N E P F N evada E ducator P erformance F ramework

N E P F

Nevada Educator Performance Framework

Southern NevadaRegional Professional Development Program

www.rpdp.net

Standard 3 Part 2Secondary Mathematics

TEACHER HIGH LEVERAGE INSTRUCTIONAL STANDARDS AND INDICATORS

STANDARD 1 STANDARD 2 STANDARD 3 STANDARD 4 STANDARD 5 N ew Learn ing is Learn ing T asks have S tud en ts E ngag e in S tuden ts E ng age in A ssessm ent is C onnec ted to P rio r H igh C ogn itive M ean in g -M aking M etacogn itiv e In teg ra ted in to Learn ing and D em an d fo r D ive rse th rough D iscourse A ctiv ity to Increase Instruc tion E xperienc e Learners and O the r U nd ers tand ing o f

S tra teg ie s and R espons ib ility fo r T he ir O w n Learn ing

Indicator 1 Indicator 1 Indicator 1 Indicator 1 Indicator 1 T he teacher activa tes all The teacher ass igns tasks T he teacher p rov ides T he teacher and all s tudents T he teacher p lans on -go ing s tuden ts ’ in it ia l that purposefu lly em ploy all opportun ities for extended , understand w ha t s tuden ts a re learn ing opportu n ities based understand ings o f new studen ts ’ cogn itive ab ilities produc tive d iscourse betw een lea rn ing, w hy they are on ev idence o f all s tudents ’ concepts and sk ills and sk ills the teacher and s tudent(s ) lea rn ing it, and how they w ill cu rrent lea rn ing s ta tus

and am ong s tuden ts know if they ha ve lea rned it

Indicator 2 Indicator 2 Indicator 2 Indicator 2 Indicator 2 T he teacher m akes T he teacher ass igns tasks T he teacher p rov ides T he teacher s tructu res T he teacher a ligns connections exp lic it betw ee n that p lace appropria te opportun ities for all s tudents opportun ities fo r se lf- assessm ent opportun ities w ith p rev ious lea rn ing and new dem ands on each stude n t to create and in te rp ret m u ltip le m on ito red lea rn ing fo r all lea rn ing goals and concepts and sk ills fo r all rep rese n tations s tudents pe rfo rm ance crite ria s tudents

Indicator 3 Indicator 3 Indicator 3 Indicator 3 Indicator 3 T he teacher m akes c lea r the The teacher ass igns tasks T he teacher ass is ts all T he teacher supports all T he teacher s tructu res pu rpose and re levance o f n ew that progress ive ly develop all s tuden ts to use ex is ting s tuden ts to take actions based opp ortun ities to genera te learn ing for all s tuden ts s tuden ts ’ cogn itive ab ilit ies know ledge and prio r on the s tuden ts ’ ow n se lf- ev idence o f lea rn ing du ring

and sk ills experience to m ake m on ito ring p rocesses the lesson o f all s tudents connections and recogn ize re la tions h ips

Indicator 4 Indicator 4 Indicator 4 Indicator 4 T he teacher p rov ides all T he teacher opera tes w ith a T he teacher s tructu res the T he teacher adap ts actions s tuden ts opportun ities to bu ild deep be lie f tha t a ll ch ild ren c lass room environm ent to based on ev idence genera ted on o r cha llenge in itia l can ach ieve reg ard less of enab le co llabo ration, in the lesson fo r all s tudents understand ing s race, pe rce ived ab ility and pa rtic ipa tion , and a pos itive

soc io -econom ic s ta tus . a ffective experien ce fo r all s tudents

NEVADA EDUCATOR PERFORM ANCE FRAMEW ORK – IMPLEMENTATION PHASE 1

Standard 3 Module for Mathematics

Part 1 – What and WhyGoal 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?

NEPF Standard 3

Students Engage in Meaning Making through

Discourse and Other Strategies

Classroom environment enables collaboration, participation and a positive, affective experience for all students.

4

Opportunities for ALL students to create and interpret multiple representations that engage student thinking.2

Opportunities for extended, productive DISCOURSE between the teacher and student(s) and among students. 1

Use existing knowledge and prior experience to make connections and recognize relationships to further acquisition of skills. 3

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); and4) 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:What artifacts are available that guide the planning of lessons?

Do teacher notes, student work, and collaborative activities show planning and forethought?

In class (teacher):How are students engaged in discourse?

How effective are aspects of classroom environment, routines, expectations, and communication?

In student work:What is the quality and depth of the discussions?

Are verbal and/or nonverbal representations seen?

In class (student):How are students engaged in discourse?

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?

!

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?”

AskHow did you do it?How do you know your solution is correct?

  What would happen if (give a

variation). . . . ?

We encourage discourse between teacher and student when we…

We can promote by engaging students in

• interactive dialogue

• meaning-making

• explaining, critiquing

• using logic and evidence to support or refute

a claim

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

How do we provide opportunities for discourse among students?…

Activity:_________________________

 Activity Purpose/Benefit ___Hear___See___Say___Do___Write___Problem-solve (Application)___Organize information___Solve___Procedures___Explain (to others/peers, class)

Level of Engagement Check List

Resources for Standard 3, Indicator 1

Check our resource list for templates, descriptions, etc. for group activities.

Look forActive 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”?

modelsdiagramswriting

digital and print mediaimages/visuals

graphs and tablesvideos

simulationspatterns

concept mapsdrawings

Challenge students to create and use representations that include:

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

N A GUse NAG to create multiple representations….

ALGEBRAICALLY

y = xGRAPHICALLY

NUMERICALLYx 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/591Start 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 StrategyIdentifying 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 & ContrastTopic:

Summary:

UNIQUE

SAME

UNIQUE

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 ClassesTo 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 CommunityTeachers 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.

While watching the following video clip, look for:Students working collaborativelyDiscourseViable suggestions/argumentsSharing ideas/thoughts

https://www.teachingchannel.org/videos/think-pair-share-lesson-idea

Standard 3 in action

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...

Teachers support students

in making meaning of their

own learning

Engage in productive discourse

Involve students in creating &

interpreting multiple

representations

Structure a positive

classroom environment

to enable collaboration

& participation

Connect what students are learning to what they

already know

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?

“3 – 2 – 1”

NEPF Standard 3:

Students Engage in Meaning Making

through Discourse and Other

Strategies

For additional NEPF resources rpdp.net

Select NEPF