Tuesday, July 17, 2012

Guided Math: Chapter 5




This post is part of my Guided Math Book Study. I will discuss each chapter in two sections: an overview of the chapter and my learning/wonderings and how this learning will affect my mathematics instruction. You can read the entire series of posts by clicking here. (Graphics for this post provided by Scrappin' Doodles.)



Using Guided Math with Small Groups


This is a really long and in-depth chapter that guides you through the process of using Guided Math with smaller groups as compared to using it with a whole group like in Chapter 4. This is not a chapter that you can get through in a few minutes; in order to process and absorb what you are learning, it is probably necessary to make notes, either in the book itself for future reference or on sticky notes or other paper as you keep track of your thoughts. This was not a chapter that I could write about in a few minutes--there is a lot of information and in order to synthesize it, it is necessary to often stop, think about what you've read, reflect on it and then keep going. So let's dive in!


Sammons begins this chapter with a quote from Debbie Miller's book Teaching with Intention which mentions that we want to create the "luscious feeling of endless time" in our classrooms (Miller, 2008, as cited in Sammons 2011). While I have not personally read Teaching with Intention, I have heard of it and this phrase speaks to me. We all want to feel like we have more than enough time in our classrooms--it's so easy to feel rushed and worry about the "getting done" and "finishing" rather than having our students "do" and "figure out". We want these things for our students in reading but it is necessary for us to desire and crave that same feeling as we teach math.

Advantages of Small-Group Instruction:
-teachers can slow down and savor the time they have with students (trying to capture that feeling of endless time)
-instruction is focused, materials can be easily managed and students can be monitored easily
-groupings vary frequently as does the time spent with each group allowing teachers to provide more 1:1 help for students who need it and less for those who don't need it
-students are more able to work in the Zone of Proximal Development when working with a teacher in smaller groups more frequently as needed
-student behavior can be monitored more easily during the group time
-students get immediate feedback during practice since the teacher is right there with the students as they practice
-students working directly with the teacher need to be encouraged to explain their answers so ensure they understand how to complete a math problem or know the process. It is difficult to see this understanding when teaching a whole class because the time to speak with each student becomes limited where in a small group, each student has the opportunity to share their thinking and reasoning with each other and the teacher

Challenges of Small-Group Instruction:
-Small group instruction requires more planning
-differentiation must be embedded by either varying the content, process or product of the lesson based upon the needs of each group; the content of the group might be the same but the product or how it is delivered changes which requires more planning on the part of the teacher
-students receive less overall direct instruction from the teacher as compared to a whole-group teaching situation
-teachers must also plan independent work that isn't busy work but is meaningful for students who are not engaged directly with the teacher

Effective Uses of Small-Group Instruction:
There are many ways in which small-group instruction can be utilized for math. Some suggestions provided include:
Differentiating Instruction: this really should be seen as a teaching philosophy because it isn't a strategy that should be used "if you have time". Often students who are high achievers miss out when teachers think they are differentiating because the higher students are given busy work or work that does not push them forward in their thinking. It is necessary to ensure that all students, even the higher achieving ones, get the benefit of small group instruction with the teacher that focuses on differentiating the process or product as well as the content (if necessary).
I think this is very important. Where I teach, we have often been told to "teach to the top" and then our strugglers fall even farther behind. On the reverse, we are told to "teach to the middle" and then our highest kids become apathetic because there is no challenge for them and learning becomes boring. It is necessary to find a way to differentiate EITHER the process/product/content, not necessarily all three so that students are still making meaning from the math work but are not becoming overwhelmed or bored in the process.

Teaching Mathematical "Hot Spots": Hot spots are defined as those concepts that year after year students have a difficult time grasping (addition and subtraction with regrouping for example). When the teacher focuses on the "hot spots" during small groups, they ensure that students are being monitored as they work through these tougher concepts and can be redirected if they are having trouble. Students don't have to wait until the next day to get feedback (which often happens in whole-group settings) and teachers can correct misconceptions faster with these concepts that are often hard for children no matter how advanced they may be.
This is a great idea. I think using the "Hot Spots" as teaching points for mini-lessons and/or small groups will be effective in helping ensure that students are mastering the concepts that they need to be successful in their current grade and the following grade. 

Teaching with Manipulatives: Manipulatives are great learning tools that can enhance student understanding of concepts as they can build visual models or use hands-on materials to help them make sense of the concepts being taught. The NCTM process standards are supported by the use of manipulatives as students need to make models and then explain their representation thereby constructing meaning through the use of the manipulatives which is what we want them to ultimately do. Small group teaching is ideal for using manipulatives because less manipulatives are out and teachers are right there with students as they use and manipulate materials which makes it easier to monitor their use and ensure that students are making the best use of the resources they have.

Formative Assessment--Assessment for Learning: Assessment it critical throughout any unit of study in order to ensure that students are learning what they need to learn and that they aren't struggling throughout the process. Assessment can not happen only at the end of a unit test. Teachers should be continuously monitoring student progress through quizzes, homework, in class practice and observation. This allows teachers to modify instruction as often as needed during the lesson and for the following day to ensure that students' aren't falling behind and are being met where they are.
Sammons points out in this section that it is important to have students participate in goal setting. Last year with my 2nd graders, each child had a data book and we made goals for our reading MAP data. We had nothing really to work on in terms of the MATH data but now with that test transitioning to the CCSS as well, we help students to identify what they need to know and help them be accountable for knowing it and making sure they remember it. Yes, teachers are responsible for the teaching but I feel that we have to instill in our students while they are little that it is THEIR responsibility that they LEARN.

Supporting Mathematics Process Standards: Students must know how to problem solve, reason through their math thinking and provide proof for their math thinking. Small group instruction allows students to feel more comfortable with sharing and exploring ideas with a group of 4-5 other children rather than the entire class. The small group time also allows more flexibility in how these standards are used and addressed based on the needs of the children and the comfort of the teacher as well as the curriculum requirements.

Forming Small Groups for Learning
Just like with Guided Reading, teachers form groups for math based upon multiple factors. As with most things, there is no one "right way" to determine your groupings. You can use whatever you feel comfortable using to determine your groups. Here are some suggestions provided in the chapter:
-Unit pretests
-Previous performance with similar concepts
-Formative tests
-Performance tasks
-Observations of student work
-Mathematical Conversations
-Benchmark tests

As I have mentioned previously in the series, I purchased the Confer app for my iPhone/iPad to use with conferences in my class. While I believe the design was intended for reading and writing workshop, you CAN use it for math. I added some fake sample data to demonstrate.

This is a screen shot as I have set it up for the 2012-2013 school year. It isn't shown but I added a class called "Fake Data" to demonstrate with to protect the identify of my upcoming students.


Here's a shot with only a few students' data added. As you confer with students, the most recent notes and entries go on the bottom and students who need to still be met with move to the top. This is a nice feature so if a student is absent, you can immediately see upon opening the app whom you need to confer with the most. The date shows the LAST time a student had notes entered. Notice that students one, four and three have a (1) behind their name which shows how many conferences you've had with that child.

Now all of the students have at least one conference and you can see under there name part of the notes that have been entered. 

I've opened up the data within that subject and can now see that my students are NOT grouped. Based upon the notes I have made for these children, I can determine a group that needs to meet. In this example, I focused on geometry, with angles and line segments.

In this final shot, you can see how I have made two groups: Angles and Line Segments. These students are now in a group with other children with similar needs based upon the notes I added into this app. 

*Note: the app isn't flawless and has some limitations but for my purposes I think that it is going to allow me to do a whole lot more with my student data than I have been able to do before. Best of all you can email the notes to yourself so you do have a hard copy if your school is one that requires you to keep student data on hand. (And no, the developer didn't pay me to say all of this nice stuff about him--although it'd be awesome if he did hehe).

Organizing for Small-Group Instruction
Clearly you can not plan a small-group lesson on the fly. You have to prepare and get the materials and information together to help you make the most of the learning time you have. It is helpful to designate an area for meeting with small groups (be it a table or on the floor) and have all of the materials necessary for teaching those groups, including manipulatives, white boards, pencils, crayons, etc.

The Lessons
There are several components to keep in mind while planning for the small groups:
-Identifying the Big Idea this is the overarching concept you want students to understand--it has to be identified for success to happen
-Establishing Criteria for Success students need to know exactly how they will be graded and how they can demonstrate proficiency
-Using Data to form groups using the information demonstrated in confer, students can be moved in/out of groups as needed, even if that is every day or after a week's instruction once they get a concept
-Determining Teaching Points using the data from all of the formative assessments helps determine the next step teaching point; curriculum guides and standards can also help determine where you should go next
-Preparing the Differentiated Lessons again the process, product or content can be differentiated and teachers can decide if they want to differentiate based upon learning styles


The chapter ends with an in-depth look at what small group instruction might look like based upon all of this information.


What a great and in-depth chapter! I have definitely had my brain spinning about this one for awhile. I really love all of the points about how using small groups improves the math process for students. I have really been conscious of my math teaching in the last few years since I have always focused mostly on literacy (my love). By taking an approach to teaching math the same way we would teach small groups, I have rekindled my desire to maximize my math instruction, especially with teaching a split class this year.

I plan to take a long look at the CCSS for both of my grades and begin to think about what my students need in terms of "Hot Spots" and how I can combine them as much as possible so that eventually my students can be mixed up between the two grades for grouping which will provide more differentiation. This may not always be possible but I'm going to experiment with it and see what works. 

I will definitely be making sure I am conscious of the notes I take, using all of the forms of formative assessment to determine my groups and not being afraid to move children when a group just isn't working for them! I think too often it is "easiest" for us to keep our groups the same for the unit instead of moving students as their needs dictate. I appreciate that Sammons points out students can be moved out of a group after only one or two meetings if they catch on with that extra support instead of making them wait for the rest of the group. 

All of this will require planning, preparation and being on top of my game always but that doesn't bother me. If it streamlines my math instruction and allows my students to make progress, it will be worth it.


Stay tuned for my thoughts and reflections on Chapter 6: Supporting Guided Math with Math Workshop!
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