NCTM Process Standards

What are you doing?

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 mode of communication

PSSM K-12 Process Standards (page 52)Introduction to the

Process Standards

The processes are not created equal – problem solving is central.

The other four connect in powerful ways to problem solving.

These are concurrent, not isolated. In a rich math activity there will be several processes going on.

PSSM K-12 Process Standards (page 52-70)

Introduction to the

Communication StandardInstructional 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.

PSSM K-12 Process Standards (page 60)Introduction to the

Communication Framework

ClearCoherentCompleteConsolidated

CCCC

Communication Standard Analogy

Unclear. What does that have to do with my question?

I’m stuck in Grand Rapids – going in circles.

I’m going to Detroit next week, can you tell me about your trip there?

Communication Standard Analogy

Clear (trip to Detroit) but incoherent (doesn’t make sense)

Isn’t this Chicago? But I was headed for Detroit.

Communication Standard Analogy

Clear and coherent but incomplete

You only made it as far as Lansing.

Communication Standard Analogy

Clear, coherent, and complete but not always consolidated

Did you learn anything from your trip? Would you go to that casino again?

mrfrumm@flickr

Communication Standard Analogy

Clear, coherent, complete and consolidated.

What a great trip – here’s what I learned...

jbcurio@flickr

Problem Solving StandardInstructional programs from prekindergarten through

grade 12 should enable all students to 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.

Introduction to thePSSM K-12 Process Standards (page 52)

Problem Solving

Georg Polya first to describe it.

It’s really a never ending cycle!

Representation Standard

Instructional programs from prekindergarten through grade 12 should enable all students to

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.

PSSM K-12 Process Standards (page 67)

Introduction to the

Representation

Make

Translate

Interpret

Model

Bruno Postle @ FlickrDiagram for

panoramic image photos

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.

PSSM K-12 Process Standards (page 64)

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 ResultP

roblem

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.

PSSM K-12 Process Standards (page 56)

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 SenseMake Conjectures

Make Arguments

Advice to Sink in Slowly