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?

The Standards for Mathematical Practice (K-1): Part 2

Recently I have did professional development for teachers in our district that included a segment on the SMPs. The purpose for discussing the SMPs was for teachers to have conversations with grade-alike colleagues around the Mathematical Practice and think about the connections and application to their specific grade level  content standards. Teachers were divided into 8 groups, one group per mathematical practice, and asked to read and discuss the Mathematical Practice. Then, create a poster that describes and shows the SMP connected to content standards at the various grades levels represented (teachers were encouraged to use words, pictures, illustrations, etc). This would allow a snapshot of a possible continuum of how that mathematical practice grows and develops from grade level to grade level. After groups finished their posters, we did a gallery walk and pairs of teachers walked around to look at, discuss, and ask questions around the other SMPs,

Standards for Mathematical Practice: Kindergarten and 1st Grade

The Kindergarten and 1st grade teachers were able to discuss the SMPs and did a great job illustrating the Mathematical Practices. Here are their posters and some descriptors of what each SMP could look like at this level. 

SMP #1 Make sense of problems and persevere in solving them.

Grade K & 1: SMP#1

• make predictions about what the answer and determine a possible strategy that might help them solve the problem.

• choose a method or strategy to solve to a problem. 

• explain mathematical problems in their own words. 

• explain how their picture, model, or equation represents the problem. 

• draw on classroom experience with variety of concrete objects, models, and pictures so that he or she can adjust his or her strategy, as needed, when solving a problem.

• check their answer using a different method or strategy and ask themselves, "Does this make sense?" 

• listen to classmates to understand the approaches of others. 

SMP#2 Reason abstractly and quantitatively.

Grade K & 1: SMP#2

• make sense of quantities by repetitive experiences with a variety of objects, models, and situations. 

• decontextualize a given situation by representing it symbolically, including acting out a situation, modeling it, drawing a picture, using manipulatives, or other representations. 

• contextualize by referencing the real-world mathematical situation to support, plan, and adjust the strategy and solution.  

• think quantitatively by making meaning of numbers, referencing units, and flexibly using different models and representations. 

SMP#3 Construct viable arguments and critique the reasoning of others.

Grade K & 1: SMP#3

• understand and use previous learning when discussing mathematics. 

• explain his or her thinking, and justify his or her answer. 

• communicated explanations and justifications to others. 

• respond to the arguments of others.

• construct arguments using concrete models such as objects, drawings, diagrams, and actions.

• make hypothesis and conjectures that build on a logical progression of statements from prior learning and experiences while connected it to current learning.  

• analyze situations and can recognize and use counterexamples that demonstrate when a mathematical idea is incorrect or a general statement cannot be made.  

• reason about data through making plausible arguments that take into account the context from which the data arose. 

• compare two ideas or arguments and determine when the thinking is correct or when the  reasoning is flawed. 

• explain the flaw in the mathematically thinking or procedure. 

• listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

SMP#4 Model with mathematics.

Grade K & 1: SMP#4

• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. 

• write simple addition or subtraction equations to describe a situation.

• identify important information required to solve the mathematical real-world problem and use tools as diagrams, tables, graphs, number lines and formulas. 

• interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

SMP#5 Use appropriate tools strategically.

Grade K & 1: SMP#5

• consider the available tools when solving a mathematical problem. These tools might include pencil and paper, base-ten blocks, linker cubes, other objects, ten-frames, counters, a hundreds charts, a number line, a ruler, etc. 

• decide when best to use a tool,  when a tool might be helpful, and recognize when a tool might not be helpful. 

SMP#6 Attend to precision.

• communicate precisely to others by using academic and mathematic vocabulary.

• explain their thinking, their mathematical expressions/sentence and their answers to classmates.

• specify units when measuring and refer to the corresponding quantities in a problem. 

• accurately and efficiently calculate addition and subtraction problems. 

SMP#7 Look for and make use of structure.

• look closely to discern patterns or structures. 

• notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. 

• look at the patterns of making ten, the basic structure of our base-ten system.  

SMP#8 Look for and express regularity in repeated reasoning.

• make connections between various counting experiences to develop a sense of numbers and their sequence, including noticing patterns within a counting sequence.

• recognize what happens to numbers when you add or subtract ten to a number, and developing an understanding of what happens when you add or subtract groups of ten to a number.

• look for and notice patterns when combining numbers.  

• evaluate the reasonableness of their results when solving problems.

Of course, these examples are not an exhaustive list of what each SMP could look like at the Kindergarten and 1st grade levels. 

Standards of Mathematical Practice Resources:

SMP Examples for Elementary Math
SMP Posters for Elementary
Standards for Mathematical Practices Progression through Grade Levels (K-12)

The Standards for Mathematical Practice: Part 1

The SMPs: Part 1

Overview

The Standards for Mathematical Practice (SMP) describe the habits of mind that all K-12 students should be developing as mathematicians. The SMPs were developed from two previous documents - the NCTM Process Standards and mathematical proficiencies describe in the National Research Council’s report Adding it Up.  

The 8 math practice standards are:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Insights from the Teaching Channel Blog

Check out the Teaching Channel Blog where Ben Curran takes time to write a 3 part series to describe specific examples of how some of the math practices can be seen in the classroom.

SMP #1 Make sense of problems and persevere in solving them.

Blog Post #1: The Key to Unlocking the Common Core Standards in Mathematics, he addresses the challenge of teaching students how to persevere in their problem solving. Curran writes:

“In math class, how often do we ask our students to persevere? We all tell our students not to give up, but this practice standard calls for us to go beyond telling to teaching students how to persevere. How often do we teach them to try different approaches, test ideas and revise their thinking?

This won’t happen in one lesson of course. So how do we do it?

One idea is to commit to presenting students with regular mathematical challenges that have multiple steps and that require close reading.”

Continue reading his blog post for ideas to support students in learning to persevere in their problem solving, click here.

SMP #3 Construct viable arguments and critique the reasoning of others

Blog Post #2: 3 Strategies for Bringing Argument and Critique in the Common Core Class, Curran examines the challenges of getting students to communicate through argument and critiquing. Curran provides 3 practical examples of including this SMP in our classrooms: (1) Be wrong more often, (2) Examine student work, and (3) Ask Why?

SMP #4 Modeling with Mathematics.

Blog Post #3: Curran writes regarding the Standards for Mathematical Practice #4 Modeling with Mathematics. His post, 3 Keys to Modeling in Mathematics in the K-8 Classroom, he challenges teachers to give it context, go deeper, and tap into resources.

-----------------------------------------------------------------------------------------

Standards for Mathematical Practice Resources

There are so many resources out there addressing the CCSSM content standards and the SMPs. When searching the vast amount of resources, I try and look for sources that are reputable. If the resource is connected to one of the writers of the Common Core, or by a state or national math organization then it most likely will have resources that truly align to the vision and purpose of the CCSSM.

Progressions

The Institute for Mathematics & Education is publishing learning progression documents for the CCSSM’s various domains and  grade spans. The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

Check out the Progression documents for SMPs:

• The Elaborations of the Standards for Mathematical Practice K-5
• The Elaborations of the STandards for Mathematical Practices 6-8

Illustrative Mathematics

Illustrative Mathematics has many resources, with a main focus on mathematical tasks aligned to the standards. Teachers can search by grade level, domain, and /or standard to locate tasks specific to their needs. The website is constantly being updated and more tasks and commentaries of tasks are being added all of the time.  One of lead writers of the CCSSM, William McCullum, is a founder of the website.

Illustrative Mathematics™ was originally developed at the University of Arizona. It was started in 2011 as an initiative of the Institute for Mathematics & Education funded by the Bill & Melinda Gates Foundation and has operated since 2013 as a 501(c)(3) nonprofit corporation.

Check out:

• Standards for Mathematical Practice section has examples at various grade levels of what that SMP could look like in the classroom.

Inside the Mathematics

Inside the Mathematics has many great resources around the CCSSM - both the content standards and mathematical practices. This initiative grew out of the Noyce Foundation’s Silicon Valley Mathematics Initiative. SVMI is based on high performance expectations, ongoing professional development, examining student work, and improved math instruction. The initiative includes a formative and summative performance assessment system, pedagogical content coaching, and leadership training and networks. Coaches in SVMI learn strategies of re-engagement with students around mathematics assessments, and Public Lessons on re-engagement are featured here.

Check out:

• Common Core Resources: Mathematical Practice Standards and Mentors of Mathematical Practices

By no means is this an exhaustive list of resources. Please take a look at a couple of these links (or all of these links) and learn more about the Standards for Mathematical Practice. Check back for Part 2 where I will share more about the SMPs.