Indicator 2d

Indicator 2d The three aspects of rigor are not always treated together and are not always

treated separately. There is a balance of the three aspects of rigor within the

grade as reflected by the standards.

Scoring

2 points

● All three aspects of rigor are present

independently and multiple aspects of rigor are

engaged simultaneously to develop students’

mathematics understanding of a single topic/unit

of study throughout the series.

0 points

● Multiple aspects of rigor are not engaged

simultaneously to develop students’ mathematical

understanding of a single topic/unit of study

throughout the series.

About this indicator:

What is the purpose of this Indicator?

This indicator, along with 2a, 2b, and 2c, determines the shift of Rigor. In order to be considered rigorous,

program materials must include a balance of conceptual understanding, procedural skills and fluencies, and

application as reflected in the standards. This balance should be evident in all aspects of the high school series

and in each course to support students as they develop mathematical understanding.

Research or Standards connection:

● Common Core State Standards for Mathematics (CCSSM)

● High School Publishers' Criteria for the CCSSM (Spring 2013)

● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics

● Achieve EQuIP Rubric for Lessons & Units

● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments

● CCSS Mathematics Curriculum Materials Analysis Project

Resources:

● SAP Coherence Map

● Institute for Mathematics Education Progressions Documents

● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)

● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)

● Reading: “Additional Aspects of the Rigor and Balance Criterion” (Publishers' Criteria, p. 10)

Indicator 2d Guiding Question:

Do the instructional materials balance the three aspects of rigor?

Evidence Collection

Review lessons, chapter/unit assessments, and homework assignments.

Look for individual lessons/topics, as well as complete units, that include more than one aspect of rigor.

Look for a balance of all three aspects of rigor, considering the program materials as a whole and as individual

units of study.

● Consider whether the content/topic is being introduced to students for the first time or is an extension of

previous learning.

● Consider whether materials in the series simultaneously develop conceptual understandings and

procedural skills.

● Be mindful of where students are encouraged to use multiple representations and written explanations to

support their work in application problems.

For this indicator, consider the intent of the series to balance the three aspects of rigor, not the quality of the

materials—indicators 2a-c focus on the quality of rigor within the materials.

Determine if the materials consistently balance the three aspects of rigor while allowing for dedicated focus

on each individual aspect. Look for the evidence in lessons, review lessons, routine daily checks, chapter and

unit assessments, homework assignments, and other sections demonstrating connections between

procedural skills and conceptual understanding.

Determine if the materials neglect to attend to all aspects of rigor specified by the standards or clusters.

Examples may include, but are not limited to:

● With A-APR.1, the materials fully develop students adding, subtracting, and multiplying polynomials, but

the materials do not engage students in understanding that polynomials form a system closed under

addition, subtraction, and multiplication.

● With A-REI.11, the materials have students find solutions to systems of equations through applications, but

the materials do not have students develop conceptual understanding by explaining why the

x-coordinates of the points where two graphs intersect are the solutions to setting the two equations

equal to each other.

Evidence must include explicit examples of where more than one aspect of rigor is present (can be two or

three aspects, but does not have to include all three). Look for lessons that call out specific components of

rigor, and lessons that focus on individual aspects of rigor.

Cluster Meeting

Do the materials intentionally focus on one aspect of rigor over the others in specific units? If so, do the

materials work to maintain balance throughout each course and the series?

In what ways do the materials maintain balance of the aspects of rigor throughout each course and the series?

In what ways do the materials neglect one, or more, aspect(s) of rigor throughout each course and the series?

Gateway 2: Rigor & Mathematical Practices

Criterion 2.2

Standards for Mathematical Practice

Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical

Practice (MPs).

What is the purpose of this Criterion?

The purpose of this criterion is to ensure the Standards for Mathematical Practice are identified and connected

to grade-level mathematical content, and the materials present opportunities for students to both learn and

independently demonstrate each of the MPs.

Research Connection

● Common Core State Standards Mathematics

Scoring

Meets Expectations

● 7-8 points

Partially Meets Expectations

● 4-6 points

Does Not Meet Expectations

● <4 points

Gateway 2: Rigor & Mathematical Practices

Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and

the Standards for Mathematical Practice.