Guided Math Chapter 5

"In spite of time constraints, which often lead teachers to emphasize procedural fluency over conceptual understanding and to use worksheets rather than problem-solving activities, we want more for our children" (p. 133).  As a teacher of English Language Learners, I think the above statement has so, so many ramifications.  We all want to be the teacher that seeks to instill conceptual understanding in our students.  While I do think they have their time and place, I am really, REALLY not a fan of worksheets.  Instead, I LOVE journals and blank paper.  With this, students are able to communicate what they know, in their language, which is so powerful for our students that have not achieved academic English fluency.

I'm so glad that Sammons explains the purpose of small group instruction as providing students with a toolbox of strategies.  This idea will really help me to focus my small group instruction (reading AND math) next year.

Advantages of Small-Group Instruction:
1) Tailored instruction to meet ALL learners' needs
2) Instruction is differentiated.
3) All students have the opportunity to engage in mathematical communication
4) Teacher monitoring of student behavior and math understanding of all students (formative assessment)

Challenges of Small-Group Instruction:
1) Planning may seem overwhelming.
2) On-going assessment.
3) Each student receives less direct-instruction time.
4) Planning independent work for students not meeting with the teacher.
5) Implementing procedures and setting expectations for math workshop.

Effective Uses of Small-Group Instruction:
1) differentiating instruction- I love that Sammons quotes Carol Ann Tomlinson (I LOVE her) as describing differentiated instruction as a teaching philosophy rather than something that we incorporate into our instruction when we have the time.  I think that it is so important that we focus on all of our students needs, not just the struggling ones.  Again, Tomlinson ROCKS when she explains (through the interpretation offered by Sammons) that what students learn is the same, but the way in which they learn it is different.
 
2) teaching mathematical "hot spots"- I love the use of this term to describe those concepts that give students a hard time year after year (such as subtraction with regrouping). 

3) teaching with manipulatives- I think that the way these tools are used makes or breaks their effectiveness.  I like that Sammons explains that using manipulatives with mathematical communication is the formula for conceptual understanding and long-term learning. 

4) assessing student learning informally- Teachers complement summative, end-of-unit tests with daily work, homework, quizzes, and projects.  Time to introduce another of my favorite technology tools and my favorite way to assess informally and continuously.  Meet, the CPS "clickers" by eInstruction:

These are such neat little tools.  They come with a receiver, and you can use them for a variety of assessments.  My favorite is "verbal mode."  In this mode, I can show a typed page of questions, allow the students to enter their answers, then grade as we go when I enter in the correct answer.  We are able to get through many questions and go over answers, offering any explanations necessary in a very efficient manner.  I check these out from my campus technology, but again, would LOVE to have some of my very own.  Of course, eInstruction does not know that I am writing about their AWESOME tool, and I have not been paid nor given anything to do so.  

I had another "Ah-ha!" when I realized (with the help of Sammons) that students can play a role in goal-setting and the formative assessment process itself.  Hello?!  How did it take me this long to figure that out? 

5) supporting mathematics process standards- It was not surprising to me that process standards get neglected in favor of content-related standards.  Again, it was unsurprising to me that many teachers are unsure how to teach process standards.  This seems like a great topic for professional development.  At the elementary level, since we are in charge of multiple disciplines, I feel like professional development tends to be more general or alternatively focused on reading. 

Forming Small Groups for Learning:
This is an area that is a bit scary for me going into next year as we switch from Envision to Investigations in math.  With Envision, I often employed pre-tests using the paper and online materials.  I think the idea of using a combination of measures will be somewhat freeing: pre-tests, evidence of learning from previous sequential concepts, formative tests, observations, conversations, and benchmark data.  I think that the most important point from this section was how important recording anecdotal notes and observations is.  I know that it is not new, but I think that I might try the labels on a clipboard, combined with a student data binder method of note-taking this year, like the example shown below (this is the year that I get SUPER organized).  :-)

I like how post-its were added to this example to allow for documentation in multiple subject areas, all kept in the same place. 

Organizing for Small-Group Instruction:
1) Identify the Big Ideas: These ideas make up the foundation for mathematical growth.
2) Establish Criteria for Success: I like the emphasis on collaboration when establishing criteria for success.
3) Use Data to Form Groups: Some things I will take from this section are her scheduling tips as well as the caution to not neglect the higher-achieving students.  I like the idea of a weekly schedule, with groups that can change each day as some students "get" concepts and need to be moved to a higher group.
4) Determine Teaching Points: Instruction is determined in response to how groups are formed by common needs.  The curriculum standards and assessment are both used to determine teaching points.
5) Prepare Differentiated Lessons: Sammons really thoroughly addressed differentiation through length and frequency of small-group lessons, content to be covered, as well as student learning styles.
6) Gather Materials: Sammons really stresses the importance of planning ahead and anticipating any materials that you might need, especially if the students struggle with the planned learning.  

Teaching a Guided Math Lesson with a Small Group:

Not my class or my classroom.  :-)

1) Introduce the Lesson- A variety of activities can be used to introduce the lesson.  Some that I hadn't thought of include: reflecting on previously-learned mathematical concepts, focusing on math vocabulary, demonstrating how to use manipulatives, emphasizing the importance of students monitoring their own work, and encouraging the use of multiple representations of mathematical ideas. 

2) Present the Activity or Task- Students should be provided rubrics, checklists, or examples of other student work for similar activities with the intention of helping them to self-monitor and produce higher-quality work that reflects deeper mathematical understanding. 

3) Encourage the Use of Multiple Strategies-I think that such a great way to do this (as suggested by Sammons) is allowing students to choose which problem-solving strategy to use.  The benefit of doing so is that student mathematical understanding will move from concrete to abstract. 

4) Scaffold Learning- Scaffolding is one of those currently hot education "buzz words."  I appreciate that it is defined here as including the following elements:

• occurs with assistance and is a social process
• involves inter-subjectivity (seeking a common view)
• is provided with warmth and a responsiveness toward students' needs
• is focused
• avoids failure
• is temporary

5) Promote Mathematical Discourse- Math communication (both oral and written) promote student understanding.  It also helps students to retain their learning longer.   

6) Promote Learning by Giving Feedback- According to Anne Davies, descriptive feedback:

• comes both during and after the learning
• is easily understood
• relates directly to the learning
• is specific, so performance can improve
• involves choice on the part of the learner as to the type of feedback and how to receive it
• is part of an ongoing conversation about the learning
• is in comparison to models, exemplars, samples, or descriptions
• is about the performance or the work-not the person

I especially am intrigued by Sammons's idea to instruct students in what exactly effective feedback is so that they may evaluate themselves and/or their peers. 

AFTER the lesson, the TEACHER should:

• keep records of informal assessments
• select the next steps for instruction
• identify students who are falling behind
• and, at times, change the composition of the groups

Wow, this chapter (and therefore, this post) was HUGE!!!  Having read only this far, I have a feeling that it will be the best chapter in the book (most applicable).  I came away from it with lots of real-world knowledge of what guided math small groups look like when implemented in the classroom.  This is SO nerdy (but I know I'm not the only one who feels this way), but I can't wait to get back to school and try it all out!!!  :-) 

I'm off to go read chapter 6, so I can get back on track with the book study.  I'll be back soon!

Technology in the Classroom and a Call for Help

Good morning!

     I want to share a direction my new campus is going (new-old, I'm going back to my first school).  :-)  The school has established a group for staff on Edmodo.  Several enterprising teachers have taken steps to utilize Edmodo in the classroom with their students.

     This is definitely one of my technology goals with my 2nd graders this year, but the learning curve is steep.  I do a good job of incorporating technology into my classroom already (one of my favorite tools is the student clickers from eInstruction that I check out from our campus technology resources-if anyone wants to buy me my own, I'd love to have them!  :-)  ), so this is the next logical step.  Do any of you use Edmodo in the classroom?  What do you use it for?  What other technology do you incorporate into your classroom?  I can't wait to learn from all of you!

Guided Math Book Study- Chapter 2 Reflection

First of all, thank you so much to those of you that are following my new blog.  I appreciate your patience and support as I learn the ropes.  One thing that I'm really enjoying about blogging is connecting with teachers and sharing ideas as part of the Guided Math book study.

With that said, here we go!  :-)  

1) The first thing that I really appreciated about this chapter was the immediate parallel that Sammons drew between guided reading and guided math.  I think that this will go along way to make teachers (myself included) feel less intimidated by guided math.  Many of the routines we already have in place for guided reading can easily be modified to be appropriate for guided math.  

2) The 7 foundational principles of a guided math classroom: All of these principles can be classified as best practices.  Students should work together, talk together, actively be involved in mathematics, and have a teacher that is ready to model, model, model.  

3) I enjoyed how Sammons addressed equity, stating that the different components of guided math help teachers to "provide scaffolding and support for all learners based on their needs" (39).  In this way, all students can be taught with equity rather than equality.  

4) I think that the importance of communication (oral and written) in math cannot be overstated.  As Sammons points out, although we realize the importance of math communication, it unfortunately has played "such a limited role in elementary-school mathematics instruction" (39).  I have only ever taught students who were learning English as a second language, so I can say with utmost confidence that achieving communication across the disciplines for these students is all about building confidence.  Students should be offered low-risk opportunities to communicate, so that they may begin to feel more and more comfortable with communicating and sharing in class.  

5) Classroom arrangement: I'm so excited to be reading this book now.  I'm one of the lucky (cursed?) teachers who keeps moving schools/classrooms, so this August, I will once again have the opportunity to build my room from scratch, arranging everything the way that I want it.  I'm making myself a mental note now to make sure that it is all set up for guided math.  Additionally, Sammons has helped me with the arrangement of my student desks.  I have always done groups in the past, but was considering rows this year (all of my teammates seat their students in rows).  I have decided to stick with groups and now I have the justification for it- yay!!!

6) A numeracy-rich environment: Wow, did this section have a lot to offer!!!  I like that Sammons teased many things that she will cover in more detail in later chapters (it just motivates me to keep. on. READING!!!).  This year is going to be a bit "funky" in math because my district is moving towards a more problem-based approach, and until I attend training on it next month, I'm completely in the dark.  I do know that many, many manipulatives will be involved, but that's pretty much it.  I would still like to do a problem of the day if I can.  I imagine that the new math curriculum will work well with math word walls, math journals, and graphic organizers.  Especially exciting, is that my district has just adopted Thinking Maps, so I know that graphic organizers can be easily incorporated into our math time.  

I feel like this blog post is just dropping off, but in closing, I'll just say that I'm looking forward to reading and discussing chapter 3.  Thanks for reading!!!

      

Guided Math Book Study-Chapter One Reflection

I'm so excited to be participating in this book study (it is largely the reason that I joined the blogosphere).  I can't wait to connect with other motivated teachers.  Here are some thoughts I had as I read chapter one:

1) I wholeheartedly agree that the main problem with the old method of mathematics instruction (teacher-centered, whole group 100% of the time) is that several students were engaged in solving problems in front of the class, but the majority of the class was disengaged.  While Sammons does not directly state this, it is heavily insinuated.

2) I'm so glad that Sammons called attention to the achievement gap related to mathematics between affluent students and minority students/students living in poverty.  I saw this first hand at my school last year, and I am ready for this gap to narrow/close.

3) I like that Sammons points out that "teachers struggle to find the time to help them [struggling students]."  I know that this book will be very helpful to teachers who are struggling with finding the time to give every student what he needs, when he needs it (aren't we all?).

4) Sammons places an importance on mathematical dialogue.  I would go even further to say that students need to develop mathematical literacy.  She previews some of her math work stations in later chapters, including math journals, so I believe that she will address this issue.  I can't wait to read what she has to say about it.  I know that this is important not only for our English Language Learners, but all of our students.

5) At this point, as Sammons has previewed her model and all of its components, I am reminded of what I know of The Daily 5 and the CAFE framework.  Both have components of whole group (I'm glad that Sammons asserts that whole group instruction still has its place, but cannot be the only method of math instruction), guided instruction, small groups for stations, as well as individual conferences.

In summary, I'm so glad that I decided to pick up a copy of this book and participate in this book study. The first chapter teases many great things to come in the remainder of the book.  I'm particularly looking forward to chapter 3.  Since I have taught older grades in the past, calendar math is somewhat new to me (I'll be teaching 2nd grade this year).  What do you include in your calendar math?