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!


  1. **I accidentally hit "delete" instead of "publish" on my phone when I was moderating this comment. Sorry Natalie!

    The Queen Bee wrote:

    Sunny, I am so glad I found this post, I just started reading "Guided Math" and I posted on my Facebook page about starting a book study...and you are doing what I was instead of me doing all the work I will keep up and comment...I'm a chapter behind, so give me a few days...I'll fall behind again because I am going on vacation again this Friday!

    1. I'm glad you're finding it useful...there is a whole book study happening on it (although I started way later so I never really joined it -- I'm just kind of doing my own thing!). Check it out here. :)