Math Trailblazers (2015)

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Report Overview

Summary of Alignment & Usability: Math Trailblazers | Math

Product Notes

Along with access to digital materials for students and teachers, the student workbooks for each grade level were also reviewed.

Math K-2

The instructional materials reviewed for Kindergarten through Grade 2 do not meet the expectations for alignment to the CCSSM. The instructional materials do not meet the expectations for Gateway 1 as they do not appropriately focus on the major work of the grades or coherence within and across the grade levels. The instructional materials were not reviewed for Gateway 2.

Kindergarten

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

1st Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

2nd Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

Math 3-5

The instructional materials reviewed for Grades 3 through 5 do not meet the expectations for alignment to the CCSSM. The instructional materials do not meet the expectations for Gateway 1 as they do not appropriately focus on the major work of the grades or coherence within and across the grade levels. The instructional materials were not reviewed for Gateway 2.

3rd Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

4th Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

5th Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Does Not Meet Expectations

Gateway 3

Usability

Not Rated

Report for Kindergarten

Alignment Summary

The instructional materials reviewed for Kindergarten do not meet the expectations for alignment to the CCSSM.

The instructional materials do not allocate a large percentage of class time to major standards of the grade, but the materials can be used to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet quality expectations for coherence. Overall, the instructional materials need to develop more consistently with the grade-by-grade progressions and foster coherence with more connections within Kindergarten. Due to the materials not meeting expectations for focusing on major work and coherence, they were not reviewed for rigor and Mathematical practices.

Kindergarten

Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Alignment (Gateway 1 & 2)

Does Not Meet Expectations

Gateway 3

Usability

Usability (Gateway 3)

Not Rated

Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Kindergarten do not meet expectations for alignment to focusing on major work of the grade and coherence. The instructional materials do not allocate a large percentage of class time to major standards of the grade, but the materials can be used to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet quality expectations for coherence. Overall, the instructional materials need to develop more consistently with the grade-by-grade progressions and foster coherence with more connections within Kindergarten.

Gateway 1

v1.0

Gateway 1

Focus & Coherence

Criterion 1.1: Focus

Criterion 1.2: Coherence

Criterion 1.3: Coherence

Does Not Meet Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Kindergarten meet the expectations for assessing material at the grade level. Although there are months and lessons noted that align to and/or assess standards that are beyond Kindergarten, the inclusion of these lessons and months is either Mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.

Indicator 1A

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Kindergarten meet expectations for assessment because above grade-level assessment items and their accompanying lessons or months could be modified or omitted without significantly impacting the underlying structure of the instructional materials. For this indicator, all of the identified assessments and end-of-month assessments for the nine months were reviewed. Months and lessons accompanying above grade-level assessment items are noted in the following list.

In month 2, lessons 2 and 4 have assessment items that align to 4.OA.C. , “Generate and analyze patterns.” The Key Assessment Opportunities Chart shows the expectation that students be able to recognize, describe, and extend a growing pattern; make predictions and solve problems from growing and repeating patterns; identify the pattern unit in a repeating pattern represented with colors, shapes, numerals, and quantities; and recognize, describe, copy, and extend a repeating pattern represented with colors, shapes, numerals, and quantities. These lessons account for two of the four lessons in month 2, so the omission or modification of these lessons would significantly impact the structure of this month. However, a significant impact on month 2 would not have a significant impact on the overall structure of the materials.
In month 5, lesson 1 has assessment items that align to 4.OA.C, “Generate and analyze patterns. The Key Assessment Opportunities Chart shows the expectation that students be able to recognize, describe, and extend a growing pattern and make predictions and solve problems from growing patterns. This lesson accounts for one of the five lessons in month 5, so the omission or modification of this lesson would not significantly impact the structure of this month.

*Evidence updated 10/27/15

Criterion 1.1: Focus

Indicator 1A

Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Kindergarten do not meet the expectations for spending the large majority of class time on the major clusters of the grade. Kindergarten Trailblazers has 135 stated objectives for the entire course. Of these, only 83 of the stated objectives are related to the major work of the grade, and this translates into about 61% of the objectives. In only six lessons does the curriculum identify that students will be comparing numbers (K.CC.C) out of the entire nine month series, and gaining foundations for place value is only explored in month 4, lesson 1, where students compose and decompose numbers. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Kindergarten or on standards that are above Kindergarten.

Indicator 1B

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Kindergarten do not meet the expectations for spending the large majority of class time on the major clusters of the grade. Overall, the materials allocate too much instructional time to clusters of standards that are not major work of Kindergarten or on standards that are above Kindergarten.

Kindergarten Trailblazers has 83 of 135 stated objectives for the entire course that are related to the major work of the grade, totaling 61% of the objectives.
In only six lessons does the curriculum identify that students will be comparing numbers (K.CC.C) out of the entire nine-month series.
Gaining foundations for place value is only explored in month 4, lesson 1, where students compose and decompose numbers.

Criterion 1.2: Coherence

Indicator 1B

Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Kindergarten do not meet the expectations for being coherent and consistent with the CCSSM. The instructional materials have some instances of supporting work fostering coherence by engaging students in major work of the grade as addressed in indicator 1c, but the amount of content designated for Kindergarten is not viable for one school year. Also, the instructional materials are not consistent with the progressions in the CCSSM, and they do not foster coherence through connections at a single grade. Overall, the instructional materials for Kindergarten exhibit some characteristics of coherence as noted in indicator 1c, but for the entire criterion, there are too many weaknesses for the materials to even partially meet the expectations.

Indicator 1C

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Kindergarten partially meet the expectations for having the supporting content enhancing focus and coherence simultaneously. Overall, the instructional materials miss opportunities to connect non-major clusters of standards to major clusters, and as a result, the supporting content does not engage students in the major work of Kindergarten.

Most of the supporting content is treated separately and does not support the major work of the grade. For example in month 4, lesson 3, identifying and describing shapes is treated separately. Again in month 6, lesson 2, identifying and describing shapes is treated separate from the major work of the grade.
The instructional materials do not state where supporting content is or how it is linked to major work of the grade.
There are content notes, for example, on page 193, but these content notes do not link major and supporting work.
In lesson 4 of month 1, students are asked to describe and sort the attributes of shoes. In this, students are sorting shoes by different attributes and then counting to find out which category has the most.
In month 1, lesson 2, students are asked to compare friends (loose connections to K.MD.A and K.MD.B), and students have to sort by birthday and height and make a visual representation. Then, students count to work on which groups have the most and the least, and give explanations.

Indicator 1D

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Kindergarten do not meet the expectations for having an amount of content designated for one grade level as viable for one school year. Overall, the amount of time needed to complete the lessons is not appropriate for a school year of approximately 170-190 days.

There are a total of 227 lessons/activities spread throughout nine months. Additionally, there are work stations and practice problems for each month.
The content has nine months of material with four to six lessons in each unit. Each lesson takes multiple days and includes multiple activities and extensions for workshops.
Each lesson is set up to cover multiple days with each having between three and 10 activities. If the text is followed as laid out using all the lessons, daily practice problems and math work stations it will not be viable for one school year.

Indicator 1E

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Kindergarten do not meet the expectations for having materials that are consistent with the progressions in the CCSSM. Overall, the materials do not give students extensive work with grade-level problems, and grade-level concepts are not always explicitly related to prior knowledge from earlier grades. Also, the materials do not develop according to the grade-by-grade progressions, with non-grade-level content not being clearly identified.

The off grade-level material is not clearly identified or connected to the related grade-level work. Examples of this includes month 2, lessons 2 and 4, where students are generating and identifying patterns.
In month 7, lesson 4 students are asked to compare areas.
Lesson 5 has students comparing capacities.
No work for future grades is clearly identified, and expectations may not be grade-level work such as when month 7, lesson 4, explores area.
Because of the amount of time spent on off grade-level standards, students do not have extensive work with grade-level problems.
Throughout the teacher manuals are green text boxes labeled "Meeting Individual Needs." These text boxes give a very brief way to change an activity, but these changes are too basic to be considered differentiation for students below or above grade level.
There are no explanations provided for the teacher or student linking prior knowledge from prior grades.
In lessons, there are no explanations of work being linked to prior grades, and additionally, there are no expectations that say this work would be review from early childhood learning standards.

Indicator 1F

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for Kindergarten do not meet the expectations for having materials foster coherence through connections at a single grade. Overall, the materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings, and the materials do not always connect two or more clusters in a domain or two or more domains in a grade when appropriate.

It is not clear that the learning objectives have been shaped by the cluster headings due to the amount of off grade-level objectives.
The months don't have names or themes that are reflective of the cluster headings, and the lesson titles do not provide evidence of being shaped by the cluster headings.
Month 1 connects K.MD.A and K.MD.B with K.CC.A-C when students are asked to compare. This was the strongest example of a connection between different clusters. Otherwise, the materials covered topics individually unless there was review in a small group or at a workstation.
There are lessons that connect two or more CCSSM clusters when appropriate, but this does not happen consistently when these connections are possible.

Criterion 1.3: Coherence

Overview of Gateway 2

Rigor & Mathematical Practices

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

Gateway 2

v1.0

Gateway 2

Rigor & Mathematical Practices

Criterion 2.1: Rigor

Criterion 2.2: Math Practices

Not Rated

Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

Indicator 2A

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Indicator 2B

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Indicator 2C

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

Indicator 2D

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

Criterion 2.2: Math Practices

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

Indicator 2E

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

Indicator 2F

Materials carefully attend to the full meaning of each practice standard

Indicator 2G

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

Indicator 2G.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

Indicator 2G.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

Indicator 2G.iii

Materials explicitly attend to the specialized language of mathematics.

Criterion 2.2: Math Practices

Overview of Gateway 3

Usability

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

Gateway 3

v1.0

Gateway 3

Usability

Criterion 3.1: Use & Design

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

Criterion 3.5: Technology

Not Rated

Criterion 3.1: Use & Design

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.

Indicator 3B

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

Indicator 3C

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

Indicator 3D

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Indicator 3E

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

Criterion 3.1: Use & Design

Criterion 3.2: Teacher Planning

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.

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.

Indicator 3H

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

Indicator 3I

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

Indicator 3J

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

Indicator 3K

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

Indicator 3L

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

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

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.

Indicator 3N

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Indicator 3O

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Indicator 3P

Materials offer ongoing formative and summative assessments:

Indicator 3P.i

Assessments clearly denote which standards are being emphasized.

Indicator 3P.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Indicator 3Q

Materials encourage students to monitor their own progress.

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

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

Indicator 3R

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

Indicator 3S

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

Indicator 3T

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

Indicator 3U

Materials suggest 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).

Indicator 3V

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Indicator 3W

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

Indicator 3X

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

Indicator 3Y

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

Criterion 3.4: Differentiation

Criterion 3.5: Technology

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

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 Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

Indicator 3AB

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

Indicator 3AC

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

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.).

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.

Criterion 3.5: Technology

Downloadable Resources

2015