High School - Gateway 3
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Usability
Gateway 3 - Meets Expectations | 83% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 7 / 8 |
Criterion 3.3: Assessment | 7 / 10 |
Criterion 3.4: Differentiation | 8 / 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 Core-Plus Mathematics integrated series meet the expectation that the materials are well-designed and take into account effective lesson structure and pacing. The design of the materials, in print and in the eBook, distinguishes between problems and exercises, and it also is not haphazard. The consistent order of the sections, Investigations followed by Applications delineated as On Your Own, Connections, Reflections, Extensions, and Review, helps to make students accustomed to the layout. Throughout the materials, students are asked to present their understanding of the mathematics in a variety of ways, and the materials also integrate the use of physical and virtual manipulatives that are faithful representations of mathematical objects.
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 Core-Plus Mathematics integrated series meet the expectation that the underlying design of the materials distinguishes between problems and exercises. The materials clearly organize learning in a specified order of an Investigation phase, sometimes with multiple concepts, followed by an On Your Own phase. Problems for learning new mathematics are within the Investigation phase, and exercises which build mastery and student capacity for a given skill with application are in the On Your Own phase. Items for application require multiple representations and extend learning, and they do build on knowledge based in the Investigation phases. Similarly, problems in the Investigation phase often contain real-world applications but use the application to introduce concepts and build knowledge. This structure is repeated throughout each of the courses. For example, in Course 2, Unit 5, Lesson 1, the Investigation phase begins on page 327 with multiple investigations followed by the On Your Own phase on page 345.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the design of assignments is not haphazard and tasks are given in intentional sequences. Throughout the curriculum, assignments are given in an intentional manner, often building capacity for the learner through reasoning. This progression includes the development of mathematically accurate vocabulary, methods, and formulas. Examples that highlight how the design of the assignments is not haphazard and tasks are given in intentional sequences include: the investigations in Lesson 2 of Unit 2 in Course 1; the applications in Lesson 2 of Unit 5 in Course 2; and the investigations in Lesson 1 of Unit 7 in Course 3.
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 Core-Plus Mathematics integrated series meet the expectation that there is variety in how students are asked to present the mathematics. The materials require students to engage in mathematics in a number of ways to solve various types of problems that include evaluating expressions, making predictions based on a set of data, estimating measurements and using geometric tools, and comparing/contrasting information from a diagram. Examples of these types of problems can be found on page 67 in the materials for Course 1. Other problems allow students to engage in the process of solving a problem through planning and to build a mathematical model from given data (Course 2, Unit 6, Lesson 2, page 435-452, applications section). At other times, students are asked to give explanations, write equations, and create a diagram (Course 3, Unit 1, Lesson 2, page 44).
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 Core-Plus Mathematics integrated series have manipulatives, both virtual and physical, that are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Physical manipulatives are utilized to introduce reasoning in problem solving. For example, counters are used in a problem referencing consecutive integers in Course 1, Unit 1, Lesson 1. In Course 1, Unit 6, Lesson 1 on page 371, virtual manipulatives are used to generate work with triangle congruence, and they are also used in Course 2, Unit 6, Overview on page T399A, to construct vertex-edge graphs to investigate problems and concepts in modeling and optimization.
The series makes use of a wide range of virtual manipulatives available within CPMP-Tools, and there are physical manipulatives needed for each course listed within the Planning Guide. A few examples of these include, but are not limited to rubber bands, meter sticks, compass, straightedge, protractor, rulers, pennies, dice, stopwatch, bouncy balls, linkage strips and pipe cleaners.
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 Core-Plus Mathematics integrated series meet the expectation for supporting teacher learning and understanding of the Standards. There are plenty of questions provided to teachers to aid in planning and providing effective learning experiences, and the materials contain numerous ways in which they help teachers present the mathematical content and use embedded technology to aid students' learning. The materials do include adult-level explanations to help teachers increase their own learning. Although there are focus and connected standards provided for each lesson, the materials do not clearly explain the vertical progression of the standards across the series or how the learning of the lessons fits into a vertical progression of learning.
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 Core-Plus Mathematics integrated series meet the expectation that teachers are provided quality questions to guide students' mathematical development. The opening page of the lessons contains a scenario that touches on the mathematics to be studied, and the next page contains a section titled Think About This Situation where students are given questions to discuss. Guiding questions are provided for teachers and students at the beginning of each investigation. The teacher edition provides typical student responses that might be expected and suggestions for follow-up questions to enrich the discussion. With the teacher edition, there is an additional Promoting Mathematical Discourse section for some lessons where a sample discussion is given for use in planning. The Implementation Guide suggests that teachers work through these pages together during planning.
In the student edition, within a lesson at the end of each Investigation, there is a Summarize the Mathematics section that provides a series of well-designed questions to have students reflect on what they have learned. The teacher edition provides the same support for Summarize the Mathematics as was mentioned above for Think About This Situation. For an example, see Course 2, Unit 4.
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 Core-Plus Mathematics integrated series meet the expectation that the teacher edition contains ample and useful annotations. There are annotations in the margins and in the narrative related to the lesson implementation. There are also boxes labeled “Instructional Notes” that cover points like specific goals for a particular question, where and how a topic was previously addressed, helpful reminders for students, thoughts on pacing, and concepts students may not yet fully understand. Other special boxes include Assignment Note, Differentiation, Teaching Resources, Key Idea, Collaboration Skills, Possible Misconception and Common Error.
CPMP Tools is an online dynamic software package embedded in the instructional materials that is referenced extensively and is freely available to the students in and out of class time. It is employed in every unit across all three courses. In the teacher edition there are boxes titled “Technology Note,” which offer guidance to teachers on the use of CPMP Tools that supports and enhances student learning. For an example, see Course 2, Unit 3, Lesson 1 starting on page T162. The use of this tool is also referenced in the planning guide at the start of each unit. (Course 2, page T161D)
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 Core-Plus Mathematics integrated series meet the expectation that the teacher edition contains adult-level discussion of the mathematics. Special boxes in the teacher edition are used to give teachers an “advanced perspective” on some of the material covered. Course 3, page T116B, has such an example. There are also “Additional Resources” that refer teachers to specific publications that may enhance their understanding of the topics (Course 1 on page T367). In some cases, there is a list of additional references in the overview of the Unit (Course 1 on page T237).
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 Core-Plus Mathematics integrated series partially meet the expectation that the teacher edition addresses the standards in the context of their place in the entire series. The materials for the series do not provide a vertical progression for the standards in the series. For some units, the materials provide general references in the Unit Overview as to how current content fits into the vertical progression of learning, for example, page T319 in Course 3, but these general references are not provided for all units, for example, page T73-73A in Course 1. At the beginning of each lesson, there is a list of standards that are "Focused on" and "Connected to" in the lesson, for example, page T462 in Course 1, but this list does not make references to any other lessons in the series. The combination of the list of standards for each lesson and the general references in the Unit Overview could explain the role of the specific standards in the context of the overall series, but the inconsistency of the general references leaves the explanation of the role of the specific standards in the context of the overall series incomplete.
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 Core-Plus Mathematics integrated series partially meet the expectation that the materials offer teachers resources and tools to collect ongoing data about student progress on the Standards. The lessons offer some opportunities to informally assess students' prior knowledge, and feedback for review and practice exercises is limited. The assessments provided do not clearly denote which standards are being emphasized, but the assessments do provide sufficient guidance for teachers in following up on student performance.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation for gathering students' prior knowledge within and across grade levels/courses. There are no formal assessments of prior knowledge or connections to learning from Grades 6-8 or previous courses. There are some instances in the materials where students' prior knowledge is assessed, for example the Lesson Launch on pages T108-109 in Course 3, and used to launch an investigation into new learning, but these informal assessments are not a part of all units or lessons. For example, in Course 2, Unit 3 addresses transformations and distance, but the materials do not include any opportunities for teachers, formally or informally, to determine what prior knowledge students might have about these topics from either Grades 6-8 or Course 1. There are some Instructional Notes that address prior knowledge, such as on page T114A in Course 3, but these Instructional Notes are inconsistently placed throughout the materials. Also, the Review section in the On Your Own homework sets provide an opportunity to review previous concepts and skills, but there is limited support for teachers as to how the information gathered from the review problems could be used in current or future lessons.
Indicator 3n
Materials provide support for teachers to identify and address common student errors and misconceptions.
The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that teachers are given support to identify and to address common student errors and misconceptions. There are multiple teaching tips provided, referred to as "Common Error," for example, page T219 in Course 1, or "Possible Misconception," for example, page T507A in Course 2, to assist teachers with addressing these needs in their classroom. Additionally, there are problems included in the materials that allow for students to identify errors and critique reasoning.
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 Core-Plus Mathematics integrated series partially meet the expectation that the materials in the series provide opportunities for ongoing review and practice of both skills and concepts. Although opportunities to review concepts and skills are provided through Summarize the Mathematics tasks, On Your Own Review practice problems, and Looking Back Lessons, attention to feedback is limited to answer guides for questions and in some Instructional Notes, for example, page T221 in Course 1 and page T328 in Course 2.
Indicator 3p
Materials offer ongoing assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that standards are clearly denoted. Assessments created in the eAssessments tool through ConnectED have the ability to denote CCSSM (listed as National Standards), but standards are not explicitly identified for formative or summative assessments that are provided. Standards are identified at the beginning of each unit/lesson, but individual problems in assessments are not labeled with 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 Core-Plus Mathematics integrated series meet the expectation that assessments provided include sufficient guidance in interpreting scores by having answer keys and solutions to all assessments, detailed answers and solutions for lesson components (On Your Own homework, Check Your Understanding, Think about the Situation, and Summarize the Mathematics), and both specific and general scoring rubrics. The implementation guide also provides guidance for how to create specific rubrics for individual questions.
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 Core-Plus Mathematics integrated series partially meet the expectation that the materials support teachers in differentiating instruction for diverse learners within and across courses. The instructional materials do not provide specific strategies to aid teachers in implementing differentiated instruction, and there is not enough scaffolding provided for students whose mathematical knowledge is not at their current course level. There is a Spanish Glossary in each student textbook, and there are boxes labeled ELL Tips that give suggestions for the teacher that could aid in instruction. Parent communication is available in Spanish.
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 Core-Plus Mathematics integrated series meet the expectation that scaffolding or sequencing strategies are provided to teachers that allows the content to be accessed by all learners. Problems are often set up to engage students at multiple levels, including Investigation, Application and Extension sections with multiple representations and questioning. Content builds throughout the lessons and units to develop comprehension. Most prominent is the use of a logical sequence of questions within context to note patterns and to help students generate solutions, for example, Lesson 2 in Unit 2, Course 3.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the materials provide teachers with strategies for meeting the needs of a range of learners. Specific strategies or materials for helping teachers implement differentiated instruction for a range of learners are limited to a brief section in the Overview of each course (page xii in Course 3) and some boxes labeled Differentiation placed at different points in the courses, for example page T202 in Course 1, page T78 in Course 2 and page T58A in Course 3. There is sufficient scaffolding provided for students to obtain new knowledge when they have the prerequisite knowledge for their current course, but the instructional materials do not provide sufficient scaffolding support for teachers to address the needs of students whose mathematical knowledge is not at their current course level. Also, complex vocabulary is used within the materials and may not be accessible to all learners, and there is limited aid provided for teachers on this issue within some of the Differentiation boxes, for example, page T216 in Course 1.
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 Core-Plus Mathematics integrated series meet the expectation that the materials provide problems with multiple entry-points that can be solved through a variety of strategies or representations. Questioning can be tiered with multiple entry points sequenced for logical reasoning and content development, for example, page T252 in Course 2. Most of the multiple step questions require a majority, if not all, of the MPs, but questions can also be specific with one solution and a single entry point. As a whole, content is experienced through a variety of mathematical representations with equations, graphs, diagrams, tables, charts, and verbal explanations consistently throughout the materials, for example, Investigation 1 in Course 1, Unit 5, Lesson 1.
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 Core-Plus Mathematics integrated series partially 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). Beyond ELL, there was no support found for special populations such as students not reading at grade level. There is a Spanish Glossary in each student textbook, and there are boxes labeled ELL Tips that give suggestions for the teacher that could aid in instruction. The location of these boxes can be found in the Index of Mathematical Topics at the back of each teacher edition.
Indicator 3v
Materials provide support for advanced students to investigate mathematics content at greater depth.
The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for providing support for advanced students to investigate mathematics content at greater depth. The Implementation Guide, on page 2, states; “Differences in student performance and interest can be accommodated by the depth and level of abstraction to which core topics are pursued, by the nature and degree of difficulty of applications, and by providing opportunities for student choice of homework tasks and projects.” The extensions tasks, included in the On Your Own section of each lesson, reveal how well students are able to extend the present content beyond the level addressed in the investigations. Teachers can pick and choose assignment problems for students to meet their level of understanding or sophistication.
The teacher edition Unit Overview contains notes of what types of enrichment are available within the lessons (Course 1, Unit 6, page T361; Course 2, Unit 1, page T1D; and Course 3, Unit 3, page T161A, paragraph 4). Within the lessons, there are Differentiation boxes that supply additional enrichment ideas. (Course 1, Unit 6, page T421; Course 2, Unit 7 page 507; and Course 3, Unit 2, page T116B). A complete list of differentiation boxes can be found in the Index of Mathematical Topics at the back of each teacher edition.
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 Core-Plus Mathematics integrated series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide access to many e-tools through ConnectEd. Additionally, the technological tools provided allow teachers to create their own assessments as well as collaborate with other teachers and their students through different features within the materials.
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.