1st Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 77% |
|---|---|
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 6 / 10 |
The materials reviewed for Grade 1 partially meet the requirements for Gateway 2. All three aspects of rigor are present in the materials and they are balanced. The MPs are listed in the specifics of the lessons and the way they are listed enhances the learning. Attention is not paid to the full meaning of each MP and one lesson in each unit focuses on MP, and not content standards. The materials are not strong in their expectation for mathematical reasoning. The students and teachers are not given enough support nor is the vocabulary development sufficient. The materials reviewed for Gateway 2 meet the expectation for rigor and partially meet expectations for mathematical practices.
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 1 meet the requirements for this criterion. All three aspects of rigor are addressed individually and all three are used to deepen the understanding of the others. Conceptual understanding, fluency and application are balanced within the Grade 1 materials.
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 in Grade 1 for this indicator meet the requirements of attending to conceptual understanding within the lessons.
- In unit 4, attention is given to understanding place value and to using that understanding in addition and subtraction.
- Students work on their understanding of place value with teen numbers in a variety of ways including visualizing, modeling, classroom routines and classroom discussion.
- In unit 4, lesson 4, students are asked to make a drawing to prove that 10+3 is the same as 9+4.
- The "Formative Assessment: Check Understanding" boxes attend to conceptual understanding. These could be used for classroom discussions instead of individual assessment checks.
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 in Grade 1 for this indicator meet the requirements by attending to fluency and procedural work within the lessons. In Grade 1 this includes the ability to add and subtract within 10 (1.OA.C.6).
- Lessons include a variety of daily routines for fluency including number partners, partner houses, and add and subtract within 10.
- Lessons attend to the use of a variety of addition and subtraction strategies including the relationship between addition and subtraction, counting on, making ten and decomposing to create equivalent sums.
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 in Grade 1 for this indicator meet the requirements by attending to application within the lessons.
- Each unit ends with a real world problem to solve.
- Word problems are interspersed throughout the lessons in all units.
- Students are given opportunities to generate their own word problems.
- Multiple problem types are attended to and described for the teacher.
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 in Grade 1 for this indicator meet the requirements of providing a balance of rigor. The three aspects are not always treated together nor are they always treated separately.
- The lessons and activities within provide ample opportunity to practice all three aspects of rigor.
- The daily routines address fluency expectations, and these expectations are also embedded throughout the lessons.
- The application problems are used to develop fluency and to deepen understanding of the mathematics at hand.
- Conceptual understanding portions of the lessons address the need for fluency and use real-world situations to further explore understanding.
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 1 partially meet the requirements for Gateway 2. All three aspects of rigor are present in the materials and they are balanced. The MPs are listed in the specifics of the lessons and the way they are listed enhances the learning. Attention is not paid to the full meaning of each MP and one lesson in each unit focuses on MP, and not content standards. The materials are not strong in their expectation for mathematical reasoning. The students and teachers are not given enough support nor is the vocabulary development sufficient. The materials reviewed for Gateway 2 meet the expectation for rigor and partially meet expectations for mathematical practices.
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 1 meet the requirement of this indicator by identifying the Standards for Mathematical Practice (MPs) and using this identification to enhance the learning.
- MPs are identified in the "Getting Ready to Teach" sections in every unit.
- MPs are identified within the lessons in a way that supports the learning. For example, MP1 is identified and used in unit 2 as students act out a scenario in order to make sense of the problem.
- MP8 is identified and used to examine fluency practice cards in unit 4. Students discuss ways to use the number 10 to subtract with teen numbers attending to repeated reasoning.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The materials reviewed for Grade 1 partially meet the requirement of this indicator.
- MP1 is consistently expected as students solve problems throughout the year.
- Within unit 4 the materials identify MPs 2, 5, 6, 7, and 8 frequently.
- The full meaning of MP5 is not attended to. MP5 is noted 22 times in unit 4, but none of these offer students the opportunity to choose their own tool.
- The final lesson in each unit focuses on all 8 MPs rather than the content standards. These lessons do not attend to the full meaning of all 8 MPs.
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 1 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.
- Students are occasionally prompted to construct viable arguments.
- In differentiation cards, students are occasionally prompted to discuss their strategies with the group.
- Most of the student pages include numbers, symbols, and spaces for answers, but they do not include spaces for students to explain their thinking or opportunities to share these explanations.
- Students are asked to analyze a response from the "Puzzled Penguin," but this analysis is an opportunity for catching errors and not an opportunity for student reasoning.
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 1 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.
- The teacher's manual provides questions to promote MP3.
- Several lessons are labeled with "Math Talk in Action" as a way to promote to high quality classroom discussions.
- Teacher questions often simply ask for the answer and not the reasoning nor the opportunity to analyze arguments of other students.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Grade 1 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.
- There are vocabulary terms listed for most lessons, however this often includes strategies specific to the curriculum instead of mathematical language. For example, the phrase "partner train" is listed as a vocabulary word in unit 1. In unit 2 the phrase "circle drawing" is listed as vocabulary.
- In unit 4 lesson 8 students are asked to explain how the numbers 2, 12, and 20 are the same and how they are different. Explanations are expected to include the number word differences and also what the digit "2" represents in each number attending to precision in mathematical language.