High School - Gateway 3
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Usability
| Score | |
|---|---|
Gateway 3 - Meets Expectations | 86% |
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 7 / 8 |
Criterion 3.3: Assessment | 6 / 10 |
Criterion 3.4: Differentiation | 10 / 10 |
Criterion 3.5: Technology Use |
Criterion 3.1: Use & Design
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials are designed well and take into account effective lesson structure and pacing. The design and layout of the materials, in print and in the eBook, are quite simple, easy to use and not distracting. In addition the consistent structure of each lesson, homework set including the Review & Preview sections and chapter closure section help to make students comfortable and confident with the lessons.
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.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. Students are learning new mathematics in each lesson and then applying what they have learned in order to build knowledge. The spaced and spiraling nature of the series helps build mastery. Each chapter, section, and lesson has a variety of problems and exercises, and has intentional purpose in developing learning and thinking.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. The materials encourage fluency through their spaced homework, helping students retain and apply new learning throughout the series. Rote procedural exercises are present, but not in mass quantities. The exercises are given in intentional sequences.
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.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that students are asked to produce a variety of products during each lesson in each chapter to demonstrate their learning. The series continuously asks students to produce models, practice fluency, create arguments, justify their answers, attend to mathematical practices and make real-world connections. This is done through homework, closure reflections, portfolios, team tasks, explanations, models, arguments (with stop light problems using error analysis), learning logs, cumulative assessments, checkpoint problems and journal entries.
Indicator 3d
Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. Each chapter in each textbook contains teacher notes in the chapter introduction that provides clarity on the lesson design and intent and a suggested assessment plan. For example Algebra 2, chapter 4 says "This chapter begins with a focus on two ways to solve equations and systems of equations: algebraically and graphically. You will build on your understanding of solving and solutions from previous courses to gain a broader and stronger understanding of the meaning of solutions. In Section 4.2, you will expand your understanding of solving and solutions to include inequalities. You will solve problems designed to illustrate how inequalities might be used for more complicated applications."
The series makes use of a wide range of virtual manipulatives. The materials have their own collection of virtual manipulatives including algebra tiles, base ten blocks, probability tools, data representation tools, transformation tools, similarity toolkit, numbers lines and graphing tools. The materials also make regular use of premade Desmos.com graphs and other applets. There are general manipulatives and tools that the materials recommend always having available. A few examples of these include, but are not limited to colored pencils, graph paper, markers, masking tape, meter sticks, rulers, scissors, and tape. Then, there are specific manipulatives and tools that will be needed for specific lessons. A few examples of these include, but are not limited to rope, foil pans, bouncy balls, candles, calculator-based rangers, digital scales and yo-yo's.
Indicator 3e
The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the visual design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. The design and layout of the materials, in print and in the eBook, are quite simple, easy to use and not distracting. The structure of the lessons and layout of the textbook in black and white help students focus on mathematics and eliminate distractions.
Criterion 3.2: Teacher Planning
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teacher learning and understanding of the standards. Overall, the materials provide the teacher necessary supports using adult-level expectations and the student with guiding questions for appropriate mathematical development and the parents with resources.
Indicator 3f
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. In many sections of the student materials, the leading paragraph of the lesson begins by listing three to four questions, then asks students to use these questions to guide the work in the lesson. In addition, the teacher resources provide teachers with guiding questions for the teacher to use when circulating the room. For example, in the teacher notes for section 3.1.1 in Algebra 1 the teacher is given the following: "As you circulate, ask questions that require students to justify their patterns or that encourage students to look for patterns, such as, “What is the exponent of the result? How is that related to the original problem?” and “How can you convince me that your shortcut works?" There are additional questions later in the teacher resources that are listed as useful questions for other parts of the lesson.
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.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Each lesson has a full printed write-up to explain the content and instructional goals as well as a video with the same purpose. Each lesson also describes how to use the supporting technology as well as how to run the lesson if technology is not available. There is a TI-83 student and teacher guide included. For example, the eBook teacher notes for the opening of Chapter 7 in Geometry includes overview paragraphs, guiding questions, a chapter outline, a teacher guide video, Smart Board file, discussion on the Standards for Mathematical Practices, a "Where's it Going?" paragraph, and a suggested assessment plan.
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.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials contain 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. Lesson videos and lesson teacher notes (both printed and in the eBook) provide teachers with a full preparation for each lesson, including historical notes, video models, mathematical background and adult-level explanations to guide the teacher. The series provides a newsletter with lesson ideas and up-to-date strategies and best practices to guide teachers in planning and in advanced learning of the mathematics. Past editions of the newsletter are archived in the teacher support of the teacher materials.
Indicator 3i
Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials explain the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve. The series makes vague reference to future and past learning but does not give clear, precise information about how current content fits into the vertical progression of learning. There is an accelerated pacing guide for Grades 7 and 8 but no other progression information of the overall mathematics curriculum for Kindergarten through Grade 12.
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).
The instructional materials reviewed for the High School CPM Traditional series provide a list of lessons, cross-referencing the standards covered. The materials in the series provide several different pacing guides, lesson sequences, and standards (both practice and content) correlations. Additionally, the materials include a quarterly benchmarks correlation that includes plus and non-plus standards.
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.
The instruction materials reviewed for the High School CPM Traditional series have an ancillary resource book for each course designed to provide parents with additional practice problems for students, including explanations for parents.
In the student resources, each lesson begins with a learning objective written for students. The lesson objectives for students are written in a way that help students make connections to previous learning concepts or experiences and to real-world contexts when appropriate. While the standards for the lesson are not explicitly written in the student text, the lesson objective is clear and aligned to the CCSSM. For example, the objective for students from Algebra I lesson 9.1.2 reads, "In the previous lesson you developed methods to solve quadratic equations. Today you will learn a new method to solve them." This lesson objective directly aligns to A-REI.4.
Indicator 3l
Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
The instructional materials reviewed for the High School CPM Traditional series provide many different instructional strategies, support on how to effectively implement these strategies and extensive research literature supporting the use of these strategies and the design of the materials.
There is an extensive research summary including research on problem based learning, mixed spaced homework, and cooperative learning found in the web-based teacher edition under the teacher tab. There is also a tab with teaching strategies included under the same teacher tab.
Criterion 3.3: Assessment
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials offer teachers resources and tools to collect ongoing data about student progress on the standards. The materials provide assessments that not only offer evidence of students’ knowledge of the CCSSM, but also elicit evidence of the students' knowledge of the MP. Unfortunately, there is a missed opportunity in identifying the specific standards that align to each of the assessment items. Additionally, there are limited strategies for gathering information about students’ prior knowledge.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that the materials provide strategies for gathering information about students' prior knowledge within and across grade levels. The materials have pre-assessments for Algebra 1. There was no indication of what to do with the information that is assessing prior knowledge from previous courses or information pinpointing standards that are being assessed. The materials do provide the opportunity within lessons to see prior knowledge being addressed.
Indicator 3n
Materials provide support for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide strategies for teachers to identify and address common student errors and misconceptions. The stoplight problems provide opportunities for students to find errors and critique reasoning. The teacher notes also provide tips for teachers to address common errors. The closure sections provide opportunities for discussion of common errors and misconceptions, along with the cooperative learning tasks.
Indicator 3o
Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The teacher materials provide rubrics along with information on giving feedback on portfolios, team tests, presentations and participation quizzes. Students also have feedback available through the eBook homework help and the animated explanations.
Every lesson has a Review & Preview section. In this section, there are homework helps that are hyperlinked to selected hints, answers and e-tools to help provide feedback to students on skills and concepts. This part of each lesson reviews problems from past learning objectives, chapters and courses within the series. One example is in section 4.1.3 of Geometry where students work 6 problems from previous chapters in Geometry.
Indicator 3p
Materials offer ongoing assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials reviewed for the High School CPM Traditional series do not meet the expectation that assessments clearly denote which standards are being emphasized. No standards are denoted on either the printed or sample digital assessments that were provided.
Indicator 3p.ii
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The instructional materials reviewed for the High School CPM Traditional series partially meet the expectation that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The materials in the series offer ongoing formative and summative assessments. The assessments include some generic rubrics. However, the rubrics are typically very general in nature and may not provide enough guidance to teachers to interpret current student performance. Assessments have answer keys but lack any guidance to the teacher on how to score or how to interpret the results.
Indicator 3q
Materials encourage students to monitor their own progress.
The materials in the series encourage students to monitor their own progress through learning logs, concept webs, closure, team activities and portfolios.
In the assessment tab of the teacher resources for each book in the series the following is provided: "Teachers require students not only to revise their incorrect solutions, but also to analyze the errors in their thinking or computations by answering a series of questions. Some examples are:
- Why did you miss the problem? (Careless error, did not know how to do it, guessed, used the wrong formula, tried a strategy inappropriate for the problem, etc.)
- What did you learn from revising the problem?
- Who (if anyone) helped you and what did they say to help you better understand the problem? Please be specific.
- Make up a new, similar problem. Show and explain to a new student (in writing) how to solve the problem. Be sure to justify your steps."
Criterion 3.4: Differentiation
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teachers in differentiating instruction for diverse learners within and across grades. The materials offer lessons that are scaffolded to allow a range of learners to gain entry into the problems. The materials provide multiple language translators so that students of various backgrounds can engage in the mathematics in their native language. Additionally, teachers are offered ideas and suggestions for grouping all learners in a variety of ways.
Indicator 3r
Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide strategies to help teachers sequence or scaffold lessons so the content is accessible to all learners. A "universal access" guide with directions on scaffolding for ELL and special needs students is provided. One strategy included is to focus on checkpoint or essential problems for struggling learners so that they have access to the same level of rigor but with fewer problems.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide teachers with strategies meeting the needs of a range of learners. There are eBook materials in the teacher resources that include a list of strategies for a wide range of learners. Specifically, the Universal Access Guidebook and Literacy Guidebook explain how to assist students who are making normal progress, or need additional help, or are underprepared for the course, or who have special needs such as English language learners, advanced learners or struggling readers.
Indicator 3t
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations. There are many investigations and modeling problems that allow for multiple solutions and strategies. Many problems encourage multiple representations (graph, verbal, analytical, numerical). Most of the beginning lessons within a chapter offer scaffolding that allows multiple entry points into the opening problem, which allows for students with a range of learning abilities to have access to the problem.
- For example, Algebra 1, lesson 5.1.1, opens the chapter on sequences with an investigation of two friends who dream of raising rabbits. The question gives a scenario and asks how many rabbits would there be after one year. There are four questions that ask students to identify patterns and make predictions, thinking in teams about the strategies they would use. Problem 5-2 is designed for further guidance for students who need more direct strategies to use. These strategies include drawing a diagram, creating a table and looking at specific patterns. Eventually, students will work their way to recursive equations, explicit equations and graphing of these equations and the functions these equations represent.
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).
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the 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. The series clearly identifies checkpoint problems and core problems with guidance on how to modify the pacing for special populations so all students have access to on grade level resources. "Math Note" sections throughout the lesson provide definitions and examples with regard to vocabulary. Additionally, every lesson is provided in Spanish, and through the eBook translator, can be translated into most languages.
Indicator 3v
Materials provide support for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. A pacing guide shows pacing for students who are at grade level as well as those who are advanced. For advanced students most lessons include enrichment and additional problems within the lesson. The teacher materials explicitly state that advanced students also benefit from the richness of the problems in the text and will often be able to develop considerable depth in their work. Examples of enrichment and additional problems include, but are not limited to:
- In Geometry lesson 6.2.3, the teacher materials note that problem 6-72 is an extension. Problem 6-68 is the core problem, while 6-69 and 6-70 are optional problems needed for further guidance.
- In Algebra 1 lesson 4.2.2, the teacher materials note the core problems as 4-42 and 4-47. Problems 4-43 through 4-45 are noted as further guidance or enrichment problems.
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
The instructional materials reviewed for the High School CPM Traditional series provide a neutral portrayal of various demographic and personal characteristics. The names and situations portrayed in the book are diverse.
Indicator 3x
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials provide opportunities and directions for teachers to use a variety of grouping strategies. The materials focus on team cooperative learning. Additionally, the materials provide activities, discussions, and tasks tailored for whole group, team and individual work. Examples include, but are not limited to:
- In Algebra 2 lesson 4.1.3, the teacher materials refer to three different grouping strategies to use throughout the lesson. When the user clicks on the strategy, a pop-up box appears that defines the purpose of the strategy and gives a full explanation of how to use the strategy. This full explanation includes materials needed, classroom management tips, the full protocol of how to use the strategy and sometimes links to other resources for more information about the strategy.
- In Geometry lesson 2.2.3, the teacher materials suggest students work in teams on three different problems. As the students are working in the teams, the teacher has been provided with specific questions to ask while circulating among the teams. The closure activity then involves a cooperative Pairs Check strategy, again that is included with a pop-up box to know how to best execute that strategy in the class. There is also a team strategy part of the lesson that supports the teacher with strategies to help the teams as they are collaborating during the lesson.
Indicator 3y
Materials encourage teachers to draw upon home language and culture to facilitate learning.
The materials encourage teachers to draw upon home language and culture to facilitate learning. The eBook materials include a translation link for every lesson. All lessons in the eBook have tabs for both English and Spanish.
Criterion 3.5: Technology Use
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
The instructional materials reviewed for the High School CPM Traditional series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide access to many e-tools through the eBook. Additionally, the materials allow teachers to create their own assessments as well as collaborate with other teachers who are also using the same materials.
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.
The digital materials are web-based and compatible with multiple internet browsers. The series uses Quicktime, YouTube, and internet resources that are accessible on multiple devices and browsers. Quicktime player needs to be installed on computers. HTML5 works on most mobile devices and on many computers. YouTube may not be allowed at all schools.
Indicator 3ab
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
The materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. Teachers have test bank available through the eBook. Assessments are not available for students through the eBook and are not adaptive, but teachers can customize assessments using the test bank.
Indicator 3ac
Materials can be easily customized for individual learners.
Indicator 3ac.i
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
The materials in the series do not provide adaptive technology.
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.
The technology components offered in the materials are not customizable for students based on their needs or interests.
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.).
The materials provide opportunities for teacher to collaborate with each other through the eBook resources via a sharing tab. There are not opportunities for student to student or student to teacher collaboration via the eBook.
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.
The materials integrate technology, manipulatives and dynamic software in ways that engage students in the MPs. The materials have their own collection of virtual manipulatives which includes algebra tiles, base ten blocks, probability tools, data representation tools, transformation tools, similarity toolkit, numbers lines and graphing tools. Additionally, the materials make regular use of pre-made Desmos.com graphs and other pre-made applets. Examples include, but are not limited to:
- In Algebra 1 lesson 6.1.4, the eBook student materials link directly to four different Desmos.com files that assist with understanding lines of best fit in the problems that are a part of that lesson.
- In Geometry lesson 3.2.1, the eBook student materials link directly to seven different CPM eTool dynamic applets to work with pre-made or to create your own sketches in thinking about and exploring similar triangles.
- In Algebra 2 lesson 7.1.3, the eBook student materials link directly to four different Desmos.com files for explorations of reference angles and trigonometric graphs.