As discussed earlier, guided math is not defined by following a curriculum; instead, guided math is the framework we put into place that allows us to meet with students for targeted instruction. The four components of guided math are simply the makeup of how to run the math block, and each of these componentsâthe math warm-up, the math mini-lesson, teacher-led small groups with concurrent workstations, and the lesson reflectionâis an essential piece of the guided math block puzzle. Taken together, these integral pieces create a well-rounded mathematician. Although this isnât just another book about the guided math structure, it is vital that we first discuss these four components in depth so that we can address common patterns and pitfalls, as well as the incredible potential of guided math.
For this reason, we will go through these four components, and I will share necessary information on the structure and focus for each. This overview of the components serves to align our understanding of the guided math structure. Once we establish a solid foundation for what the guided math components are, and what they work toward, we will discuss how to amp up those structures with the best practices that form the nextâand most substantialâportion of the book.
The Math Warm-Up
We begin the guided math block with the math warm-up. The math warm-up is a short spiral-review math activity used as a way to keep past or learned concepts fresh. Because our students must absorb a constant and large amount of new math information during their short nine months in our classrooms, we know that students cannot keep all of the new learning at the forefront of their minds. As students continually add additional, rigorous information weekly, older information will naturally become âsoftâ or âfuzzyâ as it is covered over with each new skill or concept. The math warm-up is a powerful way to begin the math learning, yet once students are trained in the process, it can be done in just five to ten minutes.
Because of the amount of new information and the pace teachers must keep to in order to adhere to the current standards framework, the math warm-up allows us a time to remind students about past concepts and skills and then have students practice and apply those concepts daily. This is an integral part of the guided math structure because it allows students to solidify information while gaining automaticity and confidence in the practice and application of older concepts. Math warm-up is also a great time to connect earlier understandings to the new learning with increasing skill as students mathematically mature through the school year.
The procedure we want to use in a math warm-up is to study the strategies and process of finding solutions, rather than just knowing an answer. When we choose a skill or problem to review as a math warm-up, our focus is on how a mathematician processes a problem. Our focus is not simply on devising the answer to a math problem. Instead, finding the correct answer is valuable because it reinforces that our strategies and steps in problem-solving, or process, were accurate. In a math warm-up, students communicate their math understanding through sharing how their mathematical thinking led them to a strategy for solving the problem. We want students to think deeply about something, reason it out loud, and listen to others doing the same. This process intrinsically builds adaptive reasoning in our students.
Whether we find ourselves in a kindergarten classroom or an AP calculus classroom, the math warm-up is a meeting of the math minds. Students are presented with a problem. This problem should be something they have been exposed to but are not currently working on in the main learning objective for that day. It serves as a review to deepen and solidify understanding. Once youâve presented students with the problem, leave time for students to work either mentally or by using a journal, turning and talking to a partner, or making a quick sketch on a personal whiteboard or scratch paper. Then, prompt students to give a signal when they have chosen a strategy and worked through the steps of problem-solving. Once most students have arrived at a strategy, invite students to share their thinking.
Academic language should be expected and used for naming problem types, strategies, methods, and steps. This approach should begin in kindergarten because it allows students to embrace the language of math while empowering them to think of themselves as mathematicians. All methods and answers should be treated with respect, as students are likely to share different strategies for solving the same problem with personal reasoning.
The Math Mini-Lesson
The second component in the guided math structure is the math mini-lesson, which refers to the point in the math block where the teacher shares new learning to the entire class at the same time. Based on curricular scope and sequence or district guidelines, teachers teach the priority standards, or new learning objectives, to their class in a whole-group setting. Because it is done in the whole-group setting and relates closely to the traditional teaching model, most teachers are familiar and competent with the idea of teaching a mini-lesson. In the context of guided math, the difference is in our purpose for and the time spent on this component.
Knowing that classrooms today have students working years above and below grade level, we want to do as much as possible to engage all learners during a whole-group mini-lesson by keeping lesson content on a level playing field. In a traditional whole-group lesson, students tend to be more passive observers and listeners. In guided math, by contrast, we want to focus on introducing new content while provoking all levels of learners to reason and conceptualize together. When I approach content for a mini-lesson, I begin by asking myself, âHow can I present this new skill or concept in a way that builds a strong foundation of understanding while pulling in all learners?â
This broad and inclusive approach sounds unrealistic, but letâs break it down so that itâs easier to realize. Cognitive structure can be a valuable way to frame mini-lessons. Cognitive structure is the schema and mental models that our students have already developed as a result of exposure to previous experiences and learningâessentially, everything we have done up to this point in time. We want to access information that students have a firm understanding of so that we can help students bridge the known and the unknown. This way, they can take in the new information and run with it.
There are three categories of mini-lessons: conceptual, strategy-based, and procedural. Each provides an important purpose to our teaching that will give a clear focus to our delivery. At the same time, each serves to impart important types of math understanding for our students. This purposeful focus takes a regular lesson and creates a dynamic and shorter mini-lesson.
Iâll say a bit more about how to run a fully AMPED mini-lesson in chapter 4. For now, though, the primary consideration is that not every student will be able to understand a mini-lessonâs new information in one sitting of the whole group. For some, it will take many exposures and formats to reinforce new math concepts. Again, though, this is where guided math is an asset, as learning will be strengthened immediately in the small-group setting, our next component. In the mini-lesson, it is vital to mentally note those who may need reinforcement while still staying on track with pacing for the rest of the students. Teachers often struggle with stopping mini-lessons to address the needs of individual students, but this approach simply is not time effective, and it saps the attention of other students. Time is better spent following up during small groups with students who were clearly out of their depth in the mini-lesson. This approach offers close proximity in a more focused setting.
Teacher-Led Small Groups and Workstations
This pair of simultaneous components is what really distinguishes a guided math block from a traditional math blockâand for a good reason! In fact, I find this part of the math block the most invigorating because it is where the most impact happens for students! Teacher-led small groups and workstations are where we implement a dynamic shift in how teachers and students work and move within the room because this component is asymmetrical: at the same time that some students meet with the teacher in small groups, the rest of the students work through learning activities in groups, as partners, or independently.
In a teacher-led small group, the teacher provides the means for students to explore math concepts in a risk-free learning environment, all while targeting their specific instructional needs. The teacher is in close proximity as students work through targeted math concepts. Teachers cultivate differentiated learning as they monitor and adapt to what students need developmentally. These are not long, drawn-out lessons but should preferably involve anywhere from ten to twenty minutes of intensive time with groups of students. Because students are grouped by ability level or by needs around a particular skill, our instruction is hyper-focused, and we can accomplish a great deal in a shorter amount of time.
Concrete, pictorial, and abstract understanding are important considerations in determining how to best cover the learning objective. All three types of learning categories can be present in small-group lessons based on each groupâs needs. In a teacher-led small group, the teacher can address the learning objective specifically for the students present by considering their developmental levels of math understanding.
These math moments are crucial for all levels of learners, and this is worth repeating. In my own experience and with other teachers, the tendency is to target students who are struggling, but all students need, and benefit from, this systematic instruction. As a result, itâs best to structure this component in such a way that you are able to see all students systematically and consistently.
Workstations
Students not involved in a teacher-led small-group lesson should move throughout the room between various workstations. At each station, students work through a set number of activities, either in a self-paced structure or in a rotation system with a set time frame. Vary activities so that some can be done independently, some as partners, and some in groups.
There are many different systems, arrangements, groupings, and choices for how to run this part of the day. Factors that play into this are the ages of students, their ability levels, your classroomâs resources, physical space, and the list goes on. Using the AMPED process outlined in this book will help you choose the best system for maximizing your learning outcomes in light of those factors.
The purpose of math workstations is for students to practice and apply known and newly learned skills and concepts through many formats and modalities. The new learning happens in the math mini-lesson and teacher-led small-group time. Therefore, the workstations allow students to practice and apply what they have already been exposed to. They deepen understanding, practice strategies, gain confidence and automaticity, and increase their cognitive structure. Independent workstations are not where we put new learning; instead, they generally offer a spiraled review of learned skills from the entire class term as we fold in freshly learned concepts from week to week. By filling our workstations with a spiral review of math skills, activities, and games, we cement past learning in the same way the math warm-up does.
I feel it necessary to mention that I do have one workstation, which I call an âApplication Station,â that focuses on newer learning. Although focused on the latest knowledge from the small-group instruction, my Application Station runs a few days behind the small-group lesson. I want students to have an understanding and a mastery of the basics before I send them over to work independently. In this way, the Application Station experience helps provide the best chance for my students to have success while providing a record of learning from which I can take a grade consistently.
As we approach guided math, we have to let go of the âmatchingâ stations. It is instructionally sound to have students working on many different skills within a math block. The purpose of math workstations is to allow students to apply and strengthen what they understand mathematically. To work independently at workstations, students must be familiar with the math topics being addressed. This desire to match our stations to our new learning objective (so that the entire room is doing place value, for instance) stems, I think, from the pressure of having our learning objectives displayed for a pop-in evaluation. If someone walks into our classroom and sees that our new learning objective is measurement, we might feel a sense of pressure that every student should be working on that skill, no matter where they are in their workstations. This effectiveness of this approach to learning new material, however, is simply not grounded in research.
Our purpose in workstations is to deepen content understanding, build fluency and automaticity, and ultimately create a well-rounded math experience for students. As students become proficient in new skills, procedures, and concepts that are taught in mini-lessons and teacher-led small groups, I begin to fold those new skills into stations so students can practice them in all the formats and modalities. Even then, I still want a variety of skills being represented in workstations at all times.
The Lesson Reflection
As our final component in the guided math block, we close out learning with a reflection. This lesson closure can look and feel different from day to day, and variety is key! Regardless of format, though, our focus is on providing ways for students to reflect, grow, and change for the better. After all, each day is an opportunity to refine and improve.
We begin lesson reflection with a whole-group reflection that provides opportunities for students to consider the thinking, learning, and work they have done withi...