8th Grade - Gateway 3
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Usability
Gateway 3 - Partially Meets Expectations | 78% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 8 / 8 |
Criterion 3.3: Assessment | 6 / 10 |
Criterion 3.4: Differentiation | 8 / 12 |
Criterion 3.5: Technology |
Criterion 3.1: Use & Design
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
The instructional materials for The Utah Middle School Math Project Grade 8 meet the expectations for use and design. Materials are well-designed, and lessons are intentionally sequenced. Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter. Students produce a variety of types of answers including both verbal and written answers. Manipulatives are used in 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 for Grade 8 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.
The chapters begin with a non-routine problem that introduces new concepts and is labeled as an Anchor Problem. The chapters are subsequently sectioned into Class Activities, Homework, and Assessments.
Generally, each Class Activity has problems to solve together as a class with instructor guidance. Occasionally, they are intended to review previous grades concepts in order to connect them to eighth grade concepts. Most often, the Class Activities are for the students to apply what they have already learned.
The mathematics taught in each Class Activity is reinforced by an accompanying Homework component.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The instructional materials for Grade 8 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.
Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter.
Within each chapter, concept development is sequential. During Class Activities, the teacher introduces new concepts or builds upon prior knowledge. Students work individually or as a whole class when engaged in the Class Activities. The Homework component reinforces the mathematical concepts taught during the previous Class Activity. Spiral Reviews are used to provide continued practice of newly learned mathematical concepts throughout the year.
The progression of lessons taught is intentional and assists students in building their mathematical understanding and skill. Students begin with activities to build conceptual understanding and procedural skill, and progress to applying the mathematics with more complex problems and procedures.
Indicator 3c
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
The instructional materials for Grade 8 meet the expectation for the variety in what students are asked to produce.
Throughout the Class Activities, students are asked to produce answers and solutions, discuss ideas, make conjectures, explain solutions and justify reasoning, make sketches and diagrams, and use appropriate models. These aspects are found individually within problems as well as in combination with others, such as provide an explanation of a solution and include a diagram.
- Chapter 1 Class Activity 1.1a: Students examine the models and write the simplified form of the expressions. Subsequent tasks require students to evaluate expressions and produce a model for a given expression.
- Chapter 1 Homework 1.1a: Students are asked to “identify the mistake, explain it, and simplify the expression correctly.”
- Chapter 1 Class Activity 1.1c: Students are asked to “model and solve the following equations. Show the solving action, and verify your solution.”
Indicator 3d
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The instructional materials for Grade 8 meet the expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models.
Algebra tiles are used to model and simplify linear expressions. In Class Activity 1.1a, Question 5 reads, “Using your tiles, model the expression 2(2???? − 1). a. Write the simplified form of this expression. b. Evaluate this expression when ???? = 0.”
Number lines are used to model the approximate location of irrational numbers. In Class Activity 7.3d, Question 1 reads, “Between which two integers does the square root of 5 lie? a. Which integer is it closest to? b. Show its approximate location on the number line below. c. Now find the square root of 5 accurate to one decimal place. Show its approximate location on the number line below.”
Indicator 3e
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.2: Teacher Planning
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
The instructional materials for The Utah Middle School Math Project Grade 8 meet the expectations for supporting teachers’ learning and understanding of the standards. The instructional materials provide questions that support teachers in delivering quality instruction. The teacher’s edition is easy to use and consistently organized and annotated. The teacher’s edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.
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 for Grade 8 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
- Anchor Problem 2.0 focuses on proportionality and unit rate as students connect prior learning from 6th and 7th grade. The teacher notes guide the students’ mathematical development for question 5 by stating, “At this point have students divide these quantities to see that they are proportional to the unit rate.”
- Class Activities are the guided lessons where a teacher facilitates students through conceptual, procedural, and application work. In Class Activity 2.2d, “Rate of Change in a Linear Relationship,” teachers are prompted to, “ask students to interpret what it means if the line is going up and if the line is going down. Also discuss the possibility of a negative rate of change.”
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 materials for Grade 8 meet expectations for containing a Teacher Workbook that has ample and useful annotations and includes suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
- The Teacher Workbook offers suggestions and annotations, labeled in red, on how to present the content.
- Section 3.0 Anchor Problem: Suggestions on how to present finding solutions to a linear equation include, “It might be helpful to demonstrate how the line is formed by the solutions to the equation above. Project the grid on the board and ask students to come up and plot an ordered pair that is a solution to the equation. They will soon see that the ordered pairs follow a pattern. Some students may even come up with solutions that include fractions. If not, ask them if there are solutions that fall between integer ordered pairs. Begin filling in all of these solutions as well. Soon a line will start to appear because all of the fractional solutions will start to “merge” together. You could have this discussion either before or after students do problems #21-23.”
- There are suggestions occasionally placed as to common student mistakes and misconceptions that teachers could expect. In Chapter 4 Class Activity 4.1b, the teacher notes read, “A common mistake here is for students to neglect the scales on the axes. You may want to remind students to take note of the scales.”
- Scaffolding is provided as, "remind students that...” or “probe students to think..."
- A small number of links are embedded to assist in presenting the material. However, geometry software and graphing calculators are mentioned for students to use.
Indicator 3h
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
The instructional materials for Grade 8 meet expectations for containing a Teacher Workbook that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
- Mathematical Foundations, written for each chapter, is a resource for teachers to understand the mathematics of the chapter and for teachers to expand their understanding of the mathematical concepts.
- Each Mathematical Foundations includes problems, explanations of problems, examples, and connections to CCSSM.
- The Teacher Workbook provides clear, step-by-step solutions.
Indicator 3i
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
The instructional materials for Grade 8 meet expectations for containing a teacher edition (in print or clearly distinguished and accessible as such in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.
- Each chapter contains an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior modules and/or grades is explicitly called out in this section. The Prior Knowledge section for chapter 7 states, “Students have worked a great deal with rational numbers up to this point. They have defined and worked with the subsets of rational numbers. They have represented rational numbers on a number line, expressed rational numbers in different but equivalent forms, and operated with rational numbers.”
- The teacher edition connects the learning from previous grade levels and explains how standards build on one another throughout the program. The chapter overview for chapter 1 states, “Later in this book, students will analyze and solve pairs of simultaneous linear equations. They will also create and solve linear equations in two-variables to solve real-world problems. A student’s understanding of how to solve a linear equation using inverse operations sets the foundation for understanding how to solve simple quadratic equations later in this course and additional types of equations in subsequent coursework.”
Indicator 3j
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
Indicator 3k
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3l
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.3: Assessment
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
The instructional materials for The Utah Middle School Math Project Grade 8 partially meet expectations for providing teachers resources and tools to collect ongoing data about student progress. There are no assessments that purposely identify prior knowledge within and across grade levels. There are some suggestions in the teacher materials that identify common misconceptions and errors, but there are no specific strategies to address these when they arise. Opportunities for ongoing review, practice, and feedback occur in various forms. Standards are identified that align to the section, and there is mapping of Standards to items for the Self-Assessments. There are opportunities for students to monitor their own progress.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
The instructional materials for Grade 8 partially meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. While no explicit method for assessing student’s prior knowledge is used, there are some ways that the materials lead to gathering this information.
The materials provide teachers with strategies on how to use the Self-Assessment for Section 2.1 as a formative assessment. The description on page (8WB2 - 37) states, “This self-assessment is meant to be used as a formative assessment and is one way to assess how students are doing toward mastery of the skills and concepts in a particular section. Teachers should guide students through this self-assessment by asking probing questions of the students. This is also a resource for teachers to analyze, to assess whether the class as a whole is ready to move on or not. There are many ways that you can use this self-assessment. For example, you could have students complete each example problem and use it as a quiz. Tell your students to read each Skill or Concept and answer the corresponding problem that relates to the skill. Then grade the quiz together as a class. At this point, have students rate their mastery level based off of how they performed on the quiz, using the rubric. Come up with the criteria for the rubric together as a class. Some sample criteria are provided.”
The teacher notes give suggestions on how to proceed with instruction when students may or may not have demonstrated mastery of a topic, however, there is no guidance on how to gather the information needed to determine mastery.
Chapter 1, Chapter Overview (8WB1 - 2) states, “It is encouraged that you move on from chapter 1 after the recommended time frame even if students have not demonstrated mastery of this topic. Students will likely require additional practice throughout the year in order to master the skill of solving complicated linear equations. We have incorporated this practice in spiral reviews, and we encourage you to continue to practice this skill throughout the year.”
Chapter 2, Section 2.1a Overview (8WB2 - 9) states, “Section 2.1a is a review of proportional relationships from 7th grade. Depending on the background knowledge of your students you may decide to skip some of the problems in this section. Be sure to assess the needs of your students as you decide which problems you are going to have them do. In addition, look at Chapter 4 in the 7th grade textbook and workbook to see examples of the foundation of which understanding is built for proportional relationships.”
Indicator 3n
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
The instructional materials for Grade 8 partially meet expectations for identifying and addressing common student errors and misconceptions. Materials provide occasional suggestions for teachers to identify and address common student errors and misconceptions.
Student misconceptions are often identified for the teachers, however, instructional plans to address these misconceptions are not detailed. The suggestions to address misconceptions consist of phrases such as, “Remind the students…, Discuss with students…, Point out that…..”
Chapter 2, Class Activity 2.2b, Representations of a Linear Pattern: “Many students will draw a continuous graph, even though this is a discrete situation. This is not the focus of this lesson, but you can discuss this if you feel it is appropriate. Students will expand their understanding of discrete functions when they study sequences in Secondary I.”
Chapter 6, Class Activity 6.2b, Fit a Linear Model to Bivariate Data: “You may want to point out to students that the plot shows a positive association, and the slope is also positive.”
Indicator 3o
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
The instructional materials for Grade 8 meet expectations for providing opportunities for ongoing review and practice for students in learning both concepts and skills.
Over the course of each chapter, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support within the Class Activities to independent problem solving within the Homework. The Anchor Problems at the beginning of each chapter incorporate review and practice of previously taught standards.
- Chapter 1. Class Activity 1.2b, Teacher Note: “Again, there are many different ways to solve the given equation and arrive at the correct solution; however some solution pathways are easier than others. Practice develops a sense of the solving sequence that is the easiest and most direct path to the solution.”
- Chapter 2, Section 2.1a, Overview contains a teacher note that states, “Section 2.1a is a review of proportional relationships from 7th grade.”
- Anchor Problems engage students in both previously-taught standards as well as standards that are to be covered in the chapter. The Anchor Problems often guide the teacher to return to the problem while working through the concepts in the chapter. Anchor Problem 5.0: Waiting at the DMV reads, “This anchor problem can be done intermittently throughout the chapter. You may choose to have students work on pieces of the problem and then return to the problem throughout the chapter. This problem could also be used as a culminating task.” The Anchor Problems are also embedded with the review of previously taught standards. Anchor Problem 7.0: Zooming in on the Number Line, states, “The problems below are a review of skills learned in 6th and 7th grade. In 6th and 7th grade, students used the number line as a model for thinking about numbers.”
- Mathematical concepts are reinforced by an accompanying Homework component for each Class Activity that is designed for individual practice.
Indicator 3p
Materials offer ongoing formative and summative assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
The instructional materials for Grade 8 partially meet expectations for offering summative Self-Assessments for the students denoting which standards are being emphasized.
- Each standard that is being emphasized is noted within the “Concepts and Skills to be Mastered” at the beginning of each section.
- There are no summative assessments provided within the instructional materials. The assessments for this program consist solely of each section's Self-Assessment.
- Self-Assessments are developed to assess particular standards, and the scoring guidelines specifically use the wording of these standards.
Indicator 3p.ii
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The instructional materials for Grade 8 partially meet expectations for assessments including scoring guidelines that provide sufficient guidance to teachers in interpreting student performance but do not include suggestions for follow-up.
- Each Self-Assessment includes a scoring guideline as well as worked-out solutions for correct responses.
- The scoring guidelines are easy to understand and interpret.
- Self-Assessment scoring guides are provided, but follow-up suggestions based on scoring criteria are not provided.
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 for The Utah Middle School Math Project Grade 8 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. Activities provide students with multiple entry points and a variety of solution strategies and representations. However, the materials provide few strategies for ELL students, special populations, or to challenge advanced students to deepen their understanding of the mathematics.
Indicator 3r
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
The instructional materials for Grade 8 partially meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
The sequencing and scaffolding are built into lesson development so that teachers pose problems as they progress through more rigorous processes or skills. However, if students need additional support, the guidance is not explicit.
The scaffolding guidance for Chapter 10, Class Activity 10.1b, “Special Angles Formed by Transversals,” reads, “Before you begin the activity below you might find it helpful to review the words in the table below with your class. Ask them, 'When you hear the following words, what do you think of? What key words or ideas will help you remember what these words mean?' Write the graphic organizer below together as a class on the board for students to refer to as they complete the activity.” There are no strategies provided for students who may still need additional support after the activity is complete.
Advanced students have “Honor” class extensions that involve more rigorous topics from later grades that can be used at teacher discretion, such as Class Activity 5.2a, question 4. The teacher notes state, “The equation that models this relationship is y = x^2 + x + 4. It is not expected that students will be able to come up with this equation in Grade 8; however, you may challenge your honors students to try to do this. One equation that models this situation is shown below. It has been color-coded to show how the equation connects to the geometric model.” Writing a quadratic equation is a high school standard.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
The instructional materials for Grade 8 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners.
The Teacher Workbook includes limited notes providing some strategies to help teachers sequence or scaffold lessons. The notes are concise, such as, "ask students," "remind students of a definition," or “point out to students.”
Chapter 5, Class Activity 5.1e, “More About Functions” contains a teacher note that reads, “This is a good time to point out to students that the independent variable is graphed on the x-axis and the dependent variable is graphed on the y-axis.”
Chapter 9, Class Activity 9.1f, “Congruence cont.” provides the following teacher note at the end of the activity: “Review with students the definition of congruence – a figure is congruent to another if the second can be obtained from the first by a sequence of rigid motions (rotations, reflections, and translations). It will help with the corresponding homework.”
Indicator 3t
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
The instructional materials for Grade 8 partially meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Tasks allow students to use multiple entry points and to solve problems using a variety of strategies, paths, and/or models. In the Chapter 5 Anchor Problem, “Waiting at the DMV,” students are asked to find an estimated time that Nazhomi will make it to the front of the line by analyzing the given information of times that others were called to the desk, time when employees are at lunch, and when Nazhomi needs to leave. This problem requires students to make their own assumptions and simplifications.
Teachers are asked to model various solution strategies and to lead students through finding a solution path.
Indicator 3u
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
The instructional materials for Grade 8 partially meet expectations for suggesting options for 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). Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners. The notes in the Teacher Workbook use suggestions like, "give students time to analyze..." or "remind students of a definition." The suggestions are not specific to the content being taught.
Indicator 3v
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
The instructional materials for Grade 8 partially meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.
- Extension problems are placed sporadically throughout the materials, however, it is unclear if extension problems are optional for the entire class, scaffolded for the class, or explicitly for students who need advanced mathematics. Chapter 2, Homework Activity 2.2a, “Connect the Rule to the Pattern” (page 8WB2 - 44): “Extension: Compare this pattern to pattern 2 in class. How are the patterns the same, and how are they different? How is the difference reflected in the rules? Will the two patterns ever have the same number of tiles?”
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
The instructional materials for Grade 8 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.
- No examples of bias were found.
- Pictures, names, and situations present a variety of ethnicities and interests. Chapter 4, Class Activity 4.2b questions 19 and 20, “Nettie’s Bargain Clothing is having a huge sale. All shirts are $3 each, and all pants are $5 each. You go to the sale and buy twice as many shirts as pants and spend $66,” and “Xavier and Carlos have a bet to see who can get more 'friends' on a social media site after 1 month. Carlos has 5 more friends than Xavier when they start the competition. After much work, Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends together.”
Indicator 3x
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3y
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.5: Technology
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
The instructional materials for The Utah Middle School Math Project Grade 8 provide limited support for the effective use of technology to enhance student learning. The materials are available for download online using Microsoft Word which would allow access from multiple operating systems. The suggested (optional) technology is intended to be used for students developing an understanding of the mathematical content. The technology provides limited opportunities to personalize instruction, and suggestions for customization are not provided. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.
Indicator 3aa
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
Indicator 3ab
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3ac
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Indicator 3ad
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
Indicator 3z
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.