Fill - Free fillable Secondary Math Handbook (Concordia College

edTPA_SecMath_05

Secondary Mathematics

Assessment Handbook

September 2016

edTPA Secondary Mathematics Assessment Handbook

edTPA stems from a twenty-five-year history of developing performance-based assessments of

teaching quality and effectiveness. The Teacher Performance Assessment Consortium (Stanford

and AACTE) acknowledges the National Board for Professional Teaching Standards, the

Interstate Teacher Assessment and Support Consortium, and the Performance Assessment for

California Teachers for their pioneering work using discipline-specific portfolio assessments to

evaluate teaching quality. This version of the handbook has been developed with thoughtful input

from over six hundred teachers and teacher educators representing various national design

teams, national subject matter organizations (ACEI, ACTFL, AMLE, CEC, IRA, NAEYC, NAGC,

NCSS, NCTE, NCTM, NSTA, SHAPE America), and content validation reviewers. All

contributions are recognized and appreciated.

This document was authored by the Stanford Center for Assessment, Learning, and Equity (SCALE)

with editorial and design assistance from Evaluation Systems.

The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the

edTPA trademarks is permitted only pursuant to the terms of a written license agreement.

edTPA Secondary Mathematics Assessment Handbook

Contents

Introduction to edTPA Secondary Mathematics............................................................................... 1

Purpose................................................................................................................................................................... 1

Overview of the Assessment ................................................................................................................................... 1

Structure of the Handbook ...................................................................................................................................... 3

edTPA Secondary Mathematics Tasks Overview ................................................................................................... 5

Planning Task 1: Planning for Instruction and Assessment .......................................................... 8

What Do I Need to Think About? ............................................................................................................................ 8

What Do I Need to Do? ........................................................................................................................................... 8

What Do I Need to Write? ..................................................................................................................................... 10

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 13

Planning Rubrics ................................................................................................................................................... 14

Instruction Task 2: Instructing and Engaging Students in Learning ........................................... 19

What Do I Need to Think About? .......................................................................................................................... 19

What Do I Need to Do? ......................................................................................................................................... 19

What Do I Need to Write? ..................................................................................................................................... 21

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 22

Instruction Rubrics ................................................................................................................................................ 23

Assessment Task 3: Assessing Student Learning ........................................................................ 28

What Do I Need to Think About? .......................................................................................................................... 28

What Do I Need to Do? ......................................................................................................................................... 28

What Do I Need to Write? ..................................................................................................................................... 29

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 32

Assessment Rubrics ............................................................................................................................................. 33

Professional Responsibilities ........................................................................................................... 38

Secondary Mathematics Context for Learning Information .......................................................... 39

Secondary Mathematics Evidence Chart ........................................................................................ 42

Planning Task 1: Artifacts and Commentary Specifications .................................................................................. 42

Instruction Task 2: Artifacts and Commentary Specifications ............................................................................... 43

Assessment Task 3: Artifacts and Commentary Specifications ............................................................................ 44

Secondary Mathematics Glossary ................................................................................................... 47

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Introduction to edTPA Secondary

Mathematics

Purpose

The purpose of edTPA Secondary Mathematics, a nationally available performance-based

assessment, is to measure novice teachers’ readiness to teach secondary mathematics.

The assessment is designed with a focus on student learning and principles from research

and theory. It is based on findings that successful teachers

develop knowledge of subject matter, content standards, and subject-specif

pedagogy

develop and apply knowledge of varied students’ needs

consider r

esearch and theory about how students learn

flect on and analyze evidence of the effects of instruction on student learning

a performance-based assessment, edTPA is designed to engage candidates in

demonstrating their understanding of teaching and student learning in authentic ways.

Overview of the Assessment

The edTPA Secondary Mathematics assessment is composed of three tasks:

1. Planning for Instruction and Assessment

2. Instructing and Engaging Students in Learning

3. Assessing Student Learning

For this assessment, you will first plan 3–5 consecutive mathematics lessons (or, if

teaching within a large time block, 3–5 hours of connected instruction) referred to as a

learning segment. Consistent with the Principles and Standards for School Mathem

atics

(NCTM 2000), a learning segment prepared for this assessment should reflect a balanced

approach t

o mathematics. This means your segment should include learning tasks in which

students have opportunities to develop

conceptual understanding

proc

edural fluency

mathemat

ical reasoning and/or

problem-solving skills

precise communication skills

You will then teach the learning segment, making a videorecording of your interactions with

tudents during instruction. You will also assess, informally and formally, students’ learning

throughout the learning segment. Upon completion of the three tasks, you will submit

artifacts from the tasks (e.g., lesson plans, clips from your videorecording, as

sessment

mat

erials, instructional materials, student work samples), as well as commentaries that you

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have written to explain and reflect on the Planning, Instruction, and Assessment

components of the tasks. The artifacts and commentaries for each task will then be

evaluated using rubrics especially developed for each task.

The edTPA Tasks and the Cycle of Effective Teaching

The three edTPA tasks represent a cycle of effective teaching (i.e., teaching that is focused

on student learning). Planning Task 1 documents your intended teaching, Instruction Task

2 documents your enacted teaching, and Assessment Task 3 documents the impact of

your teaching on student learning.

The three tasks and the evidence you provide for each are framed by your understandings

of your students and their learning. As you develop, document, and teach your lessons, you

will reflect upon the cyclical relationship among planning, instruction, and assessment with a

focus on your students’ learning needs.

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Evidence of Teaching Practice: Artifacts and Commentaries

An essential part of edTPA is the evidence you will submit of how you planned, taught, and

assessed your lessons to deepen student learning in mathematics. This evidence includes

both artifacts and commentaries:

Artifacts represent authentic work completed by you and your students. These

nclude lesson plans, copies of instructional and assessment materials, video clips of

your teaching, and student work samples.

Commentaries are y

our opportunity to describe your artifacts, explain the rationale

behind their choice, and analyze what you have learned about your teaching practice

and your students’ learning. Note that although your writing ability will not be scored

directly, commentaries must be clearly written and well focused.

When preparing your artifacts and commentaries, refer to the rubrics frequently to guide

your thinking, planning, and writing. Refer to the Secondary Mathematics Evidence Chart

for

information about how your evidence should be formatted for electronic submission.

Evaluation Criteria

The rubrics used to score your performance are included in this handbook, following the

sections describing the directions for each task. The descriptors in the five-level rubrics

address a wide range of performance, beginning with the knowledge and skills of a novice

not ready to teach (Level 1) and extending to the advanced practices of a highly

accomplished beginner (Level 5).

Structure of the Handbook

The following pages provide specific instructions on how to complete each of the three tasks

of the edTPA Secondary Mathematics assessment. After an overview of the tasks, the

handbook provides instructions for each task, organized into four sections:

1. What Do I Need to Think About?

This section provides focus questions for you to think about when completing the

task.

2. What Do I Need to Do?

This section provides specific, detailed directions for completing the task.

3. What Do I Need to Write?

This section tells you what you need to write and also provides specific and detailed

directions for writing the commentary

for the task.

4. How Will the Evidence of My Teaching Practice Be Assessed?

This section includes the rubrics that will be used to assess the evidence you provide

for the task.

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Additional requirements and resources are provided for you in this handbook:

Professional Responsibilities: guidelines for the development of your evidence

Secondary M

athematics Context for Learning Informati

on: prompts used to

collect information about your school/classroom context

Secondary Mathematics Evidence Chart: specifications for

electronic submission

of evidence (artifacts and commentaries), including templates, supported file types,

number of files, response length, and other important evidence specifications

Glossary: defini

tions of key terms can be accessed by rolling your cursor over each

glossary term marked with a dotted underline throughout the handbook or by

referring to the Secondary

Mathematics Glossary.

You should review the Mak

ing G

ood Choices document prior to beginning the planning of

the

learning segment. If you are in a preparation program, it will have additional resources

that provide guidance as you develop your evidence.

Review all instructions carefully before beginning to teach the learning segment to

ensure that you are well prepared for all tasks. Before you record your videos,

pay particular attention to the specific content focus of each video clip

submission; these foci are described in the What Do I Need to Do? sections in

Instruction Task 2 and Assessment Task 3. Refer to the Professional

Responsibilities section of this handbook for important information about

permissions, confidentiality, and other requirements.

If your program requires you to submit artifacts and commentaries for official

scoring, refer to www.edTPA.com for complete and current information before

beginning your work and to download templates for submitting materials. The

website contains information about the registration process, submission deadlines,

submission requirements, withdrawal/refund policies, and score reporting. It also

provides contact information should you have questions about your registration and

participation in edTPA.

Whether submitting directly to www.edTPA.com or via your program’s electronic

portfolio management system, follow the submission guidelines as documented in

the Evidence Chart and review edTPA Submission Requirements to ensure that

your materials conform to the required evidence specifications and requirements for

scoring.

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edTPA Secondary Mathematics Tasks Overview

Planning Task 1: Planning for Instruction and Assessment

What to Do

Select one class as a focus for this

assessment.

Provide relevant context information.

Identify a learning segment to plan, teach,

and analyze

student learning. Your

learning segment should include 3–5

consecutive lessons (or, if teaching

mathematics within a large time block,

about 3–5 hours of connected

instruction).

Determine a central focus for your

learning segment. The central focus

should support students to develop

conceptual understanding, procedural

fluency, AND mathematical reasoning

and/or problem-solving skills.

Write and submit a lesson plan for each

lesson in the learning segment.

Select and submit key instructional

materials needed to understand what you

and the students will be doing.

Choose one language function and other

language demands important to

understanding secondary mathematics in

your learning segment. Identify a learning

task where students are supported to use

this language.

Respond to commentary prompts prior to

teaching the learning segment.

Submit copies of all written assessments

and/or clear directions for any oral or

performance assessments from the

learning segment.

What to Submit

Part A: Context f

or Learning

Information

Part B: Lesson Plans for

Learnin

g Segment

Part C: Instructional Materials

Part D: A

ssessments

Part E: Planning Commentary

Evaluation Rubrics

Planning Rubrics

Rubric 1: P

lanning for

Mathematical Understandings

Rubric 2: Planning to Support

Vari

ed Student Learning

Needs

Rubric 3: Using Knowledge of

Students to Infor

m Teaching

and Learning

Rubric 4: Identifying and

Supporting Language

Demands

Rubric 5: Planning

Assessments to Monitor and

Support Student Learning

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Instruction Task 2: Instructing and Engaging Students in Learning

What to Do

Obtain required permissions for

videorecording from parents/guardians of

your students and other adults appearing

in the video.

Identify lessons from the learning segment

you planned in Planning Task 1 to be

videorecorded. You should choose

lessons that show you interacting with

students to develop their conceptual

understanding, procedural fluency, AND

mathematical reasoning and/or problem-

solving skills.

Videorecord your teaching and select 1

or 2

video clips (no more than

15 minutes total, but not less than 3

minutes).

Analyze your teaching and your students’

learning in the video clip(s) by responding

to commentary prompts.

What to Submit

Part A: V

ideo Clips

Part B: Instruction

Commentary

Evaluation Rubrics

Instruction Rubric

Rubric 6: Lea

rning

Environment

Rubric 7: Engaging Students

in Lear

ning

Rubric 8: Deepening Student

Learnin

Rubric 9: Subject-Specific

Pedagogy: Using

Representations

Rubric 10: Analyzing Teaching

Effectiveness

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Assessment Task 3: Assessing Student Learning

What to Do

Select one assessment from the learning

segment that you will use to evaluate your

students’ developing knowledge and skills.

Attach the assessment used to evaluate

student performance to the end of the

Assessment Commentary.

Define and submit the evaluation criteria

you will use to analyze student learning.

Collect and analyze student work from the

selected assessment to identify

quantitative and qualitative patterns of

learning within and across learners in the

class.

Select 3 student work samples to

illustrate your analysis of patterns of

learning within and across learners in the

class. At least 1 of the samples must be

from a student with specific learning

needs. These 3 students will be your

focus students.

Summarize the learning of the whole

class, referring to work samples from the 3

focus students to illustrate patterns in

student understanding across the class.

Submit feedback for the work samples for

the 3 focus students in written, audio, or

video form.

Analyze evidence of students’ language

use from (1) the video clip(s) from

Instruction Task 2, (2) an additional video

clip of one or more students using

language within the learning segment,

AND/OR (3) the student work samples

from Assessment Task 3.

Analyze evidence of student learning and

plan for next steps by responding to

commentary prompts.

What to Submit

Part A: S

tudent Work

Samples

Part B: Evidence of Feedback

Part C: Assessment

Commentary

Part D: Evaluation Criteria

Evaluation Rubrics

Assessment Rubrics

Rubric 11: Analysis of

Student Learning

Rubric 12: Providing

Feedback to Guide Learning

Rubric 13: Student

Understanding and Use of

Feedback

Rubric 14: Analyzing

Students’ Language Use and

Mathematics Learning

Rubric 15: Using

Assessment to Inform

Instruction

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Planning Task 1: Planning for Instruction

and Assessment

What Do I Need to Think About?

In Planning Task 1, you will describe your plans for the learning segment and explain how

your instruction is appropriate for the students and the content you are teaching. As you

develop your plans, you need to think about the following:

What do your students know, what can they do, and what are they learning to do?

What do you want your students to learn? What

are the important understandings and

core concepts you want students to develop within the learning segment?

How will

you use your knowledge of your students’ assets to inform your plans?

What instructional strategies, learning tasks, and assessments will you design to support

student learning and language use?

How will your learning segment support students to develop and use language that

deepens content understanding?

How is the teaching you propose supported by research and theory about how students

learn?

What Do I Need to Do?

Select a class. If you teach more than one class, select one focus class for this

assessment. If your placement for mathematics has you responsible for a group rather

than a whole class, plans should describe instruction for that group (minimum of 4

students). That group will constitute “the whole class” for edTPA.

Provide context information. The Secondary Mathematics Context for Learning

Information form is provided later in this handbook and must be submitted in a template.

Thi

s form provides essential information about your students and your school/classroom.

The context information you submit should be no more than 4 pages, including

prompts.

Identify a learning segment to plan, teach, and analyze. Review the curriculum with

your c

ooperating teacher and select a learning segment of 3–5 consecutive lessons. (If

teaching secondary mathematics within a large time block, select a learning segment of

about 3–5 hours of connected instruction.)

Identify

a central focus. Identify the central focus along with the content standards and

objectives you will address in the learning segment. The central focus should support

students in developing

conceptual understanding,

procedural fluency, AND

mathematical reasoning and/

or probl

em-solving skills.

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Identify and plan to support language demands. Select a key language function from

your learning objectives. Choose a learning task that provides opportunities for students

to practice using that language function. Identify additional language demands

associated with that task. Plan targeted supports that address the identified language

demands, including the language function.

Write a lesson plan for each lesson in the learning segment. Your lesson plans should

be detailed enough that a substitute or other teacher could understand them well enough

to use them.

Your lesson pl

ans must include the following information, even if your teacher

preparation program requires you to use a specific lesson plan format:

State-adop

ted student academic content standards that are the target of student

learning (Note: Please include the number and text of each standard that is being

addressed. If only a portion of a standard is being addressed, then only list the part

or parts that are relevant.)

Learning objectives ass

ociated with the content standards

Informal and formal assessments used to monitor student learning, including type(s)

of assessment and what is being assessed

Instructional strategies and learning tasks (including what you and the students will

be doing) that support diverse student needs

Inst

ructional resources and materials used to engage students in learning

Each lesson plan must be no more than 4 pages in length. You will need to

condense or excerpt lesson plans longer than 4 pages. Any explanations or rationale for

decisions should be included in your Planning Commentary and deleted from your plans.

Respond to the commentary prompts listed in the Planning Commentary section

prior to teaching the learning segment.

Submit your original lesson plans. If you make changes while teaching the learning

segment, you may offer reflection on those changes in the Instruction Task 2 and

Assessment Task 3 Commentaries. Select and submit key instructional materials

needed to understand what you and the students will be doing (no more than 5

additional pages per lesson plan). The instructional materials might include such

items as class handouts, assignments, slides, and interactive whiteboard images.

Submit copies of all written assessments and/or

directions for any oral or

performance assessments. (Submit only the blank assessment given to students; do

not submit student work samples for this task.)

Provide citations for the source of all materials that you did not create (e.g.,

published texts, websites, and material from other educators). List all citations by lesson

number at the end of the Planning Commentary. Note: Citations do not count toward the

commentary page limit.

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See the Planning Task 1: Artifacts and Commentary Specifications in the Secondary

Mathematics Evidence Chart for instructions on electronic submission of evidence.

The evidence chart identifies templates, supported file types, number of files,

response length, and other important evidence specifications. Your evidence cannot

contain hyperlinked content. Any web content you wish to include as part of your

evidence must be submitted as a document file, which must conform to the file

format and response length requirements.

What Do I Need to Write?

In Planning Task 1, you will write

a description of your Context for Learning (see “What Do I Need to Do?” above for

dir

ections)

lesson pl

ans (see “What Do I Need to Do?” above for directions)

a commentary explaining your plans (see “Planning Commentary” below for

directions)

Planning Commentary

In Planning Task 1, you will write a commentary, responding to the prompts below. Your

commentary should be no more than 9 single-spaced pages, including the prompts.

1. Central Focus

a. Describe the central focus and purpose of the content you will teach in the

learning segment.

b. Given the central focus, describe how the standards and learning objectives

within your learning segment address

conceptual understanding,

procedural fluency, AND

mathematical reasoning and/or problem-solving skills.

c. Explain how your plans build on each other to help students make connections

between concepts, computations/procedures, AND mathematical reasoning or

problem-solving strategies to build understanding of mathematics.

2. Knowledge of Students to Inform Teaching

For each of the prompts below (2a–c), describe what you know about your students

with respect to the central focus of the learning segment.

Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language learners,

struggling readers, underperforming students or those with gaps in academic

knowledge, and/or gifted students).

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a. Prior academic learning and prerequisite skills related to the central focus—Cite

evidence of what students know, what they can do, and what they are still

learning to do.

b. Personal, cultural, and community assets related to the central focus—What do

you know about your students’ everyday experiences, cultural and

language backgrounds and practices, and interests?

c. Mathematical dispositions—What do you know about the extent to which your

students

perceive mathematics as “sensible, useful, and worthwhile”

persist in applying mathematics to solve problems

believe in their own ability to learn mathematics

3. Supporting Students’ Mathematics Learning

Respond to prompts below (3a–c). To support your justifications, refer to the

instructional materials and lesson plans you have included as part of Planning

Task 1. In addition, use principles from research and/or theory to support your

justifications.

a. Justify how your understanding of your students’ prior academic learning;

personal, cultural, and community assets; and mathematical dispositions (from

prompts 2a–c above) guided your choice or adaptation of learning tasks and

materials. Be explicit about the connections between the learning tasks and

students’ prior academic learning, their assets, their mathematical dispositions,

and research/theory.

b. Describe and justify why your instructional strategies and planned supports

are

appropriate for the whole class, individuals, and/or groups of students with

specific learning needs.

Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students).

c. Describe common mathematical preconceptions, errors, or misunderstandings

within your central focus and how you will address them.

4. Supporting Mathematics Development Through Language

As you respond to prompts 4a–d, consider the range of students’ language assets

and needs—what do students already know, what are they struggling with, and/or

what is new to them?

a. Language Function. Using information about your students’ language assets

and needs, identify one language function essential for students to develop

conceptual understanding, procedural fluency, and mathematical reasoning or

problem-solving skills within your central focus. Listed below are some sample

From The Common Core State Standards for Mathematics

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language functions. You may choose one of these or another language function

more appropriate for your learning segment.

Compare/C

ontrast Justify Describe Explain Prove

Please see additional examples and non-examples of language functions in the

glossary.

b. Identify a key learning task from your plans that provides students with

opportunities to practice using the language function identified above. Identify the

lesson in which the learning task occurs. (Give lesson day/number.)

c. Additional Language Demands. Given the language function and learning task

identified above, describe the following associated language demands (written or

oral) students need to understand and/or use:

Vocabulary and/or symbols

Mathem

atical precision

(e.g., using clear definitions, labeling axes,

specifying units of measure, stating meaning of symbols), appropriate to your

students’ mathematical and language development

Plus at least one of the following:

Discourse

ntax

d. Language S

upports. Refer to y

our lesson plans and instructional materials as

needed in your response to the prompt.

Identify and describe the planned instructional s

upports (during and/or prior to

the learning task) to help students understand, develop, and use the

identified language demands (function, vocabulary and/or symbols,

mathematical precision, discourse, or syntax).

5. Monitoring Student Learning

In response to the prompts below, refer to the assessments you will submit as part of

the materials for Planning Task 1.

a. Describe how your planned formal and informal assessments will provide direct

evidence of students’ conceptual understanding, procedural fluency, AND

mathematical reasoning and/or problem-solving skills throughout the learning

segment.

b. Explain how the design or adaptation of your planned assessments allows

students with specific needs to demonstrate their learning.

Consider the variety of l

earners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students).

For an elaboration of “precision,” refer to the “Standards for Mathematical Practice” from The Common Core State Standards

for Mathematics (June 2010), which can be found at http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.

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How Will the Evidence of My Teaching Practice Be

Assessed?

For Planning Task 1, your evidence will be assessed using rubrics 1–5, which appear on the

following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, planning, and writing.

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Planning Rubrics

Rubric 1: Planning for Mathematical Understandings

How do the candidate’s plans build students’ conceptual understanding, procedural fluency, AND mathematical

reasoning and/or problem-solving skills?

Level 1

Level 2 Level 3 Level 4 Level 5

Candidate’s plans for

instruction focus solely on

facts and/or procedures with

no connections to

• concepts OR

• mathematical reasoning

and/or problem-solving

skills.

There are significant content

inaccuracies that will lead to

student misunderstandings.

Standards, objectives,

learning tasks, and materials

are not aligned with each

other.

Candidate’s plans for

instruction support student

learning of facts and

procedures with vague

connections to

• concepts AND

• mathematical reasoning

and/or problem-solving

skills.

Candidate’s plans for

instruction build on each

other to support learning of

facts and procedures with

clear connections to

• concepts AND

• mathematical reasoning

and/or problem-solving

skills.

Candidate’s plans for

instruction build on each other

to support learning of facts and

procedures with clear and

consistent connections to

• concepts AND

• mathematical reasoning

and/or problem-solving

skills.

Level 4 plus:

Candidate explains how s/he

will use learning tasks and

materials to lead students to

make clear and consistent

connections.

Text representing key differences between adjacent score levels is shown in bold. Evidence that does not meet Level 1 criteria is scored at Level 1.

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Rubric 2: Planning to Support Varied Student Learning Needs

How does the candidate use knowledge of his/her students to target support for students to develop conceptual

understanding, procedural fluency, AND mathematical reasoning and/or problem-solving skills?

Level 1 Level 2 Level 3 Level 4 Level 5

There is no evidence of

planned supports.

Candidate does not attend to

ANY INSTRUCTIONAL

requirements in IEPs and 504

plans.

Planned supports are loosely

tied to learning objectives or

the central focus of the

learning segment.

Planned supports are tied

to learning objectives and

the central focus with

attention to the

characteristics of the

class as a whole.

Planned supports are tied to

learning objectives and the

central focus. Supports

address the needs of specific

individuals or groups with

similar needs.

Level 4 plus:

Supports include specific

trategies to identify and

respond to preconceptions,

common errors, and

misunderstandings.

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Rubric 3: Using Knowledge of Students to Inform Teaching and Learning

How does the candidate use knowledge of his/her students to justify instructional plans?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate’s justification of

learning tasks is either missing

OR represents a deficit view

of students and their

backgrounds.

Candidate justifies learning

tasks with limited attention to

students’

• prior academic learning

• personal, cultural, or

community assets.

Candidate justifies why

learning tasks (or their

adaptations) are

appropriate using

examples of students’

• prior academic

learning OR

• personal, cultural, or

community assets.

Candidate makes

superficial connections

to research and/or

theory.

Candida

te justifies why learning

tasks (or their adaptations) are

appropriate using examples of

students’

• prior academic learning

AND

• personal, cultural, or

community assets.

Candida

te makes connections

to research and/or theory.

Level 4 plus:

Candidate’s justification is

upported by principles from

research and/or theory.

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Rubric 4: Identifying and Supporting Language Demands

How does the candidate identify and support language demands associated with a key mathematics learning

task?

Level 1 Level 2 Level 3 Level 4 Level 5

Language demands

identified

by the candidate are not

consistent with the selected

language function

OR task.

Language s

upports are

missing or are not aligned

with the language demand(s)

for the learning task.

Language s

upports primarily

address one language

demand (vocabulary and/or

symbols, function,

mathematical precision,

discourse, syntax).

General language supports

address use of two or more

language demands

(vocabulary and/or symbols,

function, mathematical

precision, discourse, syntax).

Targeted language supports

address use of

• vocabulary and/or

symbols,

• language function, AND

• one or more additional

language demands

(mathematical precision,

discourse, syntax).

Level 4 plus:

Language supports are

designed to meet the needs

of students with different

levels of language learning.

Language demands include: language function, vocabulary and/or symbols, syntax, and discourse (organizational structures, text structure, etc.).

Language function refers to the learning outcome (verb) selected in prompt 4a (e.g., compare/contrast, conjecture).

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Rubric 5: Planning Assessments to Monitor and Support Student Learning

How are the informal and formal assessments selected or designed to monitor students’ conceptual

understanding, procedural fluency, AND mathematical reasoning and/ or problem-solving skills?

Level 1 Level 2 Level 3 Level 4 Level 5

The assessments only provide

evidence of students'

procedural skills and/or

factual knowledge.

Candidat

e does not attend to

ANY ASSESSMENT

requirements in IEPs and 504

plans.

The assessmen

ts provide

limited evidence to monitor

students’

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning

and/or problem-solving

skills

during the learning segment.

The assessmen

ts provide

evidence to monitor students’

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning

and/or problem-solving

skills

during the learning segment.

The a

ssessments provide

multiple forms of evidence to

monitor students’ progress

toward developing

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning

and/or problem-solving

skills

throughout the learning

segment.

Level 4 plus:

The assessments are

strategically designed to

allow individuals or groups

with specific needs to

demonstrate their learning.

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Instruction Task 2: Instructing and

Engaging Students in Learning

What Do I Need to Think About?

In Instruction Task 2, you will demonstrate how you support and engage students in

learning. Before you begin your instruction, you need to thi

nk about the following:

What kind of learning env

ironment do you want to develop in order to establish

respect and rapport, and to

support students’ engagement in learning?

What kinds of learning tas

ks actively engage students in the central focus of the

learning segment?

How will you elicit and build on student responses in ways that develop and deepen

content

understanding?

In what ways will you connect new content to your students’ prior academic learning

and personal, cul

tural, or community assets during your instruction?

How wi

ll you use evidence fr

om your instruction to examine and change your

teaching practices to more effectively meet a variety of student learning needs?

What Do I Need to Do?

Obtain required permission for videorecording. Before you record your video, ensure

that you have the appropriate permission from the parents/guardians of your students

and from adults who appear in the video. Adjust the camera angle to exclude individuals

for whom you do not have permission to film.

Examine your plans for the learning segment and identify c

hallenging learning tasks

in which you and students are actively engaged. The video clip(s) you select for

submission should provide a sample of how you interact with students to support them to

develop

conceptual understanding, procedural fluency, AND mathematical reasoning

and/or problem-solving skills.

Identify lessons to videorecord.

Provide 1–2 video cli

ps (together totaling no more than 15 minutes, but not less

than 3 minutes) that demonstrate how you interact with students in a positive learning

environment to develop conceptual understanding, procedural fluency, AND

mathematical reasoning and/or problem-solving skills.

(Optional) Provide evi

dence of students’ language use. You may provide evidence

of language use with your video clip(s) from Instruction Task 2, an additional video clip of

one or more students using language within the learning segment (no more than 5

minutes in length), AND/OR through the student work samples analyzed in

Assessment Task 3.

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Determine whether you will feature the whole class or a targeted group of students

(minimum of 4 students) within the class.

Videorecord your classroom teaching. Tips for videorecording your class are

available from your teacher preparation program.

Select video clip(s) to submit and verify that the clip(s) meet the following

requirements:

Check the video and sound quality to ensure that you and your students can be seen

and heard on the video clip(s) you submit. If most of the audio in a clip cannot be

understood by a scorer, submit another clip. If there are occasional audio portions

of a clip that cannot be understood that are relevant to your commentary

responses,

do one of the following: 1) provide a transcript with time stamps of the inaudible

portion and refer to the transcript in your response; 2) embed quotes with time-stamp

references in the commentary response; or 3) insert captions in the video (captions

for this purpose will be considered permissible editing).

A video clip must be continuous and unedited, with no interruption in events.

If you have inadvertently included individuals for whom you do not have permission

to film in the video clip(s) you plan to submit, you may use software to blur the faces

of these individuals. This is not considered editing. Other portions of the submitted

video clip(s), including the classroom, your face, and the faces of individuals for

whom you have obtained permission to film should remain unblurred.

Do not include the name of the state, school, or district in your video. Use first names

only for all individuals appearing in the video.

Respond to the prompts listed in the Instruction Commentary section below after

viewing the video clip(s).

Determine if additional information is needed to understand what you and the

students are doing in the video clip(s). For example, if there are graphics, texts, or

images that are not clearly visible in the video, or comments that are not clearly heard,

you may insert digital copies or transcriptions at the end of the Instruction Commentary

(no more than 2 pages in addition to the responses to commentary prompts).

See the Instruction Task 2: Artifacts and Commentary Specifications in the

Secondary Mathematics Evidence Chart for instructions on electronic submission of

evidence. The evidence chart identifies templates, supported file types, number of

files, response length, and other important evidence specifications. Your evidence

cannot contain hyperlinked content. Any web content you wish to include as part of

your evidence must be submitted as a document file, which must conform to the file

format and response length requirements.



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What Do I Need to Write?

Instruction Commentary

In Instruction Task 2, you will write a commentary, responding to the prompts below. Your

commentary should be no more than 6 single-spaced pages, including the prompts. If

needed, insert no more than 2 additional pages of supporting documentation for the

videorecordings at the end of the commentary (e.g., digital copies of indiscernible materials

or transcriptions of inaudible comments). These additional pages do not count toward the

commentary page limit noted above.

1. Which lesson or lessons are shown in the video clip(s)? Identify the lesson(s) by

lesson plan number.

2. Promoting a Positive Learning Environment

Refer to scenes in the video clip(s) where you provided a positive learning

environment.

a. How did you demonstrate mutual respect for, rapport with, and responsiveness to

students with varied needs and backgrounds, and challenge students to engage

in learning?

3. Engaging Students in Learning

Refer to examples from the video clip(s) in your responses to the prompts.

a. Explain how your instruction engaged students in developing

conceptual understanding,

procedural fluency, AND

mathematical reasoning and/or problem-s

olving skills.

b. Describe how your instruction linked students’ prior academic learning and

personal, cultural, and/or community assets with new learning.

4. Deepening Studen

t Learning during Instruction

Refer to examples from the video clip(s) in your explanations.

a. Explain how you elicited and built on student responses to promote thinking

and develop conceptual understanding, procedural fluency, AND mathematical

reasoning and/or problem-solving skills.

b. Explain how you used representations

to support students’ understanding and

use of mathematical concepts and procedures.

5. Analyzing Teaching

Refer to examples from the video clip(s) in your responses to the prompts.

a. What changes would you make to your instruction—for the whole class and/or for

students who need greater support or challenge—to better support student

learning of the central focus (e.g., missed opportunities)?

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Consider the variety of learners in your class who may require different

strategies/support (such as students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students).

b. Why do you think these changes would improve student learning? Support your

explanati

on with evidence of student learning AND principles from theory and/or

research.

How Will the Evidence of My Teaching Practice Be

Assessed?

For Instruction Task 2, your evidence will be assessed using rubrics 6–10, which appear on

the following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, instruction, and writing.

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Instruction Rubrics

Rubric 6: Learning Environment

How does the candidate demonstrate a respectful learning environment that supports students’ engagement in

learning?

Level 1 Level 2 Level 3 Level 4 Level 5

The clip(s) reveal evidence of

disrespectful interactions

between teacher and students

or between students.

Candidate allows disruptive

behavior to interfere with

student learning.

The candidate demonstrates

respect for students.

AND

Candidate provides a learning

environment that serves

primarily to control student

behavior, and minimally

supports the learning goals.

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a

positive, low-risk learning

environment that reveals

mutual respect among

students.

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a

challenging learning

environment that promotes

mutual respect among

students.

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a

challenging learning

environment that provides

opportunities to express

varied perspectives and

promotes mutual respect

among students.

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Rubric 7: Engaging Students in Learning

How does the candidate actively engage students in developing conceptual understanding, procedural fluency,

AND/OR mathematical reasoning and/or problem-solving skills?

Level 1 Level 2 Level 3 Level 4 Level 5

Students are participating in

tasks that are vaguely or

superficially related to the

central focus.

Students are participating in

learning tasks focusing

primarily on mathematical

procedures with little

attention to understanding of

• mathematical concepts OR

• mathematical reasoning

and/or problem-solving

skills.

Students

are engaged in

learning tasks that address

understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Students ar

e engaged in

learning tasks that develop

understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Students ar

e engaged in

learning tasks that deepen

and extend their

understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

There

is little or no evidence

that the candidate links

students’ prior academic

learning or personal,

cultural, or community

assets with new learning.

Candidate makes vague or

superficial links between

prior academic learning and

new learning.

Candidate links prior

academic learning to new

learning.

Candidate links prior academic

learning AND personal,

cultural, or community

assets to new learning.

Candidate prompts students

to link prior academic learning

AND personal, cultural, or

community assets to new

learning.

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Rubric 8: Deepening Student Learning

How does the candidate elicit responses to promote thinking and to develop conceptual understanding,

procedural fluency, AND mathematical reasoning and/or problem-solving skills?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate does most of the

talking and students provide

few responses.

Candida

te responses include

significant content

inaccuracies that will lead to

student misunderstandings.

Candida

te primarily asks

surface-level questions and

evaluates student responses

as correct or incorrect.

Candidate elicits student

responses related to

understanding

• mathematical concepts,

• procedures, OR

• mathematical reasoning

and/or problem-solving

skills.

Candida

te elicits and builds

on students’ responses to

develop understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Level 4 plus:

Candida

te facilitates

interactions among students

so they can evaluate their

own abilities to understand

and apply

•

mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

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Rubric 9: Subject-Specific Pedagogy: Using Representations

How does the candidate use representations to develop students’ understanding of mathematical concepts and

procedures?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate stays focused on

facts or procedures with little

or no attention to

mathematical concepts.

Candidate uses

mathematically inappropriate

representations or uses

representations in ways that

will lead to student

misunderstandings.

Candidate makes vague or

superficial use of

representations to help

students understand

mathematical concepts and

procedures.

Candidate uses

representations in ways that

help students understand

mathematical concepts and

procedures.

Candidate provides

opportunities for students to

use representations in ways

that deepen student

understanding of

mathematical concepts and

procedures.

Level 4 plus:

Candidate facilitates

interactions among students

so they can evaluate their

own abilities to use

representations to represent

and understand mathematical

concepts and procedures.

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Rubric 10: Analyzing Teaching Effectiveness

How does the candidate use evidence to evaluate and change teaching practice to meet students’ varied

learning needs?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate suggests changes

unrelated to evidence of

student learning.

Candidate proposes changes

to teacher practice that are

superficially related to

student learning needs (e.g.,

task management, pacing,

improving directions).

Candidate proposes changes

that address students’

collective learning needs

related to the central focus.

Candidate makes superficial

connect

ions to research

and/or theory.

Candi

date proposes changes

that address individual and

collective learning needs

related to the central focus.

Candidate makes

connections to research

and/or theory.

Level 4 plus:

Candidate justifies changes

using principles from

research and/or theory.

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Assessment Task 3: Assessing Student

Learning

What Do I Need to Think About?

In Assessment Task 3, you will analyze both student learning and student use of language.

Before you begin the analysis, you need to think about the following:

How will you gather evidence and ma

ke sense of what students have learned?

How will you provide meaningful feedback to your students?

How will you use evidence of what students know and are able to do to plan next

teps

in instruction?

How will you identify evidence of and explai

n students’ use of language that

demonstrates the development of content understanding?

What Do I Need to Do?

Select one assessment from your learning segment you will use to evaluate your

students’ developing knowledge and skills. It should be an assessment that is completed

by the whole class featured in the learning segment. (If you are teaching only a group

within the class for the learning segment, that group will be “the whole class.”) The

assessment should reflect the work of individuals, not groups, but may be individual

work from a group task. The assessment should provide opportunities for students to

demonstrate

conceptual understanding,

proc

edural fluency, AND

mathe

matical reasoni

ng and/or problem-solving skills.

Define and submi

t the evaluation criteria you will use to analyze student learning

related to the mathematical goals described above.

Collect and analyze student work from

the selected assessment to identify

quantitative and qualitative patterns of learning within and across learners in the class.

You may submit text files with scanned student work, a video or audio file of a student’s

oral work, OR a student-created video or multimedia file. For each focus student, a video

or audio work sample must be no more than 5 minutes in total running time.

Select 3 student work samples th

at represent the patterns of learning (i.e., what

individuals or groups generally understood and what a number of students were still

struggling to understand) you identified in your assessment analysis. These students will

be your focus students for this task. At least one of the focus students must have

specific learning needs, for example, a student with an IEP (Individualized Education

Program) or 504 plan, an English language learner, a struggling reader, an

underperforming student or a student with gaps in academic knowledge, and/or a gifted

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student needing greater support or challenge. Note: California candidates must include

one focus student who is an English Language Learner.

Document the feedback you gave to each of the 3 focus students on the work sample

itself, as an audio clip, or as a video clip. You must submit evidence of the actual

feedback provided to each focus student, and not a description of the feedback.

If you submit a student work sample or feedback as a video or audio c

lip and comments

made by you or your focus student(s) cannot be clearly heard, do one of the following: 1)

attach a transcription of the inaudible comments (no more than 2 additional pages) to

the end of the Assessment Commentary; 2) embed quotes with time-stamp references in

the commentary response; or 3) insert captions in the video (captions for this purpose

will be considered permissible editing).

If you submit a student work sample or feedback as a video or audi

o clip and additional

students are present, clearly identify which students are your focus students in the

relevant prompts (1d and 2a) of the Assessment Commentary (in no more than 2

sentences).

Respond to the prompt

s listed in the Assessment Commentary section below after

analyzing student work from the selected assessment.

Include and submit the chosen assess

ment, including the directions/prompts

provided to students. Attach the assessment (no more than 5 additional pages) to

the end of the Assessment Commentary.

Provide evidence of students’ understanding and use of

the targeted academic

language function and other language demands. You may choose evidence from the

video clip(s) submitted in Instruction Task 2, an additional video clip of one or more

students using language within the learning segment (no more than 5 minutes in

length), AND/OR student work samples submitted in Assessment Task 3.

California candidates—If you do not have any English language learners, select a student who is challenged by academic

English.

See the Assessment Task 3: Artifacts and Commentary Specifications in the

Secondary Mathematics Evidence Chart for instructions on electronic submission of

evidence. The evidence chart identifies templates, supported file types, number of

files, response length, and other important evidence specifications. Your evidence

cannot contain hyperlinked content. Any web content you wish to include as part of

your evidence must be submitted as a document file, which must conform to the file

format and response length requirements.

What Do I Need to Write?

Assessment Commentary

In Assessment Task 3, you will write a commentary, responding to the prompts below. Your

commentary should be no more than 10 single-spaced pages, including the prompts.

Attach the assessment used to evaluate student performance (no more than 5 additional

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

pages) and, if necessary, a transcription of inaudible portions of a video or audio clip of

feedback or a student work sample (no more than 2 additional pages) to the end of the

Assessment Commentary. These additional pages do not count toward the commentary

page limit noted above.

1. Analyzing Student Learning

a. Identify the specific learning object

ives measured by the assessment you chose

for anal

ysis.

b. Provide a graphic (table or chart) or narrative that summarizes student learning

for your whole class. Be sure to summarize student learning for all evaluation

criteria submitted in Assessment Task 3, Part D.

c. Use evidence found in the 3 student work samples and the whole class

summary to analyze the patterns of learning for the whole class and

differences for groups or individual learners relative to

conceptual understanding,

ocedural fluency, AND

mathemati

cal reasoning and/or probl

em-solving skills.

Consider what students understand and do well, and where they continue to

struggle (e.g., preconceptions, common errors, common struggles, confusions,

and/or need for greater challenge).

d. If a video or audio wor

k sample occurs in a group context (e.g., discussion),

provide the name of the clip and clearly describe how the scorer can identify the

focus student(s) (e.g., position, physical description) whose work is portrayed.

2. Feedback to Guide Fu

rther Learning

Refer to specific evidence of submitted feedback to support your explanations.

a. Identify the format in which you submitted your evidence of feedback for the 3

focus students. Choose one of the following:

Written directly on work samples or in separate documents that were

provided to th

e focus students

In audio files

In video clip(s) from Instruction Task 2 (provide a time-stamp reference) or in

separate video clips

If a video or audio clip of feedback occurs in a group context (e.g., discussion),

clearly descri

be how the scorer can identify the focus student (e.g., position,

physical description) who is being given feedback.

b. Explain how feedback provided to the 3 focus students addresses their individual

strengths and needs relative to the learning objectives measured.

c. Describe how you will support each focus student to understand and use this

feedback to further their learning related to learning objectives, either within the

learning segment or at a later time.

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3. Evidence of Language Understanding and Use

When responding to the prompt below, use concrete examples from the clip(s)

and/or student work samples as evidence. Evidence from the clip(s) may focus on

one or more students.

You may provide evidence of students’ language use from ONE, TWO, OR

ALL THREE of the following sources:

1. Use the video clip(s) from Instruction Task 2 and provide time-stamp

references for evidence of language use.

2. Submit an additional video file named “Language Use” of no more than

5 minutes in length and cite language use (this can be footage of one or

more students’ language use). Submit the clip in Assessment Task 3,

Part B.

3. Use the student work samples analyzed in Assessment Task 3 and cite

language use.

a. Explain and provide concrete examples for the extent to which your students

were able to use or struggled to use the

selected language function,

vocabulary and/or symbol

s, AND

mathematical precision, di

scourse, or syntax

to develop content understandings.

4. Using Assessment to Inform Instruction

a. Based on your analysis of student learning presented in prompts 1b–c, describe

next steps for instruction to impact student learning:

For the whole class

For the 3 f

ocus students and other i

ndividuals/groups with specific needs

Consider the variety of learners in your class

who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students needing greater support or

challenge).

b. Explain how these next steps follow from your analysis of student learning.

Support your ex

planation with principles from research and/or theory.

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How Will the Evidence of My Teaching Practice Be

Assessed?

For Assessment Task 3, your evidence will be assessed using rubrics 11–15, which appear

on the following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, planning, instruction, assessment, and writing.

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Assessment Rubrics

Rubric 11: Analysis of Student Learning

How does the candidate analyze evidence of student learning of conceptual understanding, procedural fluency,

AND mathematical reasoning and/or problem-solving skills?

Level 1 Level 2 Level 3 Level 4 Level 5

The analysis is superficial or

not supported by either

student work samples or the

summary of student

learning.

The evaluation criteria,

learning objectives, and/or

analysis are not aligned with

each other.

The analysis focuses on what

students did right OR wrong.

The analysis focuses solely

on students’ ability to apply

procedures and/or their

factual knowledge.

The analysis focuses on what

students did right AND wrong.

AND

Analysis includes some

differences in whole class

learning.

Analysis uses specific

examples from work samples

to demonstrate patterns of

learning consistent with the

summary.

AND

Patterns of learning are

described for whole class.

Analysis uses specific

evidence from work samples to

demonstrate the connections

between quantitative and

qualitative patterns of learning

for individuals or groups.

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Rubric 12: Providing Feedback to Guide Learning

What type of feedback does the candidate provide to focus students?

Level 1 Level 2 Level 3 Level 4 Level 5

Feedback is unrelated to the

learning objectives OR is

developmentally

inappropriate.

Feedback cont

ains

significant content

inaccuracies.

No feedback is provided to

one or more focus students.

Feedba

ck is general and

addresses needs AND/OR

strengths related to the

learning objectives.

Feedback is specific and

addresses either needs OR

strengths related to the

learning objectives.

Feedback is specific and

addresses both strengths

AND needs related to the

learning objectives.

Level 4 plus:

Feedback for one or more

focus students

• provides a strategy to

address an individual

learning need OR

•

makes connections to

prior learning or

experience to improve

learning.

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Rubric 13: Student Understanding and Use of Feedback

How does the candidate support focus students to understand and use the feedback to guide their further

learning?

Level 1 Level 2 Level 3 Level 4 Level 5

Opportunities for

understanding or using

feedback are not described.

Candidate provides limited or

no feedback to inform

student learning.

Candidate provides vague

description of how focus

students will understand or

use feedback.

Candidate describes how

focus students will understand

or use feedback related to the

learning objectives.

Candidate describes how s/he

will support focus students to

understand and use feedback

on their strengths OR

weaknesses related to the

learning objectives.

Candidate describes how s/he

will support focus students to

understand and use feedback

on their strengths AND

weaknesses related to the

learning objectives.

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Rubric 14: Analyzing Students’ Language Use and Mathematics Learning

How does the candidate analyze students’ use of language to develop content understanding?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate identifies student

language use that is

superficially related or

unrelated to the language

demands (function,

vocabulary and/or symbols,

and additional demands).

Candidate

’s description or

explanation of language use

is not consistent with the

evidence submitted.

Candidate

describes how

students use only one

language demand

(vocabulary and/or symbols,

function, mathematical

precision, discourse,

syntax).

Candidate explains and

provides evidence of

students’ use of

• the language function

AND

• one or more additional

language demands

(vocabulary and/or

symbols, mathematical

precision, discourse,

syntax).

Candidate explains and

provides evidence of students’

use of

• the language function,

• vocabulary and/or

symbols, AND

• additional language

demand(s) (mathematical

precision, discourse,

syntax)

in ways that develop content

understa

ndings.

Level 4 plus:

Candida

te explains and

provides evidence of

language use and content

learning for students with

varied needs.

The selected language function is the verb identified in the Planning Commentary Prompt 4a (conjecture, explain, etc.).

These are the additional language demands identified in the Planning Commentary Prompt 4c (vocabulary and/or symbols, mathematical precision, plus syntax or discourse).

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Rubric 15: Using Assessment to Inform Instruction

How does the candidate use the analysis of what students know and are able to do to plan next steps in

instruction?

Level 1 Level 2 Level 3 Level 4 Level 5

Next steps do not follow from

the analysis.

Next steps ar

e not relevant to

the learning objectives

assessed.

Next steps are not described

in sufficient detail to

understand them.

Next steps p

rimarily focus on

changes to teaching

practice that are

superficially related to

student learning needs, for

example, repeating

instruction, pacing, or

classroom management

issues.

Next steps propose general

support that improves

student learning related to

assessed learning

objectives.

Next steps a

re loosely

connected with research

and/or theory.

Next steps pro

vide targeted

support to individuals or

groups to improve their

learning relative to

• conceptual understanding,

• procedural fluency,

AND/OR

• mathematical reasoning

and/or problem-solving

skills.

Next steps are connected

with research and/or theory.

Next steps pr

ovide targeted

support to individuals AND

groups to improve their

learning relative to

• conceptual understanding,

• procedural fluency,

AND/OR

• mathematical reasoning

and/or problem-solving

skills.

Next steps are justified with

principles from research

and/or theory.



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Professional Responsibilities

Refer to the following table for an overview of your professional responsibilities in

developing evidence for edTPA. If you are submitting artifacts and commentaries for official

scoring, refer to www.edTPA.com, f

or complete and current information before beginning

your work. Included here are important information and policies such as submission

requirements and deadlines, registration agreements, attestations, permissions, and

confidentiality. Whether or not you are submitting for official scoring, you should fulfill the

professional responsibilities described below.

Responsibility Description

Protect

confidentiality

To protect confidentiality, please remove your name and use pseudonyms or general

references (e.g., “the district”) for your state, school, district, and cooperating teacher. Mask or

remove all names on any typed or written material (e.g., commentaries, lesson plans, student

work samples) that could identify individuals or institutions. During videorecording, use

students’ first names only.

To ensure confidentiality of your students and yourself, do not share your video on any publicly

accessible platforms or websites (YouTube, Facebook, etc.).

Acquire

permissions

Before you record your classroom instruction, ensure that you have the appropriate permission

from the parents/guardians of your students and from adults who appear in the videorecording.

Your program will provide you with procedures and necessary forms to obtain these

permissions, according to agreements with the school or district in which you are student

teaching or completing your internship.

If your program does not provide the necessary forms, you may refer to the sample forms

found on www.edTPA.com

The release forms are not to be submitted with your materials, but you should follow your

campus policy for retaining them.

Cite sources

Provide citations for the source of all materials that you did not create (e.g., published texts,

websites, and material from other educators). List all citations by lesson number at the end of

the Planning Commentary. Note: Citations do not count toward the commentary page limit.

Align instruction

with state

standards

As part of the assessment, you will document the alignment of your lesson plans with state-

adopted academic content standards that are the target of student learning. Refer to the

education agency website for your state to obtain copies of relevant standards for this

assessment.

Follow the

guidelines for

candidate

support at

www.edTPA.com

Follow the guidelines for candidate support found at www.edTPA.com as you develop your

evidence for edTPA. Although you may seek and receive appropriate support from your

university supervisors, cooperating/master teachers, university instructors, or peers during this

process, the ultimate responsibility for completing this assessment lies with you. Therefore,

when you submit your completed work, you must be able to confirm your adherence

with certain statements, such as the following:

I have primary responsibility for teaching the students/class during the learning segment

profiled in this assessment.

I have not previously taught this learning segment to the students/class.

The video clips submitted are unedited (continuous) and show me teaching the

students/class profiled in the evidence submitted.

The student work included in the documentation is that of my students, completed during

the learning segment documented in this assessment.

I am author of the commentaries and other written responses to prompts in this

assessment.

Appropriate citations have been made for all materials in the assessment whose sources

are from published text, the Internet, or other educators.

edTPA Secondary Mathematics Assessment Handbook

39 of 51

_____

Secondary Mathematics Context for

Learning Information

Use the Context for Learning Information to supply information about your school/classroom

context.

About the School Where You Are Teaching

1. In what type of school do you teach? (Type an “X” next to the appropriate

description; if “other” applies, provide a brief description.)

Middle school:

High school:

Other (pl

ease describe):

2. Where is the school where you are teaching located? (Type an “X” next to the

appropriate description.)

City:

Subur

Town:

Rural:

3. List any special features of your school or classroom setting (e.g., charter, co-

teaching, themed magnet, remedial course, honors course) that will affect your

teaching in this learning segment.

4. Describe any district, school, or cooperating teacher requirements or expectations

that might affect your planning or delivery of instruction, such as required curricula,

pacing plan, use of specific instructional strategies, or standardized tests.

If you need guidance when making a selection, reference the NCES locale category definitions

(https://nces.ed.gov/surveys/ruraled/definitions.asp) or consult with your placement school administrator.

About the Class Featured in this Learning Segment

1. What is the name of this course?

2. What is the length of the course? (Type an “X” next to the appropriate description; if

“other” applies, provide a brief description.)

One semester:

One year:

Other (please describe):

3. What is the class schedule (e.g., 50 minutes every day, 90 minutes every other

day)?

4. Is there any ability grouping or tracking in mathematics? If so, please describe how it

affects your class.

edTPA Secondary Mathematics Assessment Handbook



40 of 51

___________________________________________________________________

_____

_____ _

____

5. Identify any textbook or instructional program you primarily use for mathematics

instruction. If a textbook, please provide the title, publisher, and date of publication.

6. List other resources (e.g., electronic whiteboard, graphing calculators, online

resources) you use for mathematics instruction in this class.

About the Students in the Class Featured in this Learning Segment

1. Grade-level composition (e.g., all seventh grade; 2 sophomores and 30 juniors):

2. Number of

students in the class:

males: females:

3. Complete the charts below to summarize required or needed supports,

accommodations, or modifications for your students that will affect your instruction in

this learning segment. As needed, consult with your cooperating teacher to complete

the charts. Some rows have been completed in italics as examples. Use as many

rows as you need.

Consider the variety of learners in your class who may require different

strategies/supports or accommodations/modifications to instruction or

assessment. For example, students

With Individualized Education Programs (IEPs) or 504 plans

With specific language needs

Needing greater challenge or support

Who struggle with reading

Who are underperforming students or have gaps in academic

knowledge

For Assessment Task 3, you will choose work samples from 3 focus

students. At least one of these students must have a specified learning need.

Note: California candidates must include one focus student who is an English

language learner.

California candidates—If you do not have any English language learners, select a student who is challenged by academic

English.

edTPA Secondary Mathematics Assessment Handbook

41 of 51

Students with IEPs/504 Plans

IEPs/504 Plans:

lassifications/Needs

Number of

Students

Supports, Accommodations,

Modifications, Pertinent IEP Goals

Example: Visual processing 2 Close monitoring, translating

nformation in word problems into

sketches

Students with Specific Language Needs

Language Needs Number of

tudents

Supports, Accommodations,

Modifications

Example: English Language

Learners with only a few

words of English

2 Pre-teach key words and phrases

through examples and graphic

organizers (e.g., word cluster,

manipulatives, visuals)

Have students use pre-taught key

ords and graphic organizers to

complete sentence starters

Example: Students who

eak a variety of English

other than that used in

textbooks

5 Make connections between the

language students bring and the

language used in the textbook

Students with Other Learning Needs

Other Learning Needs Number of

Students

Supports, Accommodations,

Modifications

Example: Struggling readers 5 Provide oral explanations for

rections and simplified text for word

problems



edTPA Secondary Mathematics Assessment Handbook

42 of 51

Secondary Mathematics Evidence Chart

Your evidence must be submitted to the electronic portfolio management system used by your teacher preparation program. Your

submission must conform to the artifact and commentary specifications for each task. This section provides instructions for all

evidence types as well as a description of supported file types for evidence submission, number of files, response lengths, and

other information regarding format specifications. Note that your evidence cannot contain hyperlinked content. Any web content

you wish to include as part of your evidence must be submitted as a document file, which must conform to the file format and

response length requirements. If you have materials that must be translated into English as per the

edTPA Submission

Requirements, those translations should be added to the original materials as part of the same file or, if applicable, to the end of

he commentary template. There is no page limit for required translations into English.

Planning Task 1: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

dditional Information

Min Max

Part A: Context for

Learning

Information

(template provided)

.doc; .docx; .odt; .pdf 1 1

No more than 4

pages, including

prompts

Use Arial 11-point type.

Single space with 1" margins on all sides.

Part B: Lesson

Plans for Learning

Segment

.doc; .docx; .odt; .pdf 1 1

No more than 4

pages per lesson

Submit 3–5 lesson plans in 1 file.

Within the file, label each lesson plan (Lesson 1, Lesson 2, etc.).

All rationale or explanation for plans should be written in the Planning

Com

mentary and removed from lesson plans.

Part C:

Instructional

Materials

.doc; .docx; .odt; .pdf 1 1

No more than 5

pages of KEY

instructional materials

per lesson plan

Submit all materials in 1 file.

Within the file, label materials by corresponding lesson (Lesson 1

Instructional Materials, Lesson 2 Instructional Materials, etc.).

Order materials as they are used in the learning segment.

Part D:

Assessments

.doc; .docx; .odt; .pdf 1 1 No limit

Submit assessments in 1 file.

Within the file, label assessments by corresponding lesson

(Lesson 1 Assessments, Lesson 2 Assessments, etc.).

Order assessments as they are used in the learning segment.

Part E: Planning

Commentary

(template provided)

.doc; .docx; .odt; .pdf 1 1

No more than 9

pages of

commentary,

including prompts

Use Arial 11-point type.

Single space with 1" margins on all sides.

Respond to prompts before teaching the learning segment.



edTPA Secondary Mathematics Assessment Handbook

43 of 51

Instruction Task 2: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

ditional Information

Min Max

Part A: Video

Clips

flv, asf, qt, mov, mpg,

mpeg, avi, wmv, mp4,

m4v

1 2

No more than

15 minutes total

running time (but

not less than 3

minutes)

Before you record your video, obtain permission from the

parents/guardians of your students and from adults who appear on

the video.

Refer to Instruction Task 2, What Do I Need to Do? for video c

lip

content and requirements.

When nami

ng each clip file, include the number of the lesson

shown in the video clip.

Part B: Instruction

Commentary

(template provided)

.doc; .docx; .odt; .pdf 1 1

No more than 6

pages of

commentary,

including prompts

If needed, no more

than 2 additional

pages of supporting

documentation

Use Arial 11-point type.

Single space with 1" margins on all sides.

IMPORTANT:

Insert documentation at the end of the commentary file if

you or the students are using graphics, texts, or images that are

not clearly visible in the video

you chose to submit a transcript for occasionally inaudible

portions of the video

If submitting documentation, include the video clip number, lesson

number, and explanatory text (e.g., “Clip 1, lesson 2, text from a

whiteboard that is not visible in the video,” “Clip 2, lesson 4,

transcription of a student response that is inaudible”).

Video file size requirements: The target file size is 200–300 MB or less. The Pearson ePortfolio System file size limit is 500 MB. Please note that each integrated platform

provider portfolio system may have additional constraints or requirements regarding video formats and file sizes. You may need to use video tools to compress or transcode your

video into smaller file sizes to facilitate uploading of the video. Refer to Recommended Video Formats and Settings on www.edtpa.com for the current requirements.



edTPA Secondary Mathematics Assessment Handbook

(Continued on next page)

44 of 51

Assessment Task 3: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Addi

tional Information

Min Max

Part A: Student

Work Samples

For written work

mples: .doc; .docx;

.odt; .pdf

For audio work

sample

s: flv, asf,

wmv, qt, mov, mpg,

avi, mp3, wav, mp4,

wma

For video work

sample

s: flv, asf, qt,

mov, mpg, mpeg, avi,

wmv, mp4, m4v

3 3

No page limit for

written work

samples

No more than 5

minutes per focus

student for video or

audio student work

samples

Use correction fluid, tape, or a felt-tip marker to

mask or remove

students’ names, your name, and the name of the school

before copying/scanning any work samples. If your students’

writing is illegible, write a transcription directly on the work sample.

On each work sample, indicate the student number (Student 1

Work Sa

mple, Student 2 Work Sample, or Student 3 Work Sample).

If more than one focus student appears in a video or audio work

sample, upload the same work sample separately for each focus

student who is seen/heard and label appropriately. Describe how to

recognize each of the focus students in the clip and provide the

label associated with the clip in prompt 1d of the Assessment

Commentary.

When naming each work sample file, include th

e student number.

If you submit a student work sample or feedback as a video or

audio clip and comments made by you or your focus student(s)

cannot be clearly heard, do one of the following: 1) attach a

transcription of the inaudible comments (no more than 2

additional pages) to the end of the Assessment Commentary

; 2)

embed quotes with time-stamp references in the commentary

response; or 3) insert captions in the video (captions for this purpose

will be considered permissible editing).

Video file size requirements: The target file size is 200–300 MB or less. The Pearson ePortfolio System file size limit is 500 MB. Please note that each integrated platform

provider portfolio system may have additional constraints or requirements regarding video formats and file sizes. You may need to use video tools to compress or transcode your

video into smaller file sizes to facilitate uploading of the video. Refer to Recommended Video Formats and Settings on www.edtpa.com for the current requirements.



edTPA Secondary Mathematics Assessment Handbook

Assessment Task 3: Artifacts and Commentary Specifications (continued)

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min Max

(Continued on next page)

45 of 51

Part B: Evidence of

Feedback

And, if included,

video evidence of

academic language

use

For written feedba

not written on the

work samples: .doc;

.docx; .odt; .pdf

For audio feedback:

flv, asf, wmv, qt, mov,

mpg

, avi, mp3, wav,

mp4, wma

For video clips

(feedback

and/or

language use): flv,

asf, qt, mov, mpg,

mpeg, avi, wmv, mp4,

m4v

0 4

No page limi

t for

written feedback

No more than 3

minutes per focus

tudent for video or

audio feedback

No more than 5

minutes for video

evidence of student

language use

Document the locati

on of your evidence of feedback in the

Assessment Commentary.

If fee

dback is not included as part of the student work samples or

recorded on the video clip(s) from Instruction Task 2, submit only 1

file for each focus student—a document, video file, OR audio file—

and label the file with the corresponding student number (Student 1

Feedback, Student 2 Feedback, or Student 3 Feedback).

If more than one focus student appears in a video or audio clip of

feedback, upload the same clip separately for each focus student

who is seen/heard and label appropriately.

When naming each feedback file, include the student number.

If you submit a student work sample or feedback as a video or

audio clip and comments made by you or your focus student(s)

cannot be clearly heard, do one of the following: 1) attach a

transcription of the inaudible comments (no more than 2

additional pages) to the end of the Assessment Commentary;

embed quotes with time-stamp references in the commentary

response; or 3) insert captions in the video (captions for this purpose

will be considered permissible editing)

For Academic Language – If you choose to submit a video clip of

student language use, it should be no more than 5 minutes. You

may identify a portion of a clip provided for Instruction Task 2 or

submit an entirely new clip.

Video file size requirements: The target file size is 200–300 MB or less. The Pearson ePortfolio System file size limit is 500 MB. Please note that each integrated platform

provider portfolio system may have additional constraints or requirements regarding video formats and file sizes. You may need to use video tools to compress or transcode your

video into smaller file sizes to facilitate uploading of the video. Refer to Recommended Video Formats and Settings on www.edtpa.com for the current requirements.



edTPA Secondary Mathematics Assessment Handbook

Assessment Task 3: Artifacts and Commentary Specifications (continued)

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min Max

46 of 51

Part C:

Assessment

Commentary

(template provided)

.doc; .docx; .odt; .pdf 1 1

No more

than 10

pages of

commentary,

including prompts

Plus

no more than 5

dditional

pages for the

chosen

assessment,

if necessary, no

more than 2

additional total

pages of

transcriptions of

video/audio

evidence for a

work sample

and feedback,

and/or video

evidence of

language use

Use Arial 11-point type.

Single space with 1" margins on all sides.

IMPORTANT: In

sert a copy of the chosen assessment, including

directions/prompts provided to students.

rt D: Evaluation

Criteria

.doc; .docx; .odt; .pdf 1 1 No limit

edTPA Secondary Mathematics Assessment Handbook



47 of 51

Secondary Mathematics Glossary

Source citations for glossary entries are provided as footnotes in this section.

academic language: Oral and written language used for academic purposes. Academic

language is the means by which students develop and express content understandings.

Academic language represents the language of the discipline that students need to learn

and use to participate and engage in the content area in meaningful ways. There are

language demands that teachers need to consider as they plan to support student learning

of content. These language demands include language functions, vocabulary and/or

symbols, discourse, and syntax.

language demands:

Specific ways that academic language (vocabulary and/or

symbols, functions, discourse, syntax) is used by students to participate in learning

tasks through reading, writing, listening, and/or speaking to demonstrate their

disciplinary understanding.

language functions: The content and language focus of the learning task,

represented by the active verbs within the learning outcomes. Common language

functions in mathematics include describing mathematical phenomena, predicting

from models and data, comparing based on common attributes, summarizing

mathematical information, recording multiple ways to solve problems, justifying

conclusions, evaluating data and mathematical representations, classifying based

on attributes, explaining how or why certain strategies work, drawing conclusions

based on data, representing mathematical information, and so on. Some specific

mathematics verbs are non-examples of language functions because they focus on a

mathematical action, not a language-based action. Examples of mathematical

functions that ARE NOT language functions include solve problems, simplify the

expressions, calculate the answers, and estimate the answers.

vocabulary: Includes words and

phrases that are used within disciplines including:

(1) words and phrases with subject-specific meanings that differ from meanings used

in everyday life (e.g., table); (2) general academic vocabulary used across disciplines

(e.g., compare, analyze, evaluate); and (3) subject-specific words defined for use in

the discipline.

discourse: Di

scourse includes the structures of written and oral language, as well as

how members of the discipline talk, write, and participate in knowledge construction.

Discipline-specific discourse has distinctive features or ways of structuring oral or

written language (text structures) that provide useful ways for the content to be

O'Hara, S., Pritchard, R., & Zwiers, J. (2012). Identifying academic language demands in support of the common core

standards. ASCD Express, 7(17). Retrieved from http://www.ascd.org/ascd-express/vol7/717-ohara.aspx

Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science

standards for English language learners: What teachers need to know. Retrieved from

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf

______ _______

edTPA Secondary Mathematics Assessment Handbook

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48 of 51

communicated.

In mathematics, language structures include symbolic

representations, such as numbers, equations, two-column proofs (which can be

translated into words), graphic representation (which is shorthand language for

complex sets of data), and narrative (e.g., to describe or compare). If the language

function is to prove, then appropriate language structures include formal two-column

proofs as well as informal explanations that begin with a statement of the problem

and known information, followed by a series of statements such as “And then, I know

because ,” ending with what is to be proved.

syntax: The set of conventions for organizing symbols, words, and phrases together

into structures

(e.g., sentences, graphs, tables).

language supports: The s

caffolds, rep

resentations, and pedagogical strategies

teachers provide to help learners understand, use, and practice the concepts and

language they need to learn within disciplines (Santos, Darling-Hammond, Cheuk,

2012).

The language supports planned within the lessons in edTPA should directly

support learners to understand and use identified language demands (vocabulary

and/or symbols, language function, and discourse or syntax) to deepen content

understandings.

aligned: Consistently address

ing the same/similar learning outcomes for students.

artifacts: Authentic work completed by you and your students including lesson plans,

copies of instructional and assessment materials, video clips of your teaching, and student

work samples. Artifacts are submitted as part of your evidence.

assessment (formal or informal): “[R]efer[s] to all those activities undertaken by teachers

and by their students

. . . that provide information to be used as feedback to modify the

teaching and learning activities”

for both students and teachers. Assessments provide

evidence of students’ prior knowledge, thinking, or learning in order to evaluate what

students understand and how they are thinking at a given point in time for the purpose of

promoting student learning. Informal assessments may include such things as student

questions and responses during instruction and teacher observations of students as they

work or perform. Formal assessments may include such things as quizzes, homework

assignments, journals, projects, and performance tasks.

assets (knowledge of students):

personal: Refers to speci

fic background information that students bring to the

learning environment. Students may bring interests, knowledge, mathematical

dispositions, everyday experiences, family backgrounds, and so on, which a teacher

can draw upon to support learning.

Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science

standards for English language learners: What teachers need to know. Retrieved from

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf

Zwiers, J. (2008). Building academic language: Essential practices for content classrooms. San Francisco, CA: Jossey-Bass.

Santos, M., Darling-Hammond, L., & Cheuk, T. (2012). Teacher development to support English language learners in the

context of common core state standards. Stanford University Understanding Language. Available at

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/10-Santos%20LDH%20Teacher%20Development%20FINAL.pdf

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan,

80(2), 139–148.

edTPA Secondary Mathematics Assessment Handbook

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49 of 51

cultural: Refers to the cultural backgrounds and practices that students bring to the

learning environment, such as traditions, languages and dialects, worldviews,

literature, art, and so on, that a teacher can draw upon to support learning.

community: Refers to com

mon backgrounds and experiences that students bring

from the community where they live, such as resources, local landmarks, community

events, practices, and so on, that a teacher can draw upon to support learning.

central focus: A desc

ription of the important understandings and core concepts that you

want students to develop w

ithin the learning segment. The central focus should go beyond a

list of facts and procedures, align with content standards and learning objectives, and

address the subject-specific components in the learning segment. For example, the subject-

specific components for secondary mathematics are: conceptual understanding, procedural

fluency, AND mathematical reasoning and/or problem-solving skills. A central focus for the

learning segment might be relationships between symbolic expressions and graphs of lines.

The learning segment would focus on conceptual understanding of linear functions, slope,

and intercepts, and the associated procedures and mathematical reasoning and/or problem-

solving skills.

commentary: Submitted as pa

rt of each task and, along with artifacts, make up your

evidence. The commentaries should be written to explain the rationale behind your teaching

decisions and to analyze and reflect on what you have learned about your teaching practice

and your students’ learning.

conceptual understanding: “Students demonstrate conceptual understanding in

mathemati

cs . . . when they recognize, label, and generate examples of concepts; use and

interrelate models, diagrams, manipulatives, and varied representations of concepts; identify

and apply principles; know and apply facts and definitions; compare, contrast, and integrate

related concepts and principles; recognize, interpret, and apply the signs, symbols, and

terms used to represent concepts.”

engaging students in learning: Using instructional and motivational strategies that

promote students’ active involvement in learning tasks that increase their knowledge, skills,

and abilities related to specific learning objectives. Engagement in learning contrasts with

student participation in learning tasks that are not well designed and/or implemented and do

not increase student learning.

evaluation criteria: Performance indicators or dimensions t

hat are used to assess evidence

of student learning. They indicate the qualities by which levels of performance can be

differentiated and that anchor judgments about the learner’s degree of success on an

assessment. Evaluation criteria can be represented in various ways, such as a rubric, a

point system for different levels of performance, or rules for awarding full versus partial

credit. Evaluation criteria may examine correctness/accuracy, cognitive complexity,

sophistication or elaboration of responses, or quality of explanations.

evidence: Consists of artifacts that document how you planned and implemented

instruction AND commentaries that explain your plans and what is seen in the

videorecording(s) or examine what you learned about your teaching practice and your

students’ learning. Evidence should demonstrate your ability to design lesson plans with

National Assessment of Educational Progress (NAEP). (2003). Conceptual understanding. In What Does the NAEP

Mathematics Assessment Measure? Retrieved from: http://nces.ed.gov/nationsreportcard/mathematics/abilities.asp

edTPA Secondary Mathematics Assessment Handbook

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instructional supports that deepen student learning, use knowledge of your students to

inform instruction, foster a positive learning environment that promotes student learning,

monitor and assess student progress toward learning objectives, and analyze your teaching

effectiveness. Your evidence must be submitted electronically using the electronic portfolio

management system used by your teacher preparation program.

learning environment: The des

igned physical and emotional context, established and

maintained throughout the learning segment to support a positive and productive learning

experience for students.

learning objectives: Student learning outcomes to be achieved by the end of the lesson or

learning segm

ent.

learning segment: A set of 3–5 lessons that build one upon another toward a central focus,

with a clearly defined beginning and end.

learning task: Includes activities, discussions, or other modes of participation that engage

students to develop, practice, and apply skills and knowledge related to a specific learning

goal. Learning tasks may be scaffolded to connect prior knowledge to new knowledge and

often include formative assessment. A sample mathematical learning task for algebra II

might be to give students an equation ax

+ bx + c. Show them how to use graphic

calculators to find a graph for y = 2x

+ 3x + 5. Then ask them to plug in different values for

a, b, and c, selecting positive and negative rational numbers, and record conjectures about

how the value of each affects the graph.

mathematical reasoning: “[T]he capacity to think logically about the relationships among

concepts and situations. Such reasoning is correct and valid, stems from careful

consideration of alternatives, and includes knowledge of how to justify the conclusions. . . .

One uses it to navigate through the many facts, procedures, concepts, and solution methods

and to see that they all fit together in some way, that they make sense.”

patterns of lear

ning: Includes both quantitative and qualitative patterns (or consistencies)

for different groups of students or individuals. Quantitative patterns indicate in a numerical

way the information understood from the assessment (e.g., 10 out of 15 students or 20% of

the students). Qualitative patterns include descriptions of understandings,

misunderstandings, and/or partial understandings that could explain the quantitative

patterns (e.g., “given that most students were able to . . . it seems that they understand”).

planned supports: Instructional strategies, learning tasks and materials, and other

resources deliberately designed to facilitate student learning of the central focus.

prior academic learning and prerequisite skills: Includes students’ content knowledge

and skills as well as academic experiences developed prior to the learning segment.

problem-solving skills: Skills to “engag[e] in a task for which the solution method is not

known in advance.”

National Research Council. (2001). Adaptive reasoning. In Adding it up: Helping children learn mathematics (p. 151).

Washington, DC: National Academy Press.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics (p. 52).

Reston, VA: NCTM.

edTPA Secondary Mathematics Assessment Handbook

51 of 51

procedural fluency: Procedural fluency is a critical component of mathematical proficiency.

Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to

transfer procedures to different problems and contexts; to build or modify procedures from

other procedures; and to recognize when one strategy or procedure is more appropriate to

apply than another. To develop procedural fluency, students need experience in integrating

concepts and procedures and building on familiar procedures as they create their own

informal strategies and procedures. Students need opportunities to justify both informal

strategies and commonly used procedures mathematically, to support and justify their

choices of appropriate procedures, and to strengthen their understanding and skill through

distributed practice.

rapport: A close and harmonious relationship in which the people or groups understand

each other’s feelings or ideas and communicate well with each other.

representation: The term representation refers both to process and to product—in other

words, to the act of capturing a mathematical concept or relationship in some form and to

the form itself. . . . Moreover, the term applies to processes and products that are

observable externally as well as to those that occur “internally,” in the minds of people doing

mathematics. All these meanings of representation are important to consider in school

mathematics. (From National Council of Teachers of Mathematics [2000]. Principles and

Standards for School Mathematics, p. 67)

respect: A positive feeling of esteem or deference for a person and specific actions and

conduct representative of that esteem. Respect can be a specific feeling of regard for the

actual qualities of the one respected. It can also be conduct in accord with a specific ethic of

respect. Rude conduct is usually considered to indicate a lack of respect, disrespect,

whereas actions that honor somebody or something indicate respect. Note that respectful

actions and conduct are culturally defined and may be context dependent.

rubrics: Subject-specific evaluation criteria used to score your performance on edTPA.

These rubrics are included in the handbook following the directions for each task. The

descriptors in the five-level rubrics address a wide range of performance, beginning with the

knowledge and skills of a novice not ready to teach (Level 1) and extending to the advanced

practices of a highly accomplished beginner (Level 5).

variety of learners: Students in your class who may require different strategies or support.

These students include but are not limited to students with IEPs or 504 plans, English

language learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students.

From "Procedural Fluency in Mathematics". Downloaded from www.nctm.org on February 9, 2016.

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