N E P F
Nevada Educator Performance Framework
Southern Nevada
Regional Professional Development Program
www.rpdp.net
Secondary Mathematics
Standard 3 Part 2
TEACHER HIGH LEVERAGE INSTRUCTIONAL STANDARDS AND INDICATORS
STANDARD 1
STANDARD 2
STANDARD 3
STANDARD 4
STANDARD 5
New Learning is
Connected to Prior
Learning and
Experience
Learning Tasks have
High Cognitive
Demand for Diverse
Learners
Students Engage in
Meaning-Making
through Discourse
and Other
Strategies
Students Engage in
Metacognitive
Activity to Increase
Understanding of
and Responsibility for
Their Own Learning
Assessment is
Integrated into
Instruction
Indicator 1
The teacher activates all
students’ initial
understandings of new
concepts and skills
Indicator 1
The teacher assigns tasks
that purposefully employ all
students’ cognitive abilities
and skills
Indicator 1
The teacher provides
opportunities for extended,
productive discourse between
the teacher and student(s)
and among students
Indicator 1
The teacher and all students
understand what students are
learning, why they are
learning it, and how they will
know if they have learned it
Indicator 1
The teacher plans on-going
learning opportunities based
on evidence of all students’
current learning status
Indicator 2
The teacher makes
connections explicit between
previous learning and new
concepts and skills for all
students
Indicator 2
The teacher assigns tasks
that place appropriate
demands on each student
Indicator 2
The teacher provides
opportunities for all students
to create and interpret multiple
representations
Indicator 2
The teacher structures
opportunities for selfmonitored learning for all
students
Indicator 2
The teacher aligns
assessment opportunities with
learning goals and
performance criteria
Indicator 3
The teacher makes clear the
purpose and relevance of new
learning for all students
Indicator 3
The teacher assigns tasks
that progressively develop all
students’ cognitive abilities
and skills
Indicator 3
The teacher assists all
students to use existing
knowledge and prior
experience to make
connections and recognize
relationships
Indicator 3
The teacher supports all
students to take actions based
on the students’ own selfmonitoring processes
Indicator 3
The teacher structures
opportunities to generate
evidence of learning during
the lesson of all students
Indicator 4
The teacher provides all
students opportunities to build
on or challenge initial
understandings
Indicator 4
The teacher operates with a
deep belief that all children
can achieve regardless of
race, perceived ability and
socio-economic status.
Indicator 4
The teacher structures the
classroom environment to
enable collaboration,
participation, and a positive
affective experience for all
students
NEVADA EDUCATOR PERFORMANCE FRAMEWORK – IMPLEMENTATION PHASE 1
Indicator 4
The teacher adapts actions
based on evidence generated
in the lesson for all students
Standard 3 Module for Mathematics
Part 1 – What and Why
 Goal 1: What is Standard 3?
 Goal 2: What are the indicators for Standard 3?
Part 2 – Implications for Mathematics
 Goal 3: What student learning tasks would provide
evidence of the standard?
 Goal 4: What specific tasks can be designed and/or
adjusted to implement them?
Opportunities for
extended,
productive
DISCOURSE
between the
teacher and
student(s) and
among students.
NEPF
Standard 3
1
Use existing
knowledge and
prior experience to
make connections
and recognize
relationships to
further acquisition
3
of skills.
Students
Engage in
Meaning
Making
through
Discourse
and Other
Strategies
Opportunities for
ALL students to
create and
interpret multiple
representations
that engage
student thinking. 2
Classroom
environment
enables
collaboration,
participation and a
positive, affective
experience for all
4
students.
THIS STANDARD IS SAYING THAT…
Students should be active
in making meaning
during their own learning.
Teachers can support students’ meaning making by:
1) engaging them in productive discourse (Indicator 1);
2) involving them in creating and interpreting multiple
representations (Indicator 2);
3) connecting what they are learning to what they already
know (Indicator 3); and
4) structuring a positive classroom environment to enable
collaboration and participation (Indicator 4).
Showing evidence…
MANDATORY EVIDENCE SOURCES
OF INSTRUCTIONAL PRACTICE
OPTIONAL EVIDENCE SOURCES OF
INSTRUCTIONAL PRACTICE
• DIRECT EVALUATOR
OBSERVATION
• ONE CONFIRMATORY ITEM
FROM OPTIONAL EVIDENCE
SOURCE
• ONE ARTIFACT OF THE
REPRESENTATION AND/OR ITS
CREATION, INTERPRETATION, OR
USE OF THE REPRESENTATION
• TEACHER PRE/POST
CONFERENCE
• TEACHER NOTES
• AUDIO/VISUAL/PRINT ARTIFACT
• LESSON PLAN
• STUDENT WORK
• STUDENT FEEDBACK
What do Teachers Need to Demonstrate as
Evidence for Standard 3?
LOOK FORS:
LISTEN FORS:
In teacher planning:
In class (teacher):
What artifacts are available that
guide the planning of lessons?
How are students engaged in
discourse?
Do teacher notes, student work, How effective are aspects of
and collaborative activities show classroom environment,
planning and forethought?
routines, expectations, and
communication?
In student work:
In class (student):
What is the quality and depth of How are students engaged in
the discussions?
discourse?
Are verbal and/or nonverbal
representations seen?
Is thinking externalized?
Are arguments, explanations,
and critiquing evident?
Teachers can support students’
meaning making by
providing opportunities for
extended, productive discourse.
How do teachers promote this
discourse?
Promoting
discourse?!
We encourage discourse between
teacher and student when we…
 Change from
“How can I teach students to get the
answer to this problem?”
to
“How can I use this problem to teach the
mathematics of this unit?”
 Ask
How did you do it?
How do you know your solution is
correct?
What would happen if (give a variation). . . . ?
How do we provide opportunities for
discourse among students?…
We can promote
• interactive dialogue
• meaning-making
• explaining, critiquing
• using logic and evidence
to support or refute
a claim
by engaging students in
Simple Paired Activities
•
•
•
•
Homework Checking Pairs
Think/Pair/Share
Question and Answer Pairs
Note-Checking Pairs
Group Activities
•
•
•
•
•
Cooperative Learning
Cubing
I Have – Who Has
Matching
Problem Solving
Level of Engagement Check List
Activity:_________________________
Activity Purpose/Benefit
___Hear
___See
___Say
___Do
___Write
___Problem-solve (Application)
___Organize information
___Solve
___Procedures
___Explain (to others/peers, class)
Resources for Standard 3, Indicator 1
Check our resource list for
templates, descriptions, etc. for
group activities. Look for
Active Learning for
Mathematics
at www.rpdp.net > NEPF >math
resources
Teachers can support students’
meaning making by
involving them in creating and
interpreting multiple representations.
How do we create tasks that
challenge students to create and
use these representations?
What are “representations”?
Challenge students to create and use representations
that include:
models
diagrams
writing
digital and print media
images/visuals
graphs and tables
videos
simulations
patterns
concept maps
drawings
Mathematical Practice # 4:
Model
with Mathematics
Modeling is a common thread found
at every grade level in the
Nevada Academic Content
Standards for Mathematics
What does Math Modeling Mean?
This video addresses the mathematical practice Create a
Mathematical Model from the Common Core. Students
are often confused about what a math model actually
encompasses.
http://www.youtube.com/watch?v=Iew9nppByKs
Start at 0:20
NAG
Use NAG to create multiple representations….
ALGEBRAICALLY
y=x
GRAPHICALLY
NUMERICALLY
x
y
1
1
2
2
3
3
MODELING: Strategies to Solve Ratio Problems
 Common Core: 6.RP.3a, by Kathryn Newmark
 “Choose a strategy to solve ratio problems”
 In this lesson you will learn to solve ratio problems by
choosing the strategy you like the best.
http://learnzillion.com/lessons/591
Start at 1:36
MODELING:
Simplify Square Roots Using Physical Models
 Common Core: N-RN.2, by Lauren Burton
 “Simplify square roots using physical models”
 In this lesson you will learn how to simplify square
roots by examining physical models.
http://learnzillion.com/lessons/2859
Teachers can support students’
meaning making by
connecting what they are
learning to what they already
know.
How do we create tasks that
help students to make these
connections?
Connect to Prior Knowledge
How?
Using graphic organizers; KWL charts, Venn diagrams, etc.
Sound familiar?
The “prior knowledge” connection is NEPF Standard 1!
Refer to the resource materials presented in the module
for Standard 1.
Use a High Yield Strategy
Identifying similarities and differences is the #1 high yield
strategy for increasing student achievement.*
STUDENTS SHOULD:
 Compare, classify, and create metaphors, analogies and
non-linguistic or graphic representations
 Use Thinking Maps, T-charts, Venn diagrams,
classifying, analogies, cause and effect links, compare
and contrast organizers
*Classroom Instruction that Works: Research-based Strategies for Increasing Student
Achievement, by Robert Marzano (2001)
Venn Diagram: Compare & Contrast
Topic:
UNIQUE
UNIQUE
SAME
Summary:
More thoughts on
making connections:
Help students use their prior
knowledge to draw analogies
that support their
understanding of the
concepts.
Using Analogies in Math Classes
To create analogies, students must understand relationships,
such as comparing, contrasting, and sequencing.
Start with a simple example from other disciplines.
hot : soup as cold : _______ (ice cream)
Then try:
straightedge : line as compass : ______ (circle)
ray : line as arc : ______ (circle)
parallel : intersecting as acute : ______ (obtuse)
4 : 12 as 1 : ___ (3)
½ : 50% as ¼ : ___ (25%)
Additional Thought on Indicator 3
Recognize that students bring a variety of personal
experiences to the classroom.
For strategies to address this diversity, refer to the
resource materials in the module for Standard 2!
Teachers can support students’
meaning making by
structuring a positive classroom
environment to enable
collaboration and participation
How do we create such an
environment?
Creating a positive classroom environment?
Building Classroom Community
Teachers need to consider factors in classroom
environment:
Classroom Culture
Classroom Management
Norms
Student behavior
Routines
Resource provision
Expectations
Organization of physical space
Communication patterns
Encouraging environment?
Notes from brain research…
 Once sensory information enters the
brain, it’s routed to one of two areas:
 (1) the prefrontal cortex, what might be
called the thinking brain, which can
consciously process and reflect on
information; OR
 (2) the lower, automatic brain, what might
be called the reactive brain, which reacts on
information instinctively rather than
through thinking.
 When a student is anxious, stressed, sad,
frustrated, confused or bored, brain filters
conduct the sensory information into their
reactive brain.
 If information gets routed to this reactive
brain, it is unlikely the brain will process the
information or remember it.
That is, unless a positive mood is restored,
the student won’t be learning much on
this particular school day.
 THEREFORE, if a student is stressed, they
CAN’T use their thinking brains…
Classroom-related stressors must be
eliminated to enable collaboration,
participation, and a positive
experience for all students.
Standard 3 in action
While watching the following video clip, look
for:
 Students working collaboratively
 Discourse
 Viable suggestions/arguments
 Sharing ideas/thoughts
 https://www.teachingchannel.org/videos/thin
k-pair-share-lesson-idea
Think-pair-share video
Did the activity (in the video) address...
Standard 3:
Students Engage in Meaning-Making
through Discourse and Other
Strategies
 Productive discourse?
 Multiple representations?
 Prior knowledge and experience?
 Conducive environment for collaboration?
In summary...
Connect what
students are
learning to what
they already
know
Engage in
productive
discourse
Teachers
support
students in
making
meaning of
their own
learning
Structure a
positive
classroom
environment to
enable
collaboration &
participation
Involve
students in
creating &
interpreting
multiple
representations
“3 – 2 – 1”
What evidence of Standard 3 can you visualize in
your classroom?
Name 3 artifacts you are already using.
What new strategies or ideas (using Standard 3) do
you think you could use in your classroom?
Give 2 such examples.
Commit to using a new strategy.
What 1 strategy will you employ?
NEPF Standard 3:
Students Engage in
Meaning Making through
Discourse and Other
Strategies
For additional NEPF
resources
rpdp.net
Select NEPF