “Compare and Connect” to learn from each other and take a step closer to owning their education. Lacking perspective taking, I am puzzled as to how to support my students to use oral discourse strategies and verbalize their thought processes using words, “I noticed…” and “I like to build on ____’s idea.” Perhaps tomorrow’s class will offer some guidance.
I feel like the more we talk about things in class, the more comfortable I am implementing them. After talking about conjectures, I feel like I was able to better explain it to my students, and in turn, got much better results!
I appreciated this class on conjectures. Using number strings will hopefully prove successful in having the students see the pattern in 0+ a number. Although, I do anticipate that it will be challenging to have kindergarteners come up with a conjecture. I am interested to hear their conclusions and see what they think. I think that introducing the pennies to the students on day one and then proceeding to the conjecture on day 2 will work well. I also think that linking the mathematical goal to the daily ball toss strategy is a great idea!!
Watching the class come up with the conjectures for fractions deepened their understanding of a possibly complicated topic. I can constantly refer to the created conjectures to help guide them through solving problems.
As a class we created a fraction conjecture that when the numerator is bigger than the dominator the fraction will be a whole number or greater. The students were able to come up with the conjecture but it felt like it took forever.
When I first introduced the study of fractions we used drawings of fraction bars and added the number line beneath to help visualize the comparison of fractions. After a time of working on other math skills such as area and perimeter and time and measurement I went back to fractions to see how much my students retained from our earlier number line work. It was frustrating and a little humbling to realize that much of the fraction concepts that I had introduced so strategically(or so I had thought) had been forgotten by many or had become confused with other concepts. I had to remind myself that with each new concept we introduce to our students we are adding on to their exposure and knowledge. It is sometimes easy for myself as a teacher to feel that my students now have this or that concept or skill "under their belt" but I realize that a better way to regard the on-going introduction of new concepts is to realize that I myself learn best through repetition and not even immediate understanding will take place. Instead, spiraling back throughout the year and revisiting all that came before. Therefore this week, as the school year draws to a close we will be reviewing fractions, using the number line rope and the cuisinaire rods and the ball toss. I have confidence that understanding will return but it will be good to review for both my students and my own understanding.
I was enlighten by the idea of looking at and using worksheets in a new way. Students don't need to do endless problems, but instead really investigate and dive in to a couple of good problems. I am looking at worksheets in a different way. It's not the number of problems that makes kids successful, it's the quality and focus on the concept at hand. i'm looking forward to adjusting how I design and implement my current curriculum.
Write something about yourself. No need to be fancy, just an overview.