PBL Icon

Project-based Learning

Creativity Icon

Creativity

DS Icon

Digital Storytelling

21st Century Icon

21st Century Classrooms

Literacy Icon

Literacy

ELA Icon

Language Acquisition

STEM Icon

STEM/STEAM

Teaching Icon

Teaching and Learning

Language Arts

Math

Science

Social Studies

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Professional Learning Icon

Professional Learning

Rubric Maker Icon

Rubric Maker

Graphic Organizer Maker Icon

Graphic Organizer Maker

PBL Icon

Project-based Learning

Creativity Icon

Creativity

DS Icon

Digital Storytelling

21st Century Icon

21st Century Classrooms

Literacy Icon

Literacy

ELA Icon

English Language Acquisition

STEM Icon

STEM/STEAM

Teaching Icon

Teaching and Learning

By Subject

Language Arts Icon

Language Arts

Math Icon

Math

Science Icon

Science

Social Studies Icon

Social Studies

By Grade Level

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Professional Learning Icon

Professional Learning

Pics4Learning Icon

Pics4Learning

Rubric Maker Icon

Rubric Maker

Graphic Organizer Icon

Graphic Organizer Maker

Beyond Understanding in Math

Promote success in math with the Common Core Standards for Mathematical Practice

description

The Common Core State Standards for Mathematics begin with eight Standards for Mathematical Practice. Unlike more common content standards, these standards describe behaviors, expertise, and habits of mind necessary for successful work with math. Great math instruction pairs content standards with these standards of practice to ensure student success with math.

The Standards for Mathematical Practice are based on “processes and proficiencies” described by the National Council of Teachers of Mathematics in their process standards and the Strands of Proficiency described in the National Research Council’s Adding It Up report.

In short, the Standards for Mathematical Practice describe students who:

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique 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.

These standards do not replace, or supersede, content standards. Without understanding of math concepts like number, value, function, and so on, there cannot be math proficiency! That being said, they are the place the Common Core State Standards for math begin. Without the productive dispositions the standards describe, student success with math in “the real world” beyond memorizing or completing formulas will be limited.

The CCSS for Mathematical Practice provide specific targets to help guide us as we develop math instruction and determine our classroom learning environment. Here are examples of what successful student math practice can look like and ways educators can build mathematics expertise in the classroom.

1. Make sense of problems and persevere in solving them

Problem solving is not simply the ability to solve an equation. Computation or application of known or expected formulas is not the same as “engaging in a task for which the solution method is NOT known in advance.” (NCTM Standards for School Mathematics, p.52)

When practicing this standard, students demonstrate:

Effective problem solvers evaluate progress, reflect, and adjust what they are doing. Teachers can foster this by creating a classroom culture where it’s okay to ask questions, take risks, and make mistakes; an environment where curiosity and persistence are rewarded and reflection is promoted. They can also explicitly teach students problem-solving skills such as looking for patterns, listing possibilities, organizing ideas, finding similar or equivalent problems or cases, and working backward.

2. Reason abstractly and quantitatively

Reasoning involves making sense of quantities and how they relate to each other, as well as the capacity to follow a rational set of steps when approaching or solving a problem. Young students may need to use physical objects, while older students can abstract and use symbols, but both groups of students are capable of making logical distinctions and decisions.

Advertisement

When practicing this standard, students demonstrate:

To reason effectively, students must follow a rational, systematic series of steps based on sound mathematical procedures. Teachers can foster this by creating a classroom culture where students are rewarded for discovery, where it’s okay to play and experiment, to guess and try along the way. They can also explicitly teach students reasoning skills such as looking for patterns, rules, and generalities, considering alternatives, and using and manipulating symbols to represent a problem.

3. Construct viable arguments and critique reasoning of others

To reason effectively students, must discover the argument (rule) then analyze and evaluate it. As they make their own arguments and evaluate the arguments of others, they apply analytical skills.

When practicing this standard, students demonstrate:

Justifying and explaining ideas improves students' reasoning skills and their conceptual understanding. Teachers can foster this by creating a classroom culture that provides interesting problems, engages in comparing, and values listening, multiple perspectives, and thinking out loud. They can also explicitly teach students analytical skills such as formulating good questions, breaking into components, seeing logic, justifying conclusions, comparing, and evaluating.

4. Model with mathematics

When students create math models, they apply what they know about math to solve problems. Effective modeling with mathematics isn’t just creating graphs and representing data. It’s the ability to represent problems in different ways.

When practicing this standard, students demonstrate:

Students must be able to use math to make sense of the world around them and solve problems they find there. Teachers can foster this by creating a classroom culture that provides interesting problems, engages in comparing, and values listening, multiple perspectives, and thinking out loud. They can also explicitly teach students analytical skills such as formulating good questions, breaking into components, seeing logic, justifying conclusions, comparing, and evaluating.

5. Use appropriate tools strategically

Students should be familiar with a variety of age-appropriate tools and choose the best one for the task at hand. Tools can be as simple as pencil and paper or as complex as today’s powerful graphing calculators. Concrete models and symbolic representations are also mathematical tools.

When practicing this standard, students demonstrate:

While they obviously need to teach students how to use tools such as calculators, protractors, and spreadsheets, teachers must also give students opportunities to make decisions about which tool to use, even if this the lesson learned is that the tool students chose wasn’t the best choice.

6. Attend to precision

Students should be concerned with precise language when communicating and accuracy when working. Building vocabulary and using precise language leads to more effective communication and is essential to mathematical communication.

When practicing this standard, students demonstrate:

Teachers can foster this by creating a classroom culture in which quality is highly prized. Rewarding students when they take their time to do work carefully and encouraging them to check their work also results in improved accuracy and lets them know that you value effort.

7. Look for and make use of structure

Students use patterns and structure to help them break down complex problems into smaller, manageable components.

When practicing this standard, students demonstrate:

Teachers can foster this by creating a classroom culture that engages students with complex questions and problems, encourages play with patterns and models, and rewards testing and trying. They can help students cope with complex problems by teaching them to see structure and patterns, to break things down into component parts, and to take a different perspective.

8. Look for and express regularity in repeated reasoning

Students are able to see repetition and use that understanding to define mathematical rules, make predictions, and develop formulas.

When practicing this standard, students demonstrate:

Teachers can foster this by creating a classroom culture that promotes comparisons, is filled with music, and egages students with sequencing and creating patterns. Teachers can help students find and express repetition by asking them to describe what is happening, identify similarities and differences, make predictions based on their observations of patterns, and combine all of this knowledge into rules and formulas.

It's the process!

The Common Core Standards for Mathematical Practice don’t so much describe “what” to teach as “how” to teach. Modeling, questioning, routines, discussions, and task selection help create an environment that gives students an opportunity to practice and develop these behaviors, skills, and habits of mind. All of these standards can be practiced in a project-based learning environment.

These standards can be addressed throughout the curriculum and aren’t limited to how we instruct in math. I would even argue that these standards provide an obvious entry point to pushing math across the curriculum and should be part of an intentional focus in all areas of learning.

Melinda Kolk

by Melinda Kolk

Melinda Kolk (@melindak) is the Editor of Creative Educator and the author of Teaching with Clay Animation. She has been helping educators implement project-based learning and creative technologies like clay animation into classroom teaching and learning for the past 15 years.

Advertisement

Using Creative Tech in Elementary Math

New approaches to math improve fluency through the use of creative technology tools.

Get this FREE guide that includes:

  • Articles and Project Ideas
  • Lesson Plans
  • Sample Student Work
Advertisement
Wixie
Advertisement
Engage digital learners.

Four ways to engage digital learners

Wixie on a stack of Chromebooks
Getting Chromebooks?
Stay creative with Wixie!
Advertisement
Creative Personalized Learning

Creative personalized learning: combining voice and choice

Advertisement
Creativity tools and math

Making in Math

Dream Room Design

Lesson: Dream Room Design

More sites to help you find success in your classroom

Rubric Maker

Rubric Maker

Create custom rubrics for your classroom.

Graphic Organizer Maker

Graphic Organizer Maker

Create custom graphic organizers for your classroom.

Building Literacy Guide

Pics4Learning

A curated, copyright-friendly image library that is safe and free for education.

Topics

Creativity

Digital Storytelling

21st Century Classrooms

Project-based Learning

Teaching and Learning

Curriculum

Literacy

English Language Aquisition

STEM

Lessons

Language Arts

Math

Science

Social Studies

Creative Educator

Professional Learning

About Us

Tech4Learning