1st Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 83% |
|---|---|
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 7 / 10 |
The instructional materials reviewed for Grade 1 partially meet the expectations for rigor and mathematical practices. The instructional materials perfectly meet the expectations for the criterion on rigor and balance, but they only partially meet the expectations of the criterion on practice-content connections because they do not fully attend to the meaning of each mathematical practice standard. Overall, the instructional materials are strong in regards to rigor, identifying mathematical practices, and the language of mathematics, but improvements can be made in consistently attending to the full meaning of practice standards where they are identified.
Criterion 2.1: Rigor
Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
The instructional materials reviewed for Grade 1 meet expectations for rigor and balance. The instructional materials give appropriate attention to conceptual understanding, procedural skill and fluency and application, and the materials address these three aspects with balance but always treating them separately and not always together. Overall, the instructional materials reflect the balances in the CCSSM, which help students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.
Indicator 2a
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The instructional materials reviewed for Grade 1 meet the expectations for giving attention to conceptual understanding. Overall, the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
- Each lesson includes a share-and-show exercise where students are asked to demonstrate conceptual understanding.
- Of the 101 lessons in the grade, 77 are primarily conceptual in nature and match the standards calling for conceptual understanding. For example, in chapter 1, lesson 6, the cluster heading for the objective is titled "Understand and Apply Properties of Operations and the Relationship between Addition and Subtraction," and the lesson uses unifix cubes to help students gain understanding of addition and subtraction.
- The beginning of each chapter has a page heading of "Teaching for Depth." For an example, see chapter 2, teacher's manual, page 65E, which identifies key ideas of which students should have a deep understanding.
- Also, all lessons have a textbox titled "Teaching for Depth," which specifically identifies what students should have conceptual understanding of in that particular lesson. For an example, see chapter 2, lesson 3, teacher's manual, page 81A.
Indicator 2b
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
The instructional materials reviewed for Grade 1 meet the expectations for giving attention to procedural skill and fluency. Overall, the materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
- In Go Math, each chapter and lesson includes connections to procedural skill and fluency. For example, in chapter 1, lesson 1, page 13A, the text identifies the "on-your-own" section to connect to this.
- In addition, there are daily routines, such as the problem of the day, where students are asked to work on their addition fluency, and the fluency builder, where students build on one at a time aloud.
- Of the 101 lessons in the grade, 24 primarily focus on procedural skill and fluency and match the standards calling for procedural skill and fluency. For example, in chapter 3, lesson 6, the objective is "add and subtract within 20, demonstrating fluency for addition and subtraction within 10," and the lesson has students practicing addition fluency.
- Each lesson has a fluency builder for the standards asking students to demonstrate fluency. For an example, see chapter 4, lesson 2, page 217B.
- See chapter 4, lesson 1, teacher's manual page 213 for an example of an "on-your-own" section.
- Each chapter has "practice and homework" to help with fluency-see chapter 4, lesson 1, teacher's manual, pages 215-16.
Indicator 2c
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
The instructional materials reviewed for Grade 1 meet the expectations for giving attention to applications. Overall, the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.
- In the section of chapter 1, lesson 1, titled "Go Deeper," teachers can have students create their own addition problem, have the class solve it and ask extending questions: "How did you find out how many there are? What is a different way to solve the problem? How did the pictures help you solve the problem? How do you know the story is an addition problem?" Also, questions 6 and 7 pay attention to an application in which students have to interpret pictures and solve a word problem.
- For example, see chapter 8, lesson 7, where questions 6 and 7 on pages 475-76 are labeled as "think smarter and go deeper" problems.
- For example, see chapter 8, lesson 9, teacher's manual, page 488.
Indicator 2d
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
The instructional materials reviewed for Grade 1 meet the expectations for balance. Overall, the three aspects of rigor are not always treated together and are not always treated separately within the materials, and there is a balance of the three aspects of rigor within the grade.
- The three aspects are all touched upon in each lesson and sometimes overlap, but they are not always treated together or always separately. For example, in chapter 1, lesson 1, question 5 is a part of the fluency portion and application portion.
- These aspects work together in some cases and are treated separately in other cases. Each chapter specifically outlines how rigor is addressed and balanced. For an example, see chapter 9, lesson 7, teacher's manual, page 549A.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The instructional materials reviewed for Grade 1 partially meet the expectations for practice-content connections. The materials meet expectations for identifying the practice standards and explicitly attending to the specialized language of mathematics, as addressed in indicators 2E and 2G.iii, respectively. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and for engaging students in mathematical reasoning as addressed in indicators 2F, 2G.i and 2G.ii. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice, the instructional materials should carefully pay attention to the full meaning of every practice standard, especially practice 3 in regards to students critiquing the reasoning of other students.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The instructional materials reviewed for Grade 1 meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the mathematical content. Overall, the instructional materials do not over-identify or under-identify the MPs, and the MPs are used within and throughout the grade.
- The identified MPs are found in the "lesson at a glance" section of each lesson. For example, in chapter 2, lesson 1, this can be found on page 69A.
- In Go Math, the MPs are identified as well as the chapters, lessons and sections where these standards are covered.
- For instance, in the teacher edition for Grade 1, chapter 8, lesson 3 covers MP3 in the "mathematics talk" section.
- More examples of MP3 are the "think smarter problems" section in chapter 12, lesson 10 and the "go deeper" section in chapter 9, lesson 7.
- In addition, each lesson identifies the individual sections where each standard for mathematical practice will be addressed.
- The practices are related to grade-level work in the "teaching for depth" section, located in the teacher's manual of each chapter-for example, see chapter 5, page 251E.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials reviewed for Grade 1 partially meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the instructional materials carefully attend to the full meaning of some of the practice standards but not all of them.
- In chapter 1, lesson 1, page 15 of the teacher edition, MP2 is referred to along with a series of questions to ask the students. The questions are very direct and do not require the students to reason abstractly or quantitatively. Another example for this practice is in chapter 7, lesson 3, page 168 of the teacher edition.
- Chapter 8 says that it will review MPs 4, 6 and 8. In the "model and draw" section, MP4 is covered. Students are asked to work through the model and the pictures together. Students are asked what they can draw to represent a problem, to represent how to find the difference, and what other ways there can be to solve a problem.
- The full meaning of MP5 is for students to consider all available tools to solve a math problem. In some instances, the Grade 1 material gives students the tool to use for solving the problem and does not ask students to choose strategically. For examples, see chapter 1, lesson 2, teacher's manual, page 21, and chapter 9, lesson 4, teacher's manual, page 532.
Indicator 2g
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2g.i
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
The instructional materials reviewed for Grade 1 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the materials consistently allow students to construct viable arguments, but they do not consistently prompt students to analyze other students' arguments.
- There are several places where MP3 is identified in the student materials, but they do not meet the intent of the practice standard. For example, in chapter 9, lessons 1, 2 and 4 identify MP3, but the question provided is a question that has a right or wrong answer and does not have students constructing viable arguments.
- In chapter 3, lesson 10, students are asked to share a strategy that they used to solve the problem. The "math talk" section prompts teachers to have students explain how they came to their answer and share their strategies, but the students are not prompted to analyze each other's strategies and answers.
Indicator 2g.ii
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
The instructional materials reviewed for Grade 1 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the materials consistently assist teachers in having students construct viable arguments, but they do not consistently assist teachers in having students analyze other students' arguments.
- There are several places where MP3 is identified, but the full meaning of the practice is not met. For example, in chapter 2, lessons 5, 7 and 8, there is no explanation for teachers on how to encourage students to participate in a conversation using viable arguments and analyzing the arguments of others. The questions often have right or wrong answers, and when they do no, they still are not asking students to explain how they went about solving a problem and then talking with others about how they solved the problem.
- When MP3 is identified, such as in the "math talk" sections, it gives students a focus. For instance, in chapter 3, lesson 10, page 185, teachers are prompted to have students share their understanding of how they combined the three addends and the strategies they use. Additionally, the curriculum provides exemplar responses, but there is no prompting for the analysis of different strategies.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The instructional materials reviewed for Grade 1 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that are consistently present throughout the materials.
- Each chapter begins with vocabulary builders and vocabulary games. An example can be found in chapter 4 on pages 209-210B.
- The lessons attend to using correct vocabulary. For example, the questions for teachers to ask use correct vocabulary. In chapter 8, lesson 3, page 454 of the teacher edition, the problems are asking students to find addends.
- In chapter 2, page 65H, there is a section on developing the language of mathematics, which identifies the vocabulary, graphic organizer strategies for teaching the vocabulary and strategies to use with English language learner (ELLs). Pages 67-68B cover strategies for building vocabulary, games to play, vocabulary flashcards, writing prompts and suggestions for how to use a mathematics journal.
- The beginning of each chapter includes a page titled "Developing Math Language." For example, see Chapter 8, teacher's manual, page 433H.