Support Candidates for
edTPA through Curriculum
Alignment and Embedded
Assignments
Mihaela Munday Ph. D.
Savannah State University
School of Teacher Education
Macon, October 22, 2015
Curriculum Mapping –
How does the edTPA align with our programs?
1.To what extent does it reflect program values?
2. Where do you predict that students would do
well? Where might they struggle?
3. What core values and program emphases are not
captured in the TPA?
4. What kinds of assessments do you currently use
(or might you need) to get at these?
Andrea Whittaker UW Whitewater Presentation January 15, 2013
Integrating the five components of
the edTPA portfolio:
 Planning
 Instruction
 Assessment
 Analysis of Teaching
 Academic Language
Element
2a
Use problem solving to develop conceptual understanding, make sense of a
wide variety of problems and persevere in solving them, apply and adapt a
variety of strategies in solving problems confronted within the field of
mathematics and other contexts, and formulate and test conjectures in order
to frame generalizations.
2b
Reason abstractly, reflectively, and quantitatively with attention to units,
constructing viable arguments and proofs, and critiquing the reasoning of
others; represent and model generalizations using mathematics; recognize
structure and express regularity in patterns of mathematical reasoning; use
multiple representations to model and describe mathematics; and utilize
appropriate mathematical vocabulary and symbols to communicate
mathematical ideas to others.
3b
Analyze and consider research in planning for and leading students in rich
mathematical learning experiences.
3c
Plan lessons and units that incorporate a variety of strategies, differentiated
instruction for diverse populations, and mathematics-specific and instructional
technologies in building all students’ conceptual understanding and procedural
proficiency.
3d
Provide students with opportunities to communicate about mathematics and
make connections among mathematics, other content areas, everyday life, and
the workplace.
3e
Implement techniques related to student engagement and communication
including selecting high quality tasks, guiding mathematical discussions,
identifying key mathematical ideas, identifying and addressing student
misconceptions, and employing a range of questioning strategies.
3f
Plan, select, implement, interpret, and use formative and summative
assessments to inform instruction by reflecting on mathematical proficiencies
essential for all students.
3g
Monitor students’ progress, make instructional decisions, and measure
students’ mathematical understanding and ability using formative and
summative assessments.
4b
Plan and create developmentally appropriate, sequential, and challenging
learning opportunities grounded in mathematics education research in which
students are actively engaged in building new knowledge from prior
knowledge and experiences.
4c
edTPA Rubric # and Level of
Support
8 – Limited
9 – Limited
3 – Moderate
3 – Moderate
8 – Moderate
7 – Moderate; 8 – Limited
5 – Strong; 10 – Limited;
11 – Limited; 13 – Limited;
15 – Limited
11 – Limited; 13 – Limited;
15 – Moderate
1 – Limited; 3 – Moderate;
7 – Limited
2 – Limited; 4 – Limited
Alignment of NCTM CAEP
Standards (2012) for
Secondary to edTPA Rubrics
Curriculum Alignment (sample)
NCTM Standards (2012) – Secondary (Initial
Preparation)
Rule 505-3-01, REQUIREMENTS AND
STANDARDS FOR APPROVING EDUCATOR
PREPARATION PROVIDERS AND EDUCATOR
PREPARATION PROGRAMS.
Georgia Intern Keys
Effectives System
Candidate
Assessment of
Performance
Standards
edPTA
Tasks and Rubrics
Courses
Secondary Mathematics Education
Curriculum Mapping
Description of the assessment system
used to provide evidence and data and
to inform continuous improvement.
1.Content Knowledge
Candidates of secondary mathematics demonstrate conceptual understanding and apply knowledge of major mathematics concepts, algorithms, procedures, connections, and applications within and among
mathematical content domains.
1a. Candidates demonstrate conceptual understanding
and apply knowledge of major mathematics concepts,
algorithms, procedures, applications in varied contexts,
and connections
within and among mathematical domains including
Number, Algebra, Geometry, Trigonometry, Statistics,
Probability, Calculus, and Discrete Mathematics as
outlined in the 2012 NCTM NCATE
Mathematics Content for Secondary.
1.Professional
Knowledge
1.1, 1.4
MAED 4416
1.State-required Licensure Test: GACE
2.Alignment to NCTM CAEP
Mathematics Content for Secondary
Task 1
Rubric 1
MATH 1113 Pre-Calculus
MATH 2111 Calculus I
MATH 3101 Linear Algebra
MATH 3201 Probability and Statistics I
MATH 3401 Modern Geometry
MATH 3211 Foundation of Higher Math
3. Individual Candidate performance data.
MAED 4417
EDUC 4475
4. Task 1 -Planning Commentary
MAED 4416
5. Course Portfolio
Developing new courses (BSED)
MAED 3000 Connections in Secondary School Mathematics
Using the NCTM Standards as a guideline and replacing traditional teaching of Algebra I,
Geometry, Algebra II, this course blends the mathematics of algebra, geometry, trigonometry,
probability, statistics, and discrete mathematics. The course bridges connections of all sorts:
those between different mathematical areas; mathematics and science; mathematics and other
subject areas; and mathematics and the real world of people, business and everyday life. The
course integrates technology through the use of graphing calculators and computers, which
students use to make conjectures; validate findings; and investigate concepts, problems, and
projects in greater depth. The emphasis on writing and the use of alternative types of assessment
in this course is designed to help the student teachers to adapt their teaching strategies in order to
meet every student’s need.
EDUC 3130 Content Area Literacy for Diverse Classroom
This course explore methods for teaching middle and high school to read, write, think, and learn in
ways that allow them to master the subject matter and meaningfully apply their understanding.
Candidates learn to plan lessons that teach content and nurture greater literacy. Pre-, during-, and
post-reading strategies are explored, along with assessment methods that give students a continual
view of their literacy progress and achievement. Classroom adaptations for culturally and
linguistically diverse population in the content areas are also addressed.
Developing new courses (BSED)
MAED 3001 Qualitative and Quantitative Research Methods in Mathematics
Education
This course will examine qualitative methods and quantitative methods. In qualitative
research, interviewing, observations and document analysis will be the major source of the
qualitative data for understanding the phenomenon under study. Observations will involve
collecting qualitative information about human actions and behaviors in social activities
and events in a real social environment, such as classroom teaching and learning.
MAED 3002 Planning, Managing & Assessing the 6-12 Divers Mathematics Classroom
The focus of the course is developing reflective teachers who draw upon a wide array of
solutions to secondary classroom challenges when planning instruction for preadolescent
and adolescent students. The class uses case studies to discuss and prepare candidates to
deal with the effects of diverse characteristics and cultures of the adolescent. The course
will provide candidates opportunities to apply conceptions of curriculum, instruction,
classroom management and discipline, multimedia, human resources, and assessment in the
context of an actual secondary classroom.
MAED 4417 Assignments
Embedded Assignments
 The balance between conceptual
understanding and computational proficiency
is achieved when the curriculum enables and
encourages students to build on the
mathematics they already know.
Substantive feedback from aligned rubrics on their
performances
MAED 4416 Mathematics Sequenced Unit Plans Rubric
Planning for
Mathematical
Understanding
CAEP 1.1, 1.3,
4(a)(d)(l)(n)
INTASC 7a-e, i-l,
n-q; 9c
NCTM 7. 2
edTPA
Rubrics1,2,4,5
Level 1
Candidate’s plans
are incomplete.
They focus solely
on facts and/or
procedures with no
connections to
concepts or
mathematical
reasoning and/or
problem solving.
Methods or
strategies of
instruction are not
evident and/or are
inappropriate for
the content.
There is little or no
Planning to
Support Varied evidence of planned
Student Learning supports.
Needs
OR
CAEP 1.2, 1.4,
Candidate does not
6c,6d
attend to
INTASC2a;2c;2d;2f requirements in IEPs
;2g;2h;2j;2k;2m;8p; and 504 plans.
9d
NCTM 7.3
edTPA Rubric 2
Level 2
Plans slavishly follow
standards with little
consideration of what
students are ready for,
making learning with
understanding difficult.
Candidate’s plans support
student learning of facts
and procedures with vague
concepts and mathematical
reasoning and/or problem
solving skills.
Planned supports are
loosely tied to learning
objectives or the central
focus of the learning
segment.
AND
Candidate attends to
requirements in IEPs and
504 plans.
Level 3
Plans for instruction
demonstrate knowledge of
content standards (CCGPS),
use of appropriate learning
materials, and commitment to
learning with understanding.
They are built on each other to
support learning of facts and
procedures with clear
connections to concepts and
mathematical reasoning and/or
problem skills.
Planned supports are tied to
learning objectives and the
central focus with attention to
the class as a whole.
AND
Candidate attends to
requirements in IEPs and 504
plans.
Level 4
Plans for instructions
demonstrate knowledge of
the content appropriate for
students,
use of stimulating curricula
that allows multiple
approaches to content, and
commitment to learning with
understanding. They are built
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.
Planned supports are tied to
learning objectives or the
central focus. Supports
address the needs of specific
individuals or groups with
similar needs.
AND
Candidate attends to
requirements in IEPs and
504 plans.
Level 5
Level 4 plus:
Candidate explains how
she/he will use learning
tasks and materials to
lead students to make
clear and consistent
connections.
Level 4 plus:
Supports include
specific strategies to
identify and respond to
preconceptions,
common errors, and
misunderstanding.
Substantive feedback from aligned rubrics on their
performances
MAED 4416 Mathematics Sequenced Unit Plans Rubric
The assessments only
provide evidence of
students’ procedural
CAEP 4(f)
INTASC6a,b, d, e,6j, skills and/or factual
knowledge.
g, m, q-u
Assessments are not
NCTM 7.5
aligned with the
edTPA Rubric 5
central focus and
standards/objectives
for the learning
segment
Assessment
Assimilation of
Knowledge
INTASC 2c,l,n
NCTM 8 .7
edTPA Rubrics
1,2,5,6,7,8
Connections
between prior
knowledge and
new learning
experiences are
not evident.
Either formal or informal
assessment strategies or
instruments are mentioned
but there are no concrete
examples. The assessments
provide limited evidence to
monitor students’
conceptual understanding,
procedural fluency, and
mathematical reasoning
and/or problem solving
skills during the learning
segment.
Provides concrete examples of at
least one question for each type
of student, and describes at least
one other informal way to gather
information about student
progress. When appropriate,
uses formal assessment to
measure student learning. The
assessments provide evidence to
monitor students’ conceptual
understanding, procedural
fluency, and mathematical
reasoning and/or problem solving
skills during the learning
segment.
Attempts to build on prior
knowledge, but is not able to
help students develop the
new concept.
Uses learning activities that
build on prior knowledge, but
students may not see how the
learning experiences develop a
new concept.
Provides examples of a
variety of questions to be
asked when students seem
to be progressing well or
when they are struggling.
Describes at least one other
method of gathering
knowledge of student
progress. When
appropriate, uses formal
assessment to measure
student learning. The
assessment provide multiple
forms of evidence to monitor
students’ conceptual
understanding, procedural
fluency, and mathematical
reasoning and/or problem
solving skills throughout the
learning segment.
Uses a variety of learning
activities that build on prior
knowledge and help students
articulate how the learning
experiences develop a new
concept.
Level 4 plus:
The assessments are
strategically designed to
allow individuals or
groups with specific
needs to demonstrate
their learning.
Level 4 plus:
Values knowledge
outside his/her own
content area and how
such knowledge
enhances learner
exploration, discovery
and expression across
content areas.
Academic Language for Secondary Mathematics
Understand Language
Demands and Resources
INTASC-2013.2.i
INTASC-2013.4.h
Level 1 (5 pts)
Level 2 (20 pts)
Level 3 (40 pts)
Level 4 (50 pts)
Candidate's description of students'
academic language proficiency at
lower levels is limited to what they
cannot do.
Candidate describes academic
language strengths and needs of
students at different levels of
academic language proficiency.
Candidate describes academic
language strengths and needs of
students at different levels of
academic language proficiency.
Candidate describes academic
language strengths and needs of
students at the full range of
academic language proficiency.
Language genre(s) discussed are
only tangentially related to the
academic purposes of the learning
segment.
The language genre(s) discussed are The language genre(s) discussed are The language genre(s) discussed are
clearly related to the academic
clearly related to the academic
clearly related to the academic
purposes of the learning and
purpose of the learning segment and purpose of the learning segment and
language demands are identified. language demands are identified. language demands are identified.
One or more linguistic features
One or more genre-related
Candidates identifies vocabulary
and/or textual resources of the
linguistic features or textual
that may be problematic for
genre are explicit identified.
resources of the specific
students.
Candidate identifies essential
tasks/materials are explicitly
vocabulary for students to actively identified and related to students'
engage in specific language tasks. varied levels of academic language
proficiency.
Candidate identifies unfamiliar
vocabulary without considering
other linguistic features.
OR
Candidate did not identify any
language demands of the learning
and assessment task.
Developing Students'
Academic Language
Repertoire
INTASC-2013.2.e
INTASC-2013.2.i INTASC2013.5.h
NCTM-K-12.8.1
The candidates gives little or
The candidate uses the scaffolding
sporadic support to students to meet or other support to address
the language demands of the
identified gaps between students'
learning tasks.
current language abilities and the
language demands of the learning
OR
tasks and assessments, including
Language and/or content is
selected genres and key linguistic
oversimplified to the point of
features.
limiting student access to the core
content of the curriculum.
Candidate identifies for instruction
related clusters of vocabulary.
The candidate's uses of scaffolding
or other support provides access to
core content while also providing
explicit models, opportunities for
practice, and feedback for students
to develop further language
proficiency for selected genres and
key linguistic features.
The candidate's use of scaffolding
or other support provides access to
core content while also providing
explicit models, opportunities for
practice, and feedback for students
to develop further language
proficiency for selected genres and
key linguistic features.
Candidate articulates why the
instructional strategies chosen are
likely to support specific aspects of
students' language development for
different levels of language
proficiency.
Candidate articulates why the
instructional strategies chosen are
likely to support specific aspects of
students' language development for
the full range of language
proficiency and projects ways in
which the scaffolds can be removed
as proficiency increases.
Language Acquisition in Mathematics Assignments
Graphing Organizers
-Verbal and Visual Word Association(VVWA) described in The teaching
of Reading in Mathematics by M.Barton and C.Heidema(2002), places a
vocabulary word into one section of a four-by-four graphic. The
remaining three sections are filled with a visual representation of the
word, a definition and/or an equation, and finally, a personal
association.
-Use of compare and contrast activities.
-Tables
-Charts
-Diagrams
VVWA(Verbal and visual word association) for the
Slope of a line
Compare and contrast activity for exponential, linear and quadratic functions
Geometry of a Circle-Semantic Map
Meaning
Semantic
Concepts
Representation Tool
Chemistry
Definitions:
Keywords
Unit Circle
-Circle
symbolizes the
expansiveness
of the cycles in
time, life and
nature itself. A
mirroring of
perception.
-Inclusion
Circle Equations
-Literature
circles are
small,
temporary
discussion
groups.
-Mathematical
circle is a plane
shape, in
which all sets
of points on a
plane are a
fixed distance
from a center.
-Wholeness Polar and Parametric
Equations
-Focus
-Unity
-Nurturing
Biology
-Cycles
-Initiation
Diameter
-Everything
-Perfection
Secto
r
Segment
Arc
Circle
-Womb
Chord
-Centering
-Revolution
-Infinity
-Mobility
Completion
Radiu
s
Circumfe
rence
Astronomy
History
The study of the circle goes back
beyond the recorded history. The
invention of the wheel is a
fundamental discovery of
properties of a circle. The Greeks
considered the Egyptians as the
inventors of geometry. Ahmes, who
is a scribe and the author of the
Rhind papyrus, gives a rule for
determining the area of a circle
that corresponds to 256/81 or
approximately 3.16. Thales found
the first theorems relating to circles
around 650 BC. The Euclid's Book
III, Euclid's Elements set to work
properties of circles and problems
of inscribing polygons. One of the
problems of Greek mathematics
was the problem of finding a
square with the same area as given
circle. Several of the 'famous
curves' were first attempted to solve
this problem. Anaxagoras in 450
BC is the first recorded
mathematician to study this
problem.
Challenging for students- Task 3
Possible reasons for low scores on Task 3:
-Fatigue by the end of this process
-Weak background in assessing student work,
developing rubrics, aligning assessments to
objectives and rubrics
Rubric 3
While preassessing students is not required by edTPA, doing so may help candidates who
are new to their placement quickly identify student learning needs and strengths.
Rubric 5



Examples of assessments: Think pair share, KWL  informal
assessments, Oral, written, diagrams, mapping
IEP/504 accommodations are met (longer time, scribe); if no
IEPs/504s than not applicable
Level 4: multiple assessments in multiple ways throughout start
out with KWL, then do think-pair-share, then do group work
where they create multimedia, then give formative assessment
 assessment is throughout.
Rubric 11
•Talking about whole class and supporting it with evidence
•Assessment and results of assessment
•Rubric results, pie chart, table of scores, etc.