6th Grade - Gateway 3
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Usability
Gateway 3 - Partially Meets Expectations | 65% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 6 / 8 |
Criterion 3.3: Assessment | 4 / 10 |
Criterion 3.4: Differentiation | 7 / 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 materials meet the criterion for use and design. The underlying design of the materials makes a distinction 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 design of assignments is not haphazard; exercises do seem to be given in intentional sequences. Furthermore, the design is not distracting or chaotic but supports students in engaging thoughtfully with the subject.
Additionally, in most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives. Overall, the materials reviewed for Grade 6 meet the expectations for this criterion.
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 underlying design of the materials does distinguish between problems and exercises meeting the expectations for this indicator.
- The lessons usually follow a typical sequence that includes classwork typically facilitated by the teacher: opening exercises, scaffold examples, exploratory challenges, discussion topics and other examples. These problems or tasks are usually labeled "examples" and are intended to be the learning portion of the lesson.
- Following the classwork, and sometimes within the class work, there is usually a set of "exercises" that are to be completed within the class period either individually or with a partner. These "exercises" generally reinforce and/or extend the process(es) explored in the classwork.
- Next, there is usually an additional set of problems that are labeled "problem set." The problems in the problem set typically mirror the problems in the class exercises but appear to be done with extra class time or outside of structured class time.
- Lastly, lessons with closure also include an "exit ticket," which is usually, but not always, aligned to problems in the exercises and the problem sets.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The design of assignments is not haphazard; exercises do seem to be given in intentional sequences meeting the expectations for this indicator.
- Problem sets typically follow the sequence in classroom work.
- Problem sets generally build from simpler problems to more complex ones with either more steps or more challenging numbers (fractions, decimals, etc.).
- Problems often allow students to both apply new knowledge (such as solving equations) to prior understandings (such as using integers, fractions, decimals) in order to solve problems.
- Therefore, it appears students are increasing fluency of prior skills while developing understanding of new math concepts.
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.
There is a variety in what students are asked to produce meeting the expectations for this indicator.
- Throughout a module-and often within a given lesson-students are asked to produce answers and solutions as well as to explain their work, justify their reasoning and use appropriate models.
- Sometimes only one aspect is specified, such as only requiring an answer, and other times a problem requires students to provide an answer, provide an explanation or steps, include a diagram and/or use a model.
- Because problems require different responses, the type of response is intentional-such as requiring models when a concept is introduced and then not requiring the same model when a more concrete or procedural method for solving similar problems is developed.
Indicator 3d
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The manipulatives are almost always faithful representations of the mathematical objectives they represent and when appropriate are connected to written models meeting the expectations for this indicator.
- In most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives.
- When appropriate, multiple models are introduced-such as using both an area and a number-line model for dividing fractions in module 2.
- However, there was an inconsistency in the model. In module 2, lesson 3, both example 1 and 2 use an area model. But in one, 8/9 is represented by shading 8 of 9 sections and using a bracket to show the whole as all 9 parts. In the other, 9/12 is shaded, but the bracket only continues to the 9 parts, Therefore, a teacher who may not be familiar with this manipulative/model may be confused by the inconsistency (there did not appear to be any other instructions about how to use these representations.)
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 materials reviewed partially meet the criterion for teacher planning and learning. The materials partially support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Materials contain a teacher edition with ample and useful annotations and, sometimes, suggestions on how to present the content in the student edition and in the ancillary materials. The strongest point is that each module has an overview section at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Overall, the material reviewed for Grade 6 partially meet the expectations for this criterion.
Indicator 3f
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
The materials partially support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
- The strength of the materials is the quality of the questions asked through the lessons (classwork) as well as the exercises, problems, exit tickets and assessments.
- However, the materials do not include instructions or guidance for how to adjust a lesson or the questions that a teacher asks to guide instruction based on the needs of students.
- The materials provide effective learning experiences if the teacher both understands the content and also has a wealth of pedagogical practices for guiding discussions through questioning strategies that they are able to incorporate with ease.
- There is not sufficient guidance for how to group students or structure questions that can support all students in accessing the material.
- If a teacher is not confident with the sequence of the math or the purpose of the scaffolded questions, she/he may struggle to guide the instruction in a meaningful way and become frustrated that the outcome is not what is expected.
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.
Materials contain a teacher's edition with ample and useful annotations and that sometimes includes 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 materials are structured in a way that teachers could present the content effectively if all students engage in the mathematics and learn in the same way.
- However, if students struggle with a concept or problem, there is little guidance for teachers in how to appropriately remediate or revisit a problem. There are no suggestions for how to address or identify common mistakes or challenges that students may have with the content.
- Often, the scaffolding provided is to "remind students." There are limited, if any, suggestions for how to modify lessons, questions and/or problem sets for students who already understand the content of the given lesson.
- Beyond an occasional link to video, there are no suggestions for teacher or student on the use of technology, including a calculator, and therefore no guidance on how to use such technology.
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 materials contain a teacher edition (in print or clearly distinguished or accessible in digital materials) that sometimes contains full explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
- The teacher edition gives a clear process for each step of the solution to the problems posed to students.
- However, there are not always consistent explanations for teachers either before or within the lessons.
- If a concept is something teachers are not familiar with, such as dividing fractions, they must study the examples given to create their own understanding of the strategies students should be using.
- Although deeper explanations should not be needed for most lessons, it would be helpful for teachers to have access to supplementary materials that further develop an idea so that they can build their understanding beyond the problems in the lesson.
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 materials do contain a teacher edition (in print or clearly distinguished or accessible 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 12.
- Each module has an overview section at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of math Kindergarten through Grade 12.
- Knowledge required from prior modules and/or grades is explicitly called out in this section.
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 materials reviewed do not meet expectations for the criterion of assessment on Grade 6.
The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Materials sometimes provide strategies for teachers to identify and address common student errors and misconceptions. A strong point is that the materials provide opportunities for ongoing review and practice.
The materials offer some formative and summative assessments, notably by the mid-module and end-of-module assessments that assess particular standards and have rubrics specifically aligned with those standards. Overall, the materials reviewed for Grade 6 do not meet the expectations for the assessment criterion.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels.
There are no strategies or assessments that are specifically for the purpose of assessing prior knowledge.
Indicator 3n
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Materials sometimes provide strategies for teachers to identify and address common student errors and misconceptions.
- Although the materials do not always provide strategies for identifying and addressing common student errors or misconceptions, there are several opportunities within each lesson where teachers can do so.
- There are no suggestions for how to address specific common errors on problem sets or homework. Such suggestions would support teachers in knowing how to intervene when these errors are observed.
Indicator 3o
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
The materials provide opportunities for ongoing review and practice.
- The materials provide several opportunities for ongoing review and practice.
- Within a lesson there are three sets of practice problems: class exercises, problem sets and exit slips. These opportunities promote both increasing understanding of a concept as well as developing procedural skill and fluency.
- Beyond a lesson or module, future modules typically incorporate practice of previous learning.
- In Grade 6, after students learn the operations with rational numbers, they are expected to use those skills in the next lessons to further develop both understanding and procedural skill and fluency.
- There are no provisions for specific feedback for teachers or instructions on how to best provide meaningful feedback to students.
Indicator 3p
Materials offer ongoing formative and summative assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
Within the teacher materials, summative assessments do clearly denote which standards are being emphasized, and items used as formative assessments do not clearly denote which standards are being emphasized.
- Each standard is aligned to one or more lessons as denoted at the beginning of each topic.
- The mid-module and end-of-module assessments appear to be developed to fully assess a particular standard, and the rubrics specify which item aligns to which standard.
- However, problems within exit slips and problem sets-which could be used as formative assessment tasks-are not explicitly aligned to a specific standard or group of standards.
- The lessons are grouped in a way that the standards are addressed, but each specific lesson and the problems within it do not necessarily align to a particular standard. Therefore, it becomes challenging for teachers to easily make notes about which students are attaining or struggling with a specific standard prior to scoring the formal assessments that are provided and clearly aligned to standards.
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.
Formative assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.
- Each mid-module and end-of-module assessment includes a rubric as well as completed solutions for correct responses.
- There are no strategies or suggestions for follow-up provided.
- There are no rubrics or scoring guidelines for any formative assessments tasks (nor are any items or tasks identified as formative assessment opportunities).
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 materials reviewed for Grade 6 do not meet expectations for the criterion for differentiated instruction. Materials sometimes provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. In the margins and boxes of the teacher materials, there are some limited notes that provide teachers with strategies for meeting the needs of a range of learners, but a variety of solution strategies are not always encouraged. Although occasionally there are challenge problems, there are minimal opportunities for advanced students to go beyond the math provided in the classroom lessons. A strong point is that the materials provide a balanced portrayal of various demographic and personal characteristics. Overall, the materials do not meet the criterion for differentiated instruction
Indicator 3r
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Materials sometimes provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
- Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
- The sequencing and scaffolding are built in to the lesson development so that teachers pose problems as they progress through more rigorous processes and skills.
- However, the reasons that the problems and/or strategies are selected for sequencing scaffolding are rarely explicit.
- The best place to find an explanation of how the lessons develop is in the module and topic overviews where the structure of how the lessons build and develop is discussed in a narrative form.
- There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The materials sometimes provide teachers with strategies for meeting the needs of a range of learners.
- The materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners.
- There are some limited notes in the margins/boxes of the teacher materials. Sometimes the suggestions are very simple-"use questioning strategies" or "remind students of a definition"-and do not offer relevant suggestions that will impact the outcome of a lesson/problem.
- The lists online mirror the strategies in the teacher's materials and do not offer additional clarification or suggestions.
Indicator 3t
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
The materials frequently (but not always) embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.
Although most tasks allow students to utilize multiple entry points and to solve problems using a variety of strategies, paths and/or models, the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.
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).
e materials suggest some options for support, accommodations and modifications for English language learners (ELLs) and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
- Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners.
- There are some limited notes in the margins and boxes of the teacher materials. Sometimes the suggestions are very simple-"use questioning strategies" or "remind students of a definition"-and do not offer relevant suggestions that will affect the outcome of a lesson or problem.
- Lists online mirror the strategies in the teacher's materials and do not offer additional clarification or suggestions.
- What is provided is not enough to guarantee that all students have content that is accessible.
Indicator 3v
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Materials sometimes provide opportunities for advanced students to investigate mathematical content at greater depth.
- Occasionally there are "challenge" problems.
- It is difficult to determine if those tasks were optional for the entire class, scaffolded for the class or if they were explicitly for students who needed advanced mathematics.
- There were minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
Materials provide a balanced portrayal of various demographic and personal characteristics.
The 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 3.5: Technology
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.
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.