Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

Teaching and Learning. An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.

The teaching of mathematics is complex. It requires teachers to have a deep understanding of the mathematical content that they are expected to teach and a clear view of how student learning of that mathematics develops and progresses across grades. It also calls for teachers to be skilled at using instructional practices that are effective in developing mathematics learning for all students. e eight Mathematics Teaching Practices (see g. 1) describe the essential teaching skills derived from the research-based learning principles, as well as other knowledge of mathematics teaching that has emerged over the last two decades.

An excellent mathematics program requires that all students have access to a high-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential.

Equitable access means high expectations, adequate time, consistent opportunities to learn, and strong support that enable students to be mathematically successful. Instead of one-size- ts-all practices and the differential expectations for students who are placed in different academic tracks, equitable access means accommodating differences to meet a common goal of high levels of learning by all students.

An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.

A robust curriculum is more than a collection of activities; instead, it is a coherent sequencing of core mathematical ideas that are well articulated across the grades. Such an effective curriculum incorporates problems in contexts from everyday life and other subjects whenever possible. These tasks engage students and generate interest and curiosity in the topics under investigation.

An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.

Available tools and technology help teachers and students visualize and concretize mathematics abstractions, and when these resources are used appropriately, they support effective teaching and meaningful learning.

An excellent mathematics program ensures that assessment is an integral part of instruction, provides evidence of proficiency with important mathematics content and practices, includes a variety of strategies and data sources, and informs feedback to students, instructional decisions, and program improvement.

Effective assessment supports and enhances the learning of important mathematics by furnishing useful formative and summative information to both teachers and students. Productive mathematics assessment is a process that is coherently aligned with learning goals and makes deliberate use of the data gathered as evidence of learning and provides guidance for next instructional steps and programmatic decision making. Students learn to assess and recognize high quality in their own work.

In an excellent mathematics program, educators hold themselves and their colleagues accountable for the mathematical success of every student and for personal and collective professional growth toward effective teaching and learning of mathematics.

Effective schools communicate a tangible sense of the professional imperative to grow personally and collectively and to hold one another accountable for this growth. Professionals who are responsible for students’ mathematics learning are never satisfied with their accomplishments and are always working to increase the impact that they have on their students’ mathematics learning. Moreover, they cultivate and support a culture of professional collaboration and continual improvement that is driven by an abiding sense of interdependence and collective responsibility.

Although principles provide guidance and structure, actions determine impact. Principles to Actions argues that ensuring mathematical success for all will take teachers who, among other actions—

• plan and implement effective instruction as described by the Mathematics Teaching Practices;
• develop socially, emotionally, and academically safe environments for mathematics teaching and learning—environments in which students feel secure and con dent in engaging with one another and with teachers;
• evaluate curricular materials and resources to determine the extent to which these materials align with the standards, ensure coherent development of topics within and across grades, promote the mathematical practices, and support e ective instruction that implements the Mathematics Teaching Practices;
• incorporate mathematical tools and technology as an everyday part of the mathematics classroom, recognizing that students should experience “mathematical action technologies” and physical or virtual manipulatives to explore important mathematics;
• provide students with descriptive, accurate, and timely feedback on assessments, including strengths, weaknesses, and next steps for progress toward the learning targets;
• work collaboratively with colleagues to plan instruction, solve common challenges, and provide mutual support as they take collective responsibility for student learning.

1. What Math Workshop model will work best for you?
2. How can you create a management board to help students identify where they will work during Math Workshop?

The power of the Guided Math framework is in the flexibility it provides teachers. Your first decision will be how you want to structure your Math Workshop. There is no right model! You have to decide what will work for you. There are models like the GUIDE or BUILD protocols. There is also the menu approach–students have a weekly list of must dos and may dos. They could choose the order that they wanted to work on the tasks. This can solve the problem of students finishing too quickly or not ever finishing. Make sure my must dos were doable for all students and the I had enough may dos to keep all students engaged. Having a structure in place can make planning easier.

Examples of Models

The GUIDE model features five workstations, each with a different focus. Students visit only one workstation each day, so each workstation must include enough tasks to keep students engaged. As with the menu model previously discussed, some tasks might be mandatory, while others are optional. Tasks don’t need to be changed each week, which makes your life a little easier. If you need to skip a Math Workshop day, the rotation just rolls over to the next day.

I realize I might be showing a little bias for the GUIDE model, but the beauty of Guided Math is that you can use the model that feels right for you!

BUILD is not a curriculum, it is a management piece for Math Stations. Each letter stands for something different and you choose activities/assignments for students to complete. The BEST thing about BUILD is that you can tweak it to fit your teaching and your classroom.

Buddy Games This is where I put games that my kiddos have practice practice practiced multiple times. They know the expectations: whisper voice, play the right way, play the whole time. My school uses Investigations as our math curriculum, so this goes perfectly b/c the basis of the curriculum is them playing games to master math skills.

Using Manipulatives This is where I put manipulatives for exploration. For the first few weeks of school I have had pattern blocks and workmats. You could also put play money, Judy Clocks, unifix cubes.

Independent Reading/Work The title on this one pretty much explains it. My kiddos read math books during this time- and amazingly they really like it. Seemingly way more than Read to Self during Literacy stations. This is where you could also have them working on something pencil and paper if you need them to.

Learning About Numbers For this one I have hundreds chart games, matching, number scrolls, student made books about numbers.

Doing Math This is where I put a game when we first learn it. After they have played it on their own a good amount of times and I have made sure that the majority of the class knows how to play- then I move it to Buddy Games.

Once you decide on the model you will use, you need to think of how you will communicate the structure to your students. What type of management board will you use? To maximize your instructional time, it’s important that students know quickly exactly what they are doing once Math Workshop starts. You have lots of options for management boards–just make it each for both you and the students.

The arrangement of your classroom significantly impacts the Math Workshop learning environment. A well-arranged room enhances learning and positively affects student behavior (Diller 2016).

Take time to consider your room arrangement. Remember, your arrangement is not set in stone. Continually reflect and assess how well it works during Math Workshop. Do not hesitate to rearrange your classroom based on your experiences as students work independently.

Keep these ideas in mind:

• Designate workstation area that can accommodate groups of different sizes. As you decide where workstations will be located, you may match tasks to spaces that best accommodate the grouping required.
• Establish specific areas for different kinds of work in which students will be engaged- whether it be independent Math Workstation tasks, games or small group lessons. Some spaces are more conducive to specific tasks. For example a game might be easily played on a carpeted area. Or a group of students creating a poster may need a large table and supplies. Or a math literature workstation might be located near the class library. Additionally, plan to have an area for a student that might need individual instruction/time to work independently.
• Create an area where you can teach small group lessons without being interrupted by the work of other students. This area should include space for storing the lesson materials. The small-group lesson are should also have ample space for students to work with manipulatives, yet be small enough that you may closely observe their work and listen to their math talk. Make sure that you have a clear view of the classroom and all workstations.
• Think about how to arrange your classroom to accommodate varying levels of noise. Some workstation tasks encourage more students interaction than others. Consider placing those workstations in areas where interruptions are less likely to occur. Additionally provide quiet areas for students who work best in calmer settings or for tasks that require quiet concentration
• Make math materials readily available to students. Some materials that students need for tasks will be stowed in workstation bins. At time, though, students may require additional material (manipulatives, paper, technology). These items should be stored so that students may easily access them as they work.
• Consider traffic flow of students during Math Workshop. Arrange you classroom so that traffic moves smoothly during transitions and as students are engaged in workstation tasks. Keep high-traffic area open and clear. Classroom furniture and other objects that are places to closely together may make it difficult for students and you to move around.
• Arrange your classroom so that it aligns with your tolerance of student activity. Some teachers are more comfortable with purposeful student movement than others. Take that into consideration as you plan where materials will be stored and where groups will work.

Use the furniture that you have creatively. Ask: Can I use this piece of furniture for more than one purpose? Can an area rug be a workspace? Can dry-erase boards be hung on the back of low bookcases for a workstations? Think outside the box to make the most of your classroom furnishing and resources.

Consult with fellow teachers to see what has worked well for them. As you plan try to eliminate clutter. A cluttered classroom often exacerbates behavior problems (Diller 2016).

Below are 2 samples of room arrangements. One is with a large group area and one without.

SPACE: TO make your mathematics resources more accessible and to rid your classroom of those you will never use, follow organization guru Julie Morgenstern's process SPACE.

Sort your math instructional items. Identify what is important for instruction based on curriculum. Categorize them by domain (Numerical Representation and Relationships, Computations and Algebraic Relationships, Geometry and Measurement and Data Analysis and Personal Financial Literacy.

Purge the materials that are deemed not important to instructions. A word of caution - review the manipulative list from the curriculum management system. These items might not be utilized to the fullest capacity.

Assign a home for your mathematics resources. Take into consideration how frequently they will be used. Also consider whether students will need ready access to them. Locate area to store them in your classroom where they are available when needed.

Containerize and store like items together to make it easy to find what you need when you need it. Use containers that are appropriately sized for the items and the storing area. Also make sure to label everything. Consider where students are and are the containers easily accessible during activities.

Equalize by continuing to assess and revise your storage system as needed with materials shared out in their appropriate places. Once your storage system is established, consistently maintain it. If you return materials to their "home" each day, it is much easier to avoid a build up of clutter. Below is an example of workshop location

A tool for designing your space that you might use is Classroom Architect

Principles of a Learning Community

The structure of guided instruction propels a Learning Community. Teach learners the value of strong work habits and instill in them a sense of being an important member of the learning community. Rely on these principles adapted from Guided Reading to establish a feeling of community among your students during Math Workshop. All members of a Math Workshop will:

• Assume responsibility for their own learning and for helping others learn
• efficiently use their time to complete assigned math takss
• monitor their behavior to maximize their own learning and that of their fellow students; and
• keep workspaces and materials in order to support a productive Math Workshop for all members of the community

Management Board

A well-planned workstation management board makes Math Workshop flow smoothly. By consulting the board, students know exactly where they will work during Math Workshop, thus eliminating the need for the teacher to give assignments orally during limited workshop time. These can be bulletin boards, magnetic boards, potable foam boards. Make it work for you and your students.