mathematics observation rubric
MATHEMATICAL RIGOR
Developed by Jaime Park, Imelda Nava and Mollie Appelgate
TEACHING
DIMENSIONS
INNOVATION
LEVEL 4
INTEGRATING
LEVEL 3
EMERGING/APPLYING
LEVEL 2
CONTEMPLATING
LEVEL 1
ENGAGING
STUDENTS
IN RIGOROUS
MATHEMATICAL
TASKS
Students engage in cognitively
high level tasks including
Common Core math practices
such as proving, making and
testing conjectures, modeling
with mathematics, and/
or connecting with multiple
representations
Students engage in cognitively high
level tasks that support procedural
knowledge with connection to
conceptual understanding or
mathematical reasoning. Students
engage in some complex thinking.
Mathematical tasks support students
to understand mathematical
concept(s).
Students engage in cognitively low level
tasks, primarily procedural and memorization tasks such as practice using algorithms and formulas, copying notes, and
recalling memorized facts that require
little/no critical thinking or connection to
mathematical concepts
Students engage in inaccurate mathematics or non-mathematics. Students engage
in inappropriate tasks that are not aligned
with the learning goals of the lesson.
Teacher uses formative
assessment(s) to monitor
student progress and uses the
information to effectively guide
instruction to meet the content
objective(s). For example, the
teacher modifies instruction,
provides feedback to students,
addresses misunderstandings,
evaluates and clarifies content.
Teacher uses formative assessment(s)
to monitor student progress and attempts to use the information to guide
instruction and may meet the content
objective(s).
Teacher uses formative assessment(s)
to monitor student progress but does not
use the information to guide instruction to
meet the content objective(s).
Teacher does not use formative
assessment(s) to monitor student progress. Teacher does not check for understanding nor provides feedback to meet
the content objective(s).
SCORE ________
CHECKING FOR
UNDERSTANDING
AND FEEDBACK
SCORE ________
EXAMPLES OF INSTRUCTIONAL
STRATEGIES
Doing Mathematics
• High Level Tasks
Problem of the Week
• Concept Maps
• Pressing for accuracy, error analysis,
testing conjectures, consensus,
justifications and explanations,
generalizations, pressing for reasoning, analysis, evaluating strategies,
connecting ideas across methods/
representations, point to key information, argumentation, math modeling
Formative Assessment
• Multiple opportunities for students
to demonstrate learning, Practicing
problems, Poster presentations
• Individual Assessment: Exit Slips,
Traffic light, thumbs down, 3-2-1,
agree/disagree, boards up, Receptive modalities: sorting, gestures,
showing. boards up, board talk,
etc. (core)
• Group Assessment: Human
Barometer, board talk, Whip Around,
Community Circles, Think-Pair-Share
MATHEMATICAL DISCOURSE
Teacher asks cognitively High Level
questions such as How and Why specific to the mathematical content
with limited scaffolds. Ex. Questions
could improve with more appropriate
scaffolds like models, graphs, visuals,
word wall, student work, etc.
Teacher asks cognitively low level questions,
such as yes/no, correct/incorrect answers,
recalling of facts, formulas and definitions
requiring little critical thinking and
mathematical reasoning. These questions
often involve IRE (initiate respond evaluate)
types of questions.
Teacher asks non-math questions
or questions that lead students to Questioning with intention:
• Essential Questions
misunderstandings.
• Asking students to predict, make
SCORE ________
Teacher asks cognitively high
jevel questions such as how and
why specific to the mathematical
content with appropriate scaffolds.
For example, the teacher
generates relevant questions
using models, data, student
work, content, evidence, prior
knowledge.
TEACHER
FACILITATION:
PARTICIPATION
STRUCTURES
Teacher facilitates participation
structures effectively to support
majority (more than ½) of students
in mathematical discourse.
Teacher facilitates participation
structures and uses instructional
strategies to support some students in
discourse.
Teacher uses
calling on students and wait-time as facilitation
strategies. Teacher does not use participation
structures to provide opportunities for students
to engage in mathematical discourse.
Teacher does not facilitate
student discourse. Students have
no opportunities to engage in
mathematical discourse. Teacher
is primarily the person who talks
in class.
TEACHER
DISCOURSE:
QUESTIONING
SCORE ________
conjectures, use evidence/ rationale
• Blooms and Costa’s levels of questioning
• Experiential Learning Cycle (80% describe/
interpret to 20%generalize/apply) (core)
• Clarifying questions that evaluate student’s
thinking or provide counter explanations.
Facilitation:
• Teacher facilitated student linking
• Teacher intentionality in moving studentcentered discussion forward
• Teacher modeling, + see strategies for
Language Support
• Talk Moves: wait time, say more, repeat/revoice, say in your own words, agree/disagree etc. (core)
* Participation structures:
STUDENT
DISCOURSE:
MATH RIGOR
SCORE ________
Student talk conveys sophisticated
mathematical reasoning around
mathematical concept(s) (e.g.,
higher level-thinking, problem solving, justifications, analyses evaluating, proving, making and testing
conjectures, math modeling, connecting with multiple representations, example/counterexample).
Student talk that conveys developing/
limited mathematical reasoning
around mathematical concept(s): ex.
mathematical explanations, examples,
counter examples.
Student talk that conveys procedural
knowledge: ex. algorithms, recalling definitions,
etc that are primarily low level.
Student talk that conveys nonmathematics
• Small, flexible, leveled groups
• Group Roles
• Think Pair Share, Write Pair Share, Multimedia Pair Share (core)
• Dyad, AB Partner, Sage & Scribe
• Whip Around
• Panels, presentations,
• Debate, Argument, claims, counter claims,
reasoning
• Whole-class discussion, Fish Bowl, Socratic
Seminar
• Peer Feedback, self evaluation
mathematics observation rubric
EQUITABLE ACCESS TO CONTENT
Developed by Jaime Park, Imelda Nava and Mollie Appelgate
TEACHING
DIMENSIONS
INNOVATION
LEVEL 4
INTEGRATING
LEVEL 3
EMERGING/APPLYING
LEVEL 2
CONTEMPLATING
LEVEL 1
EXAMPLES OF INSTRUCTIONAL STRATEGIES
SUPPORTING
DEVELOPMENT
OF ACADEMIC
LANGUAGE
Students read/write/speak to
explain mathematical concepts
and mathematical reasoning
using correct symbols, syntax,
vocabulary, and grammar. Teacher
provides feedback, models,
uses examples and instructional
strategies for language support to
meet the language demands of the
mathematical tasks.
Students engage in reading/writing/
speaking to explain mathematical
concepts or mathematical reasoning
in relation to procedures. Teacher
provides opportunities, including
mathematical tasks coupled with
literacy strategies for students to use
language.
Students engage in reading/
writing/speaking to explain
procedures, definitions and facts
Students do not engage in reading/
writing
/speaking using academic language.
For example, Students copying notes
does not count as writing.
Teacher connects content to real
world contexts to deepen content
knowledge and/or make learning
experience relevant throughout
the lesson (e.g., culturally relevant
mathematics, critical mathematics,
computational thinking using large
data sets, math modeling)
Teacher connects content to real
world contexts to deepen content
knowledge and/or make learning
experience relevant briefly without full
integration to the lesson. For example
a teacher may make brief connections
at the beginning/end of a lesson.
Teacher attempts to connect
content to real world context but
the connection to the real world is
vague and not fully integrated into
the content
No evidence connecting content to
real world contexts
Language Support
• Teacher modeling use of Academic Language
• Academic language strategies: word bank, association,
sentence frames/starters
• Use of multiple modalities – productive & receptive, visual,
kinesthetic, auditory, TPR (total physical response)
• SDAIE/sheltered strategies: group projects, choral reading,
concept mapping, graphic organizers, prediction, quick write,
quick draw, reflection, sentence starters/frames, verbalizing,
vocabulary cards,etc.
• Literacy strategies: group projects, choral reading, concept
mapping, graphic organizers, prediction, quick write, quick
draw, reflection, say-mean-matter, verbalizing
• Scaffolded writing experiences- constructed responses;
summarization, descriptions, reasoning
• Use diverse text types; texts to speak and write.
• Convert text <---> visual
Objective writing, writing conclusions.
Teacher uses differentiation
strategies to meet the diverse
needs of the majority of their
students. This includes low,
medium, high content rigor and
students with various learning
needs
Teacher uses differentiation strategies
to meet the diverse needs of some of
their students. This includes low, medium, high content rigor and students
with various learning needs
SCORE ________
MAKING
CONTENT
RELEVANT FOR
LEARNERS
SCORE ________
DIFFERENTIATION
OF CONTENT,
PROCESS AND
PRODUCT
SCORE ________
Teacher uses differentiation
strategies to meet a few of their
students.
No differentiation strategies are
used. One-size fits all teaching.
Relevance
• Accessing prior knowledge, referencing lived experiences,
Realia, Visuals
• Technology and multi-media
• Critical pedagogy, real life application, projects, Linked
Learning, multi-cultural
Differentiation
• Multi-tiered, leveled/choice tasks, application tasks
• Teacher input/ student output variations
CLASSROOM ECOLOGY
CLASSROOM
ROUTINES
SCORE ________
COMMUNITY OF
LEARNERS
SCORE ________
DEMOCRATIC
CLASSROOM
SCORE ________
Teacher or students use a few
observable classroom routines
(e.g., class running and lesson
running), however, they are
primarily teacher centered and
do not support a productive
engagement of the students.
Teacher and students use observable classroom routines and procedures to facilitate and maintain
a productive, safe, and a positive
learning environment. Thoughtful
planning for how physical components interact with students and
teacher are observable. Students
play a vital part in maintaining
classroom routines.
Teacher or students use some
observable classroom routines and
procedures that support a productive
learning environment. The classroom
may benefit from more routines or
explicit teaching of these routines to
students.
Teacher and students form a
community of learners where
internalized social norms that
facilitate as safe and respectful
environment exist. Students and
teachers work toward a common
goal through social interactions
that are mutually respectful and
supportive.
Teacher models and teaches norms
of social interaction to establish and
maintain a community of learners
where students feel safe, respected
and supported but majority (1/2 or
more) of students may not practice
these social norms.
Teacher attempts to model or
teach norms of social interaction to
establish a community of learners.
The class may benefit from more
explicit teaching of social norms.
Teacher and student input and
voice are valued. Teacher elicits
input from students and provides
opportunities for majority of the students to voice their thoughts, paying
attention to equity. Teacher-student
input, individual and cultural norms
are valued and used for instructional decision- making.
Teacher provides opportunity for some
students’ voices to be heard through
attempts at equitable participation.
Teacher attempts using student input
for instructional decision-making.
Teacher provides limited opportunity for student feedback and
input. A few of the students’ voices
are heard.
No observable classroom routines
for class-running, lesson-running
procedures. There is a lack of a
productive learning environment
Norms and Routines
•
•
•
•
Opening and Closing Routines, Instructional time is used wisely
Structure, transitions from activity to activity are planned
Preparedness/distribution of materials
Classroom routines planned:
a) class-running routines, b) lesson-running routines,
c) interaction routines
Community of Learners: Building a Supportive & Respectful
Learning Environment
Teacher does not model or teach
norms or social interaction.
Disrespectful actions/speech is
allowed in the classroom
• Teacher is professional in speech, dress, interactions with students
• Community Circle, activities from building Tribes, community building
activities, social norms, contracts, discussions, reflective conversations,
conflict resolution, empathy, I AM poems; common & explicit values,
community building activities
Democratic Classroom
Students may not feel safe asking
questions or giving feedback.
Teacher uses put downs
Teacher repeatedly dismisses
student voice.
• Opportunities for multiple student voices to be heard
• Choice, Voting, Journal Writing, Regular student feedback to teacher
and others
• Student feedback
• Student generate ideas