Guided Math Book Study-Chapter 5

“Using Guided Math With Small Groups”

Thanks to Mary at Pitner's Potpourri and Alison at Toad-ally Exceptional Learners for hosting Chapter 5.

Advantages of Small-Group Instruction
By flexibly grouping students based on their strengths and needs, teachers can tailor their teaching to provide the specific instruction that best challenges all learners.

Mathematical communication is an integral aspect of small-group mathematics lessons.  Teachers learn when to move ahead with instruction, when more teaching is needed, and what specific points need to be addressed for these learners-all of which help teachers as they plan future instruction to extend learning.

If students are making errors in their work due to misconceptions or even carelessness, the teacher notice immediately.  An essential component of instruction is assessment.  That includes formal, informal, summative, and formative assessments.  Using small-group instruction teachers learn about their students and their abilities.

Challenges of Small-Group Instruction
Teachers who use small-group instruction are involved in more complex tasks as they plan.  This type of planning is only possible when teachers know their students’ levels of achievement and learning needs extremely well.

Effective Uses of Small-Group Instruction

• differentiating instruction
• teaching mathematical “hot spots”
• teaching with manipulatives
• assessing student learning informally
• supporting mathematics process standards

Forming Small Groups for Learning

• Unit Pre-tests
• Formative Tests
• Performance Tasks
• Observations of Student Work
• Mathematical Conversations with Students
• Benchmark Tests

Organizing for Small-Group Instruction
When the meeting space is clearly defined and any materials needed are prepared and readily available at the beginning of each math class, group instruction can begin promptly.

Suggested items available during small-group instruction:

• whiteboards
• chart pad and easel
• work mats
• manipulatives
• measuring tools
• paper
• pencils
• erasers
• crayons
• markers
• specific materials for the lesson planned

Guided Math Lesson for Small Groups

Planning the Lesson

1. Determine the big ideas of the unit of study to be taught based on the standards and the needs of the students.
2. Decide what the criteria of success will be in mastering the standards of the unit.
3. Use information from assessments (both formal and informal) to form groups based on student needs.
4. Select specific teaching points for each group.
5. Prepare differentiated lessons based on the learning needs of the students in each group.
6. Gather and organize the materials necessary for the lesson.

Teaching a Guided Math Lesson with a Small Group

Guided Math in a Small Group

1. Briefly introduce the lesson by providing supportive strategies for learners through a mini lesson to introduce or extend the concepts being learned.
2. Provide students with a clear understanding of the activity or task on which they will work, including setting criteria for success.
3. Encourage students to use a variety of strategies to solve the problem or complete the activity.
4. Scaffold student learning by giving just enough support to move students to the next level of understanding and proficiency.
5. Provide ample opportunities for mathematical discourse.
6. Give students specific, descriptive feedback on their work and encourage students to engage in self-assessment based on the criteria for success.

Teacher Reflection after the Lesson

1. Record and organize informal assessment information based on observations and conversations.
2. Select the next steps in learning for the group, as well as for individual students.
3. Identify students who are struggling with specific concepts, and plan how to reteach the concept when needed.
4. Change the composition of the groups, when appropriate.

Review and Reflect

1. How does using flexible, needs-based grouping affect student learning? How can it affect teaching strategies employed by teachers? Students learning should increase as students are taught in flexible small groups. As a teacher I can target specific skills or misconceptions and focus on them with the students who need it. I will use more targeted strategies and continue to try and build conceptual understanding for struggling learners. It will also be a chance for more targeted literacy strategies to be employed.
2. Question 2 was on Guided Reading and since I only teach math I skipped it.
3. What data do you have that can guide you as you create small groups of students for Guided Math instruction? I can use MAPs data to see the math strands that groups of students struggle with. I can use pretest information for grouping students, as well as formative assessments like exit slips and in class checks. By observing students and talking to them as they work on their math I can also gain valuable information for grouping them. I will be using Carnegie math next year and there many reports that will be generated by the cognitive software that students will use. This should also prove very helpful for putting students into small groups.

Summerfest and How I Almost Fainted

Yesterday we spent a fun filled day at the opening day of Summerfest.  I believe the last time we were there was ten years ago, when my oldest was 3 and I was pregnant with my middle.  Things have not changed much, except the prices are much more pricey these days.  $20 for parking, ouch!  Greg took the day off and we arrived around 12:30 PM.

We saw Bango the Milwaukee bucks mascot, right as we arrived.  They had a "Bucks experience" that started at 1 PM so we decided to do that, BIG MISTAKE that I will elaborate on later.

We started off with Hawaiian shaved ice for the all the boys, a cold beer for my hubby, and a white wine cooler for me.  We then went to the "Bucks Debacle".  They were going around in the crowd getting kids to participate, Cooper was chosen to play "hot potato" with Brandon Jennings, Drew was supposed to be a ball boy for Brandon, and Ben was chosen for a trivia contest.  After numerous problems with their microphones (none of them would work), Cooper finally got to play (he's on the right).  I am not a Bucks follower at all, but I think the kids thought it was cool.

Well after ONE HOUR of sitting out in the blazing heat/sun, they gave up on most of the activities with the kids due to the lack of working mics.  Ben and Drew did not end up doing their activity.  It was pretty lame and we were all baked by this time.  I hope for the sake of the Bucks that they figure this out because it was really a debacle IMO.

At this point it was 2 PM and I had not eaten anything all day except a handful of chocolate covered pomegranate seed for breakfast.  I went to get my must have item at Summerfest, the eggplants strips from Venice Club.  As I was walking back, I really started to feel like I was going to pass out.  I mean it was pretty scary.  Luckily I made it to a spot in the shade and sat down, right there on the ground.  We had nothing to drink so Greg got me a bottle of water STAT and the boys all stood around encouraging me.  It was too sweet.  I guess I learned my lesson that wine cooler + an hour in the blazing sun + empty stomach = TROUBLE.  

We found a picnic table in the shade and ended up having lunch.  I was able to drink some water and eat some eggplant strips and I was back in action.  I was so looking forward to another wine cooler, but at that point I was too freaked out to have another and got an iced tea instead.

We had a nice trip across the Summerfest grounds on the Sky Glider.  Greg was in front with Cooper and Drew and Ben and I rode in next car.  Despite the 90 degree heat, it was very pleasant and there was a nice breeze.

We had a very nice day.  It was not too crowded and we left around 4 PM because Drew had a 7:30 BB game.  It was quite a change from my 20s when I would go to Summerfest multiple times every year.  One summer I even met a guy at a garbage can, while I was throwing something away and we ended up dating for three years (before I met the TRUE man of my dreams, my hubby).  Summerfest has so many great memories for me and it was great to make some new fun memories with my four favorite guys in the world!

What's your favorite summer festival?  We are so busy in the summer with baseball and other sports that it was perfect to spend the day doing something fun and local as a family.

A peek at my teacher corner (photos)

*Updated for 2012-2013 school year.  I am sharing a couple links of blogs posts with more updated photos of what my classroom looks like this year.  I changed and updated quite a few things.  I added some zebra accents to my color scheme and made a Math Focus Wall surrounding my SMARTBoard.  Classroom Photos Part I and Classroom Photos Part II.


Last fall in the rush off all things that go with getting a classroom set up for school, I posted Part I of my classroom set-up and then never got around to finishing with Part II.  As I was packing up my classroom last month I made sure that I took some photos of my "teacher corner" to share with all of you.  I have mentioned several times about our odd pentagon shaped rooms and the back corner is really wasted space, so a few years ago, I moved my desk and all teacher files/materials over there to utilize the space better.

My cozy teacher corner

My back shelves

Teacher bookcase with my binders and teacher's manuals

Another view

I love the pops of my color scheme mixed throughout

The bright colored storage containers came from Target last summer.  I made the no sew banner and it's the same as the one over my SMARTBoard.  I hope you enjoyed the tour of my "happy place"  when it comes to teaching.  I spent a lot of time (and money) last summer revamping my classroom and I could not be happier with the results.  My students really loved my classroom set-up this year.  Thanks for stopping by!

Guided Math Book Study-Chapter 4

Please join in discussing Chapter 4 of Guided Math with Brittany at Sweet Seconds and Katie at Once Upon a Teaching Blog.   Thanks for hosting ladies!

“Using Guided Math with the Whole Class”

Advantages of Whole-Class Instruction

• presenting mini lessons
• involving students in activating strategies
• reading aloud mathematics-related literature
• setting the stage for Math Workshop
• conducting a Math Huddle
• providing practice and review
• formal testing or assessments

Mini Lessons

• Connection

• With yesterday’s lesson
• With the ongoing unit of study
• With students’ work
• With an experience outside of school

• Teaching point

• Present verbally
• Demonstrate or model

• Active Engagement

• Students try out a skill or strategy
• Students act like researchers as they watch a demonstration
• Students plan their work out loud
• Students imagine trying a skill or strategy

• Link to Ongoing Student Work

• Students turn to their own work and apply the teaching point

Tips for Effective Mini Lessons

• Limit student talk
• Keep the connection brief
• State the teaching point simply and reiterate it
• Demonstrate the mathematics teaching point
• Use a familiar context for problem solving
• Match the active engagement to the mathematics teaching point

Activating Strategies

• KWL Charts
• Anticipation Guides
• Word Splashes

Reading Math-Related Children’s Literature
To encourage students to recognize these literature/math links, teachers can use a think-aloud strategy as they read a story, detailing the mathematical connections and questions that occur to them as they read the story.

Setting the Stage for Math Workshop

• creating a classroom community
• teaching procedures
• ongoing need to provide directions

Math Huddle
A math huddle is a forum for students to “communicate their ideas, solutions, problems, proofs, and conjectures with one another”

Students are held accountable

• for expressing their ideas
• for listening thoughtfully to each other
• for justifying their mathematical thinking based on their mathematical experiences

Practice and Review Sessions

• Pencil-and-Paper Tasks
• Games and Music
• SMARTBoard Reviews

Review and Reflect

1. Think back to the previous week of mathematics instruction in your classroom. How much of the instruction was whole class? Why did you choose that instructional method? Well I have been out of school for two weeks now, but when I think back to my typical instruction, I would do whole class instruction with most of our math explorations. That was the way our MathThematics text was designed to be used. Even with the whole class instruction there was lots of partner and collaborative group work throughout a lesson. On review days, a formative assessment was given to each student and it had to be completed with mastery prior to the student receiving their homework for the day.
2. In which situations do you use whole-class instruction most frequently? How effective is it in those situations? I used whole-class instruction to begin a lesson (the setting the stage and the daily warm-up) are always done whole class. This is the most effective way to do that. My class was a lot of whole class instruction with built in differentiation. I also used learning stations and when giving directions on those I would use whole-class instruction. This coming year with Carnegie there will be a large component of whole-class instruction as we work through the print materials for 60% of the class time.

What I am Loving Friday

I feel that it has been a pretty intense summer for me so far, with a week of math training after school ended and then trying to get caught up on the first three Chapters of the Guided Math book study.  I decided to do a fun post today on what is making me happy lately.

• Making my own Passion Iced Tea Lemonade.  Now I don't have to go to Starbucks and it is much less expensive to make at home.
• Going to the swimming pool with the boys.
• No alarm!  That is definitely my favorite.  We do have places to be every day, but not so early that I have to set an alarm.
• We booked The Newport Resort for our vacation this summer.  I cannot wait!  It is my happiest place in the whole wide world, or at least WI.  We are spending a week there and then finishing up at The Tundra Lodge where the guys are hoping to watch the Packers either practice or scrimmage.  The boys are so excited about our summer vacation.  We did the same thing last year (although went to GB first) and had an awesome time.
• Having the time to do some planning for school without the pressure of being in school and having no time to do it.
• Getting to go out to for a leisurely lunch instead of scarfing down my lunch in 30 minutes.
• No dress code!  It's great to wear whatever you want and getting to lounge around in jammies as long as you want.  And no someone did not come to the door the other day to drop something off at 12:30 PM and I was still in jammies so I made one of the boys answer the door.  That definitely did not happen.
• Drew was a unanimous vote for the 10 yo All-Stars which means every single coach voted for him (well except my husband who is managing the All-Stars this year, because you can only nominate your own players, you can't vote for them.  He also manages Drew's LL team and his select team.  Talk about the quality time those two spend together around baseball!)  This will of course extend our baseball season, but All-Stars is such a great experience for the kids it's definitely worth it.
• Watching all the neighborhood boys play together whether it's baseball, catching frogs in the pond, or squirt gun wars.  They spend all day outside being kids, just like the good ole days.
• The fact that nothing good is on TV over the summer (well except for my reality faves) and I am forced to watch reruns of Friends and Will and Grace, two shows that I love.
• That I have time to read a book for leisure.  Now that I finished the 50 shades trilogy, I want to read the two other books in The Girls With the Dragon Tattoo series.  I don't spend all my team reading just math related books, although it seems that way sometime.
• Having the time to keep up with my Google Reader.  I actually have had it down to zero these past few days, instead of my standard 1000+
• Having the time to blog regularly!

What are you loving this Friday?  I would love to hear about it.  

Guided Math Book Study-Chapter 3

Three posts in three days on the Guided Math book study.  Fortunately I am now caught up and will be able to share other posts other than just the book study.  I feel like I have been cramming since my book arrived on Monday.  I will be sharing some ideas of how I will be implementing components of Guided Math into my classroom next year in upcoming blog posts.  I also set a goal for myself to open up a store at either Teacher's Notebook or TPT.  Look for that coming soon.  Thanks to Michelle for hosting Chapter 3.  There is a lot of great information being shared so make sure you check it out.

“Using Math Warm-Ups in Guided Math”

Math Stretches to Begin the Day
Math stretching activities will vary according to grade level, mathematical standards being addressed, and students’ needs.  A math stretch must be relatively simple so that it doesn’t take much time, and it must be able to be completed independently by students with a minimal amount of direction by the teacher.  

Math Stretches

• Data Collection and Analysis
• Number of the Day
• What’s Next?
• How Did My Family Use Math Last Night?
• _____ Makes Me Think Of...

Planning Morning Math Stretches

• They are very brief
• They can be completed by students independently
• They prompt students to think mathematically
• They generate mathematical communication

Mathematical Current Events
When current events are included in mathematical instruction, students become aware of the ever-present relationship of mathematics to the world around them.  Mathematics becomes more meaningful and relevant, and students begin to notice how it frequently impacts their lives.  As this occurs, these connections offer teachers valuable opportunities to incorporate real-life mathematical contexts into class investigations and problem-solving activities.

Mathematics-Related Classroom Responsibilities
One way to bring real-life mathematical experiences to students is by involving them in classroom responsibilities that require the use of mathematics.  Turning the responsibility for these tasks over to students gives them practice with daily problem solving and builds a sense of community as students work together.

Calendar Board
The Calendar Board allows teachers to offer consistent, daily learning opportunities covering a range of mathematical concepts.

• gives students support in learning mathematics incrementally as they develop understanding over time
• provides visual models to help students recognize mathematical relationships
• fosters the growth of mathematical language acquisition and promotes student reasoning ability through mathematical conversations
• promotes algebraic thinking
• allows teachers to informally observe their students’ mathematical understanding and then adapt instruction to meet students’ needs.

Planning for Morning Math Warm-ups
Although the amount of time allotted to the Morning math Warm-up is relatively minor, these routine events can have a major impact on the attitudes of students as the participate in the regular mathematics lesson later that day.

Review and Reflect

1. Think about how your students begin their day in your classroom. Is there a mathematical connection? Does it involve more than a worksheet? I teach middle school so I have four separate math classes. My students begin their day by doing a warm-up that is typically on the SMARTBoard while I walk around stamping homework. After we correct the warm-up we check homework. Some days we skip the warm-up depending on what we have going on that day.
2. Why is it important to help students recognize the links between math and their own lives? What are you doing in your classroom to help students make this connection? How can you make the link even stronger? It's important that students realize math is everywhere in their lives and that the skills they learn in math class with help them with real world situations they will encounter. I try to emphasize this to my students all the time. Whenever we learn a new concept I try to link it to a real life experience they can relate to. I think the link could be stronger by doing this on a more regular basis, so it doesn't just happen when we are working on the math curriculum.

Guided Math Book Study-Chapter 2

Thanks to 3rd Grade Gridiron for hosting Chapter 2 of the Guided Math Book Study. Be sure to check the link for links to many bloggers thoughts on Chapter 2.

“Using Guided Math to Create a Classroom Environment of Numeracy”

Foundational Principles of a Guided Math Classroom

• All children can learn mathematics
• A numeracy-rich environment promotes mathematical learning by students
• Learning at its best is a social process
• Learning mathematics is a constructive process
• An organized classroom environment supports the learning process
• Modeling and think-alouds, combined with ample opportunities for guided and independent problem solving and purposeful conversations, create a learning environment in which students’ mathematical understanding grows
• Ultimately, children are responsible for their learning

Building a Classroom Learning Community
Students are not only given opportunities to learn the ‘big” ideas of mathematics; they also participate in a carefully supported climate of inquiry where ideas are generated, expressed, and justified, thus creatively exploring mathematical relationships and constructing meaning.  Teacher’s role shifts to that of model, facilitator, and at times “co-learner”.  Students become active participants in their learning.  Each member is respected and valued.

Communication is at the heart of mathematics-to clarify thinking, to express ideas, to share with others. to justify processes, and to explore relationships.

• organize and consolidate their mathematical thinking through communication
• communicate their mathematical thinking coherently and clearly to peers, teachers, and others
• analyze and evaluate the mathematical thinking and strategies of others
• use the language of mathematics to express mathematical ideas precisely

Students learn the value of being a listener,  reflector, and participant in extending and developing the ideas set forth.

Classroom Arrangement
Goals of Classroom Arrangement:

• establish appropriate spaces for each Guided Math component
• create spaces conducive to the social aspects of learning
• facilitate efficient movement within the classroom
• provide ease of access to materials needed by both students and teachers

Home Area
Students have a home space where they begin and end their days.  This can be desks grouped together or tables.

Large-Group Meeting Area
A part of the room set aside for large group gatherings or meetings (carpeted if possible)
Placement of this area should be near the calendar board.   
There should be an easel with chart paper or a whiteboard that may be used by the teacher and students for mini lessons, modeling, think-alouds, read-alouds, creation of student-created anchor charts, steps in problem solving, or the recording of student conjectures.

Small-group area
Table and chairs which accommodate up to six students.  Teacher should arrange this space to have an unobstructed view of the rest of the class.  The area should be well-equipped with everything that is needed during lessons.  Teacher should have a clipboard or other system for anecdotal notes or record keeping.  Students who join the group are told what materials they will need to bring.

Math Workshop Area
Students working independently may use space throughout the classroom.  Students are taught basic procedures concerning where they may work during the first few weeks of school.  During independent work time, students know how to access materials they need and how to return them when they are finished. Students who are not working directly with the teacher are aware of the behavioral expectations and are working independently to assure that the teacher is uninterrupted.

Organization and Storage of Materials         
An organized classroom environment supports the learning process
The first step in organizing mathematics materials is to sort through them and eliminate any that will not be needed.  They should then be separated  by whether they are for teacher-use only or also for student-use.

A Numeracy Rich Environment
Students learn best through active engagement in authentic opportunities to use and extend their number sense and develop a deep understanding of mathematical concepts.

Student Calendars or Agendas
The use of either individual calendars or agendas helps students connect the daily classroom calendar activities to their own daily lives in meaningful ways.

Manipulatives
The use of manipulatives provides a concrete representation that establishes an image of the knowledge or concepts in students’ minds.  When used appropriately and effectively, manipulatives are one of the most powerful tools in mathematics instruction.

Problems of the Day and Problems of the Week
Teachers use these to encourage students to explore, investigate, and hypothesize-all of which appeal to their inquisitiveness.  Their active engagement in problem solving provides them with opportunities to develop their mathematical skills and understandings.  Problems are posted and then, when solved, surrounded with various solutions represented in multiple ways to show student problem-solving processes.

Word Wall and Vocabulary Display
To engage students in mathematical communication, it is imperative that student learn the language of mathematics.  Focus on vocabulary is essential.  As a new term is introduced, it is added to a Math Word Wall.  Most often, the word, its definition, and a representation of the meaning are displayed.  Word walls are more than passive displays; they are instructional tools.  Students are expected to spell the word-wall words correctly and to use them appropriately when they write in their Math Journals or record their mathematical reasoning.

Math Journals
Daily use of Math Journals ensures that children engage in ongoing written mathematical communication, and is evidence of the importance placed on mathematical reasoning in the classroom environment.

Graphic Organizers
Graphic organizers assist students by providing a way to represent ideas and communicate their mathematical thinking.

Class-made Charts
These anchor charts “make our thinking permanent and visible, and so allow us to make connections from one strategy to another, clarify a point, build on earlier learning, and simply remember a specific lesson.

Review and Reflect

1. Which do you think are the two most important of the Foundational Principles of Guided Math? Why? How does your classroom reflect those principals? I think the most important principle is "Learning mathematics is a constructive process. I have a hard time picking the second one because they all seem so important. I really believe all students can learn mathematics. I try so hard to build the confidence in my math students. It never fails at open house that I will meet a few students (and parents) that claim they are no good at math. I joke around with them that we have no "negative math aura" in our classroom.. I want to prove to struggling students, that with effort and perseverance they can become good at math!
2. Do you think students feel that they are members of a mathematical learning community? If so, how did you establish that feeling of community? If not, what can you do to create it? I really hope so. I do this by building rapport with students and letting them know that, mistakes are just opportunities to learn. Students work in collaborative groups all year long and realize that every person is responsible to being an active participant. I want to student to feel that my classroom is a safe place to learn. I also want them to believe that I believe in them and will do anything in my power to help them learn their math, but ultimately they have to do the work.
3. Look at your classroom through the eyes of a new student. Walking into your class, what would he or she see that would indicate the importance of mathematics? A new student would see that math is valued and important. There is a bookshelf filled with manipulatives and games that students are able to access. My classroom is decorated to be inviting and welcoming. Various posters display important math ideas as well as math humor. I changed my classroom around quite a bit last school year and when my previous students came to visit they were so jealous of how the class looked.

Guided Math Book Study-Chapter 1

Well my book finally arrived from Amazon and I am eagerly reading the first few chapters to get myself caught up. If you are interested in joining this awesome book study please check out the Guided Math Book Study hosted by Primary Inspired. This is a book I have wanted to read since last summer when I had a goal of implementing math learning stations into my 7th grade math classroom for the 2011-2012 school year. I am hoping that other middle school math teachers join this books study to share ideas on how this framework would work in a middle school math classroom. Here is the link for Chapter 1. Please join in!

Traditional, whole class instruction is what most students still encounter in school today.  This type of whole group instruction can mislead students into thinking that there is only one "right" way to do math.  We need to get students to develop a strong conceptual foundation so they are able to move to abstract thinking (and really understand why the algorithms work, not just plug numbers in).

Teachers juggle students that need extra challenge with those who are skill deficient or lacking in conceptual knowledge.  We cannot continue to teach students math with a "one size fits all approach".

The instructional components of this model include:

1. A Classroom Environment of Numeracy  
2. Morning Math Warm-ups and Calendar board Activities  
3. Whole-Class Instruction  
4. Guided Math Instruction with Small Groups of Students
5. Math Workshop
6. Individual Conferences
7. An Ongoing System of Assessment  

Classroom Environment of Numeracy:  (Daily)

• Environments rich in mathematical opportunities
• As students recognize how numbers and problem solving affect their everyday lives, math becomes more meaningful to them
• Children learn best through active engagement in authentic opportunities to use and extend their number sense
• Encourage students to use manipulatives, compute, compare, categorize, question, estimate, solve problems, converse, and write about their thinking processes
• Through mathematical dialogue, students construct the meaning of mathematics, developing enduring understanding of the "big ideas" or concepts as they also develop procedural and computational fluency

What can teachers do to make Guided Math work in their classrooms?

• Foster the strong social aspects that are integral for learning
• Teach behaviors that promote constructive conversation
• Organize the physical aspects of their classroom for immersing students in an environment of numeracy
• Provide classroom procedures for students that allow student participation in all components of the Guided Math framework

Calendar Math and Morning Work:  (Daily)
Morning Math Warm-Ups
Math warm-ups take place in the morning to set the tone for the day.  As students arrive, they have assigned tasks to complete.  During calendar board the class discusses and analyzes their results.  Students may complete a number of the day chart.

Teacher briefly reviews previously covered mathematical skills, previews upcoming skills, provides practice in basic counting or math facts, encourages mental math skills, and engages students in problem-solving activities.

Whole-Class Instruction:  (Your choice)
Whole-class instruction remains an option within the Guided Math Framework, but rather than being limited to the traditional lesson format, a variety of instructional structures are available to teachers.

Whole-class instruction is an excellent method for presenting activating strategies or literature connections at the beginning of lessons, as well as for ongoing review of mastered concepts.

Teachers may choose to present mini lessons or model problem-solving strategies, thinking aloud as they do so.

Small-Group Instruction:  (Your choice)
Teachers use informal or formal assessment to group them according to their proficiencies at a given skill.

Groups are homogeneous, yet fluid, as students’ levels of understanding change.

Teachers work with small groups that are determined by student achievement and need.

Using this small-group instructional model, teachers can vary the amount of time they spend instructing students according the the specific needs of the student.

Offers teachers an efficient way to provide differentiated instruction to meet the needs of diverse learners.

Math  Workshop:  (Your choice)
Students who are not engaged directly with the teacher must have meaningful work to do and know how to follow established and practiced procedures for independent individual or group work.

Students are taught to work independently, and the teacher establishes expectations and routines during the first few weeks of school.

Students learn how to access materials they may need, follow rules for working with manipulatives, handle any questions they may have, and learn what to do if they complete their assigned work.

Workshop tasks might be inquiries or investigations, math-center activities, math games, problems of the week, Math Journal writing, or written practice to maintain previously learned skills.

Conferencing:  (Daily)
One-on-one work is needed to aid the teacher in assessing student understanding of mathematical skills or concepts, to clarify or correct student misunderstandings and errors, or to extend or refine student understanding.

These conferences provide rich information about how to best work with individual students.

This helps teachers identify specific teaching points for individuals and for the class as a whole.

Assessment:  (Daily)
Provides teachers with  timely information about class and individual student needs.

To maximize student learning, students themselves must be involved in assessing their own work based on criteria, rubrics, or exemplars.

Review and Reflect (My thoughts are in red)
Think of the way you currently teach mathematics.

1. What aspects of it are successful? I think that I do a lot of formative assessment to see where my individual students are at. I adapt my instruction based on that information. I think I do a good job of developing conceptual understanding in general, but there are areas I could improve. I think I do a good job of having rich discourse in my class. My students collaborate very well.
2. What aspects of it trouble you? Why? It's always finding that balance of challenging the higher level students, while also working with struggling learners. I definitely see the need for the daily review from calendar math or morning work, but as a middle school teacher I need to find something age appropriate that will serve the same purpose. I always start the year strong with daily warm-ups, but as we get going and are crunched for time, that seems to fall by the wayside.
3. Does your math instruction lead your students to a deep conceptual understanding of the math standards they are learning? If so, what are you doing that contributes to that? If not, how do you think you would like to change your teaching? I am really excited about our new math curriculum, Carnegie Learning. From what I have seen of it, it seem to do a great job of building conceptual understanding. It will be nice to have a curriculum that is common core aligned, instead of having to find materials on our own to teach the common core.