Daily Math Thinking Routines in Action

Distributed Practices Across the Year

Nicki Newton

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351164269
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

Bring math to life with routines that are academically rigorous, standards-based, and engaging! Go beyond circling ABCD on your bell ringers and do nows and get your students reasoning, modeling, and communicating about math every day! In this new book from bestselling author and consultant Dr. Nicki Newton, you'll learn how to develop effective daily routines to improve students' thinking, reasoning, and questioning about math. The book provides a wide variety of rigorous, high-interest routines and explains how to rotate and implement them into your curriculum. Inside, you'll find:

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• Questioning techniques that encourage students to think beyond the "right vs. wrong" continuum

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• Tips for building a math-learning environment that is friendly and supportive of all students

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• Math vocabulary exercises that are meaningful and fun

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• An assortment of innovative daily activities, including "Fraction of the Day, " "Truth or Fib, " "Find and Fix the Error, " "Guess My Number, " "What Doesn't Belong?" and many, many more.

Each chapter offers examples, charts, and tools that you can use immediately. With these resources and the practical advice throughout the book, you'll increase students' ability to understand math on a deeper level while keeping them engaged in their own learning processes.

Part I
Overview

1
Daily Math Thinking Routines in Action

There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.

—(Lappan & Briars, 1995, p. 139)

Classroom Vignette

Mrs. Ching has been working with her fifth graders on fractions. She is doing a Do Not Solve routine.

Mrs. Ching: OK we are going to get started. Remember that you cannot use paper and pencil. You are going to visualize the fraction models in your head and reason about the size.

She presents the following task.

• A. ¼ + ⅕
• B. ⁴⁄₆ + ⁴⁄₆
• C. ½ + ³⁄₆
• D. ⁶⁄₈ + ⁶⁄₄

1. Which expression is less than 1 whole?
2. Which expression is between 1 whole and 1½?
3. Which expression is equal to 1 whole?
4. Which expression is between 1½ and 2?

Mrs. Ching: OK, first take some private think time. [She gives them about 30 seconds.] Now, turn and talk with your shoulder buddy. Discuss Problem 1. Be sure to explain your thinking. [She waits for the children’s discussion to end.] OK who wants to share their thinking?

Tami: I think A is less than 1 whole. How I thought about it was that I know that ¼ is less than half and I know that ⅕ is less than half, so the sum has to be less than 1 whole.

Dan: I thought about the decimals and I know that ¼ is .25 and ⅕ is .2, so that is less than 1 whole.

Mrs. Ching: OK, how did you all think about Problem 2?

Kelly: I looked at the problems and I know that ⁴⁄₆ and ⁴⁄₆ is 1 whole and ²⁄₆, because I thought about the pattern blocks and ³⁄₆ is a half and then 1 more ⅙ … so that is 1 whole and ²⁄₆ … so that is between 1 and 1½.

Luke: Yeah that was what I did too.

Mrs. Ching: OK, what are your thoughts about Problem 3.

Jamal: That was easy because ³⁄₆ equals ½, and ½ and ½ makes a whole.

The students continue the discussion. Mrs. Ching asks them to explain their thinking and, at times, the thinking of others. At the end of the routine, Mrs. Ching asks the students what was easy about the routine and what was tricky. The whole discussion takes about 7 minutes.

What are Daily Math Thinking Routines?

Quick energizers and routines help students to own the math they are doing. They are quick, intentional mini-tasks based on the topics that students are learning. They incorporate the use of concrete and digital manipulatives, drawings, diagrams, and actions. These types of engaging formats help students to get on friendly terms with numbers. Students get to practice and solidify their mathematical understandings. They are “quick tasks” with engaging, standards-based, rigorous brief activities that build mathematical muscle across time.

Daily math energizers and routines help to develop mathematically proficient students. Students build conceptual understanding by playing with ideas and talking about concepts over time. They build procedural fluency and mathematical confidence because they are asked to do a variety of procedures across different mathematical topics. Resnick, Lesgold, and Bill note that it is important for students to “develop trust in their own knowledge” (1990, p. 6). Routines allow students the chance to encounter sticky situations and stuff they must keep on going with – stuff that doesn’t come immediately, stuff they have to work through – and to solve what may at times seem like daunting problems. Routines build strategic competence because they require students to think about a variety of ways to do something and to stick with it until it is accomplished. They require reasoning independently, with partners, and in groups. They build an “I can do that” mathematical disposition.

What is the Difference between an Energizer and a Routine?

An energizer is usually a short type of routine, lasting around 3 to 5 minutes. A regular routine is a bit longer – usually 5 to 10 minutes, sometimes 15. An energizer can be a routine if it is extended into one. The idea is that through distributed practice (doing something over a period of time), students gain the competency that they need. For example, the opening vignette of this chapter is a quick energizer with just a few problems put up on the board, but it could be extended with more problems being put up.

Importance of High-Level, Cognitively Demanding, Purposeful Practice

Daily Math Thinking Routines require that students take part in purposeful practice and become engaged in doing the math. They involve listening, looking, talking, discussing, agreeing, and disagreeing in meaningful ways. They are “thinking rich” mini-tasks and experiences (see below). Students look forward to doing them.

Research Note

I agree with Ritchhart et al, that we must situate "thinking routines within the larger context of our enterprise to develop thoughtful classrooms and nurture students' thinking dispositions" (Ritchhart, Palmer, Church, & Tishman, 2006, p. 2). Thinking routines are part of a bigger picture about developing a thinking culture in a classroom and developing individual thinking mindsets.

Sometimes morning routines are somewhat mindless. Students are just filling in the answers because that is what they are supposed to do. The conversation is quick and superficial, meant to finish a certain amount of problems in a few minutes. Many times schools will use “bell ringer” programs, with students reviewing concepts throughout the year. Much of this work is “fill in the blank,” “finish it and move on” - type of activities. They require a low level of cognitive demand and are “characterized as opportunities for students to demonstrate routine applications of known procedures or to work with a complex assembly of routine subtasks or non-mathematical activities” (Silver, 2010, p. 2).

Daily Math Thinking Routines are high-level, cognitively demanding mathematical structures “through which students collectively as well as individually initiate, explore, discuss, document, and manage their thinking in classrooms” (Ritchhart, 2002, p. 2). They provide “opportunities for students to explain, describe, justify, compare, or assess; to make decisions and choices; to plan and formulate questions; to exhibit creativity; and to work with more t...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Meet the Author
• Acknowledgments
• Foreword
• Introduction
• PART I OVERVIEW
• PART II DAILY MATH THINKING ROUTINES
• PART III ACTION PLANNING