Guided Math in Action

Building Each Student's Mathematical Proficiency with Small-Group Instruction

Nicki Newton

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000451863
• Edition: 2
• Topic: Education
• Subtopic: Education General

Learn how to help elementary students build mathematical proficiency with purposeful, standards-based, differentiated, engaging small-group instruction. This best-selling book from Dr. Nicki Newton provides a repertoire of in-depth strategies for conducting effective guided math lessons, scaffolding and managing learning in small groups, and assessing learning. Dr. Newton shows you the framework for guided math lessons and then helps you develop an action plan to get started.

This fully updated second edition features helpful new sections on beliefs, teacher moves, planning, talking and questioning, and kidwatching. It also contains a brand new study guide to help you get the most out of the book and use it with your colleagues. Perfect for teachers, coaches, and supervisors, this popular resource is filled with tools you can use immediately, including anchor charts, schedules, templates, and graphic organizers. With the practical help throughout, you'll be able to implement Tier 1 and 2 lessons easily. This book will help you guide all your students to becoming more competent, flexible, and confident mathematicians!

1

An Introduction

Guided Math

DOI: 10.4324/9780429283253-1

Teaching mathematics is about facilitating mathematical development. This means that you cannot get all learners to the same landmarks at the same time, in the same way, any more than you can get all toddlers to walk at the same time, in the same way! All you can do is provide a rich environment, turn your classroom into a mathematical community, and support the development of each child in the journey toward the horizon.

(Fosnot, 2007, p. 15)

A while ago, I was working with a little boy named Lulu on some math problems. He is up for most mathematical challenges even though he struggles a bit. He is quick and sharp and often gets it right away, and if not, usually after a few tries. He has a foundational understanding but very little automaticity. You know, those kids that know their fives by counting up on their fingers. So, I said to him, “Get ready, Lulu, we are about to do some tricky problems.” He looked up at me, with a broad smile and said, “My middle name is Tricky.” I laughed out loud and said, “Well then, let’s begin.”

I think Guided Math is Tricky too. It has its ins and outs and hard-to-get-to spaces. We have to stick with it, keep trying, and enter it with a sense of adventure. We have to lay it out, have a plan, and follow it. And when the going gets a little rough, we have to persist—much like we teach the children to do in our small guided math groups.

Guided Math itself is a place where we get at the Tricky parts of math. We invite the students to a front row seat, but as a participant, not a spectator. We want them to get in the game, play hard, and learn lots. We invite them to talk, to show their thinking, to question others, and to engage deeply in rich mathematical conversations. We want them to get on friendly terms with numbers, to take risks, and to go from triumph to triumph at that kidney-shaped table. We build mathematicians one problem at time in these small spaces. Let’s take a look now at one of those lessons in action (see Figure 1.1 Figure 1.2).

Figure 1.1 Guided Math Lesson Part 1

Figure 1.2 Concrete Student Activity

A Guided Math Lesson in Action

Welcome to room 307. The students are in the middle of Math Workshop. Mrs. Chi has been working with her math coach to find meaningful ways to engage her third graders. It is the middle of the year and they are working on capacity. She has a diverse class of students; today she has created a heterogenous group of students to work on learning about milliliters and liters.

Mrs. Chi wants students to do, see, and feel measurement rather than just working on a worksheet about measurement or doing an activity with Peter Liter (Gallon Man’s cousin). Mrs. Chi wants her students to play around with measurement in a real way. By having the students do this at the guided math table, she can guide them through the activity as they explore and discover different things about measurement.

Mrs. Chi then dismisses this group and begins to circulate around the room, where the other children are working on differentiated, standards-based center activities. At the first table, there are four children working on subtraction problems with base ten blocks. At the second table, there are six children and they are working in pairs playing a measurement concentration game. They have to match the unit of measure with an item that you would measure that unit in. At the third table, the children are working on problem solving with manipulatives. At the fourth table, the children are working at a “hot topics center” reviewing money. They are playing a money match card game where they match the amount to the coins. At the fifth table, the children are playing a game where they roll dice and round the number to the nearest ten, using the beaded number line as a support if needed.

Mrs. Chi is walking around the room taking anecdotals on three children whom she has chosen to observe for the day. She is getting ready to give the Big Switch Signal, where she will play the xylophone (which is her clean-up signal), so that all the children will quickly and quietly prepare to come to the rug to discuss their math work for the day. Mrs. Chi makes a written note to herself that tomorrow she definitely wants to do a math interview with Daniel about subtracting triple-digit numbers, because she is thinking he might be ready to move to a more challenging group.

This scenario shows the benefits of a guided math group. Mrs. Chi understands the benefits of differentiated, targeted, standards-based practice. In this structure, she has the flexibility to pull small groups and provide instruction at their current level of understanding while the other students stay engaged in meaningful practice in standards-based math centers. This lesson also reinforces the idea that guided math small-group experiences are about the experience. It is an opportunity to learn about math by doing it. It’s not a worksheet, a test, or even just a game or perfunctory activity: “We need to reconceptualize small groups as meeting places for thinking about, doing, reflecting on, and talking about [math]” (Wright & Hoonan, 2019, p. 3).

Summary of the Guided Math Lesson

During this guided math lesson, Mrs. Chi worked with a group of mathematicians to build conceptual understanding. Her focus for the lesson was for the students to get a hands-on feel for measurement. So often, this is taught at a procedural level, with students being told about it rather than doing it. However, oftentimes students only know how to do it but cannot explain what they are doing. So, with this group, she dives right into getting students to experience measurement with milliliters by doing a hands-on activity.

The introduction of her lesson was quick. She went over the vocabulary and the goal of the lesson, and then the students started doing the math. That is what Guided Math is all about: it is about students DOING math. She let the students engage in a guided discovery process where she was there to support their wonderings and activities. They also had to explain their thinking. Then Mrs. Chi concluded with a share period.

Goal of Guided Math

The goal of Guided Math is for students to become confident, competent, and curious mathematicians. Guided Math aims to get students comfortable with numbers and operations and mathematical concepts so that they can independently work with them in new and different contexts independently (see Figure 1.3). Guided Math is also a space to grow student communication so that they can listen to others, consider ideas, reflect, and engage in lively discussions.

Figure 1.3 Benefits of Guided Math

Source: Inspired by Fountas and Pinnell (1996).

In guided math groups, students can work on both developing content knowledge (standards) and “habits of mind” and “ways of doing” math (mathematical practices/processes). Guided Math provides “close encounters” with our students. It allows teachers to look at the work they are doing, listen closely to what they are thinking, and probe deeply into their inner thoughts. The proximity we have with our students in a guided math group provides us with the chance to get up close and personal with our students, their talk, and their work so that we can see, hear, feel, and know what they can do and then what we need to do next (Wright & Hoonan, 2019). Guided math groups allow us to look through the window to see what’s next in students’ learning journeys (see Figure 1.4).

Figure 1.4 Upgrading Guided Math

Source: Inspired by Wright & Hoonan (2019, p. 15).

Key Points

• Goals of Guided Math
• Benefits of Guided Math
• Upgrading Guided Math

Summary

Guided Math provides a powerful opportunity for students to learn math. As Yates reminds us, “Guided [math] is more than a level and a kidney table” (cited in Wright & Hoonan, 2019, p. 24). In small groups, we can meet learners where they are and take them to where they need to go. We get everyone talking within and among themselves. We coach learning. We facilitate thinking. We orchestrate masterful conversations. Everyone is invited to engage as thinking mathematicians. We get to hear how others are doing it and also to hear ourselves make sense of the math that we are doing. We also get immediate feedback so we can stay on track. It is a time for students to make more and more sense of math in its growing complexity at a pace that is appropriate for them. Guided Math is good for all students. It allows everyone to reach their next level of learning and become proficient in the grade-level standards.

Reflection Questions

1. Currently, in your class, do all of your students feel like they can learn math?
2. What do you do with the students who are frustrated?
3. Does everyone participate in mathematical conversations? Who does, how, and under what terms?
4. How do you promote perseverance in your classroom?

2

Beliefs That Frame Guided Math

DOI: 10.4324/9780429283253-2

If we are deliberately growing and changing as professionals, our cutting-edge beliefs are often ahead of our practices. We grow new beliefs and then strive to live into them.

(Wright & Hoonan, 2019, p. 33)

Guided Math is about teaching students to be proficient, engaged, rigorous mathematicians (see Figure 2.1). In order to do this, you must lead small-group lessons that have great launches, supportive structures of coaching, and engaging activities. In a guided math group, students are making meaning of the math together, they are talking about the math, they are reasoning and thinking out loud, they are modeling for one another, they are wrestling with ideas and being vulnerable, and they are constructing mathematical concepts and discovering new things. In guided math groups, students develop math muscles: “the idea of bulking up our skills and strategies so that we are more proficient [mathematicians]” (adapted from a discussion about readers from Wright & Hoonan, 2019).

Figure 2.1 Beliefs

Importance of Meeting Students Where They Are

Guided Math allows you to meet students where they are so you can take them where they need to go. Guided Math allows you to scaffold learning, so that even if you are on page 72 of the math book, you can teach everyone what they need to be ready for the current concept. So, let’s say page 72 is teaching double plus one facts. You already know that some st...