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

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.

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:

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.

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**

- 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!
- 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.
- 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.

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