2nd 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 2 partially meet the expectations for rigor and mathematical practices. The instructional materials meet the expectations for the criterion on rigor and balance with a perfect score, but they only partially meet the expectations of the criterion on practice-content connections because of not fully attending 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 2 meet expectations for rigor and balance. The instructional materials give appropriate attention to conceptual understanding, procedural skill and fluency, and application. 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 helps 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 2 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.
- In Go Math, each lesson identifies conceptual understanding that will be covered in the lesson. In chapter 1, for instance, lesson 1 identifies number concepts (2.OA.C, 2.NBT.A, and 2.NBT.B) as a conceptual concept it will cover in the "share and show" portion of the lesson.
- In chapter 3 ("Basic Facts and Relationships"), lesson 1 (2.OA.B.2) identifies that conceptual understanding will be the focus of the lesson's "share and show" segment. This happens in questions 1-6 where students are asked to solve a problem and then identify a doubles fact that they could use to help them solve the problem. Then, teachers are prompted to ask "explain your choice."
- Of the 109 lessons in the grade, 58 are primarily conceptual in nature and match the standards calling for conceptual understanding. For example, in chapter 3, lesson 10, the cluster heading for the objective is "Work with Equal Groups of Objects to Gain Foundations for Multiplication," and the lesson has students solving problems using equal groups.
- Each lesson has a textbox titled "Teaching for Depth" that specifically identifies what students should have conceptual understanding of in that particular lesson. For example, see chapter 2, lesson 1, teacher's manual, page 75A.
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 2 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 lesson identifies where it will focus on procedural skills and fluency. For instance, chapter 3, lesson 1, page 163A identifies procedural skill and fluency to be covered in the "on your own" section.
- At the beginning of each chapter and lesson, there are daily routines where students get to practice their fluency skills. In chapter 3, page 263B, the daily routine has students write a number greater than or less than the number 256.
- Of the 109 lessons in the grade, 51 deal primarily with procedural skill and fluency and match the standards calling for procedural skill and fluency. For example, in chapter 4, lesson 1, the objective is for students to "fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction," and the lesson has them practicing addition facts.
- Each lesson has a fluency builder to build fluency of the standards asking students to demonstrate fluency. For example, this can be found in chapter 9, lesson 4 on page 621B.
- Each chapter has a section called "Practice and Homework" to practice fluency. For example, see chapter 3, lesson 1, teacher's manual, page 167.
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 2 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.
- Each lesson has problems that cover application. For instance, in chapter 3, lesson 1, page 163, application is covered in sections called "Think Smarter and Go Deeper."
- In the "think smarter" section, question 15 asks students to find a doubles fact (they have to understand their addition facts and understand number sense).
- In the "go deeper" section, teachers are prompted to give children a doubles fact, 5+5=10, and then they have to write two near-doubles facts, 5+6=11 and 5+4=9. Then, teachers are prompted to ask students how they got their answer and what they notice about the answer.
- In question 17 of chapter 3, lesson 1, students are asked to solve a word problem to find a doubles fact by using clues, and in question 18, they have to use doubles facts to determine if it would help them solve the problem 4+5.
- In chapter 6, lesson 2, problem 9 from the "think smarter and go deeper" problem is an application problem.
- There are also application problems in the "think smarter and go deeper" problems found in chapter 6, lesson 4, page 412 of the teacher edition.
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 2 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.
- In each lesson and chapter in Go Math, the three elements of rigor are identified. Each element of rigor can be covered within a lesson, and sometimes they overlap. For instance in chapter 3, lesson 1, students are asked to solve problem 15, and it is considered both a procedural problem as well as an application problem.
- Each chapter specifically outlines how rigor is addressed and balanced. For example, see chapter 8, lesson 1, teacher's manual, page 541A.
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 2 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 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 attend to the full meaning of every practice standard, especially MP3 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 2 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, which are used within and throughout the grade.
- Each lesson has MPs identified, and they are used to enrich the content of the work. The identified MPs are found in the section called "Lesson at a Glance" of each lesson. For example in chapter 1, lesson 1, this can be found on page 13A.
- In the Grade 2 teacher edition's planning guide on page 23, the materials identify questions that address the standards for mathematical practice.
- On pages 24-29, the materials identify some of the sections and specific lessons that will cover each standard.
- At the beginning of each lesson and within each lesson, the standards for mathematical practice are identified.
- The practices are related to grade-level work in the "teaching for depth" section, which is located in the teacher's manual of each chapter. For example, see Chapter 7, teacher's manual, page 463E.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials reviewed for Grade 2 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 for all of them.
- In chapter 3, lesson 9, page 211 of the teacher edition, MP2 (thinking and reasoning) is referred to along with questions to ask the students. The question is direct and does not require the students to reason abstractly or quantitatively.
- In chapter 4, lesson 9, page 285 of the teacher edition, MP2 is referenced along with questions to ask the students. By asking the questions the way they are stated, the teacher is does not require students to engage in their own thinking and reasoning.
- In chapter 1, lessons 7 and 8, there are examples of MP1 (making sense of problems and persevering in solving them).
- The full meaning of MP5 is for students to consider all available tools to solve a math problem. In chapter 10, lesson 6, on page 686 of the teacher's manual, students are asked to read a line plot instead of choosing an appropriate tool.
- In chapter 9, lesson 1, page 604 of the teacher's manual under the "model and draw" section, students are given unit cubes to measure rather than choosing the best measurement tool.
- In chapter 8, lesson 2, page 548 of the teacher's manual under the "model and draw" section, students are given 8-inch paper strips and tiles to complete measurement work.
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 2 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.
- Chapter 8, lesson 8, page 586 of the student edition identifies activities in which students will engage in MP3, but it does not have any direction for having students to create an argument or engage with other students.
- Chapter 9, lesson 3, page 615 of the student edition identifies activities in which students will engage in MP3, but the students are not engaging with one another.
- An example of partially meeting the standard is found in chapter 6, lesson 8, page 435 of the student edition, where students are asked to describe how they did their subtraction. However, they are not asked to defend their argument or critique the arguments of others.
- In chapter 11, lesson 6, students are asked to write and justify rules that apply to shapes, but they are not prompted to analyze the arguments of others.
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 2 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 mathematical practice 3 is identified, however the materials do not always meet the full meaning of the practice. For example, in chapter 4, lesson 3, page 251 of the teacher edition, MP3 is listed, but instead of having students construct an argument and critique the reasoning of others, it is a right or wrong question.
- In chapter 4, lesson 8, page 281 of the teacher edition, students are paired but not constructing viable arguments.
- An example of partially meeting the standard is found in chapter 4, lesson 6, page 270 of the teacher edition. Students are critiquing the reasoning of "Abby," but they are not involved in creating their own arguments.
- Materials assist teachers in helping students make viable arguments, but the materials do not assist in analyzing the arguments of others. For examples see chapter 1, lesson 2, teacher's manual, page 21 in the "go deeper" section and chapter 4, lesson 6, teacher's manual, page 270.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The instructional materials reviewed for Grade 2 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.
- Each chapter begins with vocabulary builders and vocabulary games. An example can be found in chapter 5 on pages 315-16B.
- The lessons pay attention to using correct vocabulary. For example, the questions for teachers to ask use correct vocabulary. In chapter 5, lesson 4, page 335 of the teacher edition, the questions for teachers to ask students use correct vocabulary such as "regroup."
- In chapter 1, page 9H, "developing mathematics language" is identified as part of the chapter vocabulary, vocabulary strategies using a graphic organizer and ELL activities to help build vocabulary. Pages 11-12D include vocabulary builders, a preview, games to help review and learn vocabulary, recommendations for how to use a mathematics journal, and a writing activity involving mathematics.
- The beginning of each chapter includes a page called "Developing Math Language." For example, see chapter 9, teacher's manual, page 599H.
- The introduction of each chapter also has activity to help students build vocabulary. For example, see chapter 9, teacher's manual, page 601.
- Additionally, each chapter includes a vocabulary game. For example, see chapter 9, teacher's manual, pages 602A and 602B.