Tuesday, July 24, 2012

Guided Math: Chapter 7

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.)

Conferring with Students During Guided Math

Most teachers are familiar with conferring with students during reading and writing. We often neglect to implement this important teaching opportunity with math. This chapter focuses on how to integrate conferences during the Math Workshop.

When teachers are conferring with students, they learn about the students' work, whether students are understanding or struggling with specific concepts and what they should do next to boost the child's learning. When we confer and use that information to guide our teaching, our craft becomes more powerful than if we don't confer. 

As we confer with students, we learn immediately if the child has grasped the concept(s) we have taught and want to make sure they know and understand. If they do understand, we can continue to push them forward. If they don't, we can provide immediate remediation to help each child master the concepts we are required to help them learn. In addition to conferring with a teacher, students should be taught how to confer with each other. If Little Joe is struggling with a concept that Big Joe has mastered, it would be fair to have Little Joe seek Big Joe's help if the teacher is otherwise busy.

Conferring allows teachers to target their teaching. Every child is met at his/her level during a conference and can be given the assistance that is most appropriate to their learning needs at that moment. 

A big thing to keep in mind is how to teach students what to do if they do become stuck during workshop time. We don't want the children to interrupt our conference or small-group teaching but they need to know what they will be expected to do when this problem arises. It is mentioned that the teacher can meet with the students who needed extra help later that same day or first thing the following day so the teacher can provide the targeted help and assistance that child needed.

This got me thinking about HOW you would know a specific child needed help during the workshop. If my goal is to teach my students to be self-sufficient so that I am uninterrupted in groups and/or conferences, how would I know that someone really needed help? Years ago, in college, a strategy was presented to us about allowing children to sign up for extra conferences. If there is a write-wipe board or other signup sheet available, students can add their name and if the teacher finishes early with a small group or has time left after the day's conferences, s/he can go to the sign up sheet and meet with anyone who has signed up for an extra conference because they were struggling and needed help. I also think it is VITAL that students be taught that if they do have a problem with something they are working on and sign up for that extra conference, it doesn't mean they SIT and do nothing until the teacher comes--they go on to another task or problem until the teacher can come and provide assistance.

It is mentioned that many of our students develop "learned helplessness" because they want help instead of thinking through the options they have when they face difficulty with a problem. They don't want to work through any obstacles and would rather we continue to "spoon feed" them and walk them through the steps themselves. As a result of this, when students have to struggle to learn, they become frustrated and give up. There are also students who, for whatever reasons, dawdle getting started or finish as fast as possible without a care in the world if they are correct or not. These sorts of behaviors are what makes it crucial for teachers to spend a few minutes of the workshop surveying the room to ensure that students are working and being productive before they begin their first group. 

It is mentioned that conferences are most effective if they can occur right after a teacher observes undesirable behavior. This isn't always possible or even feasible, however, so that is something that I think needs to be handled at the discretion of the teacher. If I am working with a small group and scan the room while the kids quickly work out a problem and notice a child totally off task, I can't stop my group and go conference with this child. It might be 5, 10 or even 15 minutes or more before I would have a chance to sit with that child and talk about what I noticed. I think it is vital that teachers use what they know and use common sense when they are thinking about how to handle issues such as this.

Structure of a Conference
Conferring with children across subject areas allows the child to become more responsible for sharing the knowledge and learning they have participating in and gained. Students need to understand that it is okay to make mistakes--that's why we're here! We're here to make mistakes in a place where we can figure out how to fix those mistakes so that they won't happen out in the real world where it could cost us a job. There are four main components to a conference, again adapted from the work of Lucy Calkins and colleagues.

Research Student Understanding: it is important for the teacher to know and understand what the child has been working on. A quick scan of the child's work or even ASKING the child to share what they have been working on can provide a launch point for the rest of the conference

Decide What is Needed: once the teacher understands what the student is working on and trying to accomplish, the teacher can decide if they need to solidify or modify the child's process or strategy. If the child has grasped a concept and is using the strategies taught, that's awesome.  If not, this is the time to determine if you need to help the child make modifications to their strategy. This is the time to determine if you need to extend the learning or remediate the learning.

Teach to Student Needs: help the child, based on the need for extension or remediation, by using manipulatives or guided practice to help the child to complete the task provided.

Link to the Future: restate what this child has been working on and remind the student that they will need to work on this again in the future to provide the understanding that this is an important concept for the child to know.

Record Keeping
It is important to document the conferences that are held with students, not only to satisfy data requirements but also to ensure that you can look back and see what the child has already been working on and notice gaps that might be preventing the child from moving forward. There are so many ways to keep these kinds of records: clipboards, data binders, sticky notes, etc. As mentioned previously in this study, I plan to use the Confer app since it saves paper, allows me to print if I want/need to and allows me to group and regroup my students based on their most recent conference goals and needs.

I really enjoyed this chapter about the conferences. Most of us use this format for language arts and it makes sense to shift it over into math. I like the idea that you don't HAVE to have a set schedule for the conferences but rather can shift and roam based upon observations of students working or wanting to check in with a child who was struggling yesterday to ensure they are doing okay today.

My principal is a stickler for having posted conferences so I will likely have to do that--but the idea of having an extra conference sign up sheet is appealing so if I finish early with a group or with that day's conferences, other children know that I will have time to get to them if they really need help and couldn't get it from a peer or any other adults that might be in the class.

Stay tuned for my thoughts and reflections on Chapter 8: Assessment in Guided Math!


Sunday, July 22, 2012

Guided Math: Chapter 6

 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.)

Supporting Guided Math with Math Workshop

This chapter provides information to help teachers support using small groups with math by setting up and running a Math Workshop. 

"The Math Workshop component of Guided Math shifts much of the responsibility for learning to the students." (Sammons, pg 183).

Students need to be able to deepen their mathematical understanding and they can do this by working independently and learning skills that will help them to work independently. 

Advantages of Math Workshop
-allows for a broad variety of tasks that students can work on independently including: investigations, paper-and-pencil activities, math-facts practice, games, explorations or problem solving. You can also include journal writing related to math, computer games practice or cross-curricular activities that emphasize math.
-allows for CHOICE which helps build student independence and confidence as each child can work to his/her strengths and needs
-promotes the development of life skills such as listening carefully and anticipating questions or obstacles they may have to overcome because the teacher won't be there to simply "fix it"
-students learn to work collaboratively to complete an assignment or project

Challenges of Math Workshop
-student procedures and expectations must be taught and retaught in order for M.W. to succeed
-it may be necessary to limit the range of activities initially which could lead some students to be too challenged or not challenged enough
-planning time increases when planning for whole group, small group lessons and independent work for each student or group

Best Bets for Math Workshop Tasks
  1. Review of Previously Mastered Concepts: Since most math concepts build upon the ones previously learned (ie. there is a reason you learn to add before you learn to subtract), students can benefit from continuing to practice previous concepts that the class has mastered and moved on from. In the case of a spiral curriculum (such as Everyday Math), this review is built into the math boxes. If that component is not already embedded into the curriculum, it is worthwhile to provide review and practice activities of these concepts to ensure students don't forget the skills they have learned. This practice and review is important for standardized test preparation where students will be required to work with previously taught concepts.
  2. Practice Math Facts: Students need to know math facts from memory. It may be the only skill that teachers feel must be memorized. Students can develop this automaticity by practicing number relationships. Students can work with math facts flash cards, games or computer programs to help them build this fluency with math facts for addition, subtraction, multiplication and division.
  3. Math Games: Games for math are not a new concept. Many curriculum programs today include some form of games reinforcement. However, teachers can also create or purchase other games to reinforce the standards they are teaching. It is important to remember that these games must meet the standards in the curriculum--they are not meant to be busywork activities, they should be meaningful practice. The games should also be practiced in class before students begin to use them independently (this can be done in small groups). Students also need to be able to understand the rules of the game so they are focused on the mathematical aspect of the game rather than trying to figure out how to play it. (This is, in my opinion, a strength of Everyday Math's games component--many of the games are taught in lower grades and then just modified slightly for the upper grades so that less time has to be spent teaching the procedures of the game with the older grades. This can also be a weakness of the program if teachers at a lower grade level haven't utilized the games component because students won't have a grasp on the concepts and then they must be taught by the current teacher.)
  4. Problem Solving Practice: Problem of the Day or Problem of the Week type of problems can be used as independent work during Math Workshop once students have learned the procedures for the task. These problems should be challenging for the students as the goal is to ensure they can think about how to understand the problem. Meaningful problem solving problems should include the following criteria: a perplexing situation the child can understand, student has interest in finding the solution (it it means something to them), the student can't simply go toward a solution and the solution requires the child to think mathematically (Burns, 2000). These types of problems should be introduced to the whole class before being introduced as part of the math workshop. Students have to have comprehension skills in order to understand word problems so teachers may want to introduce graphic organizers or other strategies to help students successfully attack these sorts of problems. Due to the nature of different ways to attack these sorts of problems, it is wise to have manipulatives available for student use or to create math toolkits that students can access with the materials they will need to be able to work through these problems. 
  5. Investigations: Students can work on investigations that require data gathering and some kind of reporting back of what they have learned. Students can be assigned specific investigations (to coincide with group work) or students could select from a bank of investigations kept in the math workshop area. Students should keep a log or folder of their work with investigations to document not only the quality of their work but also to determine the strategies and resources students use to help themselves as they work through the investigation. 
  6. Math Journals: Using journals during math workshop allows students to share their mathematical ideas in writing as well as preserve strategies and concepts they have found to be useful. Students can use the journals to document the steps they took to solve a particular problem or write about something they learned or found to be difficult during a particular part of the math workshop. Questions can be posed that ask students to "dig in" to their thinking as it relates to math: What did you notice? What did you find interesting? What patterns did you notice? What surprised you? What did you predict and why? What do your findings make you wonder? What does this work remind you of? It is vital that teachers who ask students to use math journals respond to their writings with specific and descriptive feedback based upon what the student has written or shared. (Remember these can be used as part of your overall assessment.)
  7. Math Related Computer Programs: We all know students are more focused and motivated if they can use computers or other devices to help them learn. Using these programs, apps or websites to allow students to practice math skills is an easy way to keep students engaged and monitor their progress (you can use programs like Xtra Math for free and IXL which has a subscription fee but allows a certain number of "free" problems per day).
  8. Cross-curricular work from other subjects: Math is not something we see in isolation in the real world. We use it everywhere: grocery store, to balance check books, to compute earnings, etc. Students need to see and understand this and integrating work from other content areas that have a math focus is a great addition to independent work time to help students make the connections between math and the real-world scenarios in which they will find them.
  9. Complete the Work from Small-Group Instruction: Once students in a small group have demonstrated their understanding of the concept being taught, there is no need for that student to stay with the group as the other children finish. Allowing students to complete the rest of the activity or assignment from the small group time during math workshop allows the teacher to focus his/her time on the students who really need the extra support and provides the students with more time to work on other math workshop tasks once their group work is finished.

There is a great chart on pages 188-189 that provides a list of these tasks with examples of each AND the objective(s) that will be attained by using these tasks.

Managing Math Workshop
Just like with a reading or writing workshop, the teacher must teach, model, reteach and remodel the expectations and procedures that will be in place during Math Workshop. Students must understand, accept and abide by the following principles of a learning community:
  • all members have rights and responsibilities
  • all members take responsibility for their own learning and will help others learn
  • all members responsibly manage their time and activities
  • all members self-manage their learning and work
  • all members keep materials orderly so everyone can learn
If students become lax on the behaviors and expectations necessary to make the small group time effective, they must be revisited and retaught. It is a good idea to revisit the procedures and routines periodically (after long school breaks for example) to ensure that students are maximizing their learning time and the teacher is not spending the small group time managing behaviors and activities of students who should be working independently. 

When workshop is first introduced, the teacher can refrain from working with small groups to observe the students as they work. This is similar to the Stamina Building talked about in The Daily 5. When teachers notice a problem, they pull students back together and discuss what was working, what wasn't working and how the community of learners present can work to fix the problems. This can continue until students are productive enough in independent learning time for the teacher to begin to pull small groups. 

Teaching Math Workshop with a Co-Teacher or Aide
There are several options teachers can take advantage of if they have a teacher's aide or a co-teacher who works in their classroom during math. Both teachers can work with a small group or one can work with a small group while one confers. The teacher can handle the small groups and conferring and the aide or co-teacher can help students who are working independently.

As someone who has attempted portions of a Math Workshop in the past, this chapter really helped me to see where I need to make changes in my rollout of this model for it to be effective. I like the different tasks that Sammons mentions for use during the workshop portion while children are working independently because it does allow for the choice that was mentioned and provides students with a variety of tasks they can work on that will prevent them from getting discouraged if they get stuck on one activity because they can set it aside until they can get teacher help and work on something else.

I have been tossing back and forth the notion of using a form of Daily 5 Math this year as well and I think putting these tasks as choices is a great way to help students focus their learning for the day and give them a "menu" of items to work on during workshop time. It will provide the students with the opportunity to be productive and engaged in meaningful math from the moment that Math Workshop starts. 

I also like how I was able to make a connection back to the Stamina Building that is such an important part of teaching the Daily 5 (something I also plan to implement this year). We often want to jump into something but don't give our students enough time to really and truly understand what they are being asked to do which creates problems while we try to work with our small groups. Taking advice from both Guided Math and the Daily 5 framework will positively impact how I am able to teach math and maximize student learning and student time engaged in learning.

Stay tuned for my thoughts and reflections on Chapter 7: Conferring with Students During Guided Math!

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!

Sunday, July 15, 2012

Guided Math: Chapter 4

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 the 
Whole Class

This chapter focuses upon how teachers can best utilize the Guided Math model with the whole classroom. Clearly the author is a proponent of using this with small groups as she has mentioned several times throughout the first three chapters how much she modeled this after Guided Reading. 

Advantages of Whole Class Instruction
There are many ways in which teaching the entire class is appropriate and even beneficial. Examples include:
-providing active engagement strategies
-reading aloud for math
-preparing for Math Workshop
-the Math Huddle
-practice and review
-tests or assessments that are more formal

Clearly whole-class instruction requires much less planning and preparation. Teachers are able to plan one lesson and present it to the entire class. If teachers are planning to engage prior knowledge, whole class instruction is very appropriate and worthwhile. Teachers are engaged with direct teaching during whole-class instruction which can maximize the amount of time students are being taught by the teacher rather than a peer or in self-guided work. 

Working with the whole class during a Math Meeting or Math Huddle allows teachers to create a sense of community, specifically focusing upon math and math-related concepts. When students engage in conversations about math, they are more likely to understand the concepts better than if they simply read about it or listen to it described. The student conversations during this time can be monitored by the teacher and misconceptions can be addressed immediately so students are not going into independent practice with misunderstandings about the concept or process being studied.

I agree that whole-class instruction can have it's place, no matter the subject. Gathering students together to explain directions, provide brief overviews or review of concepts is probably the easiest way to give the information to everyone all at the same time. I also feel very strongly after piloting a new math review system in our district this spring that students need to be able to EXPLAIN their thinking--not just how they got an answer but how they know the answer is correct. All too often, students know the process of getting an answer but they haven't internalized it in that they can't tell someone else how to do it. The Math Huddle, which allows the entire class to meet together daily, provides time for students to engage in this talk with the teacher there to provide help or correct misconceptions. It's meant to be a very brief time but can also provide a big "bang for your buck" when students do most of the talking and explaining. 

Challenges of Whole-Class Instruction
It is nearly impossible for any teacher, no matter how good they may be at delivering instruction, to meet the needs of every student in their class when engaged in whole-class instruction all the time. Students become distracted, get lost or bored during a lesson and may not have enough active engagement if the teacher is teaching to the entire class. 

Teachers have a hard time being involved with all students when they teach in a whole-group setting all the time. They won't know if little Susie did not understand a concept until perhaps a day after she has been working on something incorrectly and ingraining the incorrect procedure or process more deeply as she works. Additionally, feedback can't be provided as readily if the teacher is trying to engage the entire class at the same time because the teacher can't be with every student during their independent practice. 

Teachers know that a balance of summative and formative assessments provide the most effective feedback for teachers in order to design their instruction. The summative assessments provide an assessment of the learning that took place while the formative assessment demonstrations what students already know (or don't) so the teacher can plan continued instruction. It is stated that the use of assessments FOR learning allow students to have tremendous gains because of the immediate feedback and change in instruction to meet their needs (pg. 110). However, it is difficult to engage in conferences and conversations when teaching the entire class and thus, some of the formative assessment information is lost because observations and conversations don't happen as often as they might.

I am a huge proponent of formative assessment--I don't want to waste my students' time teaching them something that they know. I would never know where they are and how quickly they grasp concepts and are ready to keep going if I didn't use formative assessments. It's MUCH harder to use anecdotal notes when you can't meet with students to do the observations and ask students about their thinking.

Methods of Whole Class Instruction
There are several methods that can be used during whole class instruction to engage students and maximize learning. Mini-lessons, activating strategies, preparing for Math Workshop, Math Huddle, Practice and Review sessions  and Assessment are all areas in which teachers can effectively use a whole-class model.

Mini-lessons: Just like with reading or writing workshop, this time is meant to be very brief, no more than 10 minutes in length so teachers can identify the day's learning and get students started on the work for the day. Each mini-lesson consists of four parts (as adapted from Lucy Calkins' writing mini-lessons):
Connection: make a connection to prior learning or to a real-life experience outside of school that relates to the math concept. Utilizing the connections helps engage students with something they already know so teachers can move forward.
Teaching Point: the teacher clearly states the learning for the day and then models and demonstrates the strategy being taught or the concept being used. The modeling and demonstration is vital.
Active Engagement: then students have a very short time to practice what the teacher just demonstrated. This may be individual white-board practice, a think-pair-share or restate the teaching point in their own words.
Link to Ongoing Work: the last component is to link the teaching point to something the students have already been working on. The students need to leave the mini-lesson understanding that the teaching point is something that they should remember and use when appropriate.

This is a great way to keep those mini-lessons in check. I know I am guilty of not always linking the teaching point to something we have been working on or WILL be working on. I try to remember to give them a reason (we learn X in 2nd grade because in 3rd grade you'll add Y to it so make it more challenging) but it doesn't always happen the way I intend and sometimes when things are crazy in the classroom, this part is forgotten. 

Here's a brief sample I wrote up for determining Factors with 4th graders (pulled from CCSS). Very short and sweet.

Activating Strategies: By using different strategies to activate prior knowledge and/or engage students before the lessons begin, teachers can again maximize the time they have for math instruction. Some sample strategies include:
KWL: Most teachers know what the KWL chart but there are modifications suggested for this common strategy when used with math. You can change the K to "Thinks I THINK I Know" which will help dispel anything the students thought were true about the concept but may have been incorrect. Another modification suggestion is to change it to "What do you know for sure?" "What are you trying to find out" and "Are there any special conditions in the problem?" By changing the questions to fit math, student engagement can go deeper and misconceptions can be addressed immediately.
I LOVE the modified KWLs, especially the "what do you know for sure?" question. Often students think they know a lot about how to do something and they have been doing the problem incorrectly for a long time. This will provide students with the level of comfort to still share but be open to being corrected if, in fact, their thinking is off.
Anticipation Guides: This is another strategy often used with reading. Students can provide a wealth of information to their teacher by identifying what they already know to be true or false about a concept about to be studied and can look back at the end of the unit to see their own learning. It's important to remember to explain to the students this isn't a "graded test", its purpose is to guide the instruction of the class or group so that everyone is getting their needs met. (There is a great anticipation guide sample on page 120.)
Word Splashes: Students can preview and learn vocabulary while activating prior knowledge by seeing words "splashed" across a page or charge that deals with a particular concept such as the relationships between fractions, decimals and percents.

Reading Math-Related Literature: Using stories that relate to students' lives but also teach about math can be a great way to bridge connections between concepts and reinforce ideas that students may be struggling with. 

Setting the Stage for Math Workshop: Teachers can use whole-class instruction time to set the stage for math workshop by introducing, modeling and reinforcing procedures and practices of the workshop. During the first weeks of school, procedures will be taught, practiced and reinforced. After the procedures have been taught and used successfully, time can still be set aside to discuss any problems occurring during workshop and/or for teachers to explain what students will be engaged with during individual learning time of the workshop.

Math Huddle: Like a morning meeting, this time focuses the students for learning and discussing math and math-related concepts. It can be teacher-led or student-led or a combination of both. Students share ideas, problems, solutions and provide proof during this time. Students can stretch their thinking when challenged by a classmate who may not understand how (or why) a student got a particular answer and the student who shared may experience growth as a mathematician while explaining their thinking and surely the students who are listening will gain insight as well. 
I really like the Math Huddle concept. It is important for students to discuss their thinking and engage with each other about math and other subject areas being learned. Having a set time every day for them TO engage in this kind of talk will encourage them to share, stretch their thinking and be prepared to provide proof if another student (or the teacher) isn't convinced by their statements.

Practice and Review: Students can participate in brief practice and review sessions as a whole class. Since most high-stakes state tests are done with paper-pencil, it is important that students can spend some whole-class time reviewing how to take these assessments and what they will look like. Games can be played to review math concepts as a whole class such as "Around the World" or games such as Jeopardy that use PowerPoint to be presented to the whole class.  Clickers can be used as well to review as a class where data about student responses can be graphed and displayed for students to interpret and analyze.
I love the idea of using the Clickers and we have them at my school...but the computers rarely allow them to connect so it's wasted time. There are many places around the internet to find games such as Jeopardy, Who Wants to be a Millionare? and more that are used with PowerPoint and can be played as review games with the class provided you have a computer and some kind of projection system.

Assessment: Assessment is usually conducted as a whole class so that all students can be engaged in the test at the same time. Most of the time these are paper-pencil tests and can be multiple-choice or constructed response (or a combination of both). These can be used as practice for standardized test-prep as well since most standardized tests are still done on paper.

I have done both whole-group instruction for math all year and done small group instruction for math all year. Regardless, it becomes necessary to teach the whole class sometimes, even if you are using some small groups either to provide directions or clarify things that the whole class had confusion about.

I will definitely be using the Math Huddle this year. I love the concept of it and how it doesn't have to be really long to be effective. 

I will also definitely make an effort to use more mini-lessons for math. The adaptation of Lucy Calkins' model is a great reference to have. When I wrote out that brief mini-lesson for Factors, it took me less than 10 minutes and even though I focused it for 4th grade, it is something 5th graders would benefit from reviewing (or learning!) as well. This may be a bit more challenging since I will be teaching a split grade, but I am hopeful that my using the CCSS for most of my mini-lessons I can provide a common lesson to my whole class that satisfies what both grades need to learn to maximize the time that I have with my students.

I am going to look at my math series and think about how I can integrate the Anticipation Guides and the modified KWL because I think those are strategies that would really benefit the students, especially the A.G. What better way to engage children than keep them accountable for their learning by going back to that A.G. at the end of the unit and notice how their own thinking has changed. 

Stay tuned for my thoughts and reflections on Chapter 5: Using Guided Math with Small Groups!

Tuesday, July 10, 2012

Guided Math: Chapter 3

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 Math Warm-Ups in Guided Math

This chapter focuses upon how to get students engaged mathematically from the moment they walk into the classroom each morning. Most teachers are all about their set routines as we know that routines help students perform better and they help us maintain some sense of balance in what can often be a crazy-hectic day. 

First Sammons describes Math Stretches that can be used to begin each day. These are routines that are either done daily or done once per week on a rotating basis, with some form of routine done each day to start the day off mathematically.

Some of the Math Stretches described are (my comments in blue):
-Data Collection and Analysis
Students are asked to answer questions and then use the answers provided by the class to formulate a graph and analyze that graph. Additionally, if data is gathered over time, such as the weather for the month or how many days of indoor recess they have had in January, the students can interpret and analyze that data into a graph as well.
I really like this one because throughout all of the grades I have taught, my students have had a horrendous time with graphing. Something about taking the data from a table and putting it onto a graph or chart doesn't transfer for them. Repeated practice such as this, with items that are meaningful to the students, will provide practice over time and when discussed in the Math Huddle, misconceptions can be addressed immediately.
There are also some discussion types that are identified for use when having a classroom discussion about the data collection and the subsequent graph/chart made from that data.
Think-Aloud which provides the highest level of teacher support as the teacher is modeling relevant vocabulary, records analysis on chart and discusses the reason for choosing the method of representation
Guided which helps students to join in the discussion by carefully crafting questions to help students get through their thought process. The teacher is still a dominant part of the voice in this type of discussion.
Facilitated is when students take on more of the direct role in the discussion. The teacher may pose open-ended questions but mainly ensures students are staying focused on the discussion of their observations, what they've learned and how they represented their data
Independent is when students are in control of the discussion--the teacher may record some of the discussion on chart paper but it is usually done by students entirely and the teacher may interject as students share journal reflections to dispel misconceptions

-Number of the Day
We often think of using a Number of the Day pattern with younger children, say K-3 at the most. But Sammons shows us that you can use a Number of the Day (or Number of the Week as it were), with any age. Older students can use fractions, decimals, percents to represent numbers, all students can use arrays, ten-frames, base-10 models, etc to show numbers in different ways.
This is a strength of the Everyday Math curriculum in that we often ask students to represent numbers in a variety of ways, from as early as 1st grade. What I like about this, however, is that it becomes part of a routine. With older students, I wouldn't do this every day, I would do it weekly and use numbers based upon what we are working on. For example, if we are working on converting fractions, I might provide a fraction as the number of the day and see how many ways students could represent that number--either as an equivalent fraction, a decimal, a percentage, with pictures, etc.

-What's Next?
This math stretch needs to be done on chart paper so it can be displayed and discussed during the Math Huddle (it could also be done on a small white board that is in the meeting area). The teacher starts a pattern and leaves a blank space for each student in the class. The students each fill in the "next" part of the pattern until everyone has had a turn. If there are mistakes, the KIDS have to approach each other about it and discuss the error and AGREE to fix it.
I ♥ this stretch because it really promotes TALKING about WHY the answer is (or isn't) correct. All too often we teachers do the talking during math and this promotes that discussion for the students. My only thought was really about managing it - if the students do this as they come in, it can get crazy. Routines would be a MUST and have to be modeled explicitly over and over in order for this stretch to be meaningful and worthwhile.

-How did my Family use Math Last Night?
This stretch was promoted to be used in conjunction with a homework assignment. Once a week the students record a way they or their family were using math at home. It might be during cooking, measuring for something or whatever they used math for. The following day, they take this math stretch information to school they add the information to an ongoing chart of how math is used in their every day lives. Sammons also emphasizes that students have to learn to make "Math to Self" and "Math to World" connections just like they do with reading (compared to Text to Self and Text to World connections).
I think this is a great idea and a simple homework assignment that students could do. I feel it is very important for students to make real-world connections with everything we are doing. Why do you need to study algebra? Because you will use it here, here and here sort of thing. We have to make the learning meaningful but also authentic to help the students buy into it. I love the idea of a "Math to Self" connection so students can be encouraged to think of a time when they did a similar math problem or a "Math to World" connection when they can connect something their family has done to something a lot of people in the world might do. It will broaden their math sense but also provide them with connections to the real world.

-______ Makes me Think of.....
This is another stretch that promotes making connections in math. Students can make Math to Self, Math to World and Math to Math connections by sharing words that they think of when they hear another word. The example provided (pg 84-85) is that the teacher might write Fractions make me think of.... and then students will provide a word or phrase to describe what they think of. They can ONLY use words--no pictures or number representations and there can't be any repeats. 
This activity is one that I think would help promote connections between concepts that students don't often make themselves. At least the students I have taught in the past tend to be "boxed in" with one concept at a time and unless I bring the old learning back to their attention ("Don't you remember when we did.....?" "Ooooh, yeah!"), they often don't make connections on their own. This activity would encourage them to make the connections--it might be difficult for the students to come up with 25-30 different words/phrases but that would also encourage discussion about what other words might work which, in turn, can be seen as a vocabulary booster as well.

My school has been big into DDI Strategies in the last two years (which I have mentioned before). There is a  resource with that program called "Target Tabs". 

Basically as you "target" a specific area in reading (or math), the students record a response on the tab sheet. I have only used them for reading thus far....but as I read this chapter, I thought about how I might be able to integrate the Math Stretches with the Target Tab concept. It is something the students could keep in their binders daily as a record of their progress and would allow me to see who is having trouble and who isn't. Additionally, the target tabs would be GREAT for discussion purposes. Students could use clock partners or something similar before the Math Huddle to ensure they aren't always sharing ideas with the person next to them, etc. I think this is something that I would definitely like to "guinea pig" this coming year and see how it goes.

Another thought I had with the Target Tab idea of recording the math stretches is to have the warm ups be a 10 minute opener, allow 5 minutes for sharing and then come together for 15 minutes of Calendar Math and Math Huddle time. I think this would work out well to maximize the learning time but also to ensure that kids are engaged and reviewing. I'm not positive on it simply because I ♥ the Calendar Math materials I have seen around the blogosphere recently and it seems like it might be too much to try to do both. 

At any rate, this chapter has definitely gotten me thinking more about MATH and how to approach repetitive practice and mastery of certain skills like patterning throughout the year, even with older students. I'm not sold on the idea of doing the math warm-ups first thing in the morning because while I have taught math first thing the last three years, it doesn't mean my schedule will always allow me to do so. I think as long as I can dig out a 90 minute math block in my schedule, no matter where it is, that I can feasibly do these warm-ups with my class before we begin our math lesson.  If the schedule stays relatively the same as far as lunch and recess times for upper elementary next year at my school, I could easily do my math workshop after their morning recess and still have time to fit everything in before lunch. It is the only thing that Sammons hasn't 100% sold me on--I don't think it matters when you do the warm-ups as long as you do them before you begin the workshop time.

Stay tuned for my thoughts and reflections on Chapter 4: Using Guided Math with the Whole Class on July 12!

Sunday, July 8, 2012

Guided Math: Chapter 2

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 to Create a Classroom Environment of Numeracy

Chapter Two is all about Numeracy. Numeracy includes being able to see, use and understand math and mathematics concepts. I myself nodding when Sammons pointed out that when you walk into an elementary classroom--no matter whose it is--you are pretty confident in knowing that language arts are taught in that classroom. The same isn't as true with math. Sammons asserts that we MUST provide this same framework and foundation for teaching math.

She identifies Seven Foundational Principles of Math:
1. All students can learn mathematics
2. A numeracy-rich environment promotes mathematical learning by students
3. Learning at its best is a social process
4. Learning mathematics is a constructive process
5. An organized classroom environment supports the learning process
6. Modeling and think-alouds create a learning environment in which students' mathematical understanding grows
7. Ultimately, students are responsible for their learning. 
(Sammons, 2010, pg 37)

I especially love number 7. I think that all too often we are told it is OUR responsibility to ensure students are learning and while it is, it is also the students' responsibility to understand they won't learn it if they don't own it. 

Sammons talks at length in this chapter about building a classroom learning community. We all know this is important overall but her explanations of how it pertains to math is rock solid, especially when she points out how NCTM standards dictate that students be able to problem solve, provide reasoning and proof and make connections. Students won't be as comfortable doing that if they don't feel a part of a learning community. 

It is important to understand that Sammons models much of her thinking after a Guided Reading model, just shifting it to apply to mathematics instruction. Therefore each area of the classroom is given some thought as it pertains to exactly how to set up a classroom for guided math. If you already have a whole group area, a small group area and an area for workshop materials for reading/writing, you are well on your way to being able to transition into a math workshop framework as well because they are practically identical. To me the most important part is having an area for whole group--I have found this to be important even with older students. I have always had my 4th and 5th graders gather on the floor for certain aspects of our day. I do this partly to keep them all close to me but also to increase the sense of community in the classroom. A small group area can be as simple as a stretch of carpet you meet on with your groups. One year my room wasn't big enough for two separate areas so I took out  my U-shaped table and met with my small groups on the floor where our large group area was and it worked out just fine.

The best part of this chapter, in terms of my learning, was the section providing more information about how to set up a Numeracy-Rich environment. It should include some (or best of all, ALL) of the following components:
--Student Calendar/Agenda
--Manipulatives (these can be hand-made and sometimes STUDENT made such as flip books for reference)
--Problems of the Day/Week
--Word Wall/Vocabulary*
--Math Journals**
--Graphic Organizers (I especially like the modified Frayer model!)
--Class Made Charts
--Tools for Measuring
--Literature related to math (both commercially produced and student-created)

*I went to a 3-part math workshop this year and we talked at length about how neglected math is on a word wall. My binder for that workshop is at school but there is an amazing article in there that talks a lot about how we can easily integrate math vocabulary onto our already existing (and often mandated!) word walls. I will try to remember to grab it when I go back to my classroom and add it to this post. It's worth reading!

**Math Journals is a concept I definitely love after experiencing some of the changes our district math coordinator put in place at the end of the year. I have found over the years that my students can perform a math equation or concept but they really don't own it or get it. They can't explain how they know. To me, that means they really don't understand the concept--they just know the steps to follow to get the right answer. Using math journals will provide me with a weekly look at my students' thinking in terms of HOW they process math and allow me to guide them if they are having a lot of misconceptions.

I loved this entire chapter, mostly because it validated everything I've been feeling about my math instruction! I was browsing along the web earlier this week and came across Calendar Math by Stephanie at Teaching in Room 6. I don't know if I was living under a rock but WOW. The brief encouragement that Sammons provides and Stephanie's fabulous resources (which you better believe I WILL be purchasing) make this a reality for me. Someone else did the work and I just have to implement it. No excuses there!!

I also plan to really make sure that my students have access to manipulatives. It is so easy to write it off with the older kids because of time constraints BUT it is important for them to understand that these manipulatives have a purpose. I definitely want to make sure my "big kids" know and understand ten-frames as well as base-10 because I know that numbers and operations tends to be very low across our school. They just don't have a good number sense and I need to change that.

I will definitely be using the math vocabulary/word wall. Last year I covered my shelves with posterboard but never really did much with that space. This year I will use that space as a math word wall. It will be perfect. I also definitely want to incorporate the Frayer model. Students often confuse math terms and I hope by implementing that frame with some of the more confusing words that my students will be able to enrich their vocabulary and not stumble when they come across the words in math problems which then result in them not knowing what they should do.

Stay tuned for my thoughts and reflections on Chapter 3: Using Math Warm-ups in Guided Math on July 10!