Rigor & Mathematical Practices
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
AI proposed
The materials show intentional development of both halves of MP3 in connection to grade-level content. The 'Critique, Correct, Clarify' routine [E10] explicitly engages students in analyzing others' mathematical writing, performing error analysis, and considering the author's thinking — directly meeting the 'critique the reasoning of others' intent, with teacher supports for modeling respectful critique. The 'construct viable arguments' half is supported by discourse-focused routines and discussions designed around each lesson's mathematical goal [E11], small-group grappling and synthesis [E6], and the Five Practices for facilitating argumentation [E5], with MP3 named as a core practice students 'do' [E7]. MPs are tied to grade-level content through lesson/activity narratives that explain how practices come into play [E2][E3] and via per-practice learning targets [E4].
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Evidence Guide· what the rubric asks for · click to expand
Indicator 2f Materials support the intentional development of MP3: Construct viable
arguments and critique the reasoning of others, for students, in connection to
the grade-level content standards, as expected by the mathematical practice
standards.
Scoring
2 points
● There is intentional
development of MP3 to meet its
full intent in connection to
grade-level content.
1 point
● There is intentional
development of students
constructing viable arguments
in connection to grade-level
content.
OR
● There is intentional
development of students
critiquing the reasoning of
others in connection to
grade-level content.
0 points
● There is no intentional
development of MP3 to meet its
full intent in connection to
grade-level content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2g, 2h, and 2i, determines the adherence to the Standards for Mathematical
Practice. This indicator specifically examines MP3 by examining whether the provided opportunities for student
engagement with the MP are a) connected to the mathematical content of the grade level and b) fully developed
across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP3: Construct viable arguments and critique the reasoning of others
● Mathematical Practices Compilation
Indicator 2f Guiding Questions:
Across the grade level, is MP3 identified and connected to mathematical content?
Across the grade level, is there intentional development of MP3 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP3 is occurring throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP3 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
To check that MP3 is connected to grade-level content and is developed to it full intent, look at lessons,
assessments, and any examples/descriptions of anticipated student work that require students to:
Construct Viable Arguments Critique the Reasoning of Others
Construct mathematical arguments. Perform error analysis of provided student
work/solutions/arguments.
Explain/justify their strategies and thinking orally or in
writing using concrete models, drawings, actions, or
numbers.
Listen to or read the arguments of others, decide
whether they make sense, and ask useful questions
to clarify or improve the arguments.
Create their own conjectures.
Look at teacher directions and how teachers are guided to carry out the lessons so that students are engaged
in the MPs. In particular, look for places where teachers are expected to:
● provide opportunities for students to engage in discourse to construct and/or critique mathematical
arguments,
● ask clarifying and probing questions, and
● help students compare methods and strategies.
Check to see if any of the materials address only the Standard for Mathematical Practice (meaning it is not
connected to grade-level mathematical content). Record any instances where the Standard for Mathematical
Practice is not connected to the grade-level mathematics content.
Across the grade level, verify that students use the MP to its full intent within the materials.
If the MP is only located in a specific part of the teacher manuals (e.g. the teacher-led portion of the lesson),
you will need to look at other sections (e.g. independent work, homework, assessments) to ensure that the MP
is intentionally connected to the content. Look where the MP is identified, but also look at places where it is
not identified.
Cluster Meeting
During the cluster meeting:
Consider the following question(s) as evidence is synthesized:
● When is MP3 identified and connected to grade-level mathematical content?
● In what ways do the students use MP3 to its full intent across the grade level?
● In what ways, if any, do the supports provided for teachers enable students to engage with MP3?
Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Retrieved evidence (12 chunks)
- E1 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/how-to-use-the-materials.htmlrel 0.54
- E2 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/how-to-use-the-materials.htmlrel 0.51
- E3 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/how_to.htmlrel 0.51
- E4 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/how-to-use-the-materials.htmlrel 0.50
- E5 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/design_principles.htmlrel 0.48
- E6 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/design-principles.htmlrel 0.48
- E7 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/what_is_pbc.htmlrel 0.46
- E8 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/design_principles.htmlrel 0.45
- E9 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/design_principles.htmlrel 0.44
- E10 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/mathematical-language-development.htmlrel 0.44
- E11 · k5-teacher-guide — im.kendallhunt.com/k5/teachers/teacher-guide/how-to-use-the-materials.htmlrel 0.44
- E12 · ms-teacher-guide — im.kendallhunt.com/MS/teachers/design_principles.htmlrel 0.43
Evidence is stored as references + retrieval scores (the chunk text isn’t snapshotted); open the source to read the passage in context.