Math Workshop

Math Workshop, K-8

Since the ultimate goal of mathematics instruction is to teach students to solve problems independently, the flexible nature of the Math Workshop Model encourages this through the gradual release of responsibility. The teacher provides students with various levels of scaffolds and gradually helps them take responsibility for concepts. 

 Whole-Class Instruction

The whole-class instruction option provides the maximum teacher support. Teachers may lead students through an activating activity to tap students’ background knowledge and stimulate interest. Through modeling and think-alouds, teachers can guide students through their thinking as they demonstrate mathematical concepts and problem-solving strategies. Whole-class instruction is primarily a teacher-centered activity. Students listen, answer questions, and turn-and-talk with partners when requested. The teacher has minimal opportunity to monitor comprehension or communicate with most of the class.

Many educators today are moving away from the traditional, teacher-directed method of instruction. However, this type of instruction can have a place in today’s classroom, providing it isn’t the only, or primary, method of instruction.

Whole-class instruction requires the least amount of teacher preparation. In its most common form, the teacher introduces the lesson, teaches it as students listen and are questioned, provides a practice activity for students, and either summarizes the lesson or has students summarize it. Traditionally, students remain in their desks, facing the teacher who is at the front of the classroom. Most of us are familiar with this traditional method of teaching from our own days as students. Whole-class instruction remains an option within the Guided Math framework, but rather than being limited to this 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. Using this format, teachers may choose to present mini lessons or model problem-solving strategies, thinking aloud as they do so. Moreover, this component can be used as a time for “math congress” or “math huddle” when students come together following mathematical investigations to share their discoveries (Fosnot and Dolk 2001).

Teaching to the whole class is a very straight-forward instructional method, but requires a remarkable amount of teacher skill to do it well. Although it often appears that discourse during this time is “off the cuff,” to be effective, teachers must juggle what they know of their students and the mathematical concepts on their “horizons” to guide the conversation with meaningful questions. Even a skillful teacher may be unable to reach some students because of students’ lack of attention, boredom, inability to understand the instruction, or their often incorrect confidence that they already know how to do the activity so they don’t need to listen. 

Chapter Four of Guided Math:A Framework for Mathematics Instruction by Laney Sammons, offers suggestions as to how to use this method most effectively and when it should be avoided.

Guided Math Instruction with Small Groups of Students

In the next phase of the gradual release of responsibility model, the students are expected to increase their roles in learning the concepts. When working in small, Guided Math groups, the role of the student increases. The teacher carefully provides instruction appropriate to the needs of the group and provides scaffolding to allow students to move beyond their independent capabilities, increasing student responsibility for learning.

Guided Math instruction is a method of teaching in which teachers assess their students formally or informally, and then group them according to their proficiencies at a given skill. The groups are homogeneous, yet fluid, as individual students’ levels of understanding change. This method of mathematics instruction is analogous to Guided Reading instruction as espoused by Fountas and Pinnell in their books Guided Reading: Good First Teaching for All Children and Guiding Readers and Writers Grades 3–6.

Using Guided Math instruction, teachers are able to work with small groups that are determined specifically by students’ achievement levels and needs. This allows teachers to closely observe student work, monitor student attention, provide strong support for struggling learners, and provide extra challenges for proficient learners.

Using this small-group instructional model, teachers can vary the amount of time they spend instructing students according to the specific needs of those students. For example, when a teacher is introducing a new concept, one group of students may quickly grasp the skill and be able to move on to independent practice. Another group may need significantly more time working directly with the teacher in a small group. Rather than boring those students who have already mastered the concept with continued whole-class instruction, this model allows those students to move on to independent work quickly, freeing teacher time for more intensive instruction with the struggling students.

Not only can the amount of instructional time differ, but so can the content of the material covered and the amount and level of difficulty of the practice work assigned. Guided Math groups offer teachers an efficient way to provide differentiated instruction to meet the needs of diverse learners. 

Chapter Five of Guided Math:A Framework for Mathematics Instruction examines, in greater depth, how to establish and effectively use small groups for Guided Math.

Math Workshop

The final stage of the gradual release of responsibility model enables the students to take complete responsibility for their learning. In Math Workshop, students assume full responsibility in tasks planned by the teacher. They work independently, individually, or in small groups and should not only be very familiar with the procedures and expectations of the teacher, but should also be able to carry out the assigned work with no additional teacher guidance. Students move through these components, gradually assuming more responsibility for their conceptual understanding and problem-solving skills. Since learning is not usually a completely linear process, the level of teacher support required by students varies from day-to-day and lesson-to-lesson. Guided Math offers teachers an instructional framework that encourages students to gradually assume increasing responsibility as they learn, while at the same time providing scaffolding and support when needed.

So, what are the other students doing as the teacher meets with small groups or conferences one-on-one with students? For small group instruction and conferencing to be effective, it should be uninterrupted. 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. These students participate in Math Workshop.

As the school year begins, students are taught how to work independently. 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. Periodically throughout the year, the teacher may need to revisit these expectations.

Because each instructional minute of the day is so important, it is essential that meaningful work is provided for each student. Providing something beyond busy-work also helps prevent discipline problems because students who are engaged in challenging work are less likely to disrupt the class. 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.

  In Chapter Six of Guided Math:A Framework for Mathematics Instruction, these activities are described in more detail with suggestions for establishing procedures and routines.

Individual Conferences

Guided Math offers teachers valuable opportunities to interact with students in small groups and observe communication between students as they work. Sometimes, however, 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.

At any time throughout the day, teachers can conference with individual students. In very much the same way that teachers have used reading and writing conferences, they can meet briefly with students to further those students’ understanding of mathematical concepts. These individual conferences provide rich information about how to best work with individual students. Additionally, the conferences help teachers identify specific teaching points for individuals and for the class as a whole.

In Chapter Seven of Guided Math:A Framework for Mathematics Instruction, individual conferences are covered in greater depth. Additionally, a basic structure for individual conferences is presented and methods for recording anecdotal notes are described.

An Ongoing System of Assessment

How do we know how to group students? How do we determine the needs of the class? How do we determine individual needs?

Ongoing accurate assessment provides teachers with timely information about class and individual student needs. In mathematics instruction, a student’s level of proficiency can vary drastically from concept to concept. This makes assessing mathematical knowledge and thinking skills more challenging than assessing reading ability, where periodic running records and comprehension questions provide a strong indication of reading level.

Teaching Guided Math is a more complex process than following a textbook chapter by chapter and assigning the same problems for all students in the class. With instructional time so valuable, it is important not to waste time teaching what the students already know. It is also important to refrain from moving ahead page by page, if the students are struggling. But again, how do teachers determine the needs of their students?

A balanced system of assessment gives teachers a complete picture of each child’s understanding, not just a single glimpse from a test. Formative and summative assessments, including observations of students’ work, discussions with students, and assessment of their finished products, all give valuable perspectives on their capabilities and needs. In addition, to maximize student learning, students themselves must be involved in assessing their own work based on criteria, rubrics, or exemplars. To truly “leave no child behind,” assessment should be more than just giving grades on tests and on report cards. 

Chapter Eight of Guided Math:A Framework for Mathematics Instruction examines an overview of both individual and class assessments that allow teachers to refine and extend their instruction to meet the needs of each student.