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 Traditional 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 Traditional series meet the expectation that the underlying design of the materials distinguishes 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 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 real-world problems with various contexts, embedding aspects of the modeling standards, 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 High School Discovery Traditional series meet the expectation that the materials in this series are designed and presented in intentional sequences. The series uses a consistent lesson structure throughout the courses. Each Concept is built around this lesson structure that engages students in multiple lesson sections where they Discover, Practice, and Apply what they are learning. The consistent lesson structure demonstrates an intentional sequence within a Concept, across a course, and throughout the series.
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 Traditional series meet the expectation that students are asked to produce a variety of products during each Concept in a unit to demonstrate their learning.
The series consistently asks students to share their understanding of mathematics in a variety of ways. Students produce models, make conjectures, create arguments, justify their reasoning, and make real-world connections throughout the materials. Opportunities are provided throughout the investigations for students to present their work using digital 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, 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 Traditional series meet the expectation that the manipulatives, both virtual and physical, 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, whiteboard tool, and a matrix solver tool. In some Investigations, the manipulatives embedded are specific to the lesson. Examples of this include but are not limited to:
- In Investigation 1 of Algebra I Concept 2.1 virtual algebra tiles are embedded to help students build understanding of the properties of equality.
- In Investigation 1 of Geometry Concept 7.1 the Dynamic Geometry Tool is embedded with two circles that students can manipulate to explore the possible number of intersections.
- In the Introduction to Concept 4.1 in Algebra II a technology enhanced item, Conic Section Explorer, is embedded in the lesson to allow students to determine how the cut of the plane through the cone affects the related graph of the curve to determine the relationship that results in a point, line, circle, or ellipse.
In addition to these virtual manipulatives, students use a wide collection of manipulatives when completing the hands-on activities throughout the series. These include, but are not limited to, modeling clay, straws, coffee stirrers, paper towel tubes, tools for measurement, scissors, tape, cardboard, string, a variety of sports balls, and various circular objects. Each of the manipulatives provides a representation that allows students to explore the related mathematics and connects them to procedures and written methods.
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 Traditional 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 Traditional series meet the expectation that teachers are provided quality questions to guide students' mathematical development.
The materials include a Model Lesson section and Teacher View that can be enabled as teachers navigate through the Investigation pages. Tabs, labeled as Sessions, include instructional notes for each Investigation. For example, in Algebra I Concept 7.2 Session 2 the teaching notes include questions that prompt discussion: “Why is the square root of a negative number not a real number, but the cube root is? What are some examples you can use to justify your reasoning?”
In addition, with the teacher view enabled, as teachers progress through the Investigations, blue boxes with quality questions and their connections to the mathematical practice they will enrich are included. The instructional reminders in this view are provided in a timely, and helpful way, just before 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 High School Discovery Traditional series meet the expectation that the teacher edition contains ample and useful annotations.
The Model Lesson section of the digital curriculum includes in-depth instructional notes and suggestions for both presenting and discussing the mathematical content of each Investigation, as well as use of the technology enhanced items and manipulatives embedded in the materials. For example, in the Introduction of Concept 4.1 in Algebra II a technology enhanced item, titled Conic Section Explorer, is included. In the Model Lesson Session 1 tab, teachers are provided detailed instructional notes on how to launch this technology tool, facilitate and implement it with students in a way that guides the learning, and bring closure to the exploration associated with this tool.
With the teacher view enabled, teachers have access to timely instructional notes that include useful suggestions to make sure the essential understandings are captured and the mathematical practices of focus are used to enrich the mathematics content on the Investigation pages.
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 Traditional series partially meet the expectation that the teacher edition contains adult-level discussion of the mathematics.
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 in full understanding of the standards developed in the students’ Investigations. The notes include detailed explanations of the essential and enduring understandings from the standards and any student misconceptions that may emerge.
Explanations of the responses to questions and tasks in the student Investigations are provided when the teacher view is enabled. At the end of the Concept, there is a summary tab. This tab includes a summary of the essential understandings 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. All explanations, however, focus on the mathematics of the Investigations without specific connections to mathematics outside of the instructional 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 Discovery Traditional series meet the expectation that the materials explain the role of the specific mathematics standards in the context of the overall series.
The Model Lesson section of each Concept contains a tab titled Progressions and Standards. This tab provides an overview that explains the progression of the standards including identification and detailed descriptions of Reach Back Standards (content from previous courses), standards covered in the Concept of the current course, and the Reach Ahead standards (links to future lessons and courses). Occasionally the information will include a reference to courses in higher mathematics beyond the scope of the series. For example, in Concept 1.1 of Algebra II, it is noted that, “Students will further apply their knowledge of sequences and series in calculus, analyzing both ordinary differential equations and partial differential equations, as well as integral calculus, when analyzing area under a curve (F-LE.2, F-BF.1a, F-BF.2).”
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 Traditional 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 Traditional series partially meet the expectation that they provide materials for gathering information about student’s prior knowledge within and across grade levels/courses.
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 support for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation of providing support for teachers to identify student errors. 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 Traditional series meet the expectation that materials provide support 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 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 Traditional series partially meet the expectation of clearly denoting standards on the assessments. The instructional materials include a pre-made unit assessment. The standards are identified for the unit; therefore, it is clear, as a whole, which standards are being emphasized on the unit assessment. However, there is not a standards alignment for these pre-made tests item by item, so 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. There is a Math Assessment Builder tool for teachers that will allow teachers to create their own standards-based assessment.
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 Traditional series partially meet the expectation that sufficient guidance is given 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 each score. Also, each Apply question includes a rubric with scores ranging 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 Traditional 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 Traditional series 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 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 Traditional 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, in the Summary section students are provided with online tutorial websites for instructional assistance when needed. 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 Traditional 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, Algebra I Concept 1.2 Apply 2 asks students to create a card trick and model the trick algebraically, following an example from an earlier task.
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 Traditional series 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 support for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for the High School Discovery Traditional 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 Traditional 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.