6th Grade - Gateway 3
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Usability
Gateway 3 - Partially Meets Expectations | 76% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 7 / 8 |
Criterion 3.3: Assessment | 6 / 10 |
Criterion 3.4: Differentiation | 8 / 12 |
Criterion 3.5: Technology |
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 for Discovery Education Math Techbook Grade 6 meet the expectations for use and design. Materials are well-designed, and lessons are intentionally sequenced. Students learn new mathematics in the Apply section of each Concept as they apply the mathematics and work toward mastery. Students produce a variety of types of answers including both verbal and written answers. The Discover sections introduces the mathematical concepts, and the Practice highlights connections within and between the concepts of the Concept. Manipulatives are used throughout the instructional materials as mathematical representations and to build conceptual understanding.
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 Discovery Education Math Techbook Grade 6 Mathematics meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. It is clear when the students are solving problems to learn, and when they are applying their skills to build mastery.
- Throughout the Investigations of each Concept, students explore and solve problems to learn new mathematics. The design of the instructional materials allow multiple opportunities for students to build mastery.
- Each Investigation has a Check Your Understanding for student and teachers to assess what students understood from the Investigation. Each Concept has a Practice tab with a Coach and a Play section. These sections include a variety of exercises that allow students to develop procedural skills.
- Each Concept also has an Apply tab which contains problems for students to apply their understanding of the mathematical concepts and demonstrate their mastery of mathematical concepts.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 meet the expectation for not being haphazard with exercises given in intentional sequences.
The sequencing of Units, and Concepts within the Units, develops in a way that helps to build students’ mathematical foundations.
- The Units are comprised of related content. For example, Unit 10, Data Distributions, includes Concept 10.1, Collect and Represent Data, and Concept 10.2, Describe and Compare Data.
- Within each Concept, Session development is sequential. Each Concept has numbered Sessions that include Investigations. The Investigations include different activities that build upon each other and help students develop understanding of the mathematical concepts being addressed.
- After working through the Investigations, the student has Practice (Coach and Play) and Apply sections that help students continue to sequentially build their understanding of the mathematical topics addressed in the Concept. Each Concept ends with the Apply section allowing students to consolidate and apply their new learning with a real-world problem.
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.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for having variety in what students are asked to produce.
Throughout the materials, students are asked to produce answers and solutions as well as to justify their answers and solutions, discuss ideas, make conjectures, make sketches and diagrams, and connect mathematical topics to the real world. Students are often asked to show all of their work which includes drawing visual representations in the form of figures, tables, graphs, writing equations and explaining steps and reasoning. At times, this work is presented using technologically-enhanced tools. The Model Lesson notes for teachers describe instructional strategies that ensure students produce this variety of work to demonstrate their learning.
Indicator 3d
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives.
Virtual manipulatives and tools are embedded throughout the series. Some are available on every page of the techbook and include calculators, a dynamic geometry tool, construction tool, unit convertor tool, data analysis tool, and whiteboard tool. Number tiles and Algebra tiles are the primary physical manipulatives used at this level, and there are blackline masters of these that can be copied and used during the Investigations. Each Concept has a Teacher Preparation section that lists the materials needed for all of the Sessions in the Concept. Manipulatives accurately represent the related mathematics; for example, in Unit 13 Concept 13.1 students use actual rectangular boxes to help them determine how much material is needed to make food containers in the shape of rectangular prisms.
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 3.2: Teacher Planning
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
The instructional materials for Discovery Education Math Techbook Grade 6 support teachers’ learning and understanding of the standards; however, they do not attend to learning at an adult level. The instructional materials provide Essential Questions that support teachers in delivering quality instruction. The teacher’s edition is easy to use and consistently organized and annotated. The teacher’s edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.
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 Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.
Each Concept offers essential questions to guide the teacher and students through the Concept. An example of an essential question for Concept 12.1 is, "How can you calculate the areas of trapezoids and other polygons?" In addition, with the teacher view enabled, as teachers progress through the Investigations blue boxes with quality questions, and their connections to the MPs, are included. The instructional reminders in this view are provided in a timely manner with the part of the Investigation to which it applies. This design supports teachers in both planning and implementing an effective 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 Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for containing 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. Also, where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
The Concepts have an Objectives tab with lesson objectives, essential questions, and enduring understandings. The Progressions and Standards tab includes Reach Back Standards, Standards Covered, and Reach Ahead Standards, Standards for Mathematical Practice, During previous instruction, Through the investigations, During subsequent instruction, and a graphic that shows what Conceptual Understanding, Procedural Fluency, and Application will take place in the concept. Finally, there is a Teacher Preparation tab that includes a Materials List, Common Misconceptions, and Key Vocabulary.
The Model Lesson section of the materials includes in-depth instructional notes and suggestions for both presenting and discussing the mathematical content of each Investigation, as well as how to use the technology-enhanced items and manipulatives embedded in the materials. For example, in Concept 1.2 Investigation 3 the Instructional Notes remind teachers to, “Direct students’ attention to the Snail Garden Interactive. The on-screen text will set up the scenario and direct students to look for patterns as they explore the garden. In the first tab, students will use a variety of animals to measure a rectangular garden. Each time they measure the garden, recording the length and the width, they will need to show it as a ratio. In the second tab, students will graph the data from the table using the length and width measurements as ordered pairs.”
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.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation for the teacher’s edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.
Instructional notes in the Model Lesson section of the techbook provide teachers with in-depth guidance on how to present the information in the Investigations to assist students in a full understanding of the standards developed in Investigations. The notes include detailed explanations of the essential and enduring understandings from the standards and any student misconceptions that may emerge.There is also a Professional Learning section within the materials, but neither the Instructional Notes nor Professional Learning section explain or give examples that a teacher could use to improve their content knowledge of the grade-level standards or of advanced mathematics concepts that are connected to in future grades or courses. Solutions to problems are provided for teachers, but these solutions do not always have explanations as to why an answer would be acceptable or alternate ways to solve the problem that would give support to teachers’ own understanding.
At the end of each Concept, there is a Summary, and it includes a summary of the essential understandings in the Concept and a link to Additional Assistance. The Additional Assistance provides video explanations and tutorials of the related mathematics. The Summary and Additional Assistance are available to both teachers and students, but these are not designed specifically to assist teachers in further developing their own understanding of the grade-level standards or of advanced mathematics concepts that are connected to in future grades or courses.
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.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.
The Model Lesson section of each Concept contains a tab titled Progressions and Standards that connects to standards from previous grade-levels and discusses standards that will be connected to in future grades. For example, Unit 2 Concept 2.2 makes connections to standards from 3rd grade (3.OA.5) through the 5th grade (5.NBT.6 and 5.OA.2) and to standards in 7th Grade(7.RP.1 and 7.EE.1,2). The Progressions and Standards section also includes, in paragraph form, sections that give more information on the listed connections. These sections are During previous instruction, which describes how prior standards connect to current standards, and During subsequent instruction, which describes how current standards will connect to future standards.
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 3.3: Assessment
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
The instructional materials for Discovery Education Math Techbook Grade 6 partially meet expectations for providing teachers resources and tools to collect ongoing data about student progress. There are no assessments that purposely identify prior knowledge within and across grade levels. The Teacher Preparation section identifies common misconceptions and errors, but there are no specific strategies strategies to address these when they arise. Opportunities for ongoing review, practice, and feedback occur in various forms. Standards are identified that align to the Concept; however, there is no mapping of Standards to items. There are limited opportunities for students to monitor their own progress.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.
In Progressions and Standards for each Concept, the materials provide teachers with Reach Back Standards from prior grade levels/courses to which the standards of the current Concept connect. The activities found within the Intro at the beginning of each Concept are designed to activate prior knowledge that students would have of the Reach Back Standards. Although the identification of the Reach Back Standards and their inclusion in the Intro activities could provide teachers a way to indirectly assess students’ prior knowledge, the materials do not supply specific or direct strategies for assessing students’ prior knowledge.
Indicator 3n
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions. Within each Concept in the the Teacher Preparation section, there is a bulleted list of common misconceptions about the mathematical material being taught in that Concept. During the lesson itself, though, there is no specific strategies provided for teachers to identify and address those 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.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
The materials include a Coach and Play section in each Concept that provides opportunities for review and practice of both concepts and skills. In the Coach section, the materials offer feedback when an answer is incorrect and allow the student to try again. After a third incorrect answer, the Coach section shows the student how to answer the problem correctly. The Play section allows the student to earn badges for correct answers when completed online. The Play section can also be completed offline, and if the offline version is completed, an answer key is provided. At the end of each Investigation, there is a Check for Understanding. The Check for Understanding contains problems that could be in the format of short answer, short answer with explanations, or multiple-choice questions. The materials offer feedback on review and practice in the form of instant, digital feedback or teacher-provided feedback throughout each Concept.
The teacher also has opportunities to provide the students feedback within the Dashboard, and a teacher can create an assignment in the Assignment Builder feature.
Indicator 3p
Materials offer ongoing formative and summative assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation for assessments clearly denoting which standards are being emphasized.
The materials clearly denote which assessments are intended to be formative and which are intended to be summative. The summative Unit assessments are located on the Unit-level page, and there is a tab for accessing the Unit Assessment. The formative assessments are located at the Concept level and are included in each Investigation as a Check for Understanding. The questions on the summative and formative assessments are not clearly denoted as assessing a particular standard. Each Unit has a set of standards being addressed, and each Concept has a set of standards addressed. However, the assessment questions themselves are not aligned to standards making it difficult to determine which standards are being emphasized by the assessments.
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.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The Unit Assessments include very specific and clear Evaluation Criteria for each constructed response question, and the criteria are based on a 0, 1, or 2 point scale that shows the specific criteria needed to receive that score. Also, each Apply question includes a rubric where the scores range from 0 to 4, and there are clear descriptions of what a student must do in order to earn each score. However, there are no suggestions for follow-up based on the students’ scores provided to the teachers.
There is also a dashboard that allows teachers to monitor the progress students are making as they navigate through the Discover, Practice, and Apply cycle. The dashboard indicates to a teacher where the student is performing based on a color indication as well as with points. The teacher can track scores and visually determine if a student is being successful, but there is no clear guidance given for interpreting student performance. The Teacher Notes, which are included in the Investigations before the Check for Understanding, provide some suggestions for follow-up, but these suggestions are not consistently placed throughout the materials.
Indicator 3q
Materials encourage students to monitor their own progress.
Criterion 3.4: Differentiation
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
The instructional materials for Discovery Educations Math Techbook Grade 6 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. Activities provide student with multiple entry points and a variety of solution strategies and representations. However, the materials provide few strategies for ELL, special populations, or to challenge advanced students to deepen their understanding of the mathematics. Grouping strategies are designed to ensure roles for each group member.
Indicator 3r
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Each Concept’s Discovery, Practice, and Apply sections are broken up into Sessions in which activities are sequenced for the teacher. Included in all Sessions are Instructional Notes that provide teachers with key math concepts to develop, sample questions to ask, ways in which to share student answers, and other similar instructional supports. Also, each Investigation includes Teacher Notes that assist a teacher in making the content accessible to all learners with supports similar to those found in the Instructional Notes for the Sessions.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners.
Different strategies are recommended throughout the instructional materials, but the strategies are typically intended to be used with all students and not necessarily geared toward a range of learners. For students excelling, the materials provide extension problems. For struggling learners, students are provided with online, tutorial websites for instructional assistance when needed in the Summary section. This section provides step-by-step instruction on material taught throughout the Investigations.
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 Discovery Education Math Techbook Grade 6 Mathematics meet the expectation that materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. Application tasks—particularly Apply tasks— allow for multiple solution strategies or representations, and applications are available to assign in each Concept.
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).
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics do not 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. Neither the teacher notes nor the tasks directly address support for students with a disability, students from different cultural backgrounds, or English Language Learners. A text-to-speech tool, however, is available and could be used for ELL students, and parent letters included with each unit are available in Spanish.
Indicator 3v
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. Neither the teacher notes nor the tasks directly address support for advanced students. Each Concept includes an Extension task that could be used for advanced students, though the materials do not indicate that they are designed for a particular audience.
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. The activities are diverse, meeting the interests of a demographically, diverse student population. The names, situations, videos, and images presented display 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 3.5: Technology
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 for Discovery Education Math Techbook Grade 6 support effective use of technology to enhance student learning. The materials are web-based and platform neutral. The materials embed technology enhanced, interactive virtual tools, and dynamic software that engages students with the mathematics. Opportunities to assess students through technology are embedded. The technology provides opportunities to personalize instruction; however, these are limited to the assignment of problems and exercises and cannot be customized for local use. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.
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.