2nd Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 66% |
|---|---|
Criterion 2.1: Rigor | 6 / 8 |
Criterion 2.2: Math Practices | 6 / 10 |
The materials reviewed for Grade 2 partially meet the requirements for Gateway 2. All three aspects of rigor are present in the materials, but they are not balanced. There is a prevalence of procedural lessons, problems and assessment items. There are few conceptual understanding lessons, problems or assessment items. 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 MPs separately from 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 do not align with the expectations for rigor and 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 2 partially meet the requirements for this criterion. All three aspects of rigor are present in the materials, but they are not balanced. There is a prevalence of procedural lessons, problems and assessment items. There are few conceptual understanding lessons, problems and assessment items. The balance of rigor in the standards is not present in the materials for Grade 2.
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 2 for this indicator partially meet the requirements of attending to conceptual understanding within the lessons.
- In unit 2 students use place value "secret code" cards and layered place value cards and are expected to write expanded form. Throughout the rest of the lessons there is a lack of emphasis on place value strategies.
- Place value work is often procedural and building conceptual understanding of place value is not prevalent.
- 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 2 for this indicator meet the requirements by attending to fluency and procedural work within the lessons. In Grade 2 this includes adding and subtracting single digit sums from memory (2.OA.B.2) and fluently adding and subtracting within 100 using strategies (2.NBT.B.5).
Lessons include quick practice for fluency.
Lessons include targeted practice in fluency.
● Student workbook includes opportunities 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 in Grade 2 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.
- In unit 6, students are working with mixed operation problems.
- By unit 7, students are working with 2-step 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 2 for this indicator partially meet the requirements of providing a balance of rigor. The three aspects are not always treated together nor are they always treated separately.
- While all three aspects of rigor are included, there is a heavy emphasis on procedures and a lack of emphasis on conceptual understanding.
- Within the assessments there are more procedural questions and very few conceptual or application problems.
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 2 partially meet the requirements of this criterion. 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 only on the practices and not the 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.
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 2 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, in unit 6 MP6 is identified as students are asked to explain 3-digit subtraction using place value words. This is a way to use vocabulary to enhance the learning.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The materials reviewed for Grade 2 partially meet the requirement of this indicator.
- MP1 is consistently expected as students solve problems throughout the year.
- The full meaning of MP5 is not attended to. Students rarely choose their own mathematical tools.
- The final lesson in each unit focuses on all 8 MPs instead of focusing on 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 2 partially meet the requirement of this indicator of attending to the standards' emphasis on mathematical reasoning.
- Students are rarely prompted to construct viable arguments. One example is found on the assessment for unit 6 where students are prompted to "Explain how and why you can use addition to check your answer."
- In the 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 is simply an opportunity for catching errors and not an opportunity for 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 2 partially meet the requirement of this indicator of attending to the Standards' emphasis on mathematical reasoning.
- In unit 6 teachers are given an activity called "Discuss Good Explanations." This provides students with the opportunity to construct their own arguments and help other students to make a full explanation.
- The teacher's manual provides questions to promote MP3.
- In several lessons, an element called "Math Talk in Action" is 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 2 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 "hidden information" is listed as a vocabulary word in unit 1. In unit 6, the phrases "New Groups Above" and "New Groups Below" are listed as vocabulary.