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--
Almost forgot---if you haven't already taken our poll, feel free. Just click View to see the results!
