MATHEMATICS CONTENT RUBRIC
MCR Indicators
Content Information
Provided by Teacher
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Required Classroom
Student Activities
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5
The teacher posted an accurate
definition of a term and reviewed the
definition of a term previously
defined.
The explanation or demonstration of
the new concept was accurate,
thorough, and connected to a concept
attained in a previous lesson.
The activity provided students with
multiple ways of grasping the
concept highlighted in the lesson
objective.
The activity required students to find
a pattern or build on prior
knowledge to either construct a rule
or internalize a strategy.
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3
An accurate definition of a term was
posted.
The explanation or demonstration of
the new concept was accurate and
complete.
Posting doesn’t only apply to new
concepts. Examples may be included and
necessary to clarify concepts.
 The activity required students to
investigate the concept highlighted in
the lesson objective prior to a concise
explanation or demonstration given
by the teacher.
 Proposed problems were of two
levels of difficulty and challenged
students to think on a deeper level.
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Not scoring effectiveness of the activity,
just the potential.
Answers
Provided by Teacher
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Mathematical
Academic
Language
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The teacher led students into the
accurate answer via the Socratic
method.
When two students asked the same
question, the teacher seized the
opportunity to reteach the concept or
topic at the core of the confusion.
All terms were accurate, clear, and
appropriately used.
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Answers were accurate, complete,
and justified.
When three students asked the same
question, the teacher seized the
opportunity to reteach the concept or
topic at the core of the confusion.
If questions are not audible, then score
this indicator a 1.
 One term was misused but did not
adversely impact the learning.
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1
No definitions of terms were posted.
The explanation or demonstration of
the new concept was not entirely
accurate, confusing, or difficult to
follow.
The activity provided practice in
applying knowledge attained in an
earlier lesson.
Students were required to use a
prescribed strategy or algorithm to
complete a set of problems.
Students were asked to construct
representations (graphical,
geometric, data tables, etc.) but were
not challenged to use them in
understanding the concept
highlighted in the lesson objective.
Answers were inaccurate or
incomplete.
Even though more than three
students asked the same question,
the teacher failed to reteach the
concept or topic at the core of the
confusion.
The misuse of two or more terms
adversely impacted the learning.
Mathematical Notation
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Mathematical
Connections
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Mathematical
Representations
Verbal, Numerical,
Symbolic, Graphical,
Geometric
Steps were clear and distinctly
presented.
Relational signs (e.g., equal, greater
than, approximately) connected each
step in all calculations.
Appropriate units were kept with
magnitudes throughout calculations.
Figures were accurately labeled.
Calculations were free of errors.
Two or more appropriate
connections were made to concepts
or procedures learned in a previous
lesson.
Two or more appropriate
connections were made between
mathematical representations.
All representations were effectively
incorporated and significantly
enriched the learning of the concept
or procedure.
Representations were accurate and
clear.
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Steps were clear and a majority of
them were distinctly presented.
Equal signs connected a majority of
the steps in each calculation.
Appropriate units were kept with
magnitudes throughout calculations.
A majority of the labels on the figures
were accurate.
Minor errors were made in
calculations but were immediately
addressed.
Snapshots of calculations done on the
board are evidence for this indicator.
 One appropriate connection was
made to a concept or procedure
learned in a previous lesson.
 One appropriate connection was
made between mathematical
representations.
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Three of the representations were
effectively incorporated and enriched
the learning of the concept or
procedure.
Representations were accurate and
fairly clear.
*Some overlapping is expected.
Verbal – defs paraphrased by teacher,
word problems read aloud, word
problems and Quick Polls in PDF
Numerical – equations or expressions
with values (must see)
Symbolic – formulas with/without values
(must see)
Graphical – tables, Venns, pictures,
diagrams, coordinate system, linear
graph, mapping, number line, etc. (must
see)
Geometric – shapes, angles, rays, etc.
(must see)
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Steps were missing or bunched
together.
Relational signs (e.g., equal, greater
than, approximately) were missing
between the steps of calculations.
Appropriate units were omitted in
calculations.
Figures were inaccurately labeled.
Serious errors were made in
calculations.
No appropriate connections were
made to concepts or procedures
learned in a previous lesson.
No appropriate connections were
made between mathematical
representations.
Only one representation was used to
communicate the concept or
procedure.
Considerable problems with clarity,
consistency or correctness of
representations.
Elements of
Mathematical
Abstraction
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Mathematical
Justification
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The teacher took advantage of at
more than one opportunity to teach
abstract reasoning and abstract
concepts.
Teacher identified and directly
addressed student issues with
abstract reasoning.
Teacher’s own abstract reasoning
and grasp of abstract concepts was
evident and exceptional.
Four mathematical justifications that
were given included deductive
reasoning about why a procedure
works or why something is true or
valid in general
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Teacher took advantage of at least
one opportunity to teach abstract
reasoning and abstract concepts.
Teacher was aware of student issues
with abstract reasoning and made
some attempts to directly address
those issues.
Teacher’s own abstract reasoning
appeared to be correct and clear.
Evidence that students are required to
reason to acquire a deeper
understanding than just using a formula.
Word problems that are slightly more
difficult than the ones worked by the
teacher.
 Two mathematical justifications that
were given included deductive
reasoning about why a procedure
works or why something is true or
valid in general
Defs or theorems or properties are used
to justify a procedure.
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Opportunities to teach abstract
reasoning and concepts were missed
or teacher’s own abstract reasoning
was incorrect or confusing.
Important elements of abstraction
appropriate to the lesson were
bypassed.
No justification was given for any
procedure, property, or theorem.