Alignment: Overall Summary

The instructional materials reviewed for the Springboard Traditional series do not meet expectations for alignment to the CCSSM for high school. The materials do not meet the expectations for focus and coherence as they partially meet the expectations in the following areas: attending to the full intent of the mathematical content contained in the high school standards for all students, allowing students to fully learn each standard, requiring students to engage at a level of sophistication appropriate to high school, making meaningful connections in a single course and throughout the series, and identifying and building on knowledge from Grades 6-8 to the High School Standards. Since the materials did not meet the expectations for focus and coherence, evidence for rigor and the mathematical practices in Gateway 2 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
9
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
N/A
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
21
30
36
N/A
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
9/18
+
-
Criterion Rating Details

The instructional materials reviewed for this series focus the students' time on the widely applicable prerequisites, or WAPs, for a range of college majors, postsecondary programs, and careers. There are some standards which are not fully developed throughout the series because some aspects are never addressed or there are specific methods/content identified that are not addressed. The modeling standards, standards that require students to prove concepts, and standards that require explanation, were not fully developed and did not allow students to engage deeply with the content in order to master the standards. The materials also lacked clear and coherent connections across the series and within materials to provide students with a coherent learning pathway for the mathematics being taught. In many cases, there is a lack of identification of connections for students to previous learning both with the content taught in middle grades as well as to concepts learned in previous courses in high school.

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
2/4
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. In general, the series included the majority of all of the non-plus standards, but there were some instances where the full intent of the standard was not met.

The following standards are identified as having been met in this series.

  • In Number and Quantity, there was evidence to indicate that the non-plus standards of N-CN were addressed in the Algebra 2 materials. On page 423, the Algebra 1 textbook requires students to pay particular attention to the units of quantities (N-Q.1). Additional items in Activity 33 require students to make choices about the level of accuracy needed in their answers (N-Q.3).
  • In the Algebra category, there was evidence to support student engagement with A-APR.A,B and A-REI.A,B. Many opportunities with these clusters were found across both the Algebra 1 and Algebra 2 materials.
  • Across the Algebra 1 and Algebra 2 materials, there was evidence to indicate that all aspects of the non-plus standards from the following domains and clusters were addressed: F-IF.B, F-IF.C, F-BF, F-LE.B, F-TF.A and F-TF.B.
  • The standards from the Geometry category were predominantly addressed in the Geometry materials, and there was evidence to indicate that all aspects of the non-plus standards from the following domains and clusters were addressed: G-CO; G-GMD; G-SRT.B,C; G-C.B; G-GPE.B; and G-MG.
  • In Statistics and Probability, it was determined that all aspects of the non-plus standards were met across the series.

Reviewers did not find evidence of G-SRT.1b anywhere throughout the series. The standard was not identified in the materials.

The following standards are identified as having been partially met in this series in the conceptual categories and domains listed. In general, many of the standards that are partially met earn that classification due to the lack of student opportunity to prove certain aspects stated in the standards.

  • N-RN.3: Opportunities to have students explain why the sums/products are rational or irrational are needed. While students have opportunities to predict the outcome of such sums/products (Algebra 1 Activity 20), the explanation of such is not required.
  • A-REI.5: While students were given ample opportunities to solve systems via linear combinations, there were no expectations for students to prove that linear combinations worked as a valid method of solution by showing that the sum of one equation and a multiple of the other would produce a system with the same solution.
  • A-REI.11: Students are asked to solve systems of equations graphically with a variety of equation types, but they are not asked to explain why the x-coordinates of the points were the solutions to the equation f(x) = g(x).
  • F-LE.1a: In Algebra 1, lesson 9-3, students explore the linear aspect but do not explore the exponential aspect of this standard. Also, students are not required to prove that linear functions grow by equal differences over equal intervals nor that exponential functions grow by equal factors over equal intervals.
  • G-C.3: Students are given opportunities to construct inscribed and circumscribed circles for a triangle, but they are not asked to prove the properties of angles for a quadrilateral inscribed in a circle.
  • G-GPE.1: Students are asked to derive equations using the distance formula rather than the Pythagorean theorem.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for this series do not meet the expectation for attending to the full intent of the modeling process when applied to the modeling standards. Many aspects of the modeling standards are not completely addressed with the full intent of the modeling process.

Throughout the series, many problems are labeled and identified by the publisher as modeling problems. However, students are not given opportunities to engage in the full modeling process. This process is defined for high school students in the following way:

"By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose." - www.corestandards.org

There are limited, if any, opportunities for students to make assumptions, revise their thought process, or revise and improve models. Most problems that are labeled and/or identified as a modeling problem are more of an application problem with significant scaffolding in place for the students. For a problem to be an example of modeling, students should be able to construct a hypothesis and revise their conjecture as needed.

Examples of problems that do not meet the full intent of the modeling standards include the following.

  • A-SSE.1: In Algebra 2 on page 265, there is an embedded assessment. This represents an application problem, and not the modeling process, as students do not have to engage in creating a model from a non-routine context. Likewise, the rubric does not reflect that students are expected to engage in the modeling process as described in the SMP.
  • The rubric on page 33 of Algebra 1 indicates that students are being assessed on their ability to model. Problem 2b asks students to assume, but then tells them what number to use to determine a value. The removal of students' opportunities to make assumptions keeps students from engaging in the full modeling process.
  • "Model with Mathematics" is listed many times throughout the text. However, the focus on these items is for students to compute. On page 114 of the Algebra 1 textbook, question 23 very specifically tells students how to model the problem instead of giving students choice on formulating their own model.

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.
2/2
+
-
Indicator Rating Details

The materials, when used as designed, meet the expectation for allowing students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers (WAPs). The information provided by the publisher shows a strong focus on widely applicable prerequisites for college majors, post-secondary programs, and careers. Prerequisite material is mostly limited to “Warm-Up” tasks and used in a reasonable way to support meeting high school standards. In most of the series, standards from Grades 6-8 are reviewed and do not distract students from the WAPs.

Examples include, but are not limited to:

  • F-IF.4 is addressed in activities 6, 7, 15, 22 and 29 in the Algebra 1 materials and in activities 7, 12, 14, 25 and 35 in the Algebra 2 materials. This represents a significant amount of time/attention given to this WAP from the functions category.
  • A-SSE.1 received extensive treatment through student work in Algebra 1 (activities 2, 24, 25, 26 and 31) and Algebra 2 (activities 7, 14 and 27). A-SSE received extensive work across the courses, and the domain was connected in meaningful ways to other WAPs in both the Algebra 1 and Algebra 2 materials.
  • In the Geometry materials, many of the WAPs were addressed in Unit 2 (G-CO) and Unit 3 (G-SRT).
  • Although not always specifically identified in the Geometry materials, students continue to work with WAPs from the Algebra, Functions, and Number and Quantity categories at various times throughout the series.

The materials do not include distracting content that would keep students from engaging with the standards identified as widely applicable prerequisites.

Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
2/4
+
-
Indicator Rating Details

The materials, when used as designed, partially meet the expectation for allowing students to fully learn each non-plus standard. In general, the series addressed many of the standards in a way that would allow students to learn the standards fully. However, there are cases where the standards are not fully addressed or where the instructional time devoted to the standard was insufficient. The following are examples where the materials partially meet the expectation for allowing students to fully learn a standard.

  • N-Q.2: Students are given opportunities to work with appropriate quantities when creating models for problems. However, many of these quantities are prescribed for students rather than allowing students to define their own quantities. This prescriptive definition by the materials does not allow students to develop their own understanding of how the quantities relate to the problem.
  • A-SSE.1b: Students are given minimal opportunities with this standard. An example is in Algebra 2 on page 228 where students are asked to use the discriminant to determine the nature of the solutions. Students are not asked to interpret other expressions throughout the series.
  • A-APR.4: The standard requires that students prove polynomial identities. There is one instance of this proof in Algebra 2 on page 251. This example proved the exact identity in the example in the standards. There are no other examples for proving identities. Students are also not given the opportunity to produce these proofs on their own.
  • A-REI.10: The one reference found for this standard is the Math Tip on page 92. There is no additional work to help students understand that the graph produced contains all possible solutions to the given equation.
  • F-IF.2: While students are given opportunities to evaluate functions, there are very few opportunities for students to interpret the given function in terms of the context of the given problem. In the instances where students were asked to interpret an equation in terms of a given context, function notation was not used, which is part of the standard.
  • F-IF.5: Students are not asked to determine the relationships between the domain and a graph.
  • F-LE.1a: There is one instance where students are exploring that linear functions grow by equal differences over equal intervals in Algebra 1, Lesson 9-3.
  • F-TF.8: There is a proof of the Pythagorean identity as part of the standard. In the materials, this proof is provided for the students. Students are not given the opportunity to construct the proof of the Pythagorean identity.
  • S-CP.5: Students are given the opportunity to calculate the conditional probability; however, they are not given sufficient opportunities to interpret their answers in terms of the context of the model.

There are also two examples of the materials including content that is distracting because the content is not part of the CCSSM for high school.

  • In Geometry, lesson 12-1 on page 167, the learning targets are "Write a simple flowchart proof as a two-column proof. Write a flowchart proof." While these are very explicit indications of the content in this lesson, there is no reference to specific types of proofs in the CCSSM.
  • In Algebra 2, lesson 19-3 on page 303, the learning targets are "Identify the index, lower and upper limits, and general term in sigma notation. Express the sum of a series using sigma notation. Find the sum of a series written in sigma notation." The language of the learning targets and the content of the lesson are not a part of the CCSSM.

The following are some examples of where the materials meet the expectation for allowing students to fully learn the standard:

  • G-CO.9: Starting with Lesson 6-1 in the Geometry materials, students are given multiple opportunities to use different properties and prove simple theorems about lines and angles. In Lesson 6-2, students are introduced to the Vertical Angles Theorem and use the theorem in other proofs about lines and angles. In Lesson 7-1, the materials address different angle pairs formed when a transversal intersects parallel lines and the relationships between the pairs of angles. In the remainder of the Geometry materials, there are various places where students use relationships already proven to prove new theorems about lines and angles.
  • N-Q.3: This standard is completely addressed in all courses. In Algebra 1, there is an explanation on page 489, problem 3d, in both the student and teacher editions discussing how to choose the appropriate level of accuracy. From that point on, students are expected to choose an appropriate level of accuracy in remaining lessons and courses.
  • F-IF.8 is only identified in the online version of the materials. The standard was fully addressed in the materials in the online version where identified.

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
1/2
+
-
Indicator Rating Details

The instructional materials partially meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Although students are able to experience the majority of the standards they would need to master in order to be college- and career-ready, there were several instances where students did not get to engage with content in a way that is appropriate for high school students.

Examples of where this series partially meets the expectation include:

  • Standards that require students to prove concepts or provide explanations were not fully developed and did not allow students to engage with the content in order to master the standards. An example of this is G-CO.9 where mostly teacher-given proofs were used (very few opportunities for students to generate their own proofs). G-SRT.7, problem 8, on page 310 of the Geometry textbook is one item that addresses this standard, and while the answers to problems on pages 312 and 313 address this standard as well, the explanation required from students would not fully address the relationship between the sine and cosine of complementary angles.
  • While the context provided for application problems is appropriate for high school, the contexts do not motivate the mathematics. For example, many of the Geometry contexts are superficially connected to the topic as the lessons could be completed without any knowledge of the context.
  • Most problems provide students with scaffolded steps and lead the students to the answers. For example, in the Algebra 1 textbook, lessons 7-1 and 7-2 provide students with tables, either completely or partially populated, and graphs that are completed or, at least, have scales marked and axes pre-labeled.
  • Problems presented in each section have routine answers and do not challenge students to engage fully in the mathematics required to be college- and career-ready. For example, in the Algebra 1 textbook, lesson 7-3, The Radioactive Decay Experiment, focuses on the concept of half-life for radioactive substances, but the problems in the lesson consistently use initial amounts that are even integers, which makes the computations and resulting answers much simpler than if the initial amounts were odd integers, fractions, or decimals.

When information is provided for differentiated instruction, the content does not replace what students are expected to learn in order to be college and career ready.

  • The "Getting Ready Practice" available for most units and topics is often below grade level, but it is also clearly labeled as "additional lessons and practice problems for the prerequisite skills." For example, there are "Getting Ready Practice" lessons on the distributive property (Grade 6) and operations with decimals (Grade 5), along with operations on polynomials (grade-level for Algebra 1) and graphing linear functions (Grade 8, deeper in Algebra 1). Many of the Geometry "Getting Ready Practice" topics are from the Grade 7 and 8 Geometry standards. Many of the Algebra 2 textbook "Getting Ready Practice" topics are from Algebra 1 content, but several are grade-level, such as determining asymptotic restrictions and finding inverses of functions.
  • Information presented in the sections labeled "Differentiating Instruction" or "Adapt" is not intended to replace the course-level work that students should be doing to master the standards. "Differentiating Instruction" contains directions to extend grade-level learning, and "Adapt" guides the teachers to check that students understand certain concepts and offers suggestions as to how to support students who need extra practice or what to do if re-teaching is required.

Indicator 1d

The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations that the materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and required by the Standards.

The organization of the course materials categorize units of study by related topics, and many of the activities cite multiple standards in the overview. Connections between clusters and domains are not always made for the teacher or student, and missing connections decrease the coherence of the materials across courses. The following are examples of missed opportunities for coherent connections throughout the series.

  • Although there are locations in the Algebra 1 materials where Statistics and Probability standards could be explicitly associated with the Algebra and/or Functions standards, the connections were not made. For example, a connection between standards in the Functions and Statistics and Probability categories could occur in Algebra 1, lesson 13, "Equations from Data," but it does not.
  • There are missed opportunities to connect the Statistics and Probability and Number and Quantity categories. The relationship between N-Q.1, N-Q.2, and the Statistics and Probability standards could have been made clearly in many places in Algebra 1, Unit 6. Students are working with data, yet no mention is made to whether or not the measures of center are reliable for different distribution shapes or to level of accuracy that can be expected from a line of fit for less-than-nearly-perfect correlations.
  • There are few connections between Geometry and other conceptual categories. Examples of missing connections are:
    • Proofs about various aspects of mid-segments in triangles (G-CO.10) are present in Geometry, lesson 15-1, but there are no Algebra or Functions standards listed in the lesson, such A-SSE.3 as F-IF.6.
    • Geometry activity 26 is entitled "Coordinate Proofs" and contains algebraic proofs for midpoint, slope, and concurrency (G-GPE.4,5); however, there are no Algebra or Number and Quantity standards listed in the activity, such as A-SSE.1 or N-RN.2.
    • Geometry, activity 27 uses a coordinate plane to develop the equation of a circle (G-GPE.1), which ties together the Geometry and Algebra categories through the process of completing the square, but there are no specific connections made concerning these concepts, especially A-REI.4.
    • Geometry activity 28 and Algebra 2 activity 10 (both on using focus and directrix to write the equation of a parabola) are linked, but the materials do not explicitly connect the two activities.

Some examples of how the content is coherent and provides opportunity for students to make meaningful connections are as follows:

  • In the Geometry textbook, Unit 3 is titled "Similarity and Trigonometry." Having these topics in the same chapter provides evidence that the content of the materials has been structured in terms of the connections and coherence inherent to the standards. After students learn about similarity, they engage in content specific to similarity in right triangles, which then leads to defining trigonometric ratios as a result of "understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle."
  • In Algebra 2, connections are made in the "Getting Ready" part of many sections. Unit 6 (page 476) recalls work done in Geometry (G-SRT), Algebra (A-SSE and A-CED), and Functions (F-BF), and page 477 states in the teacher materials that "students will use what they have learned in previous courses about circles, circumference, central angles, and arcs."
  • In the Algebra 1 textbook, quadratic functions are introduced through context, data, and modeling with mathematics (Lesson 29-1). Then students move into analyzing and looking at properties of quadratic functions (Lesson 29-2). In activity 30, they look at transformations of quadratic functions in the coordinate plane. Then, in activity 31, students factor quadratic expressions to find the x-intercepts of the function defined by the expression. In activity 32, students complete the square to find the vertex of a quadratic function. The portions of the materials involving quadratic functions attend to the coherence in the standards, and students have been given opportunities to see structure in expressions and think about different forms of equivalent expressions.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the series partially meet the expectation that the materials explicitly identify and build on knowledge from Grades 6-8 to the high school standards. The materials miss opportunities to identify knowledge from previous grades and move the students’ learning forward.

Below are examples of where the materials do not identify knowledge from Grades 6-8 and do not use the prior knowledge to move learning forward:

  • In Algebra 1, activity 9, the materials do not explicitly identify that students are building on their work with slope from Grade 8. The slope and rate of change portions of 8.EE.B and 8.F are not listed in the prerequisite skills for the unit. The activity does have students build on their knowledge of slope from Grade 8 to engage in F-IF.6 and F-LE.1.
  • In Algebra 1, activities 14 and 15, the materials do not identify any standards from 8.F where students defined, compared, evaluated, and used linear functions to model relationships between quantities. This domain from 8th grade forms the basis for the extension of linear concepts into piecewise-defined linear functions that occurs in activity 14 and comparing equations that occurs in activity 15.
  • In Algebra 1, activity 17, the materials do not identify any standards from 8.EE.C where students analyzed and solved pairs of simultaneous linear equations. In addition, lessons 4 and 5 in activity 17 are the only lessons that move student learning beyond what is addressed in 8.EE.C as these two lessons have students examine systems of linear equations without a unique solution and classify systems of equations, respectively.
  • In Geometry, activity 9, the materials do not identify any standards from 8.G.A or 6.NS.C where students understand congruence and similarity through transformations and recognize reflections across the axes, respectively. These clusters form the basis for the learning around transformations that occurs in activity 9.
  • In Geometry, activity 20, the materials do not explicitly identify that students are working with the Pythagorean Theorem from Grade 8. The work from Grades 6-8 is treated as a separate topic to review as opposed to being a foundation for new learning.
  • In Algebra 2, activity 25, the materials do not identify any standards from 8.EE.A where students work with radicals and integer exponents. This cluster forms the basis for working with square root and cube root functions that occurs in the four lessons of activity 25.

Each unit begins with a “Getting Ready” section that reviews prerequisite skills needed to engage in the mathematics of the upcoming section. The skills are aligned to previous grade-level CCSSM standards. Additional “Getting Ready” practice pages are available in the digital teacher resources. Although these skills are identified in the “Getting Ready” sections, connections are not made between the problem sets and the activities or lessons.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.
0/0
+
-
Indicator Rating Details

The plus standards, when included, are identified, appropriate, and support the content that students need to be college- and career-ready. For this series, the publisher identified several places where the plus standards were included and addressed.

In Algebra 1, activity 28 includes A-APR.7, which addresses closure of rational expressions. This is the only plus standard cited in the Algebra 1 textbook. It is appropriate to include this standard as closure of polynomials is discussed in Algebra 1 as well.

In Geometry, plus standards are included in activities 23, 29, 30 and 34. In activity 23, there is an appropriate introduction to the law of sines and law of cosines (G-SRT.10 and G-SRT.11). Activity 29 addresses the construction of a tangent line (G-C.4). Activity 30 asks students to derive the formula for calculating the area of the triangle (G-SRT.9), and activity 34 asks students to have an informal discussion of Cavalieri's principle (G-GMD.2). All of these plus standards are appropriate to the context of the course, and the publisher makes it clear that these standards will again be addressed and eventually mastered in later course work.

The Algebra 2 textbook includes composition of functions (F-BF.1c) in activities 5 and 6, complex conjugates (N-CN.3) and complex planes (N-CN.4) in activity 8, binomial theorem (A-APR.5) in activities 16 and 17, the fundamental theorem of algebra (N-CN.9) in activity 17, special right triangles and trigonometry (F-TF.3) in activity 32, and the unit circle (F-TF.4) in activity 34. All of these plus (+) standards are coherent with other work in the course and are presented in a way that allows both teacher and student to understand that mastery will be achieved in later course work.

The plus standards are embedded into activities/units with non-plus standards which makes it easier for teachers to include the plus standards in the normal scope of the course. However, the publisher makes it clear that the plus standards are not necessarily reached to their full intent when they are included and indicates that further work with the plus standards could be necessary to reach the full intent. For example, an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures (G-GMD.2) is identified as a plus standard and noted as an introductory skill. Likewise, function composition (F-BF.1c), included in the Algebra 2 materials in activity 5, is noted as introduced in Algebra 2 but also addressed in higher-level mathematics courses.

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
N/A

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
N/A

Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
N/A

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
N/A

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2f

The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
N/A

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners.
N/A

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
N/A

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
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Additional Publication Details

Report Published Date: 06/03/2016

Report Edition: 2015

Title ISBN Edition Publisher Year
1-4573-0151-2
1-4573-0152-0
1-4573-0153-9
978-1-4573-0151-3
978-1-4573-0152-0
978-1-4573-0153-7

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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