High School - Gateway 3
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Usability
Gateway 3 - Partially Meets Expectations | 75% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 7 / 8 |
Criterion 3.3: Assessment | 6 / 10 |
Criterion 3.4: Differentiation | 6 / 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 Discovery Integrated series meet the expectation for having a use and design to facilitate student learning. Overall, the materials are designed well and take into account effective lesson structure and pacing. The design and layout of the materials are easy to use and not distracting and support students in engaging thoughtfully with the content.
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 Discovery Education Integrated series meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson.
As the online materials organize learning in a particular order, the structure delineates between problems and exercises. This order includes the following:
- A Discover Tab which has an Intro problem followed by multiple Investigations and a Summary and Extensions. This is where problems for learning new mathematics are found.
- A Practice Tab consisting of Coach and Play sections which contain exercises.
- An Apply Tab which has one or more open-ended exercises. Exercises which build mastery and student capacity for a given skill with application are found mainly in the Practice and Apply Tabs.
This structure is repeated throughout the series.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that the design of assignments is not haphazard and that exercises are given in intentional sequences.
The basic structure of each concept includes interactive core mathematical content and concurrent formative assessment. Modeling investigations intentionally build on and extend from the core content concepts, and the Coach and Play sections assess and reinforce procedural skills.
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 Discovery Education Integrated series meet the expectation that students are asked to produce a variety of products throughout the Concepts in each Unit to demonstrate their learning of the mathematics.
The materials ask students to engage in mathematics in a variety of ways. For example, students are asked to make predictions based on a set of data, estimate measurements and use geometric tools, and compare/contrast information from a diagram.
- In Math II Concept 1.2, students are asked to make conjectures, explain their reasoning orally and through writing, and collect data.
- In Math I Concept 2.3 Apply 2 students design a chairlift by making a graph of the lift and spacing towers to adequately support the lift using ratio reasoning. Students research lifts from existing ski resorts and defend their decisions using citations. They calculate coordinates on their graphs to correspond to the towers they recommend.
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 Discovery Education Integrated series meet the expectation that manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The series makes use of a range of virtual manipulatives including, but not limited to, calculators, a geometry sketchpad, a geometry construction app, a unit converter, a data analysis app, a matrix solver, and a virtual whiteboard. General manipulatives and tools are listed in the Teacher Preparation sections. A few examples of these include, but are not limited to, paper towel tube, meter stick, measuring tape, straws, and pins. Throughout the series, students are exposed to a wide variety of manipulatives and virtual tools and are expected to utilize them as necessary.
- In Math I Concept 3.1 students explore transformations using a flip-book cut from a printable template.
- In the Math I Concept 3.3 Intro students use a construction app to reconstruct the flower of life.
- In Math II Concept 2.3 students use straws and pins.
- In Math II Concept 1.2 Investigation 1 students use the dynamic geometry tool to explore parallel and perpendicular lines and are also asked to verbalize their findings. In Investigation 2 they are asked to use patty paper and paper folding to construct different types of lines.
Indicator 3e
The visual design (whether in print or digital) 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 reviewed for the High School Discovery Integrated series meet the expectation for teacher planning and learning for success with the CCSS. Overall, the materials support teacher learning and understanding of the Standards. The materials provide the teacher necessary supports through quality questions to help guide students' mathematical development; annotations and suggestions on how to present the content; and strategies for informing students, parents, or caregivers about the mathematics program.
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 Discovery Integrated 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.
Each course contains a Course Overview which is divided into Unit Overviews and Concept Overviews explaining what students will be doing in each section. Within the Model Lesson tab of each Concept, there are tabs which contain Objectives (Lesson Objectives, Essential Questions, and Enduring Understandings), Progressions and Standards, Teacher Preparation (materials list, common misconceptions, and key vocabulary), Sessions (introduction and instructional notes), Extensions, and Apply. Throughout each lesson, additional instructional notes and guiding questions are also included in the materials. For example:
- Math II Concept 4.2 Sessions 1 and 2 Instructional Notes include the following questions:
- "How do you know that it is not possible for the graph of a quadratic function to have three x-intercepts?"
- "If the graph of a quadratic function has exactly one x-intercept, what can you conclude about the location of its vertex?"
- "If the graph of a quadratic function has no x-intercepts and a minimum point, does its vertex lie above or below the x-axis? How do you know?”
- In Math II Concept 4.2 Investigation 3 a Teacher Note states: “Have students share their reasoning for each answer and critique one another’s arguments. Analyze the graph and discuss what all of the parts mean in the context of the problem.” Though questions are provided for teachers to use, no explanation of possible answers is included.
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 Discovery Integrated series meet the expectation that 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.
Teachers are able to easily toggle a “teacher view” on or off. When the toggle is on, teacher notes and answers to all problems are visible. Throughout the teacher materials there are instructional notes for each Investigation in addition to the thorough instructional notes located in the Model Lesson tab of each Session. These notes tie directly to the Investigations found in the Discovery tab.
A dynamic geometry tool and construction tool which is referenced extensively and is freely available to the students in and out of class time is embedded within the instructional materials. It is employed in all three courses. There are “?” icons next to embedded technology where students can see explanations of how to use the technology. Additional technology support is provided in the Help menu.
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 Discovery Integrated series partially meet the expectation that 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 Progressions and Standards tab provides teachers information of the standards as well as a description of mathematics in During Previous Instruction, Through the Investigations in This Concept, and During Subsequent Instruction. The Teacher Preparation tab also provides teachers with common misconceptions. Teacher materials are written in appropriate mathematical language. This provides adult-level information specific to the course and does not provide more advanced mathematical concepts for the teachers.
The materials lack explanations for answers. Answers are either provided with no accompanying explanation or are simply listed as “answers may vary” without providing examples of acceptable answers.
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 Discovery Integrated series meet the expectation that materials contain a teachers edition that explains the role of the specific mathematics standards in the context of the overall series.
The Progressions and Standard tab in the Model Lesson provided in each concept provides teachers with an explanation of the role of specific math standards within that concept. Materials provide teachers an overview of the progression of the content standards by listing Reach Back Standards, Standards Covered, and Reach Ahead Standards. In addition, for each Concept the materials provide a narrative of mathematics learned “During Previous Instruction,” “Through the Investigations in this Concept,” and “During Subsequent Instruction.”
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).
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.
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 reviewed for the High School Discovery Integrated series partially meet the expectation for assessment and offering teachers resources and tools to collect ongoing data about student progress on the standards. The materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills, but the materials partially meet the expectations for the rest of the indicators in assessment. The materials do offer students opportunities to monitor their own progress.
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 Discovery Integrated series partially meet the expectation that the materials provide strategies for gathering information about students’ prior knowledge within and across grade levels/courses.
In the 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 Introduction 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 Introduction 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 support for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for the High School Discovery Integrated series partially meet the expectation that materials provide support for teachers to identify and address common student errors and misconceptions. The instructional materials provide a suggested list of common student misconceptions in the teacher preparation section of each concept within the unit. There is no specific support available to assist teachers in addressing those specific misconceptions.
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 Discovery Integrated series meet the expectation that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
In each concept, the Coach and Play sections provide 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 assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials reviewed for the High School Discovery Integrated series partially meet the expectation that assessments clearly denote which standards are being emphasized.
The instructional materials include a pre-made unit assessment. The standards are identified for the unit, and therefore it is clear, as a whole, what standards are being emphasized on the unit assessment. However, there is not a standards alignment item by item, and therefore, it could be challenging to determine which standards are assessed by each question. Check for Understandings and Apply problems also do not denote which standards are being emphasized. The Math Assessment Builder does clearly denote standards by allowing teachers to select questions for their assessment based on specific standards.
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 Discovery Integrated series partially meet the expectation that assessments 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, based on a 0, 1, or 2 point scale that shows the criteria needed to receive that score. 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 reviewed for the High School Discovery Integrated series partially meet the expectation for differentiated instruction for diverse learners within and across grades. The materials do embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations, and they provide strategies to help teachers sequence or scaffold lessons. The materials do not always provide teachers with strategies for meeting the needs of a range of learners or provide opportunities for advanced students to investigate mathematics content at greater depth.
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 Discovery Integrated series partially meet the expectation that the materials provide teachers with strategies to help 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 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 High School Discovery Integrated series partially meet the expectation that the materials provide 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 High School Discovery Integrated series 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. For example, Math I Concept 6.1 introduces students to the lesson using a Car Rental task. This tasks presents students with the question,”How can you use math to compare rates at two car rental companies?” Students explore the question in their own way and then through the lens of equations. Following the equation exploration, students are posed with the question, “What other solution strategies could you use to help you make decisions?” Questions such as these provide students the opportunity to expand their thinking based on their entry point and represent the solution in another way.
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 Discovery Integrated series do not meet the expectation that the materials suggest 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 support for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for the High School Discovery Integrated series 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.
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 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 Discovery Integrated series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials integrate technology in ways that engage students in the MPs, include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology, and incorporate technology that provides opportunities for teachers and/or students to collaborate.
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.
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.
Indicator 3ac.i
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
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.
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.