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Response to Sarah: Chapter 6-I also need to do a better job with explain the purpose/setting and learning expectations. Furthermore, I need to start incorporating games into my guided math groups. I liked the templates provide in this chapter. I may start to use them this year and see if they help me incorporate those portions of the guided math lessons into my own lessons.

Chapter 7- I use Math Talks in my whole group and small groups. I love the way that Math Talks focuses students on explaining their thinking to their peers. I especially use this during whole group times and try to have a high, med, and low student explain how they solved the same problems. This gives all students the chance to see multiple ways to solve a problem. This was my favorite quote so far in this book, “Mathematica proficient is way more than just knowing how to do something. It is an attitude, a way of thinking, a style of engagement mixed in with understanding and knowing how to do stuff” (Newton, p. 86).

Response to Tim: Chapter 6- I too love manipulatives. It really helps students work out problems in their head. It’s interesting to see what types of manipulative students use to solve problems. At the beginning of the year, most of my students used counting bears and liking cubs, but now most are shifting to the number grid. It gives me a good insight into evaluating which students are thinking of numbers more abstractly and which still need very concrete examples.

Chapter 7- It’s totally the self-fulfilling prophecy. If you think you can, you can. If you think you can’t, you won’t. Students that have a positive self-fulfilling prophecy will persist even if it’s challenging. It’s something that is so hard to instill in children, and adults. This year, I have made the focus of my entire classroom environment all about “it’s ok to make mistakes, we all make them”. I make it a point to always share with my students when I mess-up and that it’s ok, I will just have to try again. I am seeing this in my students. There are vocalizing that they made a mistake and are going to try again.

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Chapter 6:
1. What are the benefits of using manipulatives during guided math groups?

I love watching student use manipulatives in math because it gives me an insight into their thinking. I can evaluate if a student is understanding a math concept or not by watching how they use manipulatives. Moreover, I can also see if students are using manipulative to help them solve problems or using them as a crutch (don’t really have a concept of the problem).  Another benefit is that manipulatives give students a platform to take abstract problems and turn them into concert.

4. How often do you play games in your guided math groups lessons?

I really don’t play games in my guided math lessons. In fact, I am struggling this year to even teach many of the Everyday Math games. I feel pressured to teach the concept in the math lesson and have little time to teach the games. I also have a fear of students playing the games wrong, and in turn reinforce wrong skills. I also focus in my guided math groups on teaching concept a gradual release model. In reflecting on this chapter, guided math groups may be a great solution to teaching more math games. I could also use guided math groups to differentiate games so all students can play the same games independently.

Chapter 7:
1. How much time do you spend on building conceptual understanding of the topics you teach?

I feel like this is where I get myself in trouble. I spend way too much time on trying to build conceptual understanding which eats into my guided math groups and teaching games.

2. How much time do you build in for students to prove their thinking in more than one way? How might you improve on this?

I spend a good amount of time on giving students opportunities to share their thinking. I purposefully call on multiple students to share different ways they solved a problem. I also have students model their thinking and explain how they solved the problem in front of others.

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Sarah, I too need to do a better job making real life connections prior to lessons or during summarizing. I was happy to read about how you start the year out introducing various ways to solve problems and at this point in the year you are looking for students to solve in more than one way. This made me happy because we are beginning to do the introducing now, and I feel this is a good preview for first grade! I enjoy seeing how the standards connect and how the curriculum works together through the grade levels.

Tim, I was glad to hear that manipulatives are still used in 2nd grade. I can see how these would be useful for subtraction! We are beginning to do some one step subtraction number stories and they have been very useful! I tend to introduce partner games whole group and rarely use them during my teacher time as well. I feel this time is so short and so valuable, I like to focus on key concepts and mini-lessons, not engaged in partner games; though, they are helpful for observing how peers interact and explain their thinking to partners.

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Chapter 6:
Q3 - This chapter really resonated with me. I need to do a better job of explaining the purpose/setting the learning expectations. Typically, I will give an overview of the topic we will be learning about, but I need to give more explanation of the purpose and real world connections. I try to complete some type of summarizing activity at the end of each math group. The information gained from a summarizing problem can give much detail into how well the students grasped a concept, as well as who may need additional practice in the following days.

Q4 - My students play math games almost daily. Many times, I will introduce a new game in a whole group setting and then allow my students to practice/play on their own. As mentioned in the text, I can also have the students play games during my group. This would be a slight shift of my norm. Chapter 5 explained the importance of taking notes during all groups. I need to improve with my notes on how students are progressing with their games. If they play a game periodically during my station, I could easily take notes during this time and also re-teach if needed.

Chapter 7:
Q2 - Now that we are further into the year, I try to devote more time into having students find more than one way to solve a problem. At the beginning of the year, we focus in various ways to solve a problem. We learned about several strategies, so it is much easier for my first graders to prove their thinking now. One way to improve in my classroom is to have students begin to do this more independently without me having to ask them to try it a different way. Additionally, there are times when I feel like they give up on the second way since they already showed one way.

Q5 - Knowing your students’ mathematical disposition is critical for success in your classroom, as well as into their future education. I try to create warm, inviting environment where everyone can feel safe and respected to share their thoughts. My goal is to provide a place for all students to feel confident and be successful in our classroom (can be applied to all content areas). I do have students “wrestle with problems” frequently, but in my reflection, I need to do a better job with my scaffolding. I do see some students quickly giving up on themselves and not being able to persevere to complete the task. I need to balance how much help I give versus letting them “wrestle” without feeling too negatively about themselves.

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Chapter 6
I use manipulatives all the time! When I think about how I never used to use them (decades ago) but now I see the benefit to using them to help the children  to count, organize  thinking and prove work. I really enjoy having a very concrete model to put in front of those struggling with the concept of number .  They can see this many blocks or cubes or whatever is that number.  In my room, two of the three math groups still need that concrete representation of  place value materials to add. (showing the exchanging)  The highest group "plays with " the blocks but can do the work on their own.

I sometimes introduce new games in the guided math group with me just because without direct instruction many in my room would struggle.  After I see they understand it, I feel comfortable with putting it into the games rotation.

Chapter 7
I found myself rereading chapter 7 again and thinking to myself... hmmmmmm. Again I find myself wanting as a guided math teacher. I read the sample lessons and became enthused at some of the ideas I saw there. I plan to try out a few like "Lucky 8" I try to get my students to express themselves in writing, to explain their thought process in how they got the answer. I spend time trying to get them to understand the concept so they can go to a deeper understanding. I set the stage for the day in whole group before we go to the small group telling everyone what we are going to be working on..... and yet too often I find things don't turn out the way I planned. I try to allow the students to "struggle" so they find ways to solve on their own ( and I can see their misconceptions). However, I have a group of students that has a tendency to give up fairly early in the process.  I would like to be able to ask more effective questions to help scaffold the students who are struggling. I would like to have my room be one where every student believes they have mathematical confidence.

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Chapter 6: I think it is super important to incorporate manipulatives wherever it is possible. It provides a very concrete model for students to look at and utilize. Most recently, I've been using longs and cubes to have students show subtractions. Subtraction is tough for my kids to consider regrouping. Using the manipulatives has a been a big help. I slowly start to pull away the manipulaitves as I see my kids becoming more comfortable so they can prove to me their full thinking. I try to incorporate math games in my other stations, but I rarely use them when students are with me. I tend to focus on teaching the concept at my station and then having the students practice it with a game.

Chapter 7: I try very hard to instill a culture of mathematical confidence. So often I have kids tell me they can't do things. I reassure them that they may not be able to get it completely correct just yet, but they are closer than they used to be. We talk about how struggling is just part of the process to reach a good understanding. One way I really try to build confidence is by giving students the floor to explain their thought process. Even if I know a student is going to be incorrect I let them talk it out for a few reasons. One reason being that it helps me learn where the misconceptions lie. It also allows other students to hear a classmates struggle and then explain what they know to be true. The open and honest conversations are a wonderful way to make a group meaningful and effective.

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Chapter 6: I work hard to start insure that my students have a concrete understanding of a concept before moving into pictorial and abstract representations. Two areas that comes to mind quickly are counting groups of objects and number  stories. Early on in the year, if I show students a group of objects and ask how many they see, they might just say a number. (Quite confidently too!) We practice counting strategies and what "makes sense". Next, when we learn about number stories, some of my students can solve them abstractly if the numbers are two small. Finding a "just right" number is crucial to helping these students understand that they must have strategies and won't always "just know". I do a good job of meeting with my students prior to math groups and telling them what we will be doing today in a "meeting" type of format. They seem to be more settled and engaged when they know what is expected at each session/rotation.

Chapter 7: I spent a lot of time reflecting on Chapter 7. I enjoyed looking at how the different math strands apply and change across the grade levels. I enjoyed reading the sample lessons and considering how I can get my students to think "deeper" about math concepts. I also think knowing where they are headed in their future math careers, as well as how the standard shifts or builds will help me to be a better teacher and ask more effective math questions.

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1. How much time do you spend on building conceptual understanding of the topics you teach?
2. How much time do you  build in for students to prove their thinking in more than one way? How might you improve on this?
3. Do you have a culture of reasoning in your classrooms? How would you describe it?
4. Think about the problem-solving culture in your classroom. Do students model their thinking with numbers, words, and pictures?
5. What is the mathematical disposition of your students? What might you do to build it?

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1. What are the benefits of using manipulatives during guided math groups?
2. Do you consider how to teach a specific topic at the concrete, pictorial, and then abstract level?
3. Do you always make the math clear to the students? Do you begin the lesson by telling them what you are going to talk about and end it by summarizing what the class has done for the day?
4. How often do you play games in your guided math group lessons?