Mathematical Process Standards

NCTM Process Standards
What are you doing?

PSSM K-12 Process Standards (page 52)
Introduction to the
Process Standards
The 5 mathematical processes are:
Problem Solving – finding your own way towards a new solution or understanding
Reasoning and Proof –seeing and establishing relationships among ideas and facts
Communication –sharing or recording your understanding
Connection –relating math ideas to each other and to phenomena outside mathematics
Representation – making or understanding the modeof communication

Process Standards
PSSM K-12 Process Standards (page 52-70)
Introduction to the
The processes are not created equal – problem solving is central.
The other fourconnectin powerful ways to problem solving.
These areconcurrent, not isolated. Ina rich math activity there will be several processes going on.

Introduction to the
Communication Standard
Instructional programs from prekindergarten through grade 12 should enable all students to
Organize and consolidate their mathematical thinking through communication;
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematical ideas precisely.

Communication Framework
Clear
Coherent
Complete
Consolidated
C
C
C
C

Communication Standard Analogy
I’m going to Detroit next week, can you tell me about your trip there?
Unclear. What does that have to do with my question?
I’m stuck in Grand Rapids – going in circles.

Clear (trip to Detroit) but incoherent (doesn’t make sense)
Isn’t this Chicago? But I was headed for Detroit.

Clear and coherent but incomplete
Youonly made it as far as Lansing.

Clear, coherent, and complete but not always consolidated
Did you learn anything from your trip? Would you go to that casino again?
mrfrumm@flickr

Clear, coherent, complete and consolidated.
What a great trip – here’s what I learned...
jbcurio@flickr

Problem Solving Standard
Introduction to the
build new mathematical knowledge through problem solving;
solve problems that arise in mathematics and in other contexts;
apply and adapt a variety of appropriate strategies to solve problems;
monitor and reflect on the process of mathematical problem solving.

Problem Solving
Georg Polya first to describe it.
It’s really a never ending cycle!

Representation Standard
Introduction to the
Create and use representations to organize, record, and communicate mathematical ideas;
Select, apply, and translate among mathematical representations to solve problems;
Use representations to model and interpret physical, social, and mathematical phenomena.

Representation
Make
Interpret
Bruno Postle @ Flickr
Diagram for panoramic image photos
Translate
Model

Introduction to the Connection Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—
Recognize and use connections among mathematical ideas;
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
Recognize and apply mathematics in contexts outside mathematics.

Reading Strategy – Schema
Readers
activate schema before, during, and after reading.
add and make changes to their schema based on new information.
use schema to relate text to their world knowledge, other reading, and personal experience.

Reading Strategy – Schema
Readers
use schema to retain text information better and longer.
use their schema for specific authors and styles to better understand.
recognize their own inadequate back-ground information & can create it.
srqpix@flickr

Schema in Math
Mathematicians
use current understandings as first steps in problem-solving.
consider what they know about the general topic
consider if they have seen similar problems
connect to a simpler problem
After problem-solving, connect to harder problems.
Use schema to develop their own problems.

Schema in Research
Researchers
frequently choose topics they know and care about.
use their prior knowledge and experience to launch investigations and ask questions.
consider what they already know to decide what they need to find out
self-evaluate according to experience of what constitutes high quality products/presentations.

Connection Standard Frameworks
To Other Mathematics
To Other Subjects
To Life Experiences
To a Context
To a Similar Problem
To a Simpler Problem
To a Generalized Result
Problem

Reasoning and Proof
Instructional programs from prekindergarten through grade 12 should enable all students to—
Recognizing reasoning and proof as fundamental aspects of mathematics;
Make and investigate mathematical conjectures;
Develop and evaluate mathematical arguments and proofs;
Select and use various types of reasoning and methods of proof.

Reasoning and Proof
(56) “at all grade levels, students should see and expect that mathematics
makes sense.”

Reasoning and Proof
(57) “Doing mathematics involves discovery. Conjecture
– that is, informed guessing – is a major pathway to discovery.”

Reasoning and Proof
(58) “Along with making and investigating conjectures, students should learn to answer the question,
Why does this work?”

Reasoning
Make Sense
Make Conjectures
Make Arguments
Advice to Sink in Slowly

Mathematical Process Standards

by goldenj

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