Now What? Next Steps for Implementing Number Talks

So, you’ve heard about Number Talks or maybe your math coach has modeled a Number Talk in your classroom. Now what?

Establish the Routine:                  

• Use hand signals. 
  
•  Record all student solutions without teacher comment.
• Ask students to justify or defend an answer.
•  Provide students with sentence frames to support communication.
• Establish a classroom community that is supportive and helping everyone learn. There is not one best solution or strategy. We all can learn math.

How do I prepare for my next Number Talk?

• Consider the skills within your unit or skills that your students need more support.
•  Create or select one problem or a series of 3-4 problems. Refer to the Number Talks book by Sherry Perrish for a selection of problems. Or refer to the handout “Grades 3 through 5” by Boston Public Schools.
• Prior to the classroom Number Talks, solve each problem using strategies that students will possibly come up with. This prep work is worth the time. Consider using the Planning Guide (from Number Talks Quick Start Guide pages 15-25, Oakland by Unified School District)

Maximizing your Number Talk Experience

• Prior to the Number Talk, make sure you worked out all possible strategies. This will help you decipher students thinking and record the problem using good syntax.
• Start with easier problems. As you introduce the routine or want students to focus on a new strategy, start with problems that have smaller numbers. This will help students focus on the strategy and not get overwhelmed with the higher numbers.
• Connect the Number Talk to the math lesson for that day. This may not always be possible, but can really lead to good conversations and preloading students with strategies for that day’s lessons. 
• After the Number Talk, have students solve a problem, on paper, that is similar to the problem(s) from that day’s Number Talk. This could be an “Exit Ticket” for your Number Talk. 
• After the Number Talks have students use their math journals to answer an extension question.
• Which strategy was most efficient for “the problem”?
•  Pose a potential mistake or misconception and have students write how to fix it.
• Have students write to a friend explaining how to solve a similar problem.
• Scaffold Number Talks during the week to create problem sets that have the same strategy focus, but the numbers get increasingly bigger.

Number Talks & Talk Moves

Number Talks are powerful routines that can be used at any grade level.

What is the purpose of  number talks?

The purpose of  number talks at the beginning of kindergarten is to help students develop number sense. Later in the year, number talks should help students transition from the pictorial representation to a number sentence. (CCGPS Ongoing Standards for Mathematical Practice 1, 2, 3, 6, 7, 8).

What are Number Talks?

• Classroom conversations around purposely crafted computation problems that are solved mentally.
• The problems are designed to elicit specific strategies that focus on number relationships and number theory.
• They provide structured practice for mental math as well as promote the value in using mental math to compute.
• Number talks about the importance of being flexible with numbers and using a variety of strategies for computation.
• Students are given problems in either whole class or small-group settings and are expected to solve them accurately, efficiently, and flexibly.

Key components Number Talks

• Classroom Environment And Community
• Classroom discussion
• Teacher's role
• The Role of mental math 
• Purposeful computation problem

Number Talk Format

• Teacher presents the problem.
• Students figure out the answer on their own (use hand signals).
• Students share answers (all answers are accepted).
• Students defend their answer.
• Class Agrees on the "real" answer for the problem.
• Steps are repeated for more problems in the number string.

Note: During a number talk, the teacher only serves as a recorder and facilitator, not as a teacher


Teacher's role

• Provides a safe environment where each child's thinking is valued.
• Selects groups or strings of problems that allow access all children.
• Select problems intentionally highlight mathematical concepts.
• Focuses on how children got answer.
• Provides wait time.
• Shifts focus from "see what I see" to "what do you do see?"
• Records, clarifies, restates.
• Realizes that if the children do't "get it" then it is the teacher's responsibility to figure out the misconception  or lack of proficiency and to begin instruction at that point.

Questions for the teacher to ask

• Who would like to share their thinking?
• Who would like to defend their answer?
• What strategy did you use?
• How many people solved it the same way as (student)?
• Does anyone have any questions for (student)?
• (student), Can you tell us where you got that five from?
• How did you figure that out?
• What was the first thing your eyes saw, or your brain did?

Focus on the mathematical process process- not answer getting

• Students are asked to defend or justify their answers to prove their thinking.
• Students have a sense of shared authority In determining in determining whether the answer is accurate.
• Teacher is not the ultimate authority.
• Wrong answers are used as opportunities to unearth misconceptions.
• Students investigate their thinking and learn from their mistakes.
• Mistakes play an important role in their learningI and provide opportunities to question and analyze thinking, bring misconceptions to the forefront and solidify understanding.

Resources for Number Talks:

Elementary Math Level

• Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5, update Common Core Connections by Sherry Parrish (Math Solutions Store) *There are resources at the bottom of the page on the Math Solutions Store for the book.
• Number Talks: Building Numerical Reasoning Article by Sherry Perrish, Math Solutions published in NCTM”s Teaching Childrens Mathematics October 2011 (click here for the article)
• Sherry Perrish: Number TalksYouTube Video “Number Talks: Building Numerical Reasoning” by Sherry Parrish, Scholastic (click here)

“Until I began to make some shifts in thinking about how students learn and maybe best practices.  That I avoided writing problems horizontally. Because for the very things you're describing. I justified that if I already had it recorded vertically that they could go into that procedure and get a correct answer. Why put the confusing out there.

Now, I’m going to write just about all of my problems horizontally. I want to push on that place value piece. I want the mis conceptions to come to the forefront so that we can deal with them and have conversations around it.”  

Sherry Parrish, Number Talks: Building Numerical Reasoning on YouTube (Time 11:32 - 12:13)

Other Resources:

1. Locust Grove Elementary School: The Math Coach Locus Grove has resources by grade level - Kindergarten through Grade 5. 
2. Math Perspectives: Math Perspectives has resources, including videos and articles, for Number Talks.                             
3. Pleasanton USD - Math Moodle: The Math Coach has  resources for Number Talks oragnized by grade level. These resources follow Sherry Parrish's structure and format in her book Number Talks.   
4. Billings Public Schools: Resources from Sherry Parrish's book, broken out by grade K-5.
5. Number Strings: The blog Number Strings poses series of 4-5 math problems student do mentally. The basic structure for the classroom discussion is the same as a Number Talk. The string of problems are strategically chosen to support students thinking and possibly highlight a specific strategy students should focus on.
• Personally, I read this one and was impressed with the amount of reflection included in the Number String analysis. The teacher does a great job explaining why the number string was chosen, purpose, skills working, and analyzing the student conversation after completing in class. The teacher even includes how they would change the Number String for next time.
6. Math Talks: A variety of Number Talks can be found here and span several grade levels. Even include Pattern Talks.

Secondary Math Level

1. Number Talk Blog: A High School Math Teacher blogging about her experience using Number Talks
2. Article from Math Perspectives: Number Talks
3. Article from MathWire.com: How can Talk Moves and Mathematical Discussions support Writing?

Number Talks - Thank you Scholastic & YouTube!

I've been talking a lot about Number Talks with teachers. I am more and more convinced that this 5-15 minute routine is a powerful strategy for implementing the Common Core State Standards. 

Here are a few of the ways I think Number Talks are a powerful routine:

                 it focuses on 

mental math, 

a variety of computation strategies, 

justifying your thinking, 

defending an answer, 

proving an answer is incorrect, 

communicating you reasoning, 

listening to others, 

building off other's thinking & reasoning

Today, I listened to Sherry Parrish talk about Number Talks through a video posted on YouTube by Scholastic. What a great way to hear about Number Talks! 

I was reminding of all the ways that it supports the content of the Common Core - it helps students build fluency with computation. And incorporates so many of the habits of mind from the Standards for Mathematical Practice. 

Around 11 minutes into the video Dr. Parrish says:

“Until I began to make some shifts in thinking about how students learn and maybe best practices.  That I avoided writing problems horizontally. Because for the very things you're describing. I justified that if I already had it recorded vertically that they could go into that procedure and get a correct answer. Why put the confusing out there?

Now, I’m going to write just about all of my problems horizontally. I want to push on that place value piece. I want the misconceptions to come to the forefront so that we can deal with them and have conversations around it.”

I connect with this. I remember in my teaching being frustrated when we spent more days than planned on a topic and students still didn't quite get it. And, now what? More practice of the same? Move on? And then I started thinking about how I can make some shifts to my "first instruction". Setting things up nice and neat won't get me the results I want. As Dr. Parrish states, "[I] recorded [it] vertically [so] that they could go into that procedure and get a correct answer." But when we don't allow students to grapple with the misconceptions, we rob them of taking the understanding to a deeper level. The strategic thinking and the flexible thinking will help students build fluency with computation.

If you have read her article Number Talks: Building Numerical Reasoning (you can find it here), yet still not sure what this would look like in your classroom, take a moment to watch the video on YouTube. Its an just over an hour, but it is well worth your time. 

Math Fluency

Does Fluency = Timed Test?

What is fluency?

The word fluency surfaces a variety of emotions. Whether it brings tears of frustration or cries of joy for you, it is necessary to relook at fluency. So, let's take a look at what fluency means, activities & lessons to development fluency, and best-practices for assessing fluency.

Wherever the word fluently appears in a content standard, the word means quickly and accurately. It means more or less the same as when someone is said to be fluent in a foreign language. To be fluent is to flow: Fluent isn’t halting, stumbling, or reversing oneself. A key aspect of fluency in this sense is that it is not something that happens all at once in a single grade but requires attention to student understanding along the way. It is important to ensure that sufficient practice and extra support are provided at each grade to allow all students to meet the standards that call explicitly for fluency.

excerpt from PARCC Model Frameworks version 3.0 pg. 9

The Common Core State Standards identify fluency requirements at each grade level. Here is a chart showing the fluency requirements for K-8:

Traditionally, many of these fluencies have been assessed through timed tests. However, when I read the list and saw grade 3 has a fluency requirement for addition and subtraction within 1,000,  I wasn't  sure my definition was complete: fluency = timed tests. Time to do some research and gain a better, more well-rounded perspective.

Common Core has given us the opportunity to rethink, reflect, and retool ourselves with the best practices for our profession.  Through the process of implementing Common Core Math, I have begun my own exploration on fluency to redefine what it means, how to develop fluency, and how to assess fluency. I don't have all the answers, yet (and probably never will) but I am finding some really great resources. Let me share what I have found...

How can we development fluency with math facts?

Principles and Standards for School Mathematics states: 

“Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands well, including the structure of the base-ten number system, properties of multiplication and division, and number relationships” (p. 152).

Check out the article from NCTM President Linda Gojak from NCTM Summing It Up November 1, 2012

Using a variety of activities creates multiple experiences for students to become efficient and flexible with their math facts. Although you may use typical fluency activities like flash cards and timed-tests, consider a wider variety of activities that support students' mathematical thinking around numbers and their operations. Games and apps can be a fun way to work on basic math skills. There are a lot of games and apps available - depending on your grade level and skill of focus. Check Edutopia's list of apps to develop fluency here. Another way to address math fluency is to use problem solving activities that require students to think about efficient methods and strategies for solving 

• Incorporate a variety of activities that develop fluency: flash cards, timed tests, games, apps, problem solving activities, conceptual development lessons, math centers, etc. 
• Fluency also requires efficiency & flexibility
• Scaffold learning from concrete to semi-concrete to abstract
• Make connections among strategies 
• Have students explain their thinking
• Model your mathematical thinking 

"The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense." Jo Boaler

How can fluency be assessed?

Timed Tests are still a part of fluency. This type of assessment provides us with quick assessment data that we can gather on a regular basis. Timed tests are a clear way to assess a student's speed and accuracy for specific skills.

However, Common Core is bringing mathematics back to a place of balance. Conceptual development works together with drill and practice. Both are necessary. Both support understanding.

Some things to keep in mind:

• Timed tests can cause anxiety for some students
• Consider focusing on growth - students try to improve upon their own score
• Carefully design and plan lessons that support students' sense of a number
• Explicitly make connections within an across the mathematics content of your grade level
• Purposefully plan learning experiences that build to quick recall
• Use problem solving activities to highlight key understandings or common misconceptions
• Consider using a rubric that describes a more complete picture of fluency - a combination of evidence including timed tests, observations, and other assessments. 

Resources for Developing Fluency

Articles: 

Fluency Without Fear:  Research Evidence in the Best Ways to Learn Math Facts and Appendix A
By Jo Boaler, Professor of Mathematics Education, co-founder youcubed
with the help of Cathy Williams, co-founder you cubed & AmandaConfer, Standford University
October 24th, 2014 on youcubed.org

Fluency: Simply Fast and Accurate? I Think Not! By NCTM President Linda M. Gojak. NCTM Summing Up, November 1, 2012

Towards Meaning-Driven Math Fluency  by Dr. Jonathan Thomas, Kentucky Center for Mathematics Faculty Associate. Kentucky Center for Mathematics. 

Resources for Elementary Teachers:

Mathematically Minded & The Recovering Traditionalist
Check out the free downloads for number sense activities, number paths, subitizing, place value cards, and rekenreks activities.

Math Wire: Basic Facts Fluency
Check out the links to resources for a variety of activities to support fluency.

Fact Fluency for Addition & Subtraction, Multiplication

Howard County Public Schools - Fluency Assessment Resources
Includes Learning Targets, rubrics, assessment tasks, and scoring/recording sheets.

Grade 2: Assessing Fluency 2.OA.2

Grade 4: Assessing Fluency: 4.NBT.4

Resources for Primary Teachers:

Math Rack
Math Facts Pro
Math Wire
Web Mad Minute