8th 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 8 do not meet the expectations for rigor and balance. Conceptual understanding is not attended to by setting explicit expectations for understanding or interpreting. Each lesson is launched with a real-world situation but they often focus on practicing application and not on building conceptual understanding. There is not enough practice to build fluency. 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. There are not enough problems to support developing fluency, particularly in solving linear equations in one variable and estimating solutions by graphing the equations. The materials reviewed for Grade 8 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 are too simple with 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. The materials suggest that certain MPs are used, when they clearly are not. On other lessons, they are used well. There is too much inconsistency within this series in their use. Materials have students constructing arguments through certain routine problems such as reasoning, reflecting, writing and error analysis. The attempt is there to prompt students to construct viable arguments with some of the questions used in each lesson, but the ability to have true mathematical discourse in the lessons is not strong. The teacher notes do not indicate how they can assist their students in using the mathematical practices. This series does not meet the standard for explicitly attending 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 8 do not meet the expectations for rigor and balance. Conceptual understanding is not attended to by setting explicit expectations for understanding or interpreting. Each lesson is launched with a real-world situation, which often support application but not building conceptual understanding. There are not enough problems that support building fluency. The enrichment project for each unit is the major resource for application with multi-step problems. Within the lessons there are many real-world type problems but few that are multi-step problems.
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 8 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 attended to thoroughly by setting explicit expectations for understanding or interpreting.
Each lesson is launched with a real-world situation, but they often emphasize application instead of building conceptual understanding. For example, Lesson 6-1 has a launch about when two runners will pass one another, and later there is a problem about comparing the lengths of two shark species. These lessons begin to support the development of conceptualizing systems of equations, but are not deepened in order for students to develop a solid understanding.
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 8 partially meet expectations for attending to the expectation of procedural skill and fluency. The fluency standards for Grade 8 are 8.EE.C.7 and 8.EE.C.8.B.
Solving linear equations in one variable (8.EE.C.7) is taught in lessons 2-1, 2-2, 2-4 and 2-5. There are not many practice problems designed to promote fluency with this skill.
Topic 6 addresses 8.EE.C.8.B on solving systems of two linear equations in two variables, and there are not many practice problems designed to promote fluency with this skill.
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 8 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 application with multi-steps.
Within the lessons there are many real-world type problems, but few multi-step problems.
Students are often asked to determine the answer or explain (conceptual understanding) a problem, but 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 8 partially meet the expectations for balance between the three aspects of rigor with the grade.
Each lesson begins with a launch that is a real-world situation and conceptually based. 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.
There are not enough problems to support developing fluency, particularly in solving linear equations in one variable and estimating solutions by graphing the equations.
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 8 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. The materials have inconsistent quality in terms of implementing the MPs. Some lessons incorporate the MPs well, while others indicate that they are present where they are not.
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 MP is not able to fully develop. The attempt is there to prompt students to construct viable arguments with some of the questions used in each lesson, but the ability to have true mathematical discourse in the lessons is not strong. 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.
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 8 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 and are missing in other areas of the curriculum.
The questioning strategies offered in the program overview guide are the best example 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 these students practice these skills. For example, the teacher would need to help students recognize what practices and skills they are employing to solve problems, and to show students that they are using tools appropriately and practicing that 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 8 do not meet the expectations to carefully attend to the full meaning of each practice standard.
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.
The materials have inconsistent quality in terms of implementation. Some lessons incorporate the MPs well, while others indicate that they are present when they are not.
Even though each lesson details which MPs are correlated, only certain problems within the lessons are listed with the MPs making it difficult to determine how the lesson truly meets the practices.
The problems do not reflect the full meaning of the MP3, because they ask students to explain their work but not to critique the reasoning of others.
One example of the materials not reaching the full meaning and being inconsistent is in lesson 12-2. The launch does use MP1 and MP3 because the problem is large enough to require problem solving and perseverance and students have to construct a viable argument.
The focus question is to tell how side lengths of a right triangle and squares are related. This is a definition, so MP2 and MP8 are not used even though it is stated that they are used.
There is not evidence of the claim of MPs 6 and 7 that are listed in the program overview guide in the student or teacher materials for Lesson 12-1.
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 8 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, so the depth of the practice is not able to fully develop.
While the essence of Standard for MP3 is in lessons in Grade 8, students are not directly prompted to "construct viable arguments."
The attempt is there to prompt students to construct viable arguments with some of the questions used in each lesson, but the ability to have true mathematical discourse in the lessons is not strong.
The "Do You Understand" section attempts to do this with reasoning and error analysis questions.
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 8-6, 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 8 do not meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
The attempt is there to assist teachers in engaging students in constructing viable arguments, however, it is really only found in the program overview guide and not in the teacher notes that it will support this practice to be a major part of each day's lesson.
The teacher notes do not indicate how they can assist their students in the MP.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Grade 8 partially meet the expectations for explicitly attending to the specialized language of mathematics.
This series falls short in explicitly attending 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.
At the end of each topic is a vocabulary lesson. While this structure could support the development of mathematical language, they are presented as isolated lessons.
The focus questions to end each lesson are often based on explaining the vocabulary focus of a lesson. For example, in lesson 7-3, students must understand the term "linear function" in order to answer the focus questions, "What are linear functions? How are linear functions useful?"