Introduction and Objectives

Approximately 14 hours

Module 4 Goals

Teachers will be able to plan and conduct a Dot Talk
Teachers will be able to plan and conduct an Introductory Pattern Talk and an Extended Pattern Talk
Teachers will be able to plan and conduct a Connect with Color activity
Teachers will be able to plan and conduct a Connecting Representations activity
Teachers will be able to describe how the 5 routines work together to support the development of number sense and algebra sense
Teachers will be able to describe connections between number sense and algebra sense

Instructional Routines

This module will focus on instructional routines used to help build deep mathematical reasoning in students. Instructional routines emphasize the interconnectedness of mathematics, provide structured ways for students to learn to reason in particular ways, are “thinking specific” vs “problem specific,” and allow teachers to focus on student thinking rather than on what students should be doing. The instructional routines included in this module are:

Dot Talks
Pattern Talks
Connecting Representations
Coloring Connections
Hidden Number Word Problems
Clothesline Math
True/False & Open Number Sentences
Solving Equations on a Number Line

Introduction

This module will focus on using instructional routines to support the development of algebra sense.

Routines, like how and when to sharpen pencils or how to begin a warm-up each day at the start of class, play an important role in the day-to-day functioning in many classrooms. Instructional routines are lesson structures that proceed in a predictable way. Routines are useful in part because once they are learned by students, they allow both the teacher and the student to focus their attention on the instructional content of the activity, rather than needing to focus on how to do the activity. The routines introduced in this section are intended to be used repeatedly over the course of a school year, and become most useful in terms of developing mathematical thinking once students and teachers have learned the steps of the routine and can therefore focus their energy on the mathematical aspects. Each of these routines focuses on supporting the development of number sense and algebra sense, and the routines are designed to compliment one another.

The Five Routines

1. The first routine you will learn is a dot talk. A dot talk is a whole class discussion that starts with students mentally computing the number of "dots" (or other shapes) shown in an image. After silently thinking of one or more ways to calculate the number of dots, selected students then share their solution strategy with the class. As each student verbally shares his or her strategy for determining the total number of dots, the teacher records the student's thinking using symbols, diagrams, and/or pictures.

2. The second routine you will learn is a connect with color activity. Like a dot talk, a connect with color activity also revolves around students finding ways to describe the total number of "dots" in a given image. However, rather than being free to determine the total number of dots in any way they choose (as in a dot talk), in a connect with color activity students are given several expressions and asked to connect those expressions with the given dot image. Since all students show the connections they see between the given expressions and the dot image on a paper handout (versus mentally computing as in a number talk), a connect with color activity provides teachers with more insight into every student's way of thinking. This routine closes with a whole class discussion focused on the ways that students made and showed connections between one or more of the expressions and the image.

3/4. The third and fourth routines you will learn are different versions of a pattern talk. Like a dot talk, a pattern talk is a whole class discussion in which students determine different ways to describe the total number of dots in a given image. However, rather than showing a single dot image as in a dot talk, students are instead shown a growing pattern. In the introductory pattern talk routine, students are asked to focus on describing the way the see the pattern growing and to connect the ways they see the pattern with symbolic expressions. Students extend the pattern only to the next step. In the extended pattern talk routine, students focus on describing and extending the pattern, both visually and with symbols, ultimately determining a general rule that describes their way of seeing the pattern.

5. The final routine you will learn in this module is a connecting representations activity. In this activity, students are given several symbolic patterns and several visual patterns that have been colored in ways that relate to the symbolic patterns. Students work with a partner to make connections between the symbolic and visual patterns. Like the connect with color activity, all students show the connections they see, allowing teachers to gain insight into every student's way of thinking. Also like the connect with color activity, this routine closes with a whole class discussion focused on the ways that students made and showed connections between one or more of the expressions and the image. Note that this routine is adapted from the Connecting Representations routine described in Routines for Reasoning (2016) by Grace Kelemanik, Amy Lucenta, and Susan Janssen Creighton.

Description of Activities in the Module

Each section within this module proceeds in the same manner. First, you will learn about the routine. Next, you will practice the routine with members of your PLC. Practicing the routines will allow you to get a feel for the routine before using it with your students. Finally, you will try the routine with your class and bring back some artifact from the routine for discussion with your PLC. As these routines take time and repeated exposure for both students and teachers to learn, the closing activity of the module asks everyone in the PLC to revisit one of the routines, again trying it with their class and bringing back an artifact for discussion with the group.

Videos of the different routines in action are embedded throughout this module. While the routines will be presented in a very structured way, you will see that the video examples often show a "modified" version of the routine described in each section. This is because the presenters and teachers shown in the videos adapted the routine to fit the particular needs of the group they were working with at the time, as well as their personal teaching styles. However, in all cases, the essential elements of the routine are kept intact. We suggest you look for and discuss these "essential elements" as you work through this module with your PLC. We also suggest trying to follow the structure of each routine as closely as possible as you learn it, and that you discuss with your PLC any adjustments to the routines that you might make as you bring these routines into your classroom.