High School - Gateway 3
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Usability
| Score | |
|---|---|
Gateway 3 - Partially Meets Expectations | 63% |
Criterion 3.1: Use & Design | 7 / 8 |
Criterion 3.2: Teacher Planning | 5 / 8 |
Criterion 3.3: Assessment | 6 / 10 |
Criterion 3.4: Differentiation | 5 / 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 Mathematics Vision Project Traditional series meet expectations that the materials are well designed and take into account effective lesson structure and pacing. Overall, the materials distinguish between problems and exercises; students produce a variety of types of answers including both verbal and written answers; and 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 Mathematics Vision Project Traditional series meet the expectation that the underlying design of the materials distinguish between problems and exercises. Problems are included in “tasks”, which attend to specific standard(s) or aspect of a standard(s). There are three different kinds of tasks: Develop Understanding, Solidify Understanding, and Practice Understanding. Develop Understanding tasks introduce concepts and build on previous knowledge by providing discovery problems. Solidify Understanding tasks focus on the concepts being developed in the unit and provide students opportunities to practice what they have learned so far in the unit. Practice Understanding tasks extend learning by adding small extensions to the concepts covered in the unit. Ready, Set, Go! Exercises are designated as “homework”. Ready exercises are intended to prepare students for the upcoming work in class, Set exercises reinforce the work done in class that day, and Go exercises review concepts and skills that students learned previously.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet expectations that the design of the assignments is not haphazard and are given in intentional sequences. The materials create connections as tasks begin by re-examining mathematical content so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the material is designed to spiral concepts throughout the entire series.
Structure of the Materials states that Ready and Go exercises provide a spiraling sequence of content to help maintain skills. However, these spiraled exercises often contain concepts that are unrelated to the content of the new lesson and/or have not yet been learned in the sequence of the course or series. Examples of these exercises affecting the overall sequence of the materials include:
- In Algebra I, Module 5, Ready, Set, Go! Problem 8, students identify transformations in Ready, but this concept is not addressed until Geometry even though the concept is addressed in Grade 8 standards. The main topic of the module is systems of equations, and this practice does not provide practice that connects to the work being done in the Module or the course.
- In Algebra 1, Module 9, Ready, Set, Go! Problem 8, students create geometric constructions after learning about residuals. These topics are not related, and the materials do not address constructions until Geometry.
- In Geometry, Module 2 addresses geometric constructions and connects those to congruence of figures. In Go for Task 1, students solve systems of equations. In Go for Task 2, students write recursive and explicit formulas for sequences. While this is connected to content from Algebra I, it is not connected to new content in Module 2.
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 Mathematics Vision Project Traditional series meet expectations for having variety in how students are asked to present the mathematics. For example, students provide numerical answers, produce graphs, compile charts, draw pictures, find equations and functions, create models, describe patterns, articulate arguments, write critiques, and analyze work and possible solutions. In almost every task, students present mathematics in multiple ways. For example, in Algebra I, Module 5, Task 5, students write inequalities and create graphs. In Geometry, Module 7, Task 1, students draw three-dimensional solids and their two-dimensional cross sections. In Algebra II, Module 3, Task 2, students create area models to solve binomial multiplication.
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 Mathematics Vision Project Traditional series meet expectations that manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials occasionally instruct students to use manipulatives within the materials (for example: Algebra 2, Module 6, Task 8). On the main webpage, under the Resources header, there are links that are connected to a set of ten GeoGebra Interactive Applets (i.e. Leaping Lizards, Triangle Dilation). Directions for the interactive applets can be found within the applets and the teacher notes. A few examples of suggested physical manipulatives include dice to model a data set, and an area model for multiplying binomials, completing the square, and factoring.
Indicator 3e
The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
The instructional materials reviewed for Mathematics Vision Project Traditional series have a visual design that is not distracting or chaotic. The materials are digital versions of print books. The e-book does not have any enhancement features such as embedded media, interactivity, narration, etc. There are no places for students to enter answers that are then compiled for teachers. The index at the beginning of each module doesn’t have bookmark links to the lessons within that module, and there are no page numbers when it is a printed resource.
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 Mathematics Vision Project Traditional series partially meet expectations that materials support teacher learning and understanding of the standards. The instructional materials provide questions that support teachers in delivering quality instruction, and the teacher’s edition is easy to use and consistently organized and annotated. However, the teacher edition for the instructional materials does not contain adult-level discussions of the mathematics.
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 Mathematics Vision Project Traditional series meet the expectation for supporting teachers by providing quality questions to guide students’ mathematical development. The Teacher Notes provide suggested questions to use during the Teaching Cycle (Launch, Explore, Discuss) that aid in students’ developing understanding of the content. For example, Algebra I, Module 1, Task 6, Launch: “Then, wonder out loud whether or not it would be an arithmetic sequence if a number is subtracted to get the next term. Don’t answer the question or solicit responses.” There is also an Essential Question provided as part of the Enhanced Teacher Notes for each task, and the tasks contain questions designed to elicit discovery and exploration.
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 Mathematics Vision Project Traditional series meet the expectation that the teacher edition contains ample and useful annotations. Teacher Notes are provided for each module, and the notes contain structured guidance on how the lessons should proceed. The notes may include some or all of the following sections:
- Special Note to Teachers: highlights an aspect of the task and how it fits in the overall sequence of the three course materials.
- Purpose: describes the previous development of concepts needed for the lesson and where to place emphasis for the lesson.
- New Vocabulary: lists new vocabulary introduced in the lesson.
- CCSSM Standards focus and related Standards: lists those addressed in the lesson.
- Standards for Mathematical Practice: lists those addressed in the lesson.
- The Teaching Cycle: Launch, Explore, Discuss, provides a detailed discussion on lesson delivery.
There is also reference made to the use of technology within the teaching cycle, but there is no discussion of how to use the technology. In Algebra I, Module 9, Task 5, the introduction states, “Most graphing calculators will work well. Free computer apps would be very helpful and easy to use on this task as well (GeoGebra and Desmos, etc.).”
The MVP Enhanced Teacher Notes include the basic Teacher Notes, Essential Questions for each task, articulation of Standards of Math Practices of Focus, exit ticket ideas, instructional supports, instructional adaptations, intervention ideas, challenge activities, answer keys to in class tasks, and answer keys to Ready, Set, Go!.
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 Mathematics Vision Project Traditional series do not meet the expectation for containing adult-level discussions of the mathematics. The Teacher Notes do not contain explanations of advanced mathematical topics that advance the knowledge of the teacher. For example, in Geometry Module 5, Task 4, the purpose states, “In this task students will develop a strategy for finding the perimeter and area of regular polygons. This work will lead to informal arguments for the formulas of the circumference and area of a circle in the next task.” Teachers are not provided with further instructions within the task to advance the learning of the concept for the teacher.
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 Mathematics Vision Project Traditional series partially meet the expectation that the Teacher edition addresses the standards in the context of the overall series. An overview of each module and associated tasks is provided in the Introduction to the Materials document on the course page. An overview of each task is also provided in the Teacher Notes. The materials make occasional references to previous and future standards related to the current task. Also, occasional references are made to a course, but rarely to the module or the task. For example, in Geometry, Module 6, Task 2 states, “The purpose of this task is to prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. Students have used these theorems previously.” No precise reference about how current content fits into the vertical progression of learning is provided.
Indicator 3j
Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
The instructional materials reviewed for Mathematics Vision Project Traditional series contain Teacher Notes that include an index of Tasks within each Module with related standards. A Core Correlations document is included in the materials, which serves as a reference for standards addressed in the materials. A pacing guide for the materials was not provided, but the materials state to "usually" use/teach a task a day.
Indicator 3k
Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
The instructional materials reviewed for Mathematics Vision Project Traditional series provide a link on the main webpage for parents that contains a general, course-wide letter. If support is needed for homework, the materials suggest, “If there are areas in the Ready, Set, Go! homework assignments, where your student feels uncertain and needs guidance, please access the online help videos hosted at rsgsupport.org. For a very small subscription fee you can provide your student with help that is directly connected to his/her homework assignment. There are also print resources that can be obtained for reference.” The videos provided on rsgsuppport.org are currently available for the Integrated series. Helps, Hints and Explanations is a resource available for purchase and was developed for students and parents to assist them as they work on Ready, Set, Go! homework. This resource has explanations and examples intended to remind students of what they learned in class and provide them with support as they work on their homework.
Indicator 3l
Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
The instructional materials reviewed for Mathematics Vision Project Traditional series provide a link for professional development on the main webpage. This webpage contains past presentations, via powerpoint, on the Comprehensive Mathematics Framework, the basis of the design of MVP. Professional development options are also available for purchase about the approaches, strategies, and research.
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 Mathematics Vision Project Traditional series partially meet expectations that materials offer teachers resources and tools to collect ongoing data about students progress on the Standards. The materials provide support for teachers to identify and address common student errors and misconceptions, 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 Mathematics Vision Project Traditional series partially meet the expectation for providing materials for gathering information about student’s prior knowledge within and across grade levels/courses. The Ready exercises within a task are intended to help students review and prepare for the skills and concepts that will be needed for the task. However, there is no guidance for the teacher as to how to interpret these exercises, nor is there any discussion of possible strategies for remediation.
Indicator 3n
Materials provide support for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation for providing support for teachers to identify and address common student errors and misconceptions. The materials often include a comment related to common errors or misconceptions, but they do not always identify what these might be. For example, in Algebra I, Module 8, Task 2 Explore, the teacher notes state: “As you monitor, look for common student misconceptions to discuss during the whole group discussion. For example, some students may not realize…” and the notes go on to explain a misconception. In the same module, Task 7 Explore states: “Look for common errors among students so that you can discuss these more thoroughly during the whole group discussion”, but no indication is included of what these might be or how to address them in the whole group discussion.
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 Mathematics Vision Project Traditional series partially meet the expectation for providing opportunities for ongoing review and practice of both skills and concepts. The structure of the tasks within a module, and across modules, provides for review of concepts. However, besides the Ready, Set, Go! exercises within each task, there is no ongoing practice of skills, and there is no discussion of how to provide feedback. The Ready, Set, Go! exercises do provide students the opportunity to show proficiency on certain topics, but few resources are provided for teachers to provide feedback.
Indicator 3p
Materials offer ongoing assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that standards are clearly denoted for assessments. Assessments do indicate course, module, and task, but specific standards are not identified on the assessments. Algebra II, Module 2 Quiz, states, “Logarithmic Functions 2.1-2.4”, but it does not indicate for each question which standards are addressed. Assessments are based on modules, which include the standards of focus. Although quizzes and tests do not specifically provide standards, performance-based assessments include the standards.
Indicator 3p.ii
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Assessments typically have multiple parts including a mixture of the following types of problems: Multiple Choice, Matching, Building Tables, Short Answer, and Short Essay. Occasionally students are asked to demonstrate different methods to solve similar problems. There were few of the short answer and short essay problems, and the majority of the assessments were comprised of multiple choice/matching type problems.
Scoring rubrics for the short answer and short essay questions were not available, and grading expectations for weighted value of the assessments. Sample assessments include rubrics for the performance-based assessments which offer limited guidance, but do not provide guided feedback.
Indicator 3q
Materials encourage students to monitor their own progress.
Self assessments are included within the materials and allow students to monitor their progress. Students are expected to document evidence of their personal rating. The students have three choices for assessing, "I can do this without mistakes", "I understand most of the time…," and "I don't understand." Students are asked to give evidence of their response. No teacher materials were provided to explain what this "evidence" should or could look like or to explain how the teacher should use the "evidence".
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 Mathematics Vision Project Traditional series do not meet the expectation for differentiated instruction for diverse learners within and across courses. The instructional materials do provide opportunities for advanced students to investigate mathematics content at greater depth. However, the materials do not always provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners, provide strategies for meeting the needs of a range of learners, or embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
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 Mathematics Vision Project Traditional series partially meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. Teacher materials provide a prescribed Teaching Cycle. Each task has an Explore (Small Group) component for developing student understanding. If the students do not meet the expectations in small group, strategies are not consistently provided for how the teacher can scaffold the content of the task. An example: Algebra I, Module 5, under Explore Small Group, “watch and listen and encourage connections.”
The Enhanced Teacher Notes offer “Instructional Supports” that sometimes contain a scaffolding/intervention section, such as in Algebra I, Module 2, Task 10 which provides a graphic organizer to help students classify forms of linear equations.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners. Enhanced Teacher Notes offer “Instructional Supports”, “Instructional Adaptations”, and “Challenge Activities” as resources to differentiate instruction. These, however, are not comprehensive. The note in Geometry, Module 1, Task 5, under Instructional Adaptations states, “The use of the cutouts described in the Instructional Supports section should be sufficient intervention for this task, and provide adequate support for all students.” However, no other strategies or suggestions were given.
The Enhanced Teacher Notes list “Instructional Supports” and “Instructional Adaptations” at the end of each task. For example, Geometry, Module 1, Task 3, has these instructional supports listed:
- Relatable Context - summarizes why this context will engage students.
- Visualization - addresses the misconception that could result if students mistakenly think of this as a three-dimensional action instead of a two-dimensional action of reflecting.
And these Instructional Adaptations:
- Intervention Activity - use of tracing paper.
- Challenge Activity - “Ask students to consider this question: Is it possible to find a sequence of transformations that will carry every image to every other image in the diagram if the first transformation in the sequence is always to translate the tip of the middle fingers of the left hand of the first image to the corresponding point on the second image? What are the implications of this?”.
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 Mathematics Vision Project Traditional series partially meet the expectation for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. Most tasks do not provide multiple entry-points.
Some tasks do provide multiple entry points. For example, in Geometry, Module 7, Task 1, students explore two-dimensional cross sections of three-dimensional objects. The materials offer many different ways for students to engage in this visualization - drawing “slices” of a cube on a two-dimensional drawing, partially filling a cylinder with water and tilting and turning it different ways while watching what the surface of the water does, and finally, observing the possible shapes of shadows that can be cast by different objects.
The tasks set for the students can often be approached from many perspectives, using different strategies and representations. In some cases this is encouraged; however, in most cases the teacher is instructed to guide the students to the “desired” method of solution so as to address the standard in question.
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 Mathematics Vision Project Traditional series do not meet the expectation for providing 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). No accommodations for English Language Learners or other special populations are available.
Indicator 3v
Materials provide support for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. The Enhanced Teacher Notes offer “Challenge Activities” as resources for advanced students. For example, in Algebra I, Module 9, Task 5 the teacher is prompted to “have students find data in two way tables on the internet, then have them write a story, using relative frequency statements.”
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
The instructional materials reviewed rarely contain images of people. The names included in the problems are diverse.
Indicator 3x
Materials provide opportunities for teachers to use a variety of grouping strategies.
The instructional materials provide some suggestions for teachers to use a variety of grouping strategies. The Enhanced Teacher’s Notes have suggestions for grouping listed next to each activity. Group work is embedded in every task; MVP strongly suggests all teachers take their inservice training. No implementation guide was made available to teachers related to the pedagogy of collaborative learning, how to form and manage groups, or effective techniques that could be used.
Indicator 3y
Materials encourage teachers to draw upon home language and culture to facilitate learning.
The instructional materials did not provide references for 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 Mathematics Vision Project Traditional series inconsistently support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide few opportunities for students to use technology in effective ways for the purpose of engaging in the Mathematical Practices and few opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. The instructional materials do provide choices for teachers and/or students to collaborate with each other, and sample assessments items could be purchased and easily customized for local use.
Indicator 3aa
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
The instructional materials for the Mathematics Vision Project Traditional series are accessible within any browser. Each module is presented as a Portable Document File (pdf), which can be viewed online or printed. These files can be viewed on tablets and mobile devices.
Indicator 3ab
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
In the instructional materials for the Mathematics Vision Project Traditional series, students demonstrate knowledge and understanding through the virtual manipulatives, but other than those, there are few opportunities to show knowledge and understanding by using technology. The enhanced teacher materials provide teachers with suggestions on how technology can help students develop an understanding of concepts, but they do not provide specific instructions on the use of technology to assess understanding and procedural skills for each task.
Indicator 3ac
Materials can be easily customized for individual learners.
Indicator 3ac.i
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
The instructional materials reviewed for the Mathematics Vision Project Traditional series do not allow personalization.
Indicator 3ac.ii
Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
The instructional materials reviewed for the Mathematics Vision Project Traditional series do not offer a wide range of lessons on each topic. Each lesson involves a central task or problem. Teachers are encouraged to seek additional resources in order to give students a deeper understanding of certain topics. Teachers and individuals that have purchased the print version of Ready, Set, Go! Answer Keys and Sample Assessments can also receive Word Document files containing the sample assessment items. These sample assessment items could be easily customizable for local use.
Indicator 3ad
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
The instructional materials for the Mathematics Vision Project Traditional series do not offer opportunities for students to collaborate with each other using technology.
Mathematics Vision Project has a current Facebook page with over 1,035 likes and can be followed on Twitter at @MVPmath. Teachers can also register to receive updates related to instructional supports and materials from the MVP team.
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.
Although the instructional materials for the Mathematics Vision Project Traditional series are presented in a digital format, few opportunities are provided for students to use technology in effective ways for the purpose of engaging in the Mathematical Practices. A few virtual manipulatives are listed on the course home page (via Geogebra), but they are aligned to the courses of the integrated series. The activities are not linked to, nor referenced in, the teacher or student materials. The interactive activities give instructions for students to complete the tasks. These tasks are provided for a few lessons throughout the entire series (approximately 10 activities posted).