Tuesday, July 29, 2014

Guided Math in Action Book Study -- Chapter 7

Welcome back! Chapter 7 of Guided Math in Action is all about building students' mathematical proficiency and how guided math is the ideal framework for doing so.

Dr. Nicki outlines the five components of mathematical proficiency and how to teach each. I have included a summary of each, as presented by Dr. Nicki, and have shared a bit about how each is developed in my classroom--ultimately answering the discussion questions for chapter 7 as well.

Conceptual Understanding---Understanding how to do something on a conceptual level

What does it look like in a guided math group?
  • Use of manipulatives, scaffolds, and tools
  • Modeling/demonstrating by teacher
  • Opportunities for students to work together as a group, with partners, and independently
  • Debriefing as a group at the end of lesson

Common Core: Much focus on knowing what a concept means not just knowing how to do something

I use various tools to help students develop conceptual understanding.  In the photo below, you can see the place value tools I use with my students.  Not all tools are used by all students at the same time.  Differentiation of tools is important in my guided math groups.  For example, place value discs are only used with students after they have a firm understanding of their value (these tools are all sized the same and are labeled with the value).  On the other hand, base ten tools are partitioned and sized according to their value providing a more concrete representation.  Each tool has its own purpose and we learn about their benefits/limitations and appropriateness.  You can download FREE place value disks, place value arrows, and ten frame tools by clicking here!

Procedural Fluency---Understanding how to do mathematical procedures

What does it look like in a guided math group?
  • Students using conceptual knowledge to do the math
  • Students using different methods to compute (writing, mental math, calculators, computers, manipulatives)

Common Core:  Stresses the use of conceptual understanding to work on procedures

Once my students develop conceptual understanding of a skill, it's time to put that understanding to work.  Multiple methods are always stressed.  In the photo below, you will see how two pairs of students applied their understanding of using an open number line to two different problem situations.  When faced with the problem, the students followed various steps.  They identified what was known and what was unknown, wrote an equation to represent the situation, solved using a strategy of choice (open number line)m, and wrote their solutions in a sentence.  In this case, both pairs of students chose to use an open number line to solve similar problems.

Strategic Competence---Ability to solve problems and represent thinking

What does it look like in a guided math group?
  • Students solve problems with models
  • Students represent their thinking (using numbers, symbols, words, and pictures)
  • Students model/represent their thinking in multiple ways with discussion of the process and effectiveness (What do you think about how _____ solved? Who can explain what _____ did?, etc.)

Common Core: Standard for Mathematical Practice 4 -- Students need to find pathways rather than just jumping to a solution and use various models to explain their thinking.

Once students have learned multiple ways (pathways) for working through a problem, they begin to choose what works best for them.  They also begin to understand that some ways/tools are not as efficient as others.  For example, if a problem situation requires combining two values, 346 and 543, a ten frame model would work but would not be most appropriate/efficient.  As students work through a multitude of problem situations, they begin to see the relationship between models/ways of representation.  This enables them to look at their fellow classmates' "pathways" and understand their thinking.  In the photo below you will see a student represented his thinking in two ways (base ten and mental addition of tens and ones).

Adaptive Reasoning---Ability to think logically about math and explain and justify

What does it look like in a guided math group?
  • Students discussing in a safe environment where their ideas are valued
  • Students listening, making connections, asking questions
  • Students proving their thinking (using more than one method) and comparing/contrasting their methods, and evaluating the reasonableness of methods

Common Core: Content standards and practices require reasoning ("explain", "justify", "assess the reasonableness")

I shared my problem solving discussion fans in a previous post, but they are definitely useful in guiding student discussion away from the teacher and in small guided math groups.  My kids love these little buggers---the depth of their discussions and the affirmation given to one another is amazing. Students begin to understand the different types of questions that can be asked, and I often hear students asking thoughtful questions without the fans as the year progresses. For more information about how I use discussion fans with my students, download them here!

Mathematical Disposition---Ways of thinking, doing, being, and seeing math

What can teachers do?
  • Provide scaffolded problems that students can solve successfully
  • Talk about more than one way to do something
  • Engage students in discussions of how they got an answer, not just the correct answer
  • Give students the time to think, reason, and even struggle with a problem (with the understanding that struggling is sometime necessary before being successful)
  • Promote stick-withitness
  • Make connections to real-life
  • Provide opportunities for student reflection and the monitoring of their learning

As a teacher, I strive to do all of the above! It's all about perseverance, the celebration of successes, making connections, and multiple ways of understanding. One of the most powerful things I try to do from the first few days of school is help students see themselves as mathematicians.  This involves a beautiful discussion of what a mathematician is and what he/she does.  We create an awesome anchor chart with all of our ideas spilling over--I held on to last year's anchor chart, but I will have to share a picture later (it's packed away at school). :0)  This year, I also created a bookmark for the kids to keep in their guided math folders.  It has all of the Common Core Practice Standards stated in simple, yet specific, terms.  Please feel free to download a copy here!

The implementation of the Common Core Standards for Mathematical Practice are vital in students' development of mathematical proficiency.  Here is an excellent teacher resource dedicated entirely to implementing the standards--Putting the Practices into Action by Susan O'Connell and John SanGiovanni.  It's a must have and well worth the investment! Click here to learn more!

Such a significant chapter!  I look forward to hearing how you help your students develop mathematical proficiency---please feel free to share in a comment! PLEASE! :0) You can also read past book study posts by clicking HERE!

All the best--

AND don't forget about our Dr. Nicki Newton, Problem Solving with Models, giveaway! Click here to check out these awesome resources! The lucky winner will get to pick the grade level resource that best fits him/her.  We will be randomly drawing the winner next Sunday, August 3... Good luck!

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Saturday, July 26, 2014

Guided Math in Action Book Study -- Chapter 6

Chapter 6 was a short one, but with lots of information. This is a great chapter for anyone just beginning guided math or needing a little tune up.

Dr. Nicki outlines a framework for guided math lessons:

Presenting the Mini-Lesson
  • Hook students--make a connection to past, present, or future learning.
  • The focus of the lesson is clearly stated (concept, strategy, skill).
  • The teacher models/demonstrates and checks for understanding while doing so.
  • May include practicing what is modeled/demonstrated with the group.

**Student Practice
  • Students practice the concept, strategy, or skill on their own and explain their thinking to the group.
  • Scaffolding discussions take place. 
  • The teacher asks specific questions to facilitate mathematical thinking.
  • Students work independently and the teacher provides interventions to individual students.
  • The teacher may take anecdotal records.

**Games and manipulatives can be used to model/practice the concept, strategy, or skill.

I play games in my guided math groups as much as possible. I have found that my students seem much more engaged when they are playing a game. Even the mention of the word "game" seems to make them perk up a little more in their seats.  I have done groups with worksheets and pages from our math program during this time, but feel that the students do not get a lot of opportunities to really express their mathematical thinking because they are so worried about being wrong on the paper.

I love to play games that involve dice and playing cards mostly because these are materials that are inexpensive and many students have them at home (if they don't, I buy some at the Dollar Tree and send them home).

Here are just some of the great resources I have purchased on TPT that I use in my own classroom...

There are so many more games out there, too! Many times I will just "google" cards games for (insert CCSS standard/skill/unit), and I get lots of hits:)
I am also fortunate that several years ago I wrote a grant and purchased some board games specially for math concepts. While many have seen better days, the kids are using their math thinking skills to play.

Playing games allows me to really observe the students. Usually I will introduce the game on day 1, review it and play with them on day 2, and by day 3 they are playing with one another and I can make my observations.

Share Time
  • Students are brought back together to debrief the lesson. 
  • The teacher asks probing questions.
  • Students are asked to summarize.
  • The teacher reviews teaching points and checks for misunderstandings.
  • The teacher previews math center or homework that will follow.

A guided math lesson, with all of the components described above, is shared (p 72-75). Each component of a guided math lesson is clearly labeled for the reader.

Dr. Nicki also stresses the importance of evaluating each lesson through reflection.  See page 76 for specific questions to ask yourself about student engagement.

Question 1: Do you use guided math lesson templates? If so, what do they look like? How detailed?

This is something I have struggled with for years!! I like a nice, simple formatted planning template, but I HATE writing lessons for my overall week, my guided reading plans, and my guided math plans...it's too much!!

I saw this idea on Pinterest and it came from First Grade Nest.


I liked how simple it was and all I had to do was use sticky notes! I only have four groups that I see daily, so mine is modified.  If you want a copy of my template, you can get it here.

Dr. Nicki has some other great templates in this chapter that I may be experimenting with too. :)

Question 2: How do you teach specific concepts at a concrete, pictorial, and then abstract level?

When first introducing a concept I do what most teachers do...use manipulatives! I love base ten blocks, linking cubes, coins (real or fake), pattern blocks, geometric shapes, clocks, and the list goes on and on! I feel it is important at this young age for students to have that hands-on experience so that they can have a deeper understanding of how numbers and equations can be put together and taken apart. There are also several computer programs, websites, and apps that are available for students to use these tools digitally.

I then love to show my students how they can draw the manipulatives. I think this important because students don't have access to the tools we use in school at home, but they can use drawings to help them problem solve. This skill can also carry over not only at home, but anywhere students need to solve a math situation...even with those lovely standardized tests.  I see my students use their scratch paper and pencils, when test taking, to help them problem solve....it makes my heart so happy!

Some students have to have more exposure to the math tools in order to fully understand the mathematical skill, and then there are some students that can think abstractly a little sooner. This is another great thing about guided math groups. The group that needs that extra practice is able to spend time with the teacher manipulating math tools, and those at other mathematical levels can take that thinking and move on to more real life problem solving situations.

Now it's time to enter a fabulous giveaway! It's a Dr. Nicki Newton, Problem Solving with Models, giveaway! Click here to check out these awesome resources! The lucky winner will get to pick the grade level resource that best fits him/her.  We will be randomly drawing the winner next Sunday, August 3... Good luck!

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Stop back Wednesday for our discussion of chapter 7!  You can also read past book study posts by clicking HERE!

Friday, July 25, 2014

Five for Friday & a Giveaway!

It's Friday and our first Five for Friday!  This week we are drawing attention to a fabulous idea shared by a blogger participating in our Guided Math in Action book study as well as some other goodies.

Our book study is in full-swing, but it's NOT too late to join in!  Click here for more details!


Need a Hand?


Pam, from Pam's Place, is participating in our Guided Math in Action book study and shared a wonderful strategy for overcoming "I'm stuck!" in math-- Need a Hand? These handy-little-hands help foster her students' perseverance. Each hand gives a tip she encourages students to try before the infamous sayings, "I need help." or "I don't get this." or "I can't do this." Pam encourages her students to TRY THREE before ASKING HER. Read more about Need a Hand?!

Thinking Prompts

Guided Math in Action contains a selection of math thinking prompts to use with students. Many of the prompts are applicable to more than one discipline, and they would be great to display in the classroom.  Feel free to download the posters here!

How long have you been using guided math?: Poll Results

Thanks go out to all those who participated in our first guided math poll.  We gathered 100+ votes!  The results of the first 100 votes were used to create the graph you see above.  This first poll was set up to help everyone get to know our followers a bit better.  Additional poles will be posted as time passes, and we'd love for anyone who stops by to participate. We truly hope this new blog will offer something each follower, no matter what his/her experience is with guided math.

Dr. Nicki Q & A!

Another thank you goes out to all who sent in questions for Dr. Nicki's first Q & A! The questions have been sent on, and we will be posting her responses as soon as we receive them.  BUT---Remember, Dr. Nicki has generously agreed to do a second Q & A at the end of the book study as well--SO get those burning questions in! 

Here's how the Q & A will work:

  1. Send your questions to us at www.guidedmathadventures@gmail.com.
  2. We will pass your questions on to Dr. Nicki.
  3. She will do her best to answer your questions in an upcoming post.

We will be taking questions for Dr. Nick's second Q & A through Wednesday, August 6.  Anyone can ask a question!

A Giveaway!


Who doesn't love a giveaway--SO we have a great one for you---starting this Sunday, July 27!! It's a Dr. Nicki Newton, Problem Solving with Models, giveaway! Click here to check out these awesome resources! The lucky winner will get to pick the grade level resource that best fits him/her.  Stop back Sunday to read our Guided Math in Action chapter 6 post and enter to win. Good luck!

Don't forget to check out more Five for Fridays at Doodle Bugs Teaching...

Wishing you a fabulous weekend! See you back here on Sunday!

Tuesday, July 22, 2014

Guided Math in Action Book Study -- Chapter 5

Today we are here to discuss Chapter 5 from Dr. Nicki's Guided Math in Action book. We are only discussing one chapter today, and what a great chapter it is!

Question 1: What types of pre-assessments do you use? What new ideas have you gathered from this chapter? 

I have struggled for YEARS trying to come up with an effective way to pre-assess my students math skills in the same manner I pre-assess their reading skills. In reading, I complete a running record on each student individually. I also have a little "chat" with them about reading (likes, dislikes, what they remember from first grade, etc). But when it came to math, I would give paper and pencil pre-assessments on the unit we were going to study, but in reality, the majority wouldn't do well because WE HAVEN'T LEARNED THE MATERIAL YET! I have given pre-assessments on first grade standards, which gave me a good idea of my struggling mathematicians.

I could never find a way to do the same with math....until now! Dr. Nicki has opened my eyes and the answer is so simple, do the same thing I do with reading, but only relate it to math!  I loved how she talks about having the interviews with the students and giving a little survey. Kids eat up their individual time with me and this is something I can do when beginning a new unit.
I could relate a lot of what Dr. Nicki was saying in this chapter because it is how I assess and comprehend the individual understandings of all my students when it comes to reading. My notes I take would fit right in with the sticky note sheets Sarah made....I love it when things come together for me!

Question 2: What types on on-going assessments do you use? What new ideas have you gathered from the book?

I feel the most powerful assessments any teacher can use is teacher observations and conversations with students. I use my time during guided math groups to write what I observe and the discussions we have. These observations will then lead to my next day's lesson. It's hard for me to plan out a week of guided math groups (or reading groups for that matter) lesson plans because I go off of what we have done previously. There are times that my whole time with a group is pure discussion. Dr. Nicki said, "Small-group work is the perfect time to push on mathematical thinking so that you can build adaptive reasoning" (p. 58).

I am also one that likes a formal checklist, or graphic organizer for on-going assessments. Dr. Nicki has great examples of some in her book. 

Two things to work on:
  • Observing the students when they are not in a group. Whether doing workstations, journals, or fact practice games, observing them in other settings will give me more information on their mathematical thinking.
  • Keep anecdotal notes short and to the point....I tend to write too much!

Question 3: What types of summative assessments do you use?  What new ideas have you gathered from this chapter?

I have to honest here.....the only reason I really give a summative assessment is to get a grade.  I usually will use a test from our math program, make one up myself, or get some great assessment Sarah has made (which is always much better than what I make:). I hate feeling this way, but it's the truth. Dr. Nicki does make me feel better by saying we must use information from these assessments to make sure students are learning (I also like that she calls them "Evaluative Assessments").

I want to set goals with the students like Dr. Nicki mentions on p. 63. She says, "Students shouldn't be on a mystery train. If they know where they are going, they have a much better chance of getting there." WOW...POWERFUL!

Another goal of mine is to use student portfolios. I know how wonderful they can be for students, parents, and myself, but have failed over the years with keeping up.

I believe all three assessments are essential in all classrooms, and not just with math. Knowing our students strengths, weaknesses, and interests can make us more effective educators. They also allow a so called map into what we need to do to ensure all our students are learning!

AND, if you have not already heard the FABULOUS news...

To our surprise, Dr. Nicki recently contacted us to offer her help with the book study in any way.  She will be doing some Q & As right here!!

As of this Wednesday, we will be over half-way through our book study, so this is a great time to ask questions that have popped into your head while reading or following along on our blog.  Dr. Nicki has generously agreed to do a second Q & A at the end of the book study as well--SO start keeping track of those burning questions!

Here's how the Q & A will work:

  1. Send your questions to us at www.guidedmathadventures@gmail.com.
  2. We will pass your questions on to Dr. Nicki.
  3. She will do her best to answer your questions in an upcoming post.

We will be taking questions for Dr. Nick's first Q & A through Wednesday, July 23, so don't delay--Get your questions in! How about some questions about assessment--a big topic??

A big THANK YOU goes out to Dr. Nicki!

We will see you back here on Sunday for Chapter 6, BUT you may want to stop back this Friday to find out about a wonderful giveaway! That is--if you like giveaways!! You can also read past book study posts by clicking HERE!

Monday, July 21, 2014

Fabulous News!! Q & A with Dr. Nicki!

We come to you today with some fabulous news!

As you know, we have been hosting a book study of Guided Math in Action, by Dr. Nicki Newton.  To our surprise, Dr. Nicki recently contacted us to offer her help in any way.  She will be doing some Q & As right here!!

As of this Wednesday, we will be over half-way through our book study, so this is a great time to ask questions that have popped into your head while reading or following along on our blog.  Dr. Nicki has generously agreed to do a second Q & A at the end of the book study as well--SO start keeping track of those burning questions!

Here's how the Q & A will work:

  1. Send your questions to us at www.guidedmathadventures@gmail.com.
  2. We will pass your questions on to Dr. Nicki.
  3. She will do her best to answer your questions in an upcoming post.

We will be taking questions for Dr. Nick's first Q & A through Wednesday, July 23, so don't delay--Get your questions in!

A big THANK YOU goes out to Dr. Nicki!

If you haven't already, feel free to take our poll. Just click View to see the results.

How long have you been using guided math?
pollcode.com free polls 

AND don't forget to stop back this Wednesday for chapter 5 of our Guided Math in Action book study...

All the best--

Saturday, July 19, 2014

Guided Math in Action Book Study -- Chapters 3 & 4

Hello! Welcome back to our Guided Math in Action book study.  Today we are discussing and reflecting upon chapters 3 & 4.

Chapter Three
This chapter is all about preparing your kids for math workshop/guided math from the very first day of school. It's important to get off to a good start. Dr. Nicki recommends teachers do the following:

Establish Rules, Consequences, and Rewards

  • Rules should be clear, explicit, few, written in positive language, and agreed upon by the class.
  • Consequences should be immediate, fair/consistent. This leads to on task behavior.
  • Rewards should be given (whether intrinsic and/or extrinsic) and kept--never taken away after they have been earned.

Establish Routines

  • Students must know exactly what to do during work time.
  • Spend the first four weeks practicing math workshop/guided math routines.
  • Be consistent and predictable.
  • Set timers and stick with your schedule.
  • Have students practice working with centers independently, with partners, and in small groups.
  • Practice a variety of centers.
  • Teach students how to read task cards and transition.  
  • Practice classroom manners and good sportsmanship.

Use Math Anchor Charts

  • What do mathematicians do?
  • How can we prove our thinking?
  • How do we talk about math?
  • What is sharing?

Create Visual Schedules

  • There are many options.
  • Consider using student pictures and icons.

Dr. Nicki goes on to discuss establishing a guided math area and compiling your teacher toolkit.

Guided Math Area

  • Have a home base, yet meet in other places as well, such as at a center or an interactive whiteboard.
  • Teach students how to come to area prepared, gain teacher access, and leave the area.
  • Everything that is needed should be located in this area.
  • Observe, inquire, and take notes.
  • Do a variety of activities.

Teacher Toolkit

  • student work samples
  • record-keeping charts/forms
  • paper and pencils
  • whiteboards, markers, and erasers
  • manipulatives (specific to concepts/skills taught)
  • dice, dominoes, cards, etc.
  • number lines
  • timers
  • pointers
  • clear plastic page protectors/folders (for graphic organizers, work mats, etc.)

Question 1:
Click here to read about what is in my teacher toolkit!  

Question 2:
All of the centrally located math tools serve as my students' toolkits. Students can access any needed tools while working with centers/workstations, math journals, math vocabulary, math texts, etc.  Tools may be used at any time to reason through problems, prove thinking, illustrate problems they create, etc.  Students need not ask for permission to use a tool.  At the beginning of the year, we gather to talk about the purpose of math tools, how to use tools correctly, and how to tidy up tools for the next person.  Last year, our writing center was between our math drawers/tubs and cabinet with additional math tools.  This year, the writing center will be relocated so that everything will be housed side-by-side.

All tools are organized and clearly labeled in tubs above workstation drawers and in our math tools cabinet (sorry, some reading stuff is shown here as well).

Question 3:
I do many of the things Dr. Nicki recommends in this chapter, yet I want to incorporate the use of different timers (I need them, and so do the kids!), picture icons on my schedule, and a new record keeping system (discussed below).

You can view and read about our schedule (circle diagram) by clicking here.

One of the most important things we do the very first day of school is establish classroom responsibilities (these are our rules).  These are generated by students and agreed upon by all. They are signed and a copy is sent home to parents to discuss with their child.  Then responsibilities are posted in the classroom all year.  Students also keep a "My Responsibilities Sheet"  in their take-home binders all week, and they rate themselves daily.

We also spend valuable time talking about my role as a teacher and their roles as students during guided math time.  An anchor chart is created similar to Daily 5 t-chart--"I am..."/"Mrs. Masters is..." Courtney and I both do this and take small steps in those first weeks to ensure that students have built needed stamina.  I am off limits when meeting with a group--BUT students know what to do when I am not available (as outlined on the t-chart).  As we all know, sometimes students just think they need help, so the first question to ask is always, Do I truly need help? OR Can I think about what I need and problem solve on my own? OR Can I quickly and quietly ask another student in my area for assistance?  :0)

One the most effective things I feel I do from the very first day is expect students to take an active roll in the classroom. If they can do it, I don't do it for them.  If they can reason through a question, I expect them to answer it.  I, of course, let my students know exactly what is expected and routines are practiced over and over.  I always express my confidence in their abilities and try to instill in each a sense of pride.

Chapter 4:
Here are some highlights I pulled from chapter four:

  • All students need the teacher's attention, no matter their skill level.  Be sure to connect with every student each week.
  • Teachers must collect a variety of data for each child (using pre-assessments) to inform grouping and guided math lessons.
  • Group students into four groups: novice (no basic understanding of concept), apprentice (basic understanding), practitioners (at grade level), and experts (above level and need extension).
  • Use ongoing observation and assessments to evaluate progress.
  • Flexible grouping means students are grouped according to their ability/skill level related to a particular concept. Groups are fluid, allowing for movement in and out of each level depending on the concept/skill.

Several weekly guided math schedules are shared (p. 44-45).

Dr. Nicki ends by emphasizing the importance of keeping records--you need some way of keeping track of what you have done with students and your students' levels.  However you choose to keep records should fit your style. Some great ways to record student work, take notes, and plan are shared (p. 46-47)

Question 1:
I meet with small groups daily! Some days I meet with two guided math groups, some days three or four. 

Question 2:
Groups are very fluid--ever-changing based on constant reflection and ongoing assessments.  More about assessments when we discuss chapter 5.

Question 3:
I have to be honest and say that I need to improve in this area.  I struggle with finding a tool that is effective, yet efficient.  I keep so much "in my head"---I truly know my students, BUT I know I can do better. I have tried many systems and have yet to find one that works for me (and I have been teaching this way for many years).  I am going to try using clipboard sticky notes notes this year.

How I Will Use:
  • I will be placing sticky notes on a clipboard as I record bits of information.  One sticky note will be used per student observed or conferred with on a given day.
  • My challenge was how to easily organize/store sticky notes, so I created some simple sticky note storage sheets for collecting notes over time.  After making notes for the day, I will stick notes (not during class time) into individual student folders on these storage pages. This will house records for easy reference.
  • I plan to stick notes in four columns, using the front and back of a storage sheet, with the last few days of some months being placed in the fourth column.
  • Sticky notes will first be placed at the bottom of the sheet and then upward/overlapping as time passes.  This way I can easily flip through notes at any time.

The flipping back and forth in a folder or index file during valuable classroom time is quite frustrating to me.  I have hopes that this new system will work for me. Feel free to download the sticky note storage sheets I created!

Now it's your turn to share your thoughts about chapters 2 and 3, comment, and/or ask questions. Please! :0)

If you are a blogger and are interested in joining this book study, you may hop in at any time.  Just sent us an email at guidedmathadventures.com so we can get emails out to you.

If you haven't taken our poll, feel free. Just click View to see the results!

How long have you been using guided math?
pollcode.com free polls 

Courtney blows back into town soon, so she will be back here with you on Wednesday to discuss chapter 5!

Have a wonderful week!

Tuesday, July 15, 2014

Guided Math in Action Book Study -- Chapters 1 & 2

Good day to you!  Back with you to discuss chapters 1 & 2 of Guided Math in Action by Dr. Nicki Newton.

As we begin this book study, we look forward to hearing how each of you transacts with the text---what makes you think, what connections you make, what questions arise, what plans are put in motion, etc.  Please feel free to share any thoughts and questions that you have as you reflect on the reading and your own teaching.  

If you don't have a copy of the book, we will be summarizing portions of the text, yet other portions will be mentioned and will require the text for full understanding.  In addition, some discussion questions will require the book, and others will not.  Please feel free to share, even if you do not have the text. Of course, we DO recommend you snag yourself a copy!

The best part--with many other bloggers participating, we will gain different perspectives as various grade levels and experience are represented--SO visit fellow bloggers by clicking the links at the end of this post. Courtney and I will also be offering different perspectives as we 'tag team'--alternating posts and collaborating for some posts as well.

Just a little background about me as we begin.  From the time I was in college, I was exposed to endless experiences that helped to form some philosophies about teaching that have become even more deeply rooted as the years have passed.  The most over-reaching being the importance of differentiating to meet the diverse needs of my students.  As I began my teaching career, as a special education cross-categorical teacher of third through fifth graders, I was thrust into a setting with 16 kids who had vastly different needs, from life skills to those who truly should have been in a regular education classroom with support.  There was a half day aid, and the urgency to differentiate quickly became a reality.  I didn't see differentiating as a choice--it was something I HAD to do because that's what I was taught and believed in my heart.  Our class was an island in itself--and in those days there was not much of a support system.  I began to make my way the best way I knew how, and that was to teach my kids to be independent with differentiated tasks so that I could meet with small groups.  I remember many of the centers/workstations well--even though they were not called centers/worksations back then. :0)  How I wish I had had some of the wonderful resources available today to act as the support system that wasn't there.  Dr. Nicki's Guided Math in Action would have been a perfect companion! Even after many years of teaching, I find it to be a trusty companion that offers affirmation and has broadened my horizons.  Thank you, Dr. Nicki!

Chapter One: 
From the very first chapter of Dr. Nicki's book, we get a look into a guided math lesson in action.  Mrs. Johnson and her students are interacting in ways that help them to understand how important their knowledge of place value is when subtracting two-digit numbers and how to put that knowledge into practice using a tool (straw bundles). 

What a great way to begin! To me, Mrs. Johnson and her students were in a fishbowl as I was looking in.  I can imagine that many readers were making connections and asking themselves questions while looking into that 'fishbowl'--I've never thought of doing that before. How did she form her group? How much time is she spending on this? What are the kids outside of the 'fishbowl' doing? That's similar to what I would ask, and so on. Mrs. Johnson's guided math lesson set the stage for the rest of the text where many of those questions that readers ask are addressed.

Mrs. Johnson's guided math lesson began with a mini-lesson that tapped into her students' prior knowledge. This was essential to gain students' attention and set the stage for the day's lesson.  She also elicited students' knowledge of important vocabulary--"Who can tell me in their own words what subtraction means?"  As students shared their thinking, Mrs. Johnson used a simple thumbs up/down to check for understanding before moving on with the lesson.  Students also had access to straw bundles so they were able to actively participate and show the thinking that was being shared.  

Mrs. Johnson then went on to give each student two problems to work on, in what Dr. Nicki calls the student work period. This allowed students to have independent practice.  Mrs. Johnson observed her students as they worked, making notes and asking questions.  Students then came back together to share their solutions.

To end the lesson, Mrs. Johnson moved into what is called the share period--a time for further discussion of concepts, strategies, and understanding. Mrs. Johnson made sure students could explain what they learned by asking, "...what was the math we were working on?"--with the expectation of using math language (subtracting, tens, ones) to show their understanding of the concept. During this time, Mrs. Johnson also gave some directions about what the students would be doing when they moved on to a center as well as their homework for that night. 

Then it was time for Mrs. Johnson to observe the happenings of the rest of the class who were engaged in independent activities that were differentiated (on their own, with a partner and in small groups).  She jotted down some notes about specific students and then signaled everyone to make a switch.   

Mrs. Johnson's lesson illustrated some important aspects of guided math:

  • the flexible grouping of students according to their areas of need
  • the teaching of students at their instructional level
  • the interaction and exchange of thoughts and ideas among students and with the teacher
  • the use of appropriate tools to explore a concept at the concrete level
  • a teacher's observations and record keeping
  •  the development of students' understanding, reasoning, and confidence

The remainder of chapter one outlined some beliefs about teaching and learning mathematics that frame guided math.

  • Meeting Students Where They Are
  • Tapping into Multiple Learning Styles & Intelligences
  • Building Mathematical Confidence

A chart is also included that outlines these beliefs as they relate to students, teachers, and the development of mathematical proficiency (p. 10). 

Question 1:  
My thoughts---Go Dr. Nicki!! Stretching is a must! We are charged with meeting the diverse needs of our students--one way (or even two or three) may not cut it. Words of wisdom from the end of this passage--"You have to make sure you are using a variety of strategies, not just the ones you like and know best." As teachers, there are ways of doing things that we like, but what we like is not always what's best.  

I believe it's my responsibility to have 'withitness'.  I remember exploring classroom management theorists in college--one was Kounin who coined this term.  Withitness was described as a teacher's ability to know what is going on in his/her classroom at any given time for the purposes of classroom management.  When I think of 'withitness', I think of it as much more--a teacher's keen senses of observation and reflection that allow him/her to best meet the needs of his/her students. At any given time, I should know what each student's needs are as related to various concepts/skills. My 'withitness' makes it possible for me to stretch my own pedagogy.

Question 2: 
The use of small group, individualized instruction and providing differentiated independent tasks in themselves communicate to students that they will get what they need.  When kids know they are going to get what they need, be 'taken care of', this serves to promote perseverance.  Yet, these things in themselves are not enough. Students need to know that their ideas are valued, not just by the teacher, but by their fellow students as well.  The climate of the classroom needs to be one that encourages students to explore their thinking out loud in small and large group settings. 

From the very first day of school, I begin the quest to create what I call a 'safe place' for my students.  We talk about what we can do when someone shares something thoughtful or does something well.  We praise him/her and express exactly what we appreciate.  We also talk about how to positively respond when someone shares an idea that is different from our own or one that isn't correct. I model this myself on a daily basis, and I draw attention to students who do this well.  Students are encouraged to think out loud, and they become comfortable with this when they know their ideas are valued. As I say, we learn so much from each other when we think out loud, so we better have those eyes, ears, and brains open. :0)

As we know, not every child is as willing as the next to share publicly.  For this reason, I have an idea bulletin board that is used in many ways.  One way I use it is to have students share how they are feeling or questions they have about a specific topic, concept, new learning, etc.   Students place Post-Its on their numbers and I collect them.  Then I choose some of their feelings/questions to discuss as a class or in a small group.  In this way, only the person who shared the feeling/question knows it's his/hers when it's being discussed.  Most likely there's at least one other student who feels the same way, or has the same question, even if he/she didn't write it down.  As time goes on, more reluctant students begin to share more publicly because they have witnessed the value and care that is placed on their feelings/questions.

Encouraging the "I CAN!" and "I can't, YET!" attitudes are also important for my kids.  We learn there are things we are able to do very well (our strengths) and those we will eventually, with help, be able to do well (our struggles).  That's where our EASY button comes into play!  Many moons ago, one of my students brought in an EASY button from Staples, and I started using it with the kids right away.  The EASY button has become a thing of triumph for my second graders.  It gets pushed when a student, or small group of students ,'conquer' something that was difficult for them, and with hard work and perseverance is something that can be done well.  They slap that button, wait for "That was easy!", and they all cheer.  The pride students have when pressing the button is immense, and it's a way of receiving recognition from the masses. :0)  We are in this TOGETHER!

Wow! This is a big question! Making sure students know exactly what is expected promotes perseverance, too... As this book study unfolds, we will undoubtedly hit on other strategies... :0)

Chapter Two:
In this chapter, Dr. Nicki stresses the importance of students being able to defend their thinking and challenge the thinking of others.  These are skills that need to be taught.  She suggests posting charts that outline the ways students can prove their thinking and provides a series of thinking prompts.  She goes on to emphasize creating an atmosphere that supports reasoning out loud. Creating a numerate environment in the classroom will foster such an atmosphere.  A graphic organizer including the behaviors that exist in a numerate environment was also shared (e.g. - connecting, verifying, writing, showing, listening, and many more).

A numerate environment supports thinking with...
  • concrete manipulatives
  • counters
  • graphic organizers (number lines and grids)
  • drawings
  • acting out

Dr. Nicki goes on to discuss how math workshop is a means of establishing a strong community of learning in your classroom.  She overviews several components of a math workshop:
  • calendar (even for upper elementary)
  • problem of the day/number of the day (shared experiences)
  • whole class mini-lesson (an activity central to concept)
  • guided math groups/centers
  • math strategy practice/energizers (thinking and talking about numbers together)
  • share/class journal/individual journal (sharing related to activities done in math workshop)
Math workshop is a framework in itself, with guided math being an integral part.  You do not need to use math workshop to do guided math, yet Dr. Nicki prefers the workshop model.  If you haven't already heard, Dr. Nicki has a new book coming out soon, Math Workshop in Action, scheduled to be published this coming October. I am excited to get my hands on a copy to learn more!

Here are just a few ways I create a numerate environment in my classroom:

  • shared math journals
  • problem solving discussion prompts (discussion fans)
  • number talks, even "outside" of math time
  • use of math mentor texts
  • shared problem solving
  • number explorations (number of the day, daily math meeting)
  • reflections (e.g. - 'exit" slips used with idea board shared above)
  • math word study (words posted on word wall and the use of key vocab in context of discussions and writing)

Many of the above will be discussed in more detail in future blog posts.

To end, when I first read Guided Math in Action, I was especially taken with figure 2.2 on p. 16 that outlines some superb math thinking prompts. The more I thought about these prompts, I realized many of them are applicable to more than one discipline.   Therefore, I decided to create some letter sized signs to post in the classroom this coming school year.  I plan to post them by the ginormous question mark that reminds students to ask, WHY? Feel free to download here!

Now it's your turn! :0) We look forward to all of the ideas and thoughts that will be shared...

If you are a blogger and are interested in joining this book study, you may hop in at any time.  Just sent us an email at guidedmathadventures.com so we can get emails out to you.

See you back here on Sunday--

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