mathematical process standards
DESCRIPTION
The Process Standards from the National Council of Teachers of Mathematics, expanded with examples, analogies and frameworks.TRANSCRIPT
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