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Middle Childhood Mathematics

Assessment Handbook

Version 06.1

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 Middle Childhood Mathematics Assessment Handbook

Contents

Introduction to edTPA Middle Childhood Mathematics ................................................................... 1

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

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

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

edTPA Middle Childhood 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

Planni

ng 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 M

y 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? ........................................................................... 31

Assessment Rubrics ............................................................................................................................................. 32

Professional Responsibilities ........................................................................................................... 37

Middle Childhood Mathematics Context for Learning Information .............................................. 38

Midd

le Childhood Mathematics Evidence Chart ............................................................................ 41

Planning Task 1: Artifacts and Commentary Specifications .................................................................................. 41

Instruction Task 2: Artifacts and Commentary Specifications ............................................................................... 42

Assessment Task 3: Artifacts and Commentary Specifications ............................................................................ 43

Middle Childhood Mathematics Glossary ....................................................................................... 46

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Introduction to edTPA Middle Childhood

Mathematics

Purpose

The purpose of edTPA Middle Childhood Mathematics, a nationally available performance-

based assessment, is to measure novice teachers’ readiness to teach mathematics to

young adolescents. The assessment is designed with a focus on young adolescent learning

and principles from research and theory. It is based on findings that successful teachers

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

pedago

develop and apply knowledge of varied students’ needs

consider research and theory about how students learn

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

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

demons

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

Overview of the Assessment

The edTPA Middle Childhood 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 Mathematics

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

approach to mathematics. This means your segment should include learning tasks where

young

adolescents have opportunities to develop

conceptual understanding

procedural fluency

mathematical reasoning and/or problem-solving skills

precise communication skills

In addition, consistent with the recommendations provided by the Association for Middle

Level

Education (AMLE),

a learning segment prepared for this assessment should be

See the AMLE Middle Level Teacher Preparation Standards (2012) at

http://www.amle.org/AboutAMLE/ProfessionalPreparation/AMLEStandards/tabid/263/Default.aspx.

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“developmentally responsive, challenging, empowering, and equitable.” While the full scope

of AMLE’s recommendations will not be feasible in a short learning segment, you should

design your lessons to provide challenging and responsive opportunities for young

adolescents to learn mathematics.

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, assessment

materials, instructional materials, student work samples), as well as comm

entaries that you

hav

e 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 young adolescent learning in mathematics. This evidence

includes both artifacts and commentaries:

Artifacts represent authenti

c work completed by you and your students. These

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

your teaching, and student work samples.

Commentaries are your

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

Middle Chi

ldhood 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 Middle Childhood 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

ask.

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

or the task.

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

Professional Responsibilities: g

uidelines for the development of your evidence

Middle Childhood Mathematics Context for Learning Information: prompts used

to collect information about your school/classroom context

Middle Childhood 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: definitions

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

glossary term marked with a dotted underline throughout t

he handbook or by

referring to the Middle Childhood Mathematics Glossary.

You should review the Making Good 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 Middle Childhood 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,

ach, 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

earning segment. The central focus

should support young adolescent

learners to develop conceptual

understanding, procedural fluency, AND

mathematical reasoning and/or problem-

solving skills, as well as interdisciplinary

connections.

Write and submit a lesson plan for each

esson in the learning segment.

Select and submit key instructional

mate

rials needed to understand what you

and the students will be doing.

Choose one language function and other

anguage demands important to

understanding middle childhood

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

d/or clear directions for any oral or

performance assessments from the

learning segment.

What to Submit

Part A: Context for Learning

Information

Part B: Lesson Plans for

earning Segment

Part C: Instructional

Mate

rials

Part D: Assessments

Part E: Planning

Commen

tary

Evaluation Rubrics

Planning Rubrics

Rubric 1: Planning for

Math

ematical Understandings

Rubric 2: Planning to Support

aried Student Learning Needs

Rubric 3: Using Knowledge of

tudents to Inform Teaching and

Learning

Rubric 4: Identifying and

upporting Language Demands

Rubric 5: Planning Assessments to

Mon

itor 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

young adolescents 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 20

minutes in total, but not less than 3

minutes).

Analyze your teaching and your students’

earning in the video clip(s) by

responding to commentary prompts.

What to Submit

Part A: Video Clips

Part B: Instruction

Commentary

Evaluation Rubrics

Instruction Rubrics

Rubric 6: Learning Environment

Rubr

ic 7: Engaging Students in

Learning

Rubric 8: Deepening Student

earning

Rubric 9: Subject-Specific

edagogy: Using Representations

Rubric 10: Analyzing Teaching

ffectiveness

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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 young adolescent performance

to the end of the Assessment

Commentary.

Define and submit the evaluation criteria

you wi

ll use to analyze young adolescent

learning.

Collect and analyze young adolescent

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

lustrate your analysis of patterns of

learning within and across learners in the

class. At least 1 of the samples must be

from a young adolescent 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

young adolescent understanding across

the class.

Submit feedback for the work samples for

the 3

focus students in written, audio, or

video form.

Analyze evidence of young adolescents’

lan

guage use from (1) the video 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 young adolescent

learning, and plan for next steps by

responding to commentary prompts.

What to Submit

Part A: Student Work

Samples

Part B: Evidence of

Feedb

ack

Part C: Assessment

Commentar

Part D: Evaluation Criteria

Evaluation Rubrics

Assessment Rubrics

Rubric 11: Analysis of Student

Lear

ning

Rubric 12: Providing Feedback to

ide Learning

Rubric 13: Student

Under

standing and Use of

Feedback

Rubric 14: Analyzing Students’

Lang

uage Use and Mathematics

Learning

Rubric 15: Using Assessment to

Infor

m 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 developmentally appropriate for young adolescents 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 ar

e the important understandings,

core concepts, and interdisciplinary connections you want students to develop within

he learning segment?

How will you use your knowledge of your students’ assets to inform

your plans?

What instructional strategies, learning task

s, and assessments will you design to

upport young adolescent 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

tudents 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 Middle Childhood Mathematics Context for Learning

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

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

teaching 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

obj

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

young adolescents in developing

conceptual understanding

procedural fluency

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mathematical reasoning and/or problem-solving skills

interdisciplinary connections as relevant

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 plans must include the following information, even if your teacher

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

State-adopted 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 (subject-specific and, as relevant, interdisciplinary) associated

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

Instructional resources and materials used to engage young adolescents 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 Middle

Childhood 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

rections)

lesson plans (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

earning segment.

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

ithin your learning segment address

conceptual understanding,

edural fluency, AND

mathematical reasoning and/or problem-solving skills.

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

bet

ween concepts, computations/procedures, AND mathematical reasoning

and/or problem-solving strategies to build understanding of mathematics.

d. Explain how you will help young adolescents make interdisciplinary or integrative

connections between the central focus of the learning segment and other subject

areas.

2. Knowledge of Students to Inform Teaching

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

ith respect to the central focus of the learning segment.

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Consider the variety of young adolescent 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).

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

evidence of what young adolescents 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. Young adolescent developmental assets related to the central focus—What do

you know about your students’ cognitive, physical, and

social and

emotional development?

d. 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 Lea

rning

Respond to prompts 3a–d below. To support your justifications, refer to the

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

1. In addition, support your justifications using principles from research and/or

theory, including how the research/theory reflects elements of young

adolescent development.

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

prompt 2a 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 and research/theory.

b. Justify how your understanding of your students’ personal, cultural, community,

and developmental assets (from prompts 2b–c above) guided your choice or

adaptation of learning tasks and materials. Be explicit about the connections

between the learning tasks and students’ assets and research/theory.

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

are

appropriate for the whole class, individuals, and groups of young

adolescents with specific learning needs.

Consider the variety of young adolescent learners in your class who may require

different strategies/support (e.g., young adolescents with IEPs or 504 plans,

English language learners, struggling readers, underperforming students or those

with gaps in academic knowledge, and/or gifted students).

From the Common Core State Standards for Mathematics

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d. 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 al

ready know, what are they struggling with, and/or

what is new to them?

a. Language Function. Using i

nfo

rmation about your students’ language assets

and needs, identify one language function essential for young adolescents to

develop conceptual understanding, procedural fluency, and mathematical

reasoning or problem-solving skills within your central focus. Listed below are

some sample language functions. You may choose one of these or another more

appropriate for your learning segment.

Compare/contrast Describe Expla

in Justify 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 young adolescents with

opportunities to practice using the language function. 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) young adolescents need to understand and/or use:

Vocabulary and/or symbols

Mathematical 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:

Syntax

Discourse

d. Language Supports. Refer to your lesson plans and instructional materials as

needed in your response to the prompt below.

Identify and describe the planned instructional supports (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, syntax, or discourse).

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.

For an elaboration of “precision,” refer to the Standards for Mathematical Practice in 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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a. Describe how your planned formal and informal assessments will provide direct

evidence of young adolescents’ 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 young

adolescents with specific needs to demonstrate their learning.

Consider the vari

ety of young adolescent learners in your class who may require

different strategies/support (e.g., young adolescents with IEPs or 504 plans,

English language learners, struggling readers, underperforming students or those

with gaps in academic knowledge, and/or gifted students).

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 young adolescents’ 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

ina

ccuracies that will lead to

young adolescent

misunderstandings.

Standards, objectives,

learning t

asks, and materials

are not aligned with each

other.

Candidate’s plans for

instr

uction support 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

nstruction 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.

Plans support

mathematics

learning and imply

interdisciplinary

connections.

Level 4 plus:

Candidate explains how s/he

will use

learning tasks and

materials to lead young

adolescents to make clear

and consistent connections

within mathematics, as well

as explicit and relevant,

interdisciplinary

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 young adolescents 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

ied 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

strategies 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 young

adolescents and their

backgrounds.

Candidate justifies learning

sks with limited attention to

young adolescents’

• prior academic learning

• personal, cultural,

community, or

developmental assets.

Candi

date justifies why

learning tasks (or their

adaptations) are appropriate

using examples of young

adolescents’

• prior academic learning

• personal, cultural,

community, or

developmental assets.

Candidat

e makes superficial

connections to research

and/or theory.

Candidate justifies why

earning tasks (or their

adaptations) are appropriate

using examples of young

adolescents’

• prior academic learning

AND

• personal, cultural,

community, or

developmental assets.

Candi

date makes

connections to research

and/or theory, including young

adolescent development.

Level 4 plus:

Candidate’s justification is

supported by principles

from research and/or theory,

including young adolescent

development.

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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 supports are

mis

sing or are not aligned

with the language

demand(s) for the learning

task.

Language supports primarily

address

one language

demand (vocabulary and/or

symbols, function,

mathematical precision,

syntax, discourse).

General language supports

address use of two or more

language demands

(vocabulary and/or symbols,

function, mathematical

precision, syntax, discourse).

Targeted language supports

address use of

• vocabulary and/or

symbols,

• language function, AND

• one or more additional

language demands

(mathematical precision,

syntax, discourse).

Level 4 plus:

Langua

ge supports are

designed t

o meet the needs

of young adolescents with

different levels of language

learning.

Language demands include: language function, vocabulary and/or symbols, mathematical precision, 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 young adolescents’ 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.

Candidate does not attend to

ANY

ASSESSMENT

requirements in IEPs and 504

plans.

The assessments provide

lim

ited evidence to monitor

young adolescents’

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning

and/or problem-solving

skills

during the lea

rning segment.

The assessments provide

vidence to monitor young

adolescents’

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning

and/or problem-solving

skills

dur

ing the learning segment.

The assessments provide

ultiple forms of evidence

to monitor young adolescents’

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 young adolescents

in learning. Before you begin your instruction, you need to think about the following:

What kind of learning environment do you want to develop in order to establish

respect and rapport, and to support young adolescents’ engagement in learning?

What kinds of learning tasks actively engage young adolescents in the central focus

of the learning segment?

How will you elicit and build on young adolescents’ responses in ways that develop

and deepen c

ontent understanding?

In what ways will you connect new content to young adolescents’ prior academic

earning and personal, cultural, community, or developmental assets during your

nstruction?

How will you use evidence from your instruction to examine and change your

eaching practices to more effectively meet a variety of young adolescent 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 challenging learning tasks

in which you and young adolescents are actively engaged. The video clip(s) you select

for submission should provide a sample of how you interact with young adolescents 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 clips (no more than 20 minutes total, but not less than 3

inutes) that demonstrate how you interact with young adolescents in a positive

learning environment to develop

conceptual understanding,

procedural fluency, AND

mathematical reasoning and/or problem-solving skills.

(Optional) Provide evidence of students’ language use. You may provide evidence

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

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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.

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

adolescents (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 Middle

Childhood Mathematics Evidence Chart for instructions on electronic submission of

evidence. This 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. Wh

ich lesson or lessons are shown in the video clip(s)? Identify the lesson(s) by lesson

plan number.

2. Pr

omoting a Positive Learning Environment

fer 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

young adolescents with varied needs (academic and developmental) and

backgrounds, and challenge young adolescents to engage in learning?

3. Engagi

ng Students in Learning

Ref

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

a. Ex

plain how your instruction engaged young adolescents in developing

conc

eptual understanding

procedural fluency

mathematical reasoning and/or problem-solving skills

b. Des

cribe how your instruction linked young adolescents’ prior academic learning and

personal, cultural, community, or developmental assets with new learning.

4. Deepeni

ng Student Learning during Instruction

Ref

er 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. Ex

plain how you used representations to support young adolescents’ understanding

and use of mathematical concepts and procedures.

5. Analyzing Teaching

Ref

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

a. Wh

at changes would you make to your instruction—for the whole class and/or for

young adolescents 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 young adolescent 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 young adolescent learning? Support

your explanation with evidence of young adolescent learning AND principles from

theory and/or research, including young adolescent development.

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 young adolescents’

engagement in learning?

Level 1 Level 2 Level 3 Level 4 Level 5

The clip(s) reveal evidence of

disrespectful interactions

between teacher and young

adolescents or between young

adolescents.

Candidate allows disruptive

beha

vior to interfere with

young adolescent learning.

The candidate demonstrates

spect for young

adolescents.

AND

Candidate provides a learning

env

ironment that serves

primarily to control young

adolescent behavior, and

minimally supports the

learning goals.

The candidate demonstrates

rapport with and respect for

young adolescents.

AND

Candidate provides a

posit

ive, low-risk learning

environment that reveals

mutual respect among

young adolescents.

The candidate demonstrates

rapport with and respect for

young adolescents.

AND

Candidate provides a

hallenging learning

environment that promotes

mutual respect among young

adolescents.

The candidate demonstrates

rapport with and respect for

young adolescents.

AND

Candidate provides a

allenging learning

environment that provides

opportunities to express

varied perspectives and

promotes mutual respect

among young adolescents.

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Rubric 7: Engaging Students in Learning

How does the candidate actively engage young adolescents 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

Young adolescents are

participating in tasks that are

vaguely or superficially related

• mathematical concepts,

• procedures, OR

• mathematical reasoning

and/or problem-solving

skills.

ung adolescents 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.

Young adolescents are

engaged in learning tasks that

address understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Young

adolescents are

engaged in learning tasks that

develop understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Young

adolescents are

engaged in learning tasks that

deepen and extend their

understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Ther

e is little or no evidence

that the candidate links

young adolescents’ prior

academic learning or

personal, cultural,

community, or

developmental 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,

community, or

developmental assets to new

learning.

Candidate prompts young

adolescents to link prior

academic learning AND

personal, cultural, community,

or developmental 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 young

adolescents provide few

responses.

Candidate responses include

signif

icant content

inaccuracies that will lead to

student misunderstandings.

Candidate primarily asks

surf

ace-level questions and

evaluates young adolescents’

responses as correct or

incorrect.

Candidate elicits young

adolescents’ responses

related to understanding

• mathematical concepts,

• procedures, OR

• mathematical reasoning

and/or problem-solving

skills.

Candi

date elicits and builds

on young adolescents’

responses to develop

understanding of

• mathematical concepts,

• procedures, AND

• mathematical reasoning

and/or problem-solving

skills.

Level 4 plus:

Candidate facilitates

int

eractions among young

adolescents 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 young adolescents’ 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

athematically inappropriate

representations or uses

representations in ways that

will lead to young

adolescents’

misunderstandings.

Candidate makes vague or

supe

rficial use of

representations to help

young adolescents understand

mathematical concepts and

procedures.

Candidate uses

representations in ways that

address young adolescents’

understanding of

mathematical concepts and

procedures.

Candidate provides

opportunities for students to

use representations in ways

that deepen young

adolescents’ understanding

of mathematical concepts

and procedures.

Level 4 plus:

Candidate facilitates

interactions among young

adolescents 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 young adolescents’

varied learning needs?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate suggests changes

unrelated to evidence of

young adolescent 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 young

adolescents’ collective

learning needs related to the

central focus.

Candidate makes superficial

conne

ctions to research

and/or theory.

Candidate proposes changes

at address individual and

collective learning needs

related to the central focus.

Candidate makes

connections to research

and/or theory, including young

adolescent development.

Level 4 plus:

Candidate justifies changes

using principles from

research and/or theory,

including young adolescent

development.

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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 evi

dence and make 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 expl

ain 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 young

adolescents to demonstrate

conceptual understanding

procedural fluency

mathematical reasoning and/or

problem-solving skills

Define and submit

the evaluation criteria you will use to analyze young adolescent

earning 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.

ou 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 that

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

individuals or groups generally understood and what a number of young adolescents

were still struggling to understand) you identified in your assessment analysis. These

young adolescents 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

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knowledge, and/or a gifted 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 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).

If you submit a student work sample or feedback as a video or audio clip and additional

udents 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 prompts listed in the Assessment Commentary section below after

analyzing student work from the selected assessment.

Include and submit the chosen assessment, including the directions/prompts provided to

udents. Attach the assessment (no more than 5 additional pages) to the end of the

Assessment Commentary.

Provide evidence of young adolescents’ understanding and use of the targeted

academi

c language function and other language demands. You may choose

evi

dence 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 Middle

Childhood Mathematics Evidence Chart for instructions on electronic submission of

evidence. This 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 objectives measured by the assessment you chose

for analysis.

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,

procedural fluency, AND

mathematical reasoning and/or problem-solving skills.

Consider what young adolescents understand and do well, and where they

continue to struggle (e.g., preconceptions, common errors, common struggles,

confusions, need for greater challenge).

d. If a video or audio work 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 Further 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 the 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 describe 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

REE 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. Subm

it 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. Us

e 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

ere able to use or struggled to use the

sel

ected language function,

vocabulary and/or symbols, AND

mathematical precision, syntax, or discourse

to develop content understandings.

4. Using Assessment to Inform Instruction

a. Bas

ed on your analysis of young adolescent learning presented in prompts 1b–c,

describe next steps for instruction to impact student learning:

For

the whole class

For the 3 focus students and other individuals/groups with specific needs

Consider the variety of young adolescent learners in your class who may require

fferent 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 young adolescent

learning. Support your explanation with principles from research and/or theory as

well as young adolescent development.

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 young adolescent 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 work

samples or the summary of

young adolescent learning.

The evaluation criteria,

earning objectives, and/or

analysis are not aligned with

each other.

The analysis focuses on what

young a

dolescents did right

OR wrong.

The analysis focuses solely

young adolescents’ ability

to apply procedures and/or

their factual knowledge.

The analysis focuses on what

young adolescents did right

AND wrong.

AND

Analysis includes some

dif

ferences 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

des

cribed for whole class.

Analysis uses specific

vidence 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 contains

signif

icant content

inaccuracies.

No feedback is provided to

one or m

ore focus students.

Feedback is general and

addre

sses 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

ocus 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 f

eedback to inform

student learning.

Candidate provides vague

des

cription 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 young adolescents’ use of language to develop content understanding?

Level 1 Level 2 Level 3 Level 4 Level 5

Candidate identifies young

adolescent 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

young adolescents

use only

one language demand

(vocabulary and/or symbols,

function, mathematical

precision, syntax, or

discourse).

Candidate explains and

provides evidence of young

adolescents’ use of

• the language function

AND

• one or more additional

language demands

(vocabulary and/or

symbols, mathematical

precision, syntax,

discourse).

Candidate explains and

provides evidence of young

adolescents’ use of

• the language function,

• vocabulary and/or

symbols, AND

• additional language

demand(s) (mathematical

precision, syntax,

discourse)

in ways that develop content

understandi

ngs.

Level 4 plus:

Candidate explains and

provides evidence of

language use and content

learning for young

adolescents with varied

needs.

Previous footnote is now obsolete and has been deleted.

9 Previous footnote is now obsolete and has been deleted.

edTPA Middle Childhood Mathematics Assessment Handbook

Assessment Rubrics continued

36 of 51

Rubric 15: Using Assessment to Inform Instruction

How does the candidate use the analysis of what young adolescents 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 are not relevant to

he learning objectives

assessed.

Next steps are not described

in s

ufficient detail to

understand them.

Next steps primarily focus on

cha

nges 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

young adolescent learning

related to assessed learning

objectives.

Next steps are loosely

onnected with research

and/or theory.

Next steps provide targeted

upport 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 a

re connected with

research and/or theory,

including young adolescent

development.

Next steps provide targeted

pport 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 a

re justified with

principles from research

and/or theory, including young

adolescent development.

edTPA Middle Childhood Mathematics Assessment Handbook

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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, for 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

acc

essible 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

cam

pus 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

prof

iled in this assessment.

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

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

udents/class profiled in the evidence submitted.

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

the l

earning segment documented in this assessment.

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

asse

ssment.

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

are f

rom published text, the Internet, or other educators.

edTPA Middle Childhood Mathematics Assessment Handbook

_____

____

_____

38 of 51

Middle Childhood 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.)

Elementary school (K–6):

Middle school (6–8):

K–8:

7–9:

Other (please describe):

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

appropr

iate description.)

City:

Suburb:

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, interdisciplinary teaming, 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

fects your class.

edTPA Middle Childhood Mathematics Assessment Handbook

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39 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

res

ources) you use for mathematics instruction in this class.

About the Young Adolescents in the Class Featured in this

Learning Segment

1. Grade level:

Age range of students:

2. Number of

students in the class:

males: females:

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

acc

ommodations, 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 young adolescent learners in your class who may

quire 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

know

ledge

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

udents. 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 Middle Childhood Mathematics Assessment Handbook

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Students with IEPs/504 Plans

IEPs/504 Plans:

Classifications/Needs

Number of

Students

Supports, Accommodations,

Modifications, Pertinent IEP Goals

Example: Visual processing 2 Close monitoring, translating

information in word problems into

sketches

Students with Specific Language Needs

Language Needs Number of

Students

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

words and graphic organizers to

complete sentence starters

Example: Students who

speak 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

directions and simplified text for word

problems

edTPA Middle Childhood Mathematics Assessment Handbook

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Middle Childhood 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

Requi

rements, 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

Additional Information

Min Max

Part A: Context for

Learning

Information

(template provided)

.doc; .docx; .odt; .pdf

1 1 No more than

4 page

s, including

prompts

Use Arial 11-poin

t type.

Single space with 1" margins on all sides.

Part B: Lesson

ans for Learning

Segment

.doc; .docx; .odt; .pdf

1 1 No more than 4

page

s per lesson

Submit 3–5 lesson plans in 1 file.

Within the fi

le, label each lesson plan (Lesson 1, Lesson 2, etc.).

All rationale or explanation for plans should be written in the

anning Commentary and removed from lesson plans.

Part C:

Instr

uctional

Materials

.doc; .docx; .odt; .pdf

1 1 No more than

5 pages of KE

instructional materials

per lesson plan

Submit all material

s in 1 file.

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

Instr

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

Order materials as they are used in the learning segment.

Part D:

Asse

ssments

.doc; .docx; .odt; .pdf

1 1

No limit

Submit assessments in 1 file.

Within the file, label assessments by corresponding lesson

(Le

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

Order assessments as they are used in the learning segment.

Part E: Planning

Commentar

(template provided)

.doc; .docx; .odt; .pdf

1 1 No more than

9 pages o

commentary,

including prompts

Use Arial 11-poin

t type.

Single space with 1" margins on all sides.

Respond to prompts before teaching the learning segment.

edTPA Middle Childhood Mathematics Assessment Handbook

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42 of 51

Instruction Task 2: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min Max

Part A: Video

Clips

flv, asf, qt, mov, mpg,

mpeg, avi, wmv, mp4,

m4v

1 2 No more than

20 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 in

the video.

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

deo clip

content and requirements.

When naming each clip file, include the number of the lesson

shown

in the video clip.

Part B: Instruction

Commentar

(template

pro

vided)

.doc; .docx; .odt; .pdf

1 1 No more than

6 pages of

mmentary,

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 occasional inaudible

por

tions of the video

If submitting documentation, include the video clip number, lesson

numbe

r, 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 requirem

ents.

edTPA Middle Childhood Mathematics Assessment Handbook



(Continued on next page)

43 of 51

Assessment Task 3: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min Max

Part A: Student

Work Samples

For written work

samples: .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 f

ocus

student for video or

audio student work

samples

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

student

s’ 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 Sample, 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 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; 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 Middle Childhood 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)

44 of 51

Part B: Evidence

of Feedback

And, if included,

video evidence of

academic

language use

For written feedback

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 limit for

written feedback

No more than 3

minutes per focus

student for video or

audio feedback

No more than 5

minutes for video

evidence of

student language

use

Document the location of your evidence of feedback in the

Assessment Commentary.

If feedback 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; 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).

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 Middle Childhood 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



45 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

additional pages

for the chosen

assessment

if necessary, no

more than 2

additional total

pages of

transcription of

video/audio

evidence for a

work sample,

feedback, and/or

video evidence of

language use

Use Arial 11-point type.

Single space with 1" margins on all sides.

IMPORTANT: Insert a copy of the chosen assessment, including

directions/prompts provided to students.

Part D: Evaluation

Criteria

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

No limit

edTPA Middle Childhood Mathematics Assessment Handbook

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46 of 51

Middle Childhood 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,

discourse, and syntax.

language demands:

Specific ways that academic language (vocabulary, 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, 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) w

ords 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: Discourse 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

communicated.

In mathematics, language structures include symbolic

representations such as numbers, equations, two-column proofs (which can 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 ELLs. Retrieved from http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%

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

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

standards for ELLs. Retrieved from http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%

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

edTPA Middle Childhood Mathematics Assessment Handbook

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47 of 51

_______ _______

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 scaffolds, representations, 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 addressing 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 and 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

teaching and learning activities.”

Assessments provide evidence of students’ prior

knowledge, thinking, or learning in order to evaluate what students understand and how they

are thinking. 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 specific background information that young adolescents bring to

the learning environment. Students may bring interests, knowledge, mathematical

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

draw upon to support learning.

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 common backgrounds and experiences that students bring

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

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

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 Middle Childhood Mathematics Assessment Handbook

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developmental: Refers to specific background information about cognitive, physical,

social, and emotional development that a teacher can draw upon to support student

learning. See below for definitions of each aspect of development.

central focus: A description of the important understandings and core concepts that you

want students to develop within 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 middle childhood 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.

cognitive development: Refers to the changes and advancement that occur in intellectual

development during adolescence, such as the shift from concrete operational thinking to

formal abstract thinking.

commentary: Submitted as part 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

mathematics . . . 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 that 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

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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.

integrative: The Association for Middle Level Education (AMLE) encourages middle grades

teachers to design curriculum and select materials that are integrative, challenging, and

grounded in the ideas, interests, and experiences of all young adolescents. In an integrative

curriculum, a problem or issue, often initiated by the learners, is the driving force for

organizing the curriculum.

interdisciplinary: An interdisciplinary curriculum makes connections across several

disciplines through a theme that crosses curricular lines. The learning experiences require

that knowledge from several disciplines be utilized to explore the concepts and skills of the

curriculum.

learning environment: The designed 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 segment.

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 learning: 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”).

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

Washington, DC: National Academy Press.

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physical development: Refers to the growth and development of skeletal, structural, and

muscular systems that includes the changes brought about by puberty.

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.”

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 pos

itive 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).

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

Reston, VA: NCTM.

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

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social and emotional development: Refers to the ways in which adolescents develop

understandings of self and others. Milestones at various levels of development include

identity formation, self-awareness/self-concept, pro-social behavior, peer relationships,

social responsibility, and moral reasoning.

variety of young adolescent learners: Students in your class who may require different

strategies or support. These young adolescents 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.

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