6th Grade - Gateway 2
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Rigor & Mathematical Practices
| Score | |
|---|---|
Gateway 2 - Does Not Meet Expectations | 38% |
Criterion 2.1: Rigor | 4 / 8 |
Criterion 2.2: Math Practices | 3 / 10 |
The materials reviewed for Grade 6 do not meet the expectations for rigor and balance. Conceptual understanding is not attended to thoroughly setting explicit expectations for understanding or interpreting. Each lesson is launched with a real-world situation but they are often application problems that do not support building conceptual understanding. There are insufficient problems designed to build fluency, particularly within dividing multi-digit numbers and adding, subtracting, multiplying and dividing multi-digit decimals. The enrichment project for each unit is the major resource for application with multi-steps. Within the lessons there are many real-world problems, but few that are also multi-step problems. There is an attempt to balance conceptual and procedural work. The materials reviewed for Grade 6 do not meet the expectations for practice-content connections. While the MPs are included and labeled in the launch of each lesson and the focus question, they are not identified in the in-class teaching notes and are missing in other areas of the curriculum. A teacher who is not familiar with the MPs would not be able to use the information given on the individual lessons to educate the students on how to use the MPs to assist in solving a math problem. On some lessons the MPs are used well, and other lessons are mislabeled as being aligned to certain MP. Materials have students constructing arguments through certain routine problems such as reasoning, reflecting, writing and error analysis. These problems appear in each lesson in the same way, so the depth of the MPs is not able to fully develop. Students are prompted to construct arguments through some of the questions, but the students frequently do not need to analyze problems in-depth in order to make these arguments. The teacher notes do not indicate how they can assist their students in the MP. This series does not meet the standard to explicitly attend to the specialized language of mathematics. It often uses vocabulary that is not precise and does not allow for the student to be completely immersed in the language of mathematics.
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 materials reviewed for Grade 6 do not meet the expectations for rigor and balance. Conceptual understanding is not attended to by thoroughly setting explicit expectations for understanding or interpreting. Each lesson is launched with a real-world situation, but these launches prioritize application over building conceptual understanding. There are too few problems and practice designed to build fluency, particularly in dividing multi-digit numbers and adding, subtracting, multiplying and dividing multi-digit decimals. The enrichment project for each unit is the major resource for application with multi-steps. Within the lessons there are many real-world type problems but very few that are multi-step problems. There is an attempt to balance conceptual and procedural work.
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 materials reviewed for Grade 6 partially meet the expectations for developing conceptual understanding of key mathematical concepts.
- There are multiple representations used including verbal descriptions, graphs, number lines, tables and equations.
- Conceptual understanding is not thoroughly addressed by setting explicit expectations for understanding or interpreting. For example, 6.RP.A.3 specifically calls for tape diagrams and double number lines to show student understanding in regards to ratios. There is one number line in Digits.
- Each lesson is launched with a real-world situation, emphasizing application but not supporting building conceptual understanding.
- One example of building conceptual understanding is topic 6 on the division of fractions.
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 materials reviewed for Grade 6 partially meet expectations for attending to the expectation of procedural skill and fluency.
- The fluency standards for Grade 6 are 6.NS.B.2 and 6.NS.B.3. Lesson 7-3 is the only lesson focused on fluently dividing multi-digit numbers (6.NS.B.2).
- Lessons 7-1 through 7-4 address 6.NS.B.3 to fluently add, subtract, multiply and divide multi-digit decimals for each operation.
- Lessons 7-5 and 7-6 compare decimals and fractions.
- Lesson 7-7 solves real-world problems involving the operations with decimals.
- The materials do not include many opportunities for students to practice fluency.
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 materials reviewed for Grade 6 partially meet the expectations for spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.
- The enrichment project for each unit is the major resource for multi-step application problems.
- There are many real-world type problems, but few multi-step problems within the lessons.
- Students do not have many chances to model their thinking in a variety of instances while solving problems.
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 materials reviewed for Grade 6 partially meet the expectations for balance between the three aspects of rigor with the grade.
- Each lesson begins with a launch that includes a real world situation and conceptual base.
- In the "Got It" sections, there are problems that are procedural and applications of the mathematical topic.
- There is an attempt to balance conceptual and procedural work.
- The piece missing is enough practice for fluency of dividing multi-digit numbers; and adding, subtracting, multiplying and dividing multi-digit decimals.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The materials reviewed for Grade 6 do not meet the expectations for practice-content connections. While the MPs are included and labeled in the launch of each lesson and the focus question, they are not identified anywhere in the in-class teaching notes and are missing in other areas of the curriculum. Problems often include too much scaffolding to enrich the mathematics for students. A teacher who is not familiar with the MPs would not be able to use the information given on the individual lessons to educate the students on how to use the MPs to assist in solving a math problem. On some lessons the MPs are used well and other lessons are mislabeled as being aligned to certain MPs. Materials have students constructing arguments through certain routine problems such as reasoning, reflecting, writing and error analysis. Students are prompted to construct arguments through some of the questions; however, the students frequently do not need to analyze problems in-depth in order to make these arguments. The teacher notes do not indicate how they can assist their students in the MPs. This series does not meet the standard to explicitly attend to the specialized language of mathematics. It often uses vocabulary that is not precise and does not allow for the student to be completely immersed in the language of mathematics.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The materials reviewed for Grade 6 partially meet the expectations for identifying and using the Standards for Mathematical Practice (MPs) to enrich mathematics content.
- While the MPs are included and labeled in the launch of each lesson and the focus question, they are not identified anywhere in the in-class teaching notes or in other areas of the curriculum.
- The questioning strategies offered in the program overview guide are the best examples of how to assist the educator to lead their students into applying the MPs to enrich the mathematics content.
- Each lesson has students using a variety of MPs to enrich the lesson, but need explicit teacher support in order to ensure students practice these skills. The teacher would need to help students recognize what practices and skills they are employing to solve problems, and ensure students are using tools appropriately in practicing a standard.
- MP4 on modeling is referred to often, but these lessons miss the opportunity to also practice MP5, which requires students to select the appropriate tool, in order to solve real-world problems.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The materials reviewed for Grade 6 do not meet the expectations to carefully attend to the full meaning of each practice standard.
- A teacher who is not familiar with MPs would not be able to use the information given in the individual lessons to educate the students on how to use the MPs to assist in solving a math problem.
- The materials have inconsistent quality in terms of implementing the MPs. Some lessons incorporate the MPs well, while others indicate that practices are present where they are not.
- Even though each lesson details which practices are correlated, only certain problems within the lessons are labeled as meeting the MPs, making it difficult to determine how the lesson truly meets the standards.
- The problems do not reflect the full meaning of the MPs. For example, the problems want students to explain their work in order to satisfy MP3 and do not ask students to critique the reasoning of others.
- One example of the materials not reaching the full meaning of MP3 and being inconsistent is in lesson 1-1.
- In Lesson 1-1, the launch is a broad problem with multiple answers that uses MPs 1 and 2 well. Students would be making conjectures and planning solutions. They would make sense of quantities and their relationships.
- The focus question for Lesson 1-1 is labeled as aligned to MPs 2 and 4; however, the students neither reason abstractly nor model in order to answer the question.
- There is no evidence of MPs 3, 6, 7 and 8 in the materials for lesson 1-1; however, the program overview guide lists those MPs next to the lesson.
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 materials reviewed for Grade 6 partially meet the expectations for prompting students to construct viable arguments and analyzing the arguments of others.
- Materials have students constructing arguments through certain routine problems such as reasoning, reflecting, writing and error analysis.
- These problems appear in each lesson in the same manner, which leads to less depth in the practice of the MP.
- While the essence of standard for MP3 is in lessons in Grade 6, students are not directly prompted to "construct viable arguments."
- Students are prompted to construct arguments through some of the questions in each lesson, but in many cases parts of the answers are already given to the students in advance and they do not need to think deeply about the answer. For example, in the lesson 4-4, "Do You Understand," there is an error analysis on writing an equation for a situation and students have to find the error. This question does not require the students to fully reason and construct arguments because they have already been told it is incorrect.
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 materials reviewed for Grade 6 do not meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
- The attempt is present to assist teachers in engaging students in constructing viable arguments, but it is only found in the program overview guide and it is not embedded in the teacher notes or instructions to be included in each lesson.
- The teacher notes do not indicate how to assist their students in the MPs.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Grade 6 partially meet the expectations for explicitly attending to the specialized language of mathematics.
- This series does not explicitly attend to the specialized language of mathematics.
- The materials often use vocabulary that is not precise and does not allow for the student to be immersed in the language of mathematics.
- A vocabulary lesson is at the end of each topic. While this structure could support the development of mathematical language, they are isolated lessons.
- The focus questions that conclude each lesson are often based on explaining the vocabulary focus of a lesson. For example, in Lesson 1-2, students need to understand the term "variable" to answer the question, "What does a variable allow you to do that you couldn't do before?"