Guided Math
In looking for ways to help teachers in the North American Division, our committee examined a textbook written by Laney Sammons entitled, Guided Math: A Framework for Mathematics Instruction. It presents a “new” way of teaching math that supports both single and multi-grade teaching practices. Here we share some of the highlights of that text, but we strongly recommend reading it in its entirety.
A Numeracy Rich Classroom
A numeracy rich classroom walks hand-in-hand with a literacy rich classroom. This is one way in which we make mathematics part of our students’ everyday lives. A numeracy rich classroom includes:
- A supportive classroom learning environment.
- A classroom organized for productive math work.
- A numeracy-rich environment.
A supportive classroom environment is necessary to all subject areas. Organizing your classroom for math productivity is simply a matter of making sure that all materials are available for students to use with ease. It also includes making sure that there is space provided for work in varying sizes of groups and individual work. Much like a literacyrich environment, a numeracy rich environment means having math words and concepts presented throughout the classroom for reference and use by students.
Math Warm-Up
Math Warm-ups can be used wherever they fit in your day to start minds moving and keep them moving in mathematical directions. Warm-ups may include:
Math stretches are short, student-led activities that review concepts. These may include gathering and graphing classroom data, examining a number of the day, or even discussing how families used math at home last night. The purpose is to get students recognizing where math plays a part in their life.
Using the morning newspaper or news video clips with mathematical significance, teachers can draw attention to math as well. Political polls, stock market reports, sports statistics, etc. all utilize mathematical references.
- Classroom Responsibilities
Many teachers use student helpers to complete tasks in the morning or clean things up in the afternoon. Some examples of this are taking attendance, collecting lunch money, feeding classroom pets, watering classroom plants, etc. These jobs can be used to teach fractions, percentages, decimals, etc.
For many teachers, the Calendar Board is habitual by now. On the calendar board, teachers and students review the date, counting and math fact skills, time, temperature, money, etc.
Guided Math with Large Groups
Whole class instruction allows the teacher to introduce new concepts in a brief way. Teachers can use large group instruction for:
- Presenting mini-lessons which include:
Connection – This element connects the current concept with a lesson taught before, something in the students’ work, or something in the students’ experience.
Teaching Point – The new teaching point should be presented verbally and demonstrated or modeled.
Active Engagement – This is the students’ opportunity to try out their skill and investigate its possibilities. This can be done with manipulatives, pen and paper, or even orally.
Link to Ongoing Student Work – Students then turn to their own work and apply the teaching point.
As in other content areas, an activating strategy can be used to get students focused on the topic, especially when new concepts are being introduced. These strategies include KWL charts, anticipation guides, word splashes or brain storms, etc.
- Reading Aloud Mathematic Related Literature
Students love a good story. Math literature can often inspire students and motivate them. Teachers can use think-alouds to relate mathematical concepts within the story.
- Setting the Stage for Math Workshop
Whole-group instruction time is the time to explain and practice procedures, or give specific directions for the workshop time. Math Huddle
A “Math Huddle” or math meeting is an opportunity for students to gather to discuss and learn from each other. They can talk about the discoveries, solutions, and learning that has occurred during math exploration.
- Practice and Review Sessions
Practice and review sessions work well in large group settings utilizing pencil and paper tasks, games, music, technology etc., anything that allows the group to be refreshed and reminded of the concepts that have been taught. This allows students to prepare for tests and solidify their understanding of what they have learned.
A variety of assessment styles and formats can be used for both formative and summative purposes in a large group setting.
Guided Math in Small Groups
The overarching goal for our students is a deeper understanding of math leading to an understanding of concepts, rather than a simple mastery of procedures. Unfortunately, time constraints can sometimes get in the way of this. Using Guided Math with small groups helps to solve some of the time constraint issues. Small group instruction can be useful for:
- Differentiated instruction
Even within a single-grade and similar age groupings, there can be a wide variety in ability and understanding. Too often this leaves a teacher targeting the middle range students and those with lower or higher abilities get left out. By keeping groupings dynamic and tailoring small group instruction to meet the needs of the various groups, teachers can reach all students at their level of need.
- Teaching Mathematical “Critical Learning Areas”
A “Critical Learning Area” is an integral Core Curriculum Item which needs to be mastered at a particular grade level such as 2-digit addition in the second grade, or multiplication in third grade. Teaching a small group of students at a time allows teachers to closely monitor understanding of these concepts throughout the instructional process.
- Teaching with Manipulatives
Manipulatives allow students to better visualize the process they are learning. By working with manipulatives within a small group rather than a whole-class setting, teachers can monitor their use and discern if students are grasping the process.
By observing the work with manipulatives or written tasks and asking specific questions of students, teachers are able to quickly assess understanding and re-direct misunderstandings before they have been practiced repeatedly.
- Supporting Mathematics Process Standards
The eight standards for mathematical practice are intended to help students learn the processes of mathematics. Small group work is a good format in which to have students practice the skills defined by these standards.
Teaching Guided Lessons in Small Groups
Teachers generally follow a 6 step format for teaching a small math group.
- Teach a mini-lesson to introduce the skill.
- Provide an activity or task that will help build clear understanding. This will include clear instructions and criteria.
- Encourage students to use a variety of strategies in solving the problem.
- Provide scaffolding as necessary to help students move to the next level.
- Allow a variety of opportunities for students to have math talk and interaction.
- Give students specific feedback and encourage them to review and selfassess. Math Workshop
Math workshop is basically an exploratory time for students to work on problems. This is particularly helpful when teachers are working with a variety of grades, or with a small group. Like writing and reading workshops, math workshop is a time for students to develop skills and put them into practice. Math workshop may include:
- Reviewing concepts that have already been learned
- Practicing for mastery of math facts
- Using math games for reinforcement
- Solving problems
- Investigating math concepts
- Writing in their math journals
- Working with technology tools
- Completing work from small-group instruction
Most teachers have used games, computer software, flash cards, etc. for math review and facts practice. Math workshop is the perfect time for these, as well as mad minutes, and spiral review – anything that students can do to practice math that requires minimal supervision.
In their Math journals, students collect math learning. They begin with any new vocabulary words and write their meaning, along with a definition, an example and a non-example that will help them to remember the concepts learned.
Real-world problems may be presented to students during this time, letting them explore to find the answer. This might involve some measurement, research, use of math journals, etc. The problem might be solved individually or with collaboration. The key to making sure that Math Workshop goes smoothly is that you establish and practice routines, keep materials organized, and review as needed. Each task for Math workshop should be introduced and explained in a way that students will be able to work on them independently.
Conferences
Much like reading and writing conferences, math conferences give teachers a chance to spend a short, one-on-one time with students. This allows teachers to find out what a student really understands, decide what a student needs, design lessons that meet students needs and then link this to future learning. It is important to keep records of student conferences, even if they are just simple notes on a sticky pad, to help in guiding future instruction and learning practices.
Assessment
Assessment is key in Guided Math. It is used to guide teaching and evaluate progress. It is necessary on both a formal and informal level. The more teachers know about their students’ learning, the better they can meet their needs.
Criterion referenced checklists and rubrics can be used to evaluate student progress toward standards. These can be used to provide timely and descriptive feedback that can help students move toward their goals.
Ultimately, all instruction and assessment should work toward the goal of helping students develop a deep and lasting understanding of mathematics.
Summary
We believe that by the use of these strategies, teachers will be able to use the Go Math! and Big Ideas Math series to their fullest potential.
You can order the book at http://estore.seppub.com/estore/product/50534.
Works Cited: Sammons, L. 2010. Guided Math. A Framework for Mathematics Instruction. Huntington Beach, CA: Shell Education.
For more on the MATH K-8 program, visit our friends at Houghton Mifflin Harcourt.
