edTPA_SecMath_05
Secondary Mathematics
Assessment Handbook
September 2016
edTPA Secondary Mathematics Assessment Handbook
edTPA stems from a twenty-five-year history of developing performance-based assessments of
teaching quality and effectiveness. The Teacher Performance Assessment Consortium (Stanford
and AACTE) acknowledges the National Board for Professional Teaching Standards, the
Interstate Teacher Assessment and Support Consortium, and the Performance Assessment for
California Teachers for their pioneering work using discipline-specific portfolio assessments to
evaluate teaching quality. This version of the handbook has been developed with thoughtful input
from over six hundred teachers and teacher educators representing various national design
teams, national subject matter organizations (ACEI, ACTFL, AMLE, CEC, IRA, NAEYC, NAGC,
NCSS, NCTE, NCTM, NSTA, SHAPE America), and content validation reviewers. All
contributions are recognized and appreciated.
This document was authored by the Stanford Center for Assessment, Learning, and Equity (SCALE)
with editorial and design assistance from Evaluation Systems.
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University. All rights reserved.
The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the
edTPA trademarks is permitted only pursuant to the terms of a written license agreement.
edTPA Secondary Mathematics Assessment Handbook
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
i
Contents
Introduction to edTPA Secondary Mathematics............................................................................... 1
Purpose................................................................................................................................................................... 1
Overview of the Assessment ................................................................................................................................... 1
Structure of the Handbook ...................................................................................................................................... 3
edTPA Secondary Mathematics Tasks Overview ................................................................................................... 5
Planning Task 1: Planning for Instruction and Assessment .......................................................... 8
What Do I Need to Think About? ............................................................................................................................ 8
What Do I Need to Do? ........................................................................................................................................... 8
What Do I Need to Write? ..................................................................................................................................... 10
How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 13
Planning Rubrics ................................................................................................................................................... 14
Instruction Task 2: Instructing and Engaging Students in Learning ........................................... 19
What Do I Need to Think About? .......................................................................................................................... 19
What Do I Need to Do? ......................................................................................................................................... 19
What Do I Need to Write? ..................................................................................................................................... 21
How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 22
Instruction Rubrics ................................................................................................................................................ 23
Assessment Task 3: Assessing Student Learning ........................................................................ 28
What Do I Need to Think About? .......................................................................................................................... 28
What Do I Need to Do? ......................................................................................................................................... 28
What Do I Need to Write? ..................................................................................................................................... 29
How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 32
Assessment Rubrics ............................................................................................................................................. 33
Professional Responsibilities ........................................................................................................... 38
Secondary Mathematics Context for Learning Information .......................................................... 39
Secondary Mathematics Evidence Chart ........................................................................................ 42
Planning Task 1: Artifacts and Commentary Specifications .................................................................................. 42
Instruction Task 2: Artifacts and Commentary Specifications ............................................................................... 43
Assessment Task 3: Artifacts and Commentary Specifications ............................................................................ 44
Secondary Mathematics Glossary ................................................................................................... 47
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edTPA Secondary Mathematics Assessment Handbook
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This document contains both information and definition pop-ups. To read information, use the Down Arrow from a form field.
Introduction to edTPA Secondary
Mathematics
Purpose
The purpose of edTPA Secondary Mathematics, a nationally available performance-based
assessment, is to measure novice teachers’ readiness to teach secondary mathematics.
The assessment is designed with a focus on student learning and principles from research
and theory. It is based on findings that successful teachers
develop knowledge of subject matter, content standards, and subject-specif
ic
pedagogy
develop and apply knowledge of varied students’ needs
consider r
esearch and theory about how students learn
re
flect on and analyze evidence of the effects of instruction on student learning
As
a performance-based assessment, edTPA is designed to engage candidates in
demonstrating their understanding of teaching and student learning in authentic ways.
Overview of the Assessment
The edTPA Secondary Mathematics assessment is composed of three tasks:
1. Planning for Instruction and Assessment
2. Instructing and Engaging Students in Learning
3. Assessing Student Learning
For this assessment, you will first plan 3–5 consecutive mathematics lessons (or, if
teaching within a large time block, 3–5 hours of connected instruction) referred to as a
learning segment. Consistent with the Principles and Standards for School Mathem
atics
(NCTM 2000), a learning segment prepared for this assessment should reflect a balanced
approach t
o mathematics. This means your segment should include learning tasks in which
students have opportunities to develop
conceptual understanding
proc
edural fluency
mathemat
ical reasoning and/or
problem-solving skills
precise communication skills
You will then teach the learning segment, making a videorecording of your interactions with
s
tudents during instruction. You will also assess, informally and formally, students’ learning
throughout the learning segment. Upon completion of the three tasks, you will submit
artifacts from the tasks (e.g., lesson plans, clips from your videorecording, as
sessment
mat
erials, instructional materials, student work samples), as well as commentaries that you
edTPA Secondary Mathematics Assessment Handbook
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have written to explain and reflect on the Planning, Instruction, and Assessment
components of the tasks. The artifacts and commentaries for each task will then be
evaluated using rubrics especially developed for each task.
The edTPA Tasks and the Cycle of Effective Teaching
The three edTPA tasks represent a cycle of effective teaching (i.e., teaching that is focused
on student learning). Planning Task 1 documents your intended teaching, Instruction Task
2 documents your enacted teaching, and Assessment Task 3 documents the impact of
your teaching on student learning.
The three tasks and the evidence you provide for each are framed by your understandings
of your students and their learning. As you develop, document, and teach your lessons, you
will reflect upon the cyclical relationship among planning, instruction, and assessment with a
focus on your students’ learning needs.
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edTPA Secondary Mathematics Assessment Handbook
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Evidence of Teaching Practice: Artifacts and Commentaries
An essential part of edTPA is the evidence you will submit of how you planned, taught, and
assessed your lessons to deepen student learning in mathematics. This evidence includes
both artifacts and commentaries:
Artifacts represent authentic work completed by you and your students. These
i
nclude lesson plans, copies of instructional and assessment materials, video clips of
your teaching, and student work samples.
Commentaries are y
our opportunity to describe your artifacts, explain the rationale
behind their choice, and analyze what you have learned about your teaching practice
and your students’ learning. Note that although your writing ability will not be scored
directly, commentaries must be clearly written and well focused.
When preparing your artifacts and commentaries, refer to the rubrics frequently to guide
your thinking, planning, and writing. Refer to the Secondary Mathematics Evidence Chart
for
information about how your evidence should be formatted for electronic submission.
Evaluation Criteria
The rubrics used to score your performance are included in this handbook, following the
sections describing the directions for each task. The descriptors in the five-level rubrics
address a wide range of performance, beginning with the knowledge and skills of a novice
not ready to teach (Level 1) and extending to the advanced practices of a highly
accomplished beginner (Level 5).
Structure of the Handbook
The following pages provide specific instructions on how to complete each of the three tasks
of the edTPA Secondary Mathematics assessment. After an overview of the tasks, the
handbook provides instructions for each task, organized into four sections:
1. What Do I Need to Think About?
This section provides focus questions for you to think about when completing the
task.
2. What Do I Need to Do?
This section provides specific, detailed directions for completing the task.
3. What Do I Need to Write?
This section tells you what you need to write and also provides specific and detailed
directions for writing the commentary
for the task.
4. How Will the Evidence of My Teaching Practice Be Assessed?
This section includes the rubrics that will be used to assess the evidence you provide
for the task.
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Additional requirements and resources are provided for you in this handbook:
Professional Responsibilities: guidelines for the development of your evidence
Secondary M
athematics Context for Learning Informati
on: prompts used to
collect information about your school/classroom context
Secondary Mathematics Evidence Chart: specifications for
electronic submission
of evidence (artifacts and commentaries), including templates, supported file types,
number of files, response length, and other important evidence specifications
Glossary: defini
tions of key terms can be accessed by rolling your cursor over each
glossary term marked with a dotted underline throughout the handbook or by
referring to the Secondary
Mathematics Glossary.
You should review the Mak
ing G
ood Choices document prior to beginning the planning of
the
learning segment. If you are in a preparation program, it will have additional resources
that provide guidance as you develop your evidence.
Review all instructions carefully before beginning to teach the learning segment to
ensure that you are well prepared for all tasks. Before you record your videos,
pay particular attention to the specific content focus of each video clip
submission; these foci are described in the What Do I Need to Do? sections in
Instruction Task 2 and Assessment Task 3. Refer to the Professional
Responsibilities section of this handbook for important information about
permissions, confidentiality, and other requirements.
If your program requires you to submit artifacts and commentaries for official
scoring, refer to www.edTPA.com for complete and current information before
beginning your work and to download templates for submitting materials. The
website contains information about the registration process, submission deadlines,
submission requirements, withdrawal/refund policies, and score reporting. It also
provides contact information should you have questions about your registration and
participation in edTPA.
Whether submitting directly to www.edTPA.com or via your program’s electronic
portfolio management system, follow the submission guidelines as documented in
the Evidence Chart and review edTPA Submission Requirements to ensure that
your materials conform to the required evidence specifications and requirements for
scoring.
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edTPA Secondary Mathematics Assessment Handbook
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edTPA Secondary Mathematics Tasks Overview
Planning Task 1: Planning for Instruction and Assessment
What to Do
Select one class as a focus for this
assessment.
Provide relevant context information.
Identify a learning segment to plan, teach,
and analyze
student learning. Your
learning segment should include 3–5
consecutive lessons (or, if teaching
mathematics within a large time block,
about 3–5 hours of connected
instruction).
Determine a central focus for your
learning segment. The central focus
should support students to develop
conceptual understanding, procedural
fluency, AND mathematical reasoning
and/or problem-solving skills.
Write and submit a lesson plan for each
lesson in the learning segment.
Select and submit key instructional
materials needed to understand what you
and the students will be doing.
Choose one language function and other
language demands important to
understanding secondary mathematics in
your learning segment. Identify a learning
task where students are supported to use
this language.
Respond to commentary prompts prior to
teaching the learning segment.
Submit copies of all written assessments
and/or clear directions for any oral or
performance assessments from the
learning segment.
What to Submit
Part A: Context f
or Learning
Information
Part B: Lesson Plans for
Learnin
g Segment
Part C: Instructional Materials
Part D: A
ssessments
Part E: Planning Commentary
Evaluation Rubrics
Planning Rubrics
Rubric 1: P
lanning for
Mathematical Understandings
Rubric 2: Planning to Support
Vari
ed Student Learning
Needs
Rubric 3: Using Knowledge of
Students to Infor
m Teaching
and Learning
Rubric 4: Identifying and
Supporting Language
Demands
Rubric 5: Planning
Assessments to Monitor and
Support Student Learning
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Instruction Task 2: Instructing and Engaging Students in Learning
What to Do
Obtain required permissions for
videorecording from parents/guardians of
your students and other adults appearing
in the video.
Identify lessons from the learning segment
you planned in Planning Task 1 to be
videorecorded. You should choose
lessons that show you interacting with
students to develop their conceptual
understanding, procedural fluency, AND
mathematical reasoning and/or problem-
solving skills.
Videorecord your teaching and select 1
or 2
video clips (no more than
15 minutes total, but not less than 3
minutes).
Analyze your teaching and your students’
learning in the video clip(s) by responding
to commentary prompts.
What to Submit
Part A: V
ideo Clips
Part B: Instruction
Commentary
Evaluation Rubrics
Instruction Rubric
s
Rubric 6: Lea
rning
Environment
Rubric 7: Engaging Students
in Lear
ning
Rubric 8: Deepening Student
Learnin
g
Rubric 9: Subject-Specific
Pedagogy: Using
Representations
Rubric 10: Analyzing Teaching
Effectiveness
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Assessment Task 3: Assessing Student Learning
What to Do
Select one assessment from the learning
segment that you will use to evaluate your
students’ developing knowledge and skills.
Attach the assessment used to evaluate
student performance to the end of the
Assessment Commentary.
Define and submit the evaluation criteria
you will use to analyze student learning.
Collect and analyze student work from the
selected assessment to identify
quantitative and qualitative patterns of
learning within and across learners in the
class.
Select 3 student work samples to
illustrate your analysis of patterns of
learning within and across learners in the
class. At least 1 of the samples must be
from a student with specific learning
needs. These 3 students will be your
focus students.
Summarize the learning of the whole
class, referring to work samples from the 3
focus students to illustrate patterns in
student understanding across the class.
Submit feedback for the work samples for
the 3 focus students in written, audio, or
video form.
Analyze evidence of students’ language
use from (1) the video clip(s) from
Instruction Task 2, (2) an additional video
clip of one or more students using
language within the learning segment,
AND/OR (3) the student work samples
from Assessment Task 3.
Analyze evidence of student learning and
plan for next steps by responding to
commentary prompts.
What to Submit
Part A: S
tudent Work
Samples
Part B: Evidence of Feedback
Part C: Assessment
Commentary
Part D: Evaluation Criteria
Evaluation Rubrics
Assessment Rubrics
Rubric 11: Analysis of
Student Learning
Rubric 12: Providing
Feedback to Guide Learning
Rubric 13: Student
Understanding and Use of
Feedback
Rubric 14: Analyzing
Students’ Language Use and
Mathematics Learning
Rubric 15: Using
Assessment to Inform
Instruction
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Planning Task 1: Planning for Instruction
and Assessment
What Do I Need to Think About?
In Planning Task 1, you will describe your plans for the learning segment and explain how
your instruction is appropriate for the students and the content you are teaching. As you
develop your plans, you need to think about the following:
What do your students know, what can they do, and what are they learning to do?
What do you want your students to learn? What
are the important understandings and
core concepts you want students to develop within the learning segment?
How will
you use your knowledge of your studentsassets to inform your plans?
What instructional strategies, learning tasks, and assessments will you design to support
student learning and language use?
How will your learning segment support students to develop and use language that
deepens content understanding?
How is the teaching you propose supported by research and theory about how students
learn?
What Do I Need to Do?
Select a class. If you teach more than one class, select one focus class for this
assessment. If your placement for mathematics has you responsible for a group rather
than a whole class, plans should describe instruction for that group (minimum of 4
students). That group will constitute “the whole class” for edTPA.
Provide context information. The Secondary Mathematics Context for Learning
Information form is provided later in this handbook and must be submitted in a template.
Thi
s form provides essential information about your students and your school/classroom.
The context information you submit should be no more than 4 pages, including
prompts.
Identify a learning segment to plan, teach, and analyze. Review the curriculum with
your c
ooperating teacher and select a learning segment of 3–5 consecutive lessons. (If
teaching secondary mathematics within a large time block, select a learning segment of
about 3–5 hours of connected instruction.)
Identify
a central focus. Identify the central focus along with the content standards and
objectives you will address in the learning segment. The central focus should support
students in developing
conceptual understanding,
procedural fluency, AND
mathematical reasoning and/
or probl
em-solving skills.
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Identify and plan to support language demands. Select a key language function from
your learning objectives. Choose a learning task that provides opportunities for students
to practice using that language function. Identify additional language demands
associated with that task. Plan targeted supports that address the identified language
demands, including the language function.
Write a lesson plan for each lesson in the learning segment. Your lesson plans should
be detailed enough that a substitute or other teacher could understand them well enough
to use them.
Your lesson pl
ans must include the following information, even if your teacher
preparation program requires you to use a specific lesson plan format:
State-adop
ted student academic content standards that are the target of student
learning (Note: Please include the number and text of each standard that is being
addressed. If only a portion of a standard is being addressed, then only list the part
or parts that are relevant.)
Learning objectives ass
ociated with the content standards
Informal and formal assessments used to monitor student learning, including type(s)
of assessment and what is being assessed
Instructional strategies and learning tasks (including what you and the students will
be doing) that support diverse student needs
Inst
ructional resources and materials used to engage students in learning
Each lesson plan must be no more than 4 pages in length. You will need to
condense or excerpt lesson plans longer than 4 pages. Any explanations or rationale for
decisions should be included in your Planning Commentary and deleted from your plans.
Respond to the commentary prompts listed in the Planning Commentary section
prior to teaching the learning segment.
Submit your original lesson plans. If you make changes while teaching the learning
segment, you may offer reflection on those changes in the Instruction Task 2 and
Assessment Task 3 Commentaries. Select and submit key instructional materials
needed to understand what you and the students will be doing (no more than 5
additional pages per lesson plan). The instructional materials might include such
items as class handouts, assignments, slides, and interactive whiteboard images.
Submit copies of all written assessments and/or
directions for any oral or
performance assessments. (Submit only the blank assessment given to students; do
not submit student work samples for this task.)
Provide citations for the source of all materials that you did not create (e.g.,
published texts, websites, and material from other educators). List all citations by lesson
number at the end of the Planning Commentary. Note: Citations do not count toward the
commentary page limit.
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edTPA Secondary Mathematics Assessment Handbook
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See the Planning Task 1: Artifacts and Commentary Specifications in the Secondary
Mathematics Evidence Chart for instructions on electronic submission of evidence.
The evidence chart identifies templates, supported file types, number of files,
response length, and other important evidence specifications. Your evidence cannot
contain hyperlinked content. Any web content you wish to include as part of your
evidence must be submitted as a document file, which must conform to the file
format and response length requirements.
What Do I Need to Write?
In Planning Task 1, you will write
a description of your Context for Learning (see “What Do I Need to Do?” above for
dir
ections)
lesson pl
ans (see “What Do I Need to Do?” above for directions)
a commentary explaining your plans (see “Planning Commentary” below for
directions)
Planning Commentary
In Planning Task 1, you will write a commentary, responding to the prompts below. Your
commentary should be no more than 9 single-spaced pages, including the prompts.
1. Central Focus
a. Describe the central focus and purpose of the content you will teach in the
learning segment.
b. Given the central focus, describe how the standards and learning objectives
within your learning segment address
conceptual understanding,
procedural fluency, AND
mathematical reasoning and/or problem-solving skills.
c. Explain how your plans build on each other to help students make connections
between concepts, computations/procedures, AND mathematical reasoning or
problem-solving strategies to build understanding of mathematics.
2. Knowledge of Students to Inform Teaching
For each of the prompts below (2a–c), describe what you know about your students
with respect to the central focus of the learning segment.
Consider the variety of learners in your class who may require different
strategies/support (e.g., students with IEPs or 504 plans, English language learners,
struggling readers, underperforming students or those with gaps in academic
knowledge, and/or gifted students).
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edTPA Secondary Mathematics Assessment Handbook
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a. Prior academic learning and prerequisite skills related to the central focusCite
evidence of what students know, what they can do, and what they are still
learning to do.
b. Personal, cultural, and community assets related to the central focusWhat do
you know about your students’ everyday experiences, cultural and
language backgrounds and practices, and interests?
c. Mathematical dispositionsWhat do you know about the extent to which your
students
perceive mathematics as “sensible, useful, and worthwhile
1
persist in applying mathematics to solve problems
believe in their own ability to learn mathematics
3. Supporting StudentsMathematics Learning
Respond to prompts below (3a–c). To support your justifications, refer to the
instructional materials and lesson plans you have included as part of Planning
Task 1. In addition, use principles from research and/or theory to support your
justifications.
a. Justify how your understanding of your students’ prior academic learning;
personal, cultural, and community assets; and mathematical dispositions (from
prompts 2a–c above) guided your choice or adaptation of learning tasks and
materials. Be explicit about the connections between the learning tasks and
students’ prior academic learning, their assets, their mathematical dispositions,
and research/theory.
b. Describe and justify why your instructional strategies and planned supports
are
appropriate for the whole class, individuals, and/or groups of students with
specific learning needs.
Consider the variety of learners in your class who may require different
strategies/support (e.g., students with IEPs or 504 plans, English language
learners, struggling readers, underperforming students or those with gaps in
academic knowledge, and/or gifted students).
c. Describe common mathematical preconceptions, errors, or misunderstandings
within your central focus and how you will address them.
4. Supporting Mathematics Development Through Language
As you respond to prompts 4ad, consider the range of students’ language assets
and needswhat do students already know, what are they struggling with, and/or
what is new to them?
a. Language Function. Using information about your students’ language assets
and needs, identify one language function essential for students to develop
conceptual understanding, procedural fluency, and mathematical reasoning or
problem-solving skills within your central focus. Listed below are some sample
1
From The Common Core State Standards for Mathematics
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edTPA Secondary Mathematics Assessment Handbook
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language functions. You may choose one of these or another language function
more appropriate for your learning segment.
Compare/C
ontrast Justify Describe Explain Prove
Please see additional examples and non-examples of language functions in the
glossary.
b. Identify a key learning task from your plans that provides students with
opportunities to practice using the language function identified above. Identify the
lesson in which the learning task occurs. (Give lesson day/number.)
c. Additional Language Demands. Given the language function and learning task
identified above, describe the following associated language demands (written or
oral) students need to understand and/or use:
Vocabulary and/or symbols
Mathem
atical precision
2
(e.g., using clear definitions, labeling axes,
specifying units of measure, stating meaning of symbols), appropriate to your
students’ mathematical and language development
Plus at least one of the following:
Discourse
Sy
ntax
d. Language S
upports. Refer to y
our lesson plans and instructional materials as
needed in your response to the prompt.
Identify and describe the planned instructional s
upports (during and/or prior to
the learning task) to help students understand, develop, and use the
identified language demands (function, vocabulary and/or symbols,
mathematical precision, discourse, or syntax).
5. Monitoring Student Learning
In response to the prompts below, refer to the assessments you will submit as part of
the materials for Planning Task 1.
a. Describe how your planned formal and informal assessments will provide direct
evidence of students’ conceptual understanding, procedural fluency, AND
mathematical reasoning and/or problem-solving skills throughout the learning
segment.
b. Explain how the design or adaptation of your planned assessments allows
students with specific needs to demonstrate their learning.
Consider the variety of l
earners in your class who may require different
strategies/support (e.g., students with IEPs or 504 plans, English language
learners, struggling readers, underperforming students or those with gaps in
academic knowledge, and/or gifted students).
2
For an elaboration of “precision,” refer to the Standards for Mathematical Practicefrom 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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edTPA Secondary Mathematics Assessment Handbook
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How Will the Evidence of My Teaching Practice Be
Assessed?
For Planning Task 1, your evidence will be assessed using rubrics 1–5, which appear on the
following pages. When preparing your artifacts and commentaries, refer to the rubrics
frequently to guide your thinking, planning, and writing.
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edTPA Secondary Mathematics Assessment Handbook
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Planning Rubrics
Rubric 1: Planning for Mathematical Understandings
How do the candidate’s plans build students’ conceptual understanding, procedural fluency, AND mathematical
reasoning and/or problem-solving skills?
Level 1
3
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.
OR
There are significant content
inaccuracies that will lead to
student misunderstandings.
OR
Standards, objectives,
learning tasks, and materials
are not aligned with each
other.
Candidate’s plans for
instruction support student
learning of facts and
procedures with vague
connections to
concepts AND
mathematical reasoning
and/or problem-solving
skills.
Candidate’s plans for
instruction build on each
other to support learning of
facts and procedures with
clear connections to
concepts AND
mathematical reasoning
and/or problem-solving
skills.
Candidate’s plans for
instruction build on each other
to support learning of facts and
procedures with clear and
consistent connections to
concepts AND
mathematical reasoning
and/or problem-solving
skills.
Level 4 plus:
Candidate explains how s/he
will use learning tasks and
materials to lead students to
make clear and consistent
connections.
3
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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edTPA Secondary Mathematics Assessment Handbook
Planning Rubrics continued
15 of 51
Rubric 2: Planning to Support Varied Student Learning Needs
How does the candidate use knowledge of his/her students to target support for students to develop conceptual
understanding, procedural fluency, AND mathematical reasoning and/or problem-solving skills?
Level 1 Level 2 Level 3 Level 4 Level 5
There is no evidence of
planned supports.
OR
Candidate does not attend to
ANY INSTRUCTIONAL
requirements in IEPs and 504
plans.
Planned supports are loosely
tied to learning objectives or
the central focus of the
learning segment.
Planned supports are tied
to learning objectives and
the central focus with
attention to the
characteristics of the
class as a whole.
Planned supports are tied to
learning objectives and the
central focus. Supports
address the needs of specific
individuals or groups with
similar needs.
Level 4 plus:
Supports include specific
s
trategies to identify and
respond to preconceptions,
common errors, and
misunderstandings.
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edTPA Secondary Mathematics Assessment Handbook
Planning Rubrics continued
16 of 51
Rubric 3: Using Knowledge of Students to Inform Teaching and Learning
How does the candidate use knowledge of his/her students to justify instructional plans?
Level 1 Level 2 Level 3 Level 4 Level 5
Candidate’s justification of
learning tasks is either missing
OR represents a deficit view
of students and their
backgrounds.
Candidate justifies learning
tasks with limited attention to
students’
prior academic learning
OR
personal, cultural, or
community assets.
Candidate justifies why
learning tasks (or their
adaptations) are
appropriate using
examples of students’
prior academic
learning OR
personal, cultural, or
community assets.
Candidate makes
superficial connections
to research and/or
theory.
Candida
te justifies why learning
tasks (or their adaptations) are
appropriate using examples of
students’
prior academic learning
AND
personal, cultural, or
community assets.
Candida
te makes connections
to research and/or theory.
Level 4 plus:
Candidate’s justification is
s
upported by principles from
research and/or theory.
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Planning Rubrics continued
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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
4
identified
by the candidate are not
consistent with the selected
language function
5
OR task.
OR
Language s
upports are
missing or are not aligned
with the language demand(s)
for the learning task.
Language s
upports primarily
address one language
demand (vocabulary and/or
symbols, function,
mathematical precision,
discourse, syntax).
General language supports
address use of two or more
language demands
(vocabulary and/or symbols,
function, mathematical
precision, discourse, syntax).
Targeted language supports
address use of
vocabulary and/or
symbols,
language function, AND
one or more additional
language demands
(mathematical precision,
discourse, syntax).
Level 4 plus:
Language supports are
designed to meet the needs
of students with different
levels of language learning.
4
Language demands include: language function, vocabulary and/or symbols, syntax, and discourse (organizational structures, text structure, etc.).
5
Language function refers to the learning outcome (verb) selected in prompt 4a (e.g., compare/contrast, conjecture).
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Planning Rubrics continued
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Rubric 5: Planning Assessments to Monitor and Support Student Learning
How are the informal and formal assessments selected or designed to monitor students’ conceptual
understanding, procedural fluency, AND mathematical reasoning and/ or problem-solving skills?
Level 1 Level 2 Level 3 Level 4 Level 5
The assessments only provide
evidence of students'
procedural skills and/or
factual knowledge.
OR
Candidat
e does not attend to
ANY ASSESSMENT
requirements in IEPs and 504
plans.
The assessmen
ts provide
limited evidence to monitor
students’
conceptual understanding,
procedural fluency, AND
mathematical reasoning
and/or problem-solving
skills
during the learning segment.
The assessmen
ts provide
evidence to monitor students’
conceptual understanding,
procedural fluency, AND
mathematical reasoning
and/or problem-solving
skills
during the learning segment.
The a
ssessments provide
multiple forms of evidence to
monitor students’ progress
toward developing
conceptual understanding,
procedural fluency, AND
mathematical reasoning
and/or problem-solving
skills
throughout the learning
segment.
Level 4 plus:
The assessments are
strategically designed to
allow individuals or groups
with specific needs to
demonstrate their learning.
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Instruction Task 2: Instructing and
Engaging Students in Learning
What Do I Need to Think About?
In Instruction Task 2, you will demonstrate how you support and engage students in
learning. Before you begin your instruction, you need to thi
nk about the following:
What kind of learning env
ironment do you want to develop in order to establish
respect and rapport, and to
support students’ engagement in learning?
What kinds of learning tas
ks actively engage students in the central focus of the
learning segment?
How will you elicit and build on student responses in ways that develop and deepen
content
understanding?
In what ways will you connect new content to your students’ prior academic learning
and personal, cul
tural, or community assets during your instruction?
How wi
ll you use evidence fr
om your instruction to examine and change your
teaching practices to more effectively meet a variety of student learning needs?
What Do I Need to Do?
Obtain required permission for videorecording. Before you record your video, ensure
that you have the appropriate permission from the parents/guardians of your students
and from adults who appear in the video. Adjust the camera angle to exclude individuals
for whom you do not have permission to film.
Examine your plans for the learning segment and identify c
hallenging learning tasks
in which you and students are actively engaged. The video clip(s) you select for
submission should provide a sample of how you interact with students to support them to
develop
conceptual understanding, procedural fluency, AND mathematical reasoning
and/or problem-solving skills.
Identify lessons to videorecord.
Provide 1–2 video cli
ps (together totaling no more than 15 minutes, but not less
than 3 minutes) that demonstrate how you interact with students in a positive learning
environment to develop conceptual understanding, procedural fluency, AND
mathematical reasoning and/or problem-solving skills.
(Optional) Provide evi
dence of students’ language use. You may provide evidence
of language use with your video clip(s) from Instruction Task 2, an additional video clip of
one or more students using language within the learning segment (no more than 5
minutes in length), AND/OR through the student work samples analyzed in
Assessment Task 3.
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Determine whether you will feature the whole class or a targeted group of students
(minimum of 4 students) within the class.
Videorecord your classroom teaching. Tips for videorecording your class are
available from your teacher preparation program.
Select video clip(s) to submit and verify that the clip(s) meet the following
requirements:
Check the video and sound quality to ensure that you and your students can be seen
and heard on the video clip(s) you submit. If most of the audio in a clip cannot be
understood by a scorer, submit another clip. If there are occasional audio portions
of a clip that cannot be understood that are relevant to your commentary
responses,
do one of the following: 1) provide a transcript with time stamps of the inaudible
portion and refer to the transcript in your response; 2) embed quotes with time-stamp
references in the commentary response; or 3) insert captions in the video (captions
for this purpose will be considered permissible editing).
A video clip must be continuous and unedited, with no interruption in events.
If you have inadvertently included individuals for whom you do not have permission
to film in the video clip(s) you plan to submit, you may use software to blur the faces
of these individuals. This is not considered editing. Other portions of the submitted
video clip(s), including the classroom, your face, and the faces of individuals for
whom you have obtained permission to film should remain unblurred.
Do not include the name of the state, school, or district in your video. Use first names
only for all individuals appearing in the video.
Respond to the prompts listed in the Instruction Commentary section below after
viewing the video clip(s).
Determine if additional information is needed to understand what you and the
students are doing in the video clip(s). For example, if there are graphics, texts, or
images that are not clearly visible in the video, or comments that are not clearly heard,
you may insert digital copies or transcriptions at the end of the Instruction Commentary
(no more than 2 pages in addition to the responses to commentary prompts).
See the Instruction Task 2: Artifacts and Commentary Specifications in the
Secondary Mathematics Evidence Chart for instructions on electronic submission of
evidence. The evidence chart identifies templates, supported file types, number of
files, response length, and other important evidence specifications. Your evidence
cannot contain hyperlinked content. Any web content you wish to include as part of
your evidence must be submitted as a document file, which must conform to the file
format and response length requirements.
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What Do I Need to Write?
Instruction Commentary
In Instruction Task 2, you will write a commentary, responding to the prompts below. Your
commentary should be no more than 6 single-spaced pages, including the prompts. If
needed, insert no more than 2 additional pages of supporting documentation for the
videorecordings at the end of the commentary (e.g., digital copies of indiscernible materials
or transcriptions of inaudible comments). These additional pages do not count toward the
commentary page limit noted above.
1. Which lesson or lessons are shown in the video clip(s)? Identify the lesson(s) by
lesson plan number.
2. Promoting a Positive Learning Environment
Refer to scenes in the video clip(s) where you provided a positive learning
environment.
a. How did you demonstrate mutual respect for, rapport with, and responsiveness to
students with varied needs and backgrounds, and challenge students to engage
in learning?
3. Engaging Students in Learning
Refer to examples from the video clip(s) in your responses to the prompts.
a. Explain how your instruction engaged students in developing
conceptual understanding,
procedural fluency, AND
mathematical reasoning and/or problem-s
olving skills.
b. Describe how your instruction linked students’ prior academic learning and
personal, cultural, and/or community assets with new learning.
4. Deepening Studen
t Learning during Instruction
Refer to examples from the video clip(s) in your explanations.
a. Explain how you elicited and built on student responses to promote thinking
and develop conceptual understanding, procedural fluency, AND mathematical
reasoning and/or problem-solving skills.
b. Explain how you used representations
to support students’ understanding and
use of mathematical concepts and procedures.
5. Analyzing Teaching
Refer to examples from the video clip(s) in your responses to the prompts.
a. What changes would you make to your instructionfor the whole class and/or for
students who need greater support or challengeto better support student
learning of the central focus (e.g., missed opportunities)?
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Consider the variety of learners in your class who may require different
strategies/support (such as students with IEPs or 504 plans, English language
learners, struggling readers, underperforming students or those with gaps in
academic knowledge, and/or gifted students).
b. Why do you think these changes would improve student learning? Support your
explanati
on with evidence of student learning AND principles from theory and/or
research.
How Will the Evidence of My Teaching Practice Be
Assessed?
For Instruction Task 2, your evidence will be assessed using rubrics 610, which appear on
the following pages. When preparing your artifacts and commentaries, refer to the rubrics
frequently to guide your thinking, instruction, and writing.
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Instruction Rubrics
Rubric 6: Learning Environment
How does the candidate demonstrate a respectful learning environment that supports students’ engagement in
learning?
Level 1 Level 2 Level 3 Level 4 Level 5
The clip(s) reveal evidence of
disrespectful interactions
between teacher and students
or between students.
OR
Candidate allows disruptive
behavior to interfere with
student learning.
The candidate demonstrates
respect for students.
AND
Candidate provides a learning
environment that serves
primarily to control student
behavior, and minimally
supports the learning goals.
The candidate demonstrates
rapport with and respect for
students.
AND
Candidate provides a
positive, low-risk learning
environment that reveals
mutual respect among
students.
The candidate demonstrates
rapport with and respect for
students.
AND
Candidate provides a
challenging learning
environment that promotes
mutual respect among
students.
The candidate demonstrates
rapport with and respect for
students.
AND
Candidate provides a
challenging learning
environment that provides
opportunities to express
varied perspectives and
promotes mutual respect
among students.
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Instruction Rubrics continued
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Rubric 7: Engaging Students in Learning
How does the candidate actively engage students in developing conceptual understanding, procedural fluency,
AND/OR mathematical reasoning and/or problem-solving skills?
Level 1 Level 2 Level 3 Level 4 Level 5
Students are participating in
tasks that are vaguely or
superficially related to the
central focus.
Students are participating in
learning tasks focusing
primarily on mathematical
procedures with little
attention to understanding of
mathematical concepts OR
mathematical reasoning
and/or problem-solving
skills.
Students
are engaged in
learning tasks that address
understanding of
mathematical concepts,
procedures, AND
mathematical reasoning
and/or problem-solving
skills.
Students ar
e engaged in
learning tasks that develop
understanding of
mathematical concepts,
procedures, AND
mathematical reasoning
and/or problem-solving
skills.
Students ar
e engaged in
learning tasks that deepen
and extend their
understanding of
mathematical concepts,
procedures, AND
mathematical reasoning
and/or problem-solving
skills.
There
is little or no evidence
that the candidate links
students’ prior academic
learning or personal,
cultural, or community
assets with new learning.
Candidate makes vague or
superficial links between
prior academic learning and
new learning.
Candidate links prior
academic learning to new
learning.
Candidate links prior academic
learning AND personal,
cultural, or community
assets to new learning.
Candidate prompts students
to link prior academic learning
AND personal, cultural, or
community assets to new
learning.
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Instruction Rubrics continued
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Rubric 8: Deepening Student Learning
How does the candidate elicit responses to promote thinking and to develop conceptual understanding,
procedural fluency, AND mathematical reasoning and/or problem-solving skills?
Level 1 Level 2 Level 3 Level 4 Level 5
Candidate does most of the
talking and students provide
few responses.
OR
Candida
te responses include
significant content
inaccuracies that will lead to
student misunderstandings.
Candida
te primarily asks
surface-level questions and
evaluates student responses
as correct or incorrect.
Candidate elicits student
responses related to
understanding
mathematical concepts,
procedures, OR
mathematical reasoning
and/or problem-solving
skills.
Candida
te elicits and builds
on students’ responses to
develop understanding of
mathematical concepts,
procedures, AND
mathematical reasoning
and/or problem-solving
skills.
Level 4 plus:
Candida
te facilitates
interactions among students
so they can evaluate their
own abilities to understand
and apply
mathematical concepts,
procedures, AND
mathematical reasoning
and/or problem-solving
skills.
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Instruction Rubrics continued
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Rubric 9: Subject-Specific Pedagogy: Using Representations
How does the candidate use representations to develop students’ understanding of mathematical concepts and
procedures?
Level 1 Level 2 Level 3 Level 4 Level 5
Candidate stays focused on
facts or procedures with little
or no attention to
mathematical concepts.
OR
Candidate uses
mathematically inappropriate
representations or uses
representations in ways that
will lead to student
misunderstandings.
Candidate makes vague or
superficial use of
representations to help
students understand
mathematical concepts and
procedures.
Candidate uses
representations in ways that
help students understand
mathematical concepts and
procedures.
Candidate provides
opportunities for students to
use representations in ways
that deepen student
understanding of
mathematical concepts and
procedures.
Level 4 plus:
Candidate facilitates
interactions among students
so they can evaluate their
own abilities to use
representations to represent
and understand mathematical
concepts and procedures.
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Instruction Rubrics continued
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Rubric 10: Analyzing Teaching Effectiveness
How does the candidate use evidence to evaluate and change teaching practice to meet students’ varied
learning needs?
Level 1 Level 2 Level 3 Level 4 Level 5
Candidate suggests changes
unrelated to evidence of
student learning.
Candidate proposes changes
to teacher practice that are
superficially related to
student learning needs (e.g.,
task management, pacing,
improving directions).
Candidate proposes changes
that address students’
collective learning needs
related to the central focus.
Candidate makes superficial
connect
ions to research
and/or theory.
Candi
date proposes changes
that address individual and
collective learning needs
related to the central focus.
Candidate makes
connections to research
and/or theory.
Level 4 plus:
Candidate justifies changes
using principles from
research and/or theory.
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Assessment Task 3: Assessing Student
Learning
What Do I Need to Think About?
In Assessment Task 3, you will analyze both student learning and student use of language.
Before you begin the analysis, you need to think about the following:
How will you gather evidence and ma
ke sense of what students have learned?
How will you provide meaningful feedback to your students?
How will you use evidence of what students know and are able to do to plan next
s
teps
in instruction?
How will you identify evidence of and explai
n students’ use of language that
demonstrates the development of content understanding?
What Do I Need to Do?
Select one assessment from your learning segment you will use to evaluate your
students’ developing knowledge and skills. It should be an assessment that is completed
by the whole class featured in the learning segment. (If you are teaching only a group
within the class for the learning segment, that group will be “the whole class.”) The
assessment should reflect the work of individuals, not groups, but may be individual
work from a group task. The assessment should provide opportunities for students to
demonstrate
conceptual understanding,
proc
edural fluency, AND
mathe
matical reasoni
ng and/or problem-solving skills.
Define and submi
t the evaluation criteria you will use to analyze student learning
related to the mathematical goals described above.
Collect and analyze student work from
the selected assessment to identify
quantitative and qualitative patterns of learning within and across learners in the class.
You may submit text files with scanned student work, a video or audio file of a student’s
oral work, OR a student-created video or multimedia file. For each focus student, a video
or audio work sample must be no more than 5 minutes in total running time.
Select 3 student work samples th
at represent the patterns of learning (i.e., what
individuals or groups generally understood and what a number of students were still
struggling to understand) you identified in your assessment analysis. These students will
be your focus students for this task. At least one of the focus students must have
specific learning needs, for example, a student with an IEP (Individualized Education
Program) or 504 plan, an English language learner, a struggling reader, an
underperforming student or a student with gaps in academic knowledge, and/or a gifted
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student needing greater support or challenge. Note: California candidates must include
one focus student who is an English Language Learner.
6
Document the feedback you gave to each of the 3 focus students on the work sample
itself, as an audio clip, or as a video clip. You must submit evidence of the actual
feedback provided to each focus student, and not a description of the feedback.
If you submit a student work sample or feedback as a video or audio c
lip and comments
made by you or your focus student(s) cannot be clearly heard, do one of the following: 1)
attach a transcription of the inaudible comments (no more than 2 additional pages) to
the end of the Assessment Commentary; 2) embed quotes with time-stamp references in
the commentary response; or 3) insert captions in the video (captions for this purpose
will be considered permissible editing).
If you submit a student work sample or feedback as a video or audi
o clip and additional
students are present, clearly identify which students are your focus students in the
relevant prompts (1d and 2a) of the Assessment Commentary (in no more than 2
sentences).
Respond to the prompt
s listed in the Assessment Commentary section below after
analyzing student work from the selected assessment.
Include and submit the chosen assess
ment, including the directions/prompts
provided to students. Attach the assessment (no more than 5 additional pages) to
the end of the Assessment Commentary.
Provide evidence of students’ understanding and use of
the targeted academic
language function and other language demands. You may choose evidence from the
video clip(s) submitted in Instruction Task 2, an additional video clip of one or more
students using language within the learning segment (no more than 5 minutes in
length), AND/OR student work samples submitted in Assessment Task 3.
6
California candidatesIf you do not have any English language learners, select a student who is challenged by academic
English.
See the Assessment Task 3: Artifacts and Commentary Specifications in the
Secondary Mathematics Evidence Chart for instructions on electronic submission of
evidence. The evidence chart identifies templates, supported file types, number of
files, response length, and other important evidence specifications. Your evidence
cannot contain hyperlinked content. Any web content you wish to include as part of
your evidence must be submitted as a document file, which must conform to the file
format and response length requirements.
What Do I Need to Write?
Assessment Commentary
In Assessment Task 3, you will write a commentary, responding to the prompts below. Your
commentary should be no more than 10 single-spaced pages, including the prompts.
Attach the assessment used to evaluate student performance (no more than 5 additional
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pages) and, if necessary, a transcription of inaudible portions of a video or audio clip of
feedback or a student work sample (no more than 2 additional pages) to the end of the
Assessment Commentary. These additional pages do not count toward the commentary
page limit noted above.
1. Analyzing Student Learning
a. Identify the specific learning object
ives measured by the assessment you chose
for anal
ysis.
b. Provide a graphic (table or chart) or narrative that summarizes student learning
for your whole class. Be sure to summarize student learning for all evaluation
criteria submitted in Assessment Task 3, Part D.
c. Use evidence found in the 3 student work samples and the whole class
summary to analyze the patterns of learning for the whole class and
differences for groups or individual learners relative to
conceptual understanding,
pr
ocedural fluency, AND
mathemati
cal reasoning and/or probl
em-solving skills.
Consider what students understand and do well, and where they continue to
struggle (e.g., preconceptions, common errors, common struggles, confusions,
and/or need for greater challenge).
d. If a video or audio wor
k sample occurs in a group context (e.g., discussion),
provide the name of the clip and clearly describe how the scorer can identify the
focus student(s) (e.g., position, physical description) whose work is portrayed.
2. Feedback to Guide Fu
rther Learning
Refer to specific evidence of submitted feedback to support your explanations.
a. Identify the format in which you submitted your evidence of feedback for the 3
focus students. Choose one of the following:
Written directly on work samples or in separate documents that were
provided to th
e focus students
In audio files
In video clip(s) from Instruction Task 2 (provide a time-stamp reference) or in
separate video clips
If a video or audio clip of feedback occurs in a group context (e.g., discussion),
clearly descri
be how the scorer can identify the focus student (e.g., position,
physical description) who is being given feedback.
b. Explain how feedback provided to the 3 focus students addresses their individual
strengths and needs relative to the learning objectives measured.
c. Describe how you will support each focus student to understand and use this
feedback to further their learning related to learning objectives, either within the
learning segment or at a later time.
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3. Evidence of Language Understanding and Use
When responding to the prompt below, use concrete examples from the clip(s)
and/or student work samples as evidence. Evidence from the clip(s) may focus on
one or more students.
You may provide evidence of students’ language use from ONE, TWO, OR
ALL THREE of the following sources:
1. Use the video clip(s) from Instruction Task 2 and provide time-stamp
references for evidence of language use.
2. Submit an additional video file named “Language Use” of no more than
5 minutes in length and cite language use (this can be footage of one or
more students’ language use). Submit the clip in Assessment Task 3,
Part B.
3. Use the student work samples analyzed in Assessment Task 3 and cite
language use.
a. Explain and provide concrete examples for the extent to which your students
were able to use or struggled to use the
selected language function,
vocabulary and/or symbol
s, AND
mathematical precision, di
scourse, or syntax
to develop content understandings.
4. Using Assessment to Inform Instruction
a. Based on your analysis of student learning presented in prompts 1b–c, describe
next steps for instruction to impact student learning:
For the whole class
For the 3 f
ocus students and other i
ndividuals/groups with specific needs
Consider the variety of learners in your class
who may require different
strategies/support (e.g., students with IEPs or 504 plans, English language
learners, struggling readers, underperforming students or those with gaps in
academic knowledge, and/or gifted students needing greater support or
challenge).
b. Explain how these next steps follow from your analysis of student learning.
Support your ex
planation with principles from research and/or theory.
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How Will the Evidence of My Teaching Practice Be
Assessed?
For Assessment Task 3, your evidence will be assessed using rubrics 1115, which appear
on the following pages. When preparing your artifacts and commentaries, refer to the rubrics
frequently to guide your thinking, planning, instruction, assessment, and writing.
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Assessment Rubrics
Rubric 11: Analysis of Student Learning
How does the candidate analyze evidence of student learning of conceptual understanding, procedural fluency,
AND mathematical reasoning and/or problem-solving skills?
Level 1 Level 2 Level 3 Level 4 Level 5
The analysis is superficial or
not supported by either
student work samples or the
summary of student
learning.
OR
The evaluation criteria,
learning objectives, and/or
analysis are not aligned with
each other.
The analysis focuses on what
students did right OR wrong.
OR
The analysis focuses solely
on students’ ability to apply
procedures and/or their
factual knowledge.
The analysis focuses on what
students did right AND wrong.
AND
Analysis includes some
differences in whole class
learning.
Analysis uses specific
examples from work samples
to demonstrate patterns of
learning consistent with the
summary.
AND
Patterns of learning are
described for whole class.
Analysis uses specific
evidence from work samples to
demonstrate the connections
between quantitative and
qualitative patterns of learning
for individuals or groups.
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Assessment Rubrics continued
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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.
OR
Feedback cont
ains
significant content
inaccuracies.
OR
No feedback is provided to
one or more focus students.
Feedba
ck is general and
addresses needs AND/OR
strengths related to the
learning objectives.
Feedback is specific and
addresses either needs OR
strengths related to the
learning objectives.
Feedback is specific and
addresses both strengths
AND needs related to the
learning objectives.
Level 4 plus:
Feedback for one or more
focus students
provides a strategy to
address an individual
learning need OR
makes connections to
prior learning or
experience to improve
learning.
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Rubric 13: Student Understanding and Use of Feedback
How does the candidate support focus students to understand and use the feedback to guide their further
learning?
Level 1 Level 2 Level 3 Level 4 Level 5
Opportunities for
understanding or using
feedback are not described.
OR
Candidate provides limited or
no feedback to inform
student learning.
Candidate provides vague
description of how focus
students will understand or
use feedback.
Candidate describes how
focus students will understand
or use feedback related to the
learning objectives.
Candidate describes how s/he
will support focus students to
understand and use feedback
on their strengths OR
weaknesses related to the
learning objectives.
Candidate describes how s/he
will support focus students to
understand and use feedback
on their strengths AND
weaknesses related to the
learning objectives.
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Rubric 14: Analyzing Students’ Language Use and Mathematics Learning
How does the candidate analyze studentsuse of language to develop content understanding?
Level 1 Level 2 Level 3 Level 4 Level 5
Candidate identifies student
language use that is
superficially related or
unrelated to the language
demands (function,
7
vocabulary and/or symbols,
and additional demands).
OR
Candidate
s description or
explanation of language use
is not consistent with the
evidence submitted.
Candidate
describes how
students use only one
language demand
(vocabulary and/or symbols,
function, mathematical
precision, discourse,
syntax).
Candidate explains and
provides evidence of
students’ use of
the language function
AND
one or more additional
language demands
(vocabulary and/or
symbols, mathematical
precision, discourse,
syntax).
8
Candidate explains and
provides evidence of students’
use of
the language function,
vocabulary and/or
symbols, AND
additional language
demand(s) (mathematical
precision, discourse,
syntax)
in ways that develop content
understa
ndings.
Level 4 plus:
Candida
te explains and
provides evidence of
language use and content
learning for students with
varied needs.
7
The selected language function is the verb identified in the Planning Commentary Prompt 4a (conjecture, explain, etc.).
8
These are the additional language demands identified in the Planning Commentary Prompt 4c (vocabulary and/or symbols, mathematical precision, plus syntax or discourse).
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edTPA Secondary Mathematics Assessment Handbook
Assessment Rubrics continued
37 of 51
Rubric 15: Using Assessment to Inform Instruction
How does the candidate use the analysis of what students know and are able to do to plan next steps in
instruction?
Level 1 Level 2 Level 3 Level 4 Level 5
Next steps do not follow from
the analysis.
OR
Next steps ar
e not relevant to
the learning objectives
assessed.
OR
Next steps are not described
in sufficient detail to
understand them.
Next steps p
rimarily focus on
changes to teaching
practice that are
superficially related to
student learning needs, for
example, repeating
instruction, pacing, or
classroom management
issues.
Next steps propose general
support that improves
student learning related to
assessed learning
objectives.
Next steps a
re loosely
connected with research
and/or theory.
Next steps pro
vide targeted
support to individuals or
groups to improve their
learning relative to
conceptual understanding,
procedural fluency,
AND/OR
mathematical reasoning
and/or problem-solving
skills.
Next steps are connected
with research and/or theory.
Next steps pr
ovide targeted
support to individuals AND
groups to improve their
learning relative to
conceptual understanding,
procedural fluency,
AND/OR
mathematical reasoning
and/or problem-solving
skills.
Next steps are justified with
principles from research
and/or theory.
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edTPA Secondary Mathematics Assessment Handbook
38 of 51
Professional Responsibilities
Refer to the following table for an overview of your professional responsibilities in
developing evidence for edTPA. If you are submitting artifacts and commentaries for official
scoring, refer to www.edTPA.com, f
or complete and current information before beginning
your work. Included here are important information and policies such as submission
requirements and deadlines, registration agreements, attestations, permissions, and
confidentiality. Whether or not you are submitting for official scoring, you should fulfill the
professional responsibilities described below.
Responsibility Description
Protect
confidentiality
To protect confidentiality, please remove your name and use pseudonyms or general
references (e.g., “the district”) for your state, school, district, and cooperating teacher. Mask or
remove all names on any typed or written material (e.g., commentaries, lesson plans, student
work samples) that could identify individuals or institutions. During videorecording, use
students’ first names only.
To ensure confidentiality of your students and yourself, do not share your video on any publicly
accessible platforms or websites (YouTube, Facebook, etc.).
Acquire
permissions
Before you record your classroom instruction, ensure that you have the appropriate permission
from the parents/guardians of your students and from adults who appear in the videorecording.
Your program will provide you with procedures and necessary forms to obtain these
permissions, according to agreements with the school or district in which you are student
teaching or completing your internship.
If your program does not provide the necessary forms, you may refer to the sample forms
found on www.edTPA.com
.
The release forms are not to be submitted with your materials, but you should follow your
campus policy for retaining them.
Cite sources
Provide citations for the source of all materials that you did not create (e.g., published texts,
websites, and material from other educators). List all citations by lesson number at the end of
the Planning Commentary. Note: Citations do not count toward the commentary page limit.
Align instruction
with state
standards
As part of the assessment, you will document the alignment of your lesson plans with state-
adopted academic content standards that are the target of student learning. Refer to the
education agency website for your state to obtain copies of relevant standards for this
assessment.
Follow the
guidelines for
candidate
support at
www.edTPA.com
Follow the guidelines for candidate support found at www.edTPA.com as you develop your
evidence for edTPA. Although you may seek and receive appropriate support from your
university supervisors, cooperating/master teachers, university instructors, or peers during this
process, the ultimate responsibility for completing this assessment lies with you. Therefore,
when you submit your completed work, you must be able to confirm your adherence
with certain statements, such as the following:
I have primary responsibility for teaching the students/class during the learning segment
profiled in this assessment.
I have not previously taught this learning segment to the students/class.
The video clips submitted are unedited (continuous) and show me teaching the
students/class profiled in the evidence submitted.
The student work included in the documentation is that of my students, completed during
the learning segment documented in this assessment.
I am author of the commentaries and other written responses to prompts in this
assessment.
Appropriate citations have been made for all materials in the assessment whose sources
are from published text, the Internet, or other educators.
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edTPA Secondary Mathematics Assessment Handbook
39 of 51
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
Secondary Mathematics Context for
Learning Information
Use the Context for Learning Information to supply information about your school/classroom
context.
About the School Where You Are Teaching
1. In what type of school do you teach? (Type an “X” next to the appropriate
description; if “other” applies, provide a brief description.)
Middle school:
High school:
Other (pl
ease describe):
2. Where is the school where you are teaching located? (Type an “X” next to the
appropriate description.)
9
City:
Subur
b:
Town:
Rural:
3. List any special features of your school or classroom setting (e.g., charter, co-
teaching, themed magnet, remedial course, honors course) that will affect your
teaching in this learning segment.
4. Describe any district, school, or cooperating teacher requirements or expectations
that might affect your planning or delivery of instruction, such as required curricula,
pacing plan, use of specific instructional strategies, or standardized tests.
9
If you need guidance when making a selection, reference the NCES locale category definitions
(https://nces.ed.gov/surveys/ruraled/definitions.asp) or consult with your placement school administrator.
About the Class Featured in this Learning Segment
1. What is the name of this course?
2. What is the length of the course? (Type an “X” next to the appropriate description; if
“other” applies, provide a brief description.)
One semester:
One year:
Other (please describe):
3. What is the class schedule (e.g., 50 minutes every day, 90 minutes every other
day)?
4. Is there any ability grouping or tracking in mathematics? If so, please describe how it
affects your class.
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edTPA Secondary Mathematics Assessment Handbook
40 of 51
___________________________________________________________________
_____
_____ _
____
5. Identify any textbook or instructional program you primarily use for mathematics
instruction. If a textbook, please provide the title, publisher, and date of publication.
6. List other resources (e.g., electronic whiteboard, graphing calculators, online
resources) you use for mathematics instruction in this class.
About the Students in the Class Featured in this Learning Segment
1. Grade-level composition (e.g., all seventh grade; 2 sophomores and 30 juniors):
2. Number of
students in the class:
males: females:
3. Complete the charts below to summarize required or needed supports,
accommodations, or modifications for your students that will affect your instruction in
this learning segment. As needed, consult with your cooperating teacher to complete
the charts. Some rows have been completed in italics as examples. Use as many
rows as you need.
Consider the variety of learners in your class who may require different
strategies/supports or accommodations/modifications to instruction or
assessment. For example, students
With Individualized Education Programs (IEPs) or 504 plans
With specific language needs
Needing greater challenge or support
Who struggle with reading
Who are underperforming students or have gaps in academic
knowledge
For Assessment Task 3, you will choose work samples from 3 focus
students. At least one of these students must have a specified learning need.
Note: California candidates must include one focus student who is an English
language learner.
10
10
California candidatesIf you do not have any English language learners, select a student who is challenged by academic
English.
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edTPA Secondary Mathematics Assessment Handbook
41 of 51
Students with IEPs/504 Plans
IEPs/504 Plans:
C
lassifications/Needs
Number of
Students
Supports, Accommodations,
Modifications, Pertinent IEP Goals
Example: Visual processing 2 Close monitoring, translating
i
nformation in word problems into
sketches
Students with Specific Language Needs
Language Needs Number of
S
tudents
Supports, Accommodations,
Modifications
Example: English Language
Learners with only a few
words of English
2 Pre-teach key words and phrases
through examples and graphic
organizers (e.g., word cluster,
manipulatives, visuals)
Have students use pre-taught key
w
ords and graphic organizers to
complete sentence starters
Example: Students who
sp
eak a variety of English
other than that used in
textbooks
5 Make connections between the
language students bring and the
language used in the textbook
Students with Other Learning Needs
Other Learning Needs Number of
Students
Supports, Accommodations,
Modifications
Example: Struggling readers 5 Provide oral explanations for
di
rections and simplified text for word
problems
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edTPA Secondary Mathematics Assessment Handbook
42 of 51
Secondary Mathematics Evidence Chart
Your evidence must be submitted to the electronic portfolio management system used by your teacher preparation program. Your
submission must conform to the artifact and commentary specifications for each task. This section provides instructions for all
evidence types as well as a description of supported file types for evidence submission, number of files, response lengths, and
other information regarding format specifications. Note that your evidence cannot contain hyperlinked content. Any web content
you wish to include as part of your evidence must be submitted as a document file, which must conform to the file format and
response length requirements. If you have materials that must be translated into English as per the
edTPA Submission
Requirements, those translations should be added to the original materials as part of the same file or, if applicable, to the end of
t
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
A
dditional Information
Min Max
Part A: Context for
Learning
Information
(template provided)
.doc; .docx; .odt; .pdf 1 1
No more than 4
pages, including
prompts
Use Arial 11-point type.
Single space with 1" margins on all sides.
Part B: Lesson
Plans for Learning
Segment
.doc; .docx; .odt; .pdf 1 1
No more than 4
pages per lesson
Submit 35 lesson plans in 1 file.
Within the file, label each lesson plan (Lesson 1, Lesson 2, etc.).
All rationale or explanation for plans should be written in the Planning
Com
mentary and removed from lesson plans.
Part C:
Instructional
Materials
.doc; .docx; .odt; .pdf 1 1
No more than 5
pages of KEY
instructional materials
per lesson plan
Submit all materials in 1 file.
Within the file, label materials by corresponding lesson (Lesson 1
Instructional Materials, Lesson 2 Instructional Materials, etc.).
Order materials as they are used in the learning segment.
Part D:
Assessments
.doc; .docx; .odt; .pdf 1 1 No limit
Submit assessments in 1 file.
Within the file, label assessments by corresponding lesson
(Lesson 1 Assessments, Lesson 2 Assessments, etc.).
Order assessments as they are used in the learning segment.
Part E: Planning
Commentary
(template provided)
.doc; .docx; .odt; .pdf 1 1
No more than 9
pages of
commentary,
including prompts
Use Arial 11-point type.
Single space with 1" margins on all sides.
Respond to prompts before teaching the learning segment.
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edTPA Secondary Mathematics Assessment Handbook
43 of 51
Instruction Task 2: Artifacts and Commentary Specifications
What to
Submit
Supported File
Types
Number of Files
Response
Length
Ad
ditional Information
Min Max
Part A: Video
Clips
11
flv, asf, qt, mov, mpg,
mpeg, avi, wmv, mp4,
m4v
1 2
No more than
15 minutes total
running time (but
not less than 3
minutes)
Before you record your video, obtain permission from the
parents/guardians of your students and from adults who appear on
the video.
Refer to Instruction Task 2, What Do I Need to Do? for video c
lip
content and requirements.
When nami
ng each clip file, include the number of the lesson
shown in the video clip.
Part B: Instruction
Commentary
(template provided)
.doc; .docx; .odt; .pdf 1 1
No more than 6
pages of
commentary,
including prompts
If needed, no more
than 2 additional
pages of supporting
documentation
Use Arial 11-point type.
Single space with 1" margins on all sides.
IMPORTANT:
Insert documentation at the end of the commentary file if
you or the students are using graphics, texts, or images that are
not clearly visible in the video
you chose to submit a transcript for occasionally inaudible
portions of the video
If submitting documentation, include the video clip number, lesson
number, and explanatory text (e.g., “Clip 1, lesson 2, text from a
whiteboard that is not visible in the video,” “Clip 2, lesson 4,
transcription of a student response that is inaudible”).
11
Video file size requirements: The target file size is 200300 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.
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
(Continued on next page)
44 of 51
Assessment Task 3: Artifacts and Commentary Specifications
What to
Submit
Supported File
Types
Number of Files
Response
Length
Addi
tional Information
Min Max
Part A: Student
Work Samples
12
For written work
sa
mples: .doc; .docx;
.odt; .pdf
For audio work
sample
s: flv, asf,
wmv, qt, mov, mpg,
avi, mp3, wav, mp4,
wma
For video work
sample
s: flv, asf, qt,
mov, mpg, mpeg, avi,
wmv, mp4, m4v
3 3
No page limit for
written work
samples
No more than 5
minutes per focus
student for video or
audio student work
samples
Use correction fluid, tape, or a felt-tip marker to
mask or remove
students’ names, your name, and the name of the school
before copying/scanning any work samples. If your students’
writing is illegible, write a transcription directly on the work sample.
On each work sample, indicate the student number (Student 1
Work Sa
mple, Student 2 Work Sample, or Student 3 Work Sample).
If more than one focus student appears in a video or audio work
sample, upload the same work sample separately for each focus
student who is seen/heard and label appropriately. Describe how to
recognize each of the focus students in the clip and provide the
label associated with the clip in prompt 1d of the Assessment
Commentary.
When naming each work sample file, include th
e student number.
If you submit a student work sample or feedback as a video or
audio clip and comments made by you or your focus student(s)
cannot be clearly heard, do one of the following: 1) attach a
transcription of the inaudible comments (no more than 2
additional pages) to the end of the Assessment Commentary
; 2)
embed quotes with time-stamp references in the commentary
response; or 3) insert captions in the video (captions for this purpose
will be considered permissible editing).
12
Video file size requirements: The target file size is 200300 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.
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
Assessment Task 3: Artifacts and Commentary Specifications (continued)
What to
Submit
Supported File
Types
Number of Files
Response
Length
Additional Information
Min Max
(Continued on next page)
45 of 51
Part B: Evidence of
Feedback
13
And, if included,
video evidence of
academic language
use
For written feedba
ck
not written on the
work samples: .doc;
.docx; .odt; .pdf
For audio feedback:
flv, asf, wmv, qt, mov,
mpg
, avi, mp3, wav,
mp4, wma
For video clips
(feedback
and/or
language use): flv,
asf, qt, mov, mpg,
mpeg, avi, wmv, mp4,
m4v
0 4
No page limi
t for
written feedback
No more than 3
minutes per focus
s
tudent for video or
audio feedback
No more than 5
minutes for video
evidence of student
language use
Document the locati
on of your evidence of feedback in the
Assessment Commentary.
If fee
dback is not included as part of the student work samples or
recorded on the video clip(s) from Instruction Task 2, submit only 1
file for each focus studenta 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.
13
Video file size requirements: The target file size is 200300 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.
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
Assessment Task 3: Artifacts and Commentary Specifications (continued)
What to
Submit
Supported File
Types
Number of Files
Response
Length
Additional Information
Min Max
46 of 51
Part C:
Assessment
Commentary
(template provided)
.doc; .docx; .odt; .pdf 1 1
No more
than 10
pages of
commentary,
including prompts
Plus
no more than 5
a
dditional
pages for the
chosen
assessment,
if necessary, no
more than 2
additional total
pages of
transcriptions of
video/audio
evidence for a
work sample
and feedback,
and/or video
evidence of
language use
Use Arial 11-point type.
Single space with 1" margins on all sides.
IMPORTANT: In
sert a copy of the chosen assessment, including
directions/prompts provided to students.
Pa
rt D: Evaluation
Criteria
.doc; .docx; .odt; .pdf 1 1 No limit
edTPA Secondary Mathematics Assessment Handbook
47 of 51
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
Secondary Mathematics Glossary
Source citations for glossary entries are provided as footnotes in this section.
academic language: Oral and written language used for academic purposes. Academic
language is the means by which students develop and express content understandings.
Academic language represents the language of the discipline that students need to learn
and use to participate and engage in the content area in meaningful ways. There are
language demands that teachers need to consider as they plan to support student learning
of content. These language demands include language functions, vocabulary and/or
symbols, discourse, and syntax.
language demands:
14
Specific ways that academic language (vocabulary and/or
symbols, functions, discourse, syntax) is used by students to participate in learning
tasks through reading, writing, listening, and/or speaking to demonstrate their
disciplinary understanding.
language functions: The content and language focus of the learning task,
represented by the active verbs within the learning outcomes. Common language
functions in mathematics include describing mathematical phenomena, predicting
from models and data, comparing based on common attributes, summarizing
mathematical information, recording multiple ways to solve problems, justifying
conclusions, evaluating data and mathematical representations, classifying based
on attributes, explaining how or why certain strategies work, drawing conclusions
based on data, representing mathematical information, and so on. Some specific
mathematics verbs are non-examples of language functions because they focus on a
mathematical action, not a language-based action. Examples of mathematical
functions that ARE NOT language functions include solve problems, simplify the
expressions, calculate the answers, and estimate the answers.
vocabulary: Includes words and
phrases that are used within disciplines including:
(1) words and phrases with subject-specific meanings that differ from meanings used
in everyday life (e.g., table); (2) general academic vocabulary used across disciplines
(e.g., compare, analyze, evaluate); and (3) subject-specific words defined for use in
the discipline.
15
discourse: Di
scourse includes the structures of written and oral language, as well as
how members of the discipline talk, write, and participate in knowledge construction.
Discipline-specific discourse has distinctive features or ways of structuring oral or
written language (text structures) that provide useful ways for the content to be
14
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
15
Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science
standards for English language learners: What teachers need to know. Retrieved from
http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-
Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf
______ _______
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All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
48 of 51
communicated.
16
In mathematics, language structures include symbolic
representations, such as numbers, equations, two-column proofs (which can be
translated into words), graphic representation (which is shorthand language for
complex sets of data), and narrative (e.g., to describe or compare). If the language
function is to prove, then appropriate language structures include formal two-column
proofs as well as informal explanations that begin with a statement of the problem
and known information, followed by a series of statements such as “And then, I know
because ,” ending with what is to be proved.
syntax: The set of conventions for organizing symbols, words, and phrases together
into structures
(e.g., sentences, graphs, tables).
17
language supports: The s
caffolds, rep
resentations, and pedagogical strategies
teachers provide to help learners understand, use, and practice the concepts and
language they need to learn within disciplines (Santos, Darling-Hammond, Cheuk,
2012).
18
The language supports planned within the lessons in edTPA should directly
support learners to understand and use identified language demands (vocabulary
and/or symbols, language function, and discourse or syntax) to deepen content
understandings.
aligned: Consistently address
ing the same/similar learning outcomes for students.
artifacts: Authentic work completed by you and your students including lesson plans,
copies of instructional and assessment materials, video clips of your teaching, and student
work samples. Artifacts are submitted as part of your evidence.
assessment (formal or informal): “[R]efer[s] to all those activities undertaken by teachers
and by their students
. . . that provide information to be used as feedback to modify the
teaching and learning activities
19
for both students and teachers. Assessments provide
evidence of students’ prior knowledge, thinking, or learning in order to evaluate what
students understand and how they are thinking at a given point in time for the purpose of
promoting student learning. Informal assessments may include such things as student
questions and responses during instruction and teacher observations of students as they
work or perform. Formal assessments may include such things as quizzes, homework
assignments, journals, projects, and performance tasks.
assets (knowledge of students):
personal: Refers to speci
fic background information that students bring to the
learning environment. Students may bring interests, knowledge, mathematical
dispositions, everyday experiences, family backgrounds, and so on, which a teacher
can draw upon to support learning.
16
Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science
standards for English language learners: What teachers need to know. Retrieved from
http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-
Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf
17
Zwiers, J. (2008). Building academic language: Essential practices for content classrooms. San Francisco, CA: Jossey-Bass.
18
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
19
Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan,
80(2), 139148.
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All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
49 of 51
cultural: Refers to the cultural backgrounds and practices that students bring to the
learning environment, such as traditions, languages and dialects, worldviews,
literature, art, and so on, that a teacher can draw upon to support learning.
community: Refers to com
mon backgrounds and experiences that students bring
from the community where they live, such as resources, local landmarks, community
events, practices, and so on, that a teacher can draw upon to support learning.
central focus: A desc
ription of the important understandings and core concepts that you
want students to develop w
ithin the learning segment. The central focus should go beyond a
list of facts and procedures, align with content standards and learning objectives, and
address the subject-specific components in the learning segment. For example, the subject-
specific components for secondary mathematics are: conceptual understanding, procedural
fluency, AND mathematical reasoning and/or problem-solving skills. A central focus for the
learning segment might be relationships between symbolic expressions and graphs of lines.
The learning segment would focus on conceptual understanding of linear functions, slope,
and intercepts, and the associated procedures and mathematical reasoning and/or problem-
solving skills.
commentary: Submitted as pa
rt of each task and, along with artifacts, make up your
evidence. The commentaries should be written to explain the rationale behind your teaching
decisions and to analyze and reflect on what you have learned about your teaching practice
and your students’ learning.
conceptual understanding: “Students demonstrate conceptual understanding in
mathemati
cs . . . when they recognize, label, and generate examples of concepts; use and
interrelate models, diagrams, manipulatives, and varied representations of concepts; identify
and apply principles; know and apply facts and definitions; compare, contrast, and integrate
related concepts and principles; recognize, interpret, and apply the signs, symbols, and
terms used to represent concepts.”
20
engaging students in learning: Using instructional and motivational strategies that
promote students’ active involvement in learning tasks that increase their knowledge, skills,
and abilities related to specific learning objectives. Engagement in learning contrasts with
student participation in learning tasks that are not well designed and/or implemented and do
not increase student learning.
evaluation criteria: Performance indicators or dimensions t
hat are used to assess evidence
of student learning. They indicate the qualities by which levels of performance can be
differentiated and that anchor judgments about the learner’s degree of success on an
assessment. Evaluation criteria can be represented in various ways, such as a rubric, a
point system for different levels of performance, or rules for awarding full versus partial
credit. Evaluation criteria may examine correctness/accuracy, cognitive complexity,
sophistication or elaboration of responses, or quality of explanations.
evidence: Consists of artifacts that document how you planned and implemented
instruction AND commentaries that explain your plans and what is seen in the
videorecording(s) or examine what you learned about your teaching practice and your
students’ learning. Evidence should demonstrate your ability to design lesson plans with
20
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
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
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instructional supports that deepen student learning, use knowledge of your students to
inform instruction, foster a positive learning environment that promotes student learning,
monitor and assess student progress toward learning objectives, and analyze your teaching
effectiveness. Your evidence must be submitted electronically using the electronic portfolio
management system used by your teacher preparation program.
learning environment: The des
igned physical and emotional context, established and
maintained throughout the learning segment to support a positive and productive learning
experience for students.
learning objectives: Student learning outcomes to be achieved by the end of the lesson or
learning segm
ent.
learning segment: A set of 35 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
2
+ bx + c. Show them how to use graphic
calculators to find a graph for y = 2x
2
+ 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.
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patterns of lear
ning: Includes both quantitative and qualitative patterns (or consistencies)
for different groups of students or individuals. Quantitative patterns indicate in a numerical
way the information understood from the assessment (e.g., 10 out of 15 students or 20% of
the students). Qualitative patterns include descriptions of understandings,
misunderstandings, and/or partial understandings that could explain the quantitative
patterns (e.g., “given that most students were able to . . . it seems that they understand”).
planned supports: Instructional strategies, learning tasks and materials, and other
resources deliberately designed to facilitate student learning of the central focus.
prior academic learning and prerequisite skills: Includes students’ content knowledge
and skills as well as academic experiences developed prior to the learning segment.
problem-solving skills: Skills to engag[e] in a task for which the solution method is not
known in advance.
22
21
National Research Council. (2001). Adaptive reasoning. In Adding it up: Helping children learn mathematics (p. 151).
Washington, DC: National Academy Press.
22
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics (p. 52).
Reston, VA: NCTM.
Copyright © 2016 Board of Trustees of the Leland Stanford Junior University.
All rights reserved.
edTPA Secondary Mathematics Assessment Handbook
51 of 51
procedural fluency: Procedural fluency is a critical component of mathematical proficiency.
Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to
transfer procedures to different problems and contexts; to build or modify procedures from
other procedures; and to recognize when one strategy or procedure is more appropriate to
apply than another. To develop procedural fluency, students need experience in integrating
concepts and procedures and building on familiar procedures as they create their own
informal strategies and procedures. Students need opportunities to justify both informal
strategies and commonly used procedures mathematically, to support and justify their
choices of appropriate procedures, and to strengthen their understanding and skill through
distributed practice.
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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 productin other
words, to the act of capturing a mathematical concept or relationship in some form and to
the form itself. . . . Moreover, the term applies to processes and products that are
observable externally as well as to those that occur internally,” in the minds of people doing
mathematics. All these meanings of representation are important to consider in school
mathematics. (From National Council of Teachers of Mathematics [2000]. Principles and
Standards for School Mathematics, p. 67)
respect: A positive feeling of esteem or deference for a person and specific actions and
conduct representative of that esteem. Respect can be a specific feeling of regard for the
actual qualities of the one respected. It can also be conduct in accord with a specific ethic of
respect. Rude conduct is usually considered to indicate a lack of respect, disrespect,
whereas actions that honor somebody or something indicate respect. Note that respectful
actions and conduct are culturally defined and may be context dependent.
rubrics: Subject-specific evaluation criteria used to score your performance on edTPA.
These rubrics are included in the handbook following the directions for each task. The
descriptors in the five-level rubrics address a wide range of performance, beginning with the
knowledge and skills of a novice not ready to teach (Level 1) and extending to the advanced
practices of a highly accomplished beginner (Level 5).
variety of learners: Students in your class who may require different strategies or support.
These students include but are not limited to students with IEPs or 504 plans, English
language learners, struggling readers, underperforming students or those with gaps in
academic knowledge, and/or gifted students.
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From "Procedural Fluency in Mathematics". Downloaded from www.nctm.org on February 9, 2016.