2nd Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 71% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 4 / 8 |
The instructional materials reviewed for Grade 2 enVision Math 2.0 partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Grade 2, but the materials do not always meet the full depth of the standards.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 2 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades within the assessments provided.
Indicator 1a
The assessment materials reviewed for Grade 2 meet expectations for focus within assessment. Content from future grades was found to be introduced; however, above grade-level assessment items, and their accompanying lessons, could be modified or omitted without significantly impacting the underlying structure of the instructional materials.
Probability, statistical distributions, and/or similarity, transformations and congruence do not appear in the Grade 2 materials.
The series is divided into topics and each topic has a topic assessment and a topic performance assessment. Additional assessments include a placement test found in Topic 1, four cumulative/benchmark assessments, and a End-of-Year Assessment.
The topic assessments have a few items which assess future grade level standards.
- Topic 3, Question 1 should say mass instead of weight because balances measure mass, which is a Grade 3 standard 3.MD.1.
- In Topic 4, page 252A, questions 3 and 4 ask about "regrouping." In lesson 4-3 on page 206, a step-by-step procedure is taught, the standard algorithm; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction, and this procedure is used throughout the topic.
- In Topic 4, page 252, item 3, students are directed to use regrouping with a procedure, which is a Grade 4 standard 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- In Topic 6, pages 383-386, items 1, 2, 5, 6, 7, 8, 9 and 13 all include regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard 4.NBT.4; students are not directed to place value, properties of operations and the relationship between addition and subtraction.
- In Topic 6, page 386A, items 1, 5, 6, 7, 8, 9 and 13 all include regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- Topic 1-8 Cumulative Review, page 502B, item 21, includes regrouping which is treated in Topic 6 as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- Topic 10, page 634, item 4, asks students to critique a solution strategy that is using a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- Topic 10, page 534A, item 4, asks students to critique a solution strategy using a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- Topic 11, page 684A, item 7, asks students to solve a subtraction problem that is represented as a procedure, a Grade 4 standard, 4.NBT.4; students are not directed to attend to place value, properties of operations and the relationship between addition and subtraction.
- Topic 8 Topic Assessment item 2 and Topic 8 Performance Assessment item 4b assess adding minutes to time; this is a Grade 3 standard, 3.MD.1.
The off-grade level items could be removed without affecting the sequence of learning for the students.
Note:
- In Topic 12, item 2, the student is expected to answer that the scarf is 1 yard and the shoe is 1 foot. In the picture, the scarf and shoe are the same size.
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials reviewed for Grade 2 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters of the grade which include 2.OA.A, 2.OA.B, 2.NBT, 2.MD.A and 2.MD.B.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Grade 2 meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade which includes 2.OA.A, 2.OA.B, 2.NBT, 2.MD.A and 2.MD.B.
To determine this, three perspectives were evaluated: 1) the number of topics devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days is the same as the number of lessons. A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent, and we drew our conclusion based on that data.
Grade 2 enVision Math 2.0 includes 15 Topics with 116 lessons.
At the topic level, 9 of the 15 topics focus on major work. 2.5 of the 15 topics focus on supporting work and connect to the major work of the grade, 1.5 of the 15 topics focus on supporting work without connecting to the major work, and 2 topics focus on the off-grade level work of 4.NBT.4 using procedures to solve addition and subtraction instead of attending to place value, order of operations and the relationship between addition and subtraction. Approximately 77 percent of the topics are focused on major work (counting the 2.5 topics which somewhat supports major work), approximately 10 percent of the topics are focused on supporting clusters and do not support the major work of the grade, and approximately 13 percent of the topics are focused on off-grade level topics.
A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level 70 lessons focus on major work, 17 lessons focus on supporting work and the major work of the grade, 10 lessons focus on the supporting work without connecting to the major work, and 20 lessons focus on off-grade level work that consists of having students use procedures to solve addition and subtraction problems. At the lesson level approximately 59 percent of the lessons focus solely on major work, approximately 15 percent of the lessons focus on supporting work connected to major work, approximately 9 percent of the lessons focus on supporting work which does not support the major work, and approximately 17 percent focus on off-grade level work. At the lesson level, approximately 74 percent of the lessons focus on major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 2 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do not have enough materials to be viable for a school year and do not always meet the depth of the standards. The majority of instructional materials do not have supporting content enhancing focus and coherence simultaneously but do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 2 do not exhibit the characteristics of coherence.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Grade 2 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade, and many natural connections are missed.
The following details supporting work in the instructional materials.
- Topic 2 is focused on working with equal groups. It supports the major work of the grade. The lessons each have questions about adding and subtracting within 20.
- Topic 8 is focused on time and money. The money lessons support the major work of the grade by adding and subtracting within 100. For example, lessons 8-1 through 8-4 focus on solving problems with money. Students count coin and dollar values to find sums. At times directions ask students to "count on" to find the total value. There is a missed opportunity here to support major work through a connection to addition and subtraction; this connection isn't introduced until 8-4. Lesson 8-5 focuses on reasoning and has students showing values in different ways. There is a missed opportunity to make connections to place value as the coin values could also be seen as distinct units. For example a dime is a ten, composed of 10 ones, or pennies. There could also be a connection to composing any given number in multiple ways. The lessons on time are treated separately from the major work of the grade. There are missed opportunities to connect time to counting by fives 2.NBT.2.
- Topic 14 is focused on graphs and data. This topic minimally supports the major work of the grade. Students could be answering compare, put-together, and take-apart problems with graphs. The majority of the questions associated with the graphs do not ask these types of questions but instead simply ask how many.
- Topic 15 is focused on equal shares of circles and rectangles. This topic is treated separately with the exception of one lesson; 15-5 supports adding within 100.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-23A. The enVision Math 2.0 Grade 2 program consists of 116 lessons, grouped in 15 topics. Assessments are not included in this count; if the 15 days of assessment are added in this would bring the count to 131 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to be viable for one school year and for the students to meet the expectations of the grade-level standards.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Grade 2 partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade level.
Material related to future grade-level content is not clearly identified or related to grade level work. The exception is the topic titled "Step up to 3rd grade" where the materials are clearly identified as Grade 3 materials. The Grade 2 materials have some instances where future grade-level content is present and not identified as such. For example, lesson 4-4 teaches students to add without attending to strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
The content does not always meet the full depth of the standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:
- There are six lessons which address 2.NBT.1, all of which fall in Topic 9. This standard, understanding the values of 3-digit numbers, is the foundation for students to understand numbers from 100-999 and "use place value and properties of operations ...," and this standard supports the development of "level 3 strategies" as explained on page 6 of the Operations and Algebraic Thinking progression document.
- A second example is 2.OA.C, work with equal groups of objects to gain foundations for multiplication. There are five lessons that address this standard, all in Topic 2.
- A third example is major clusters 2.MD.A and 2.MD.B, for which there are two lessons addressing 2.MD.2, two lessons addressing 2.MD.4, and 2 lessons addressing 2.MD.6.
The materials extensively work with grade-level problems, for example:
- All students complete grade-level materials, and suggestions for re-teaching and intervention are included with each lesson and at the end of each topic.
- Online resources include extra, on-level and advanced-practice materials.
- Interventions provided with lessons for students most often engage students more deeply in the work of the grade level than the lesson itself. Often, students are simply following directions instead of being engaged in problems.
- The numbers of topics addressing Grade 2 domains are as follows: 7 out of 15 topics address numbers in base ten; 3 out of 15 topics address operations and algebraic thinking; 4 out of 15 topics address measurement and data; and 1 out of 15 topics address geometry.
The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:
- "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 2, explaining connections to the content within the topic, and explaining what will come later in Grades 2 and 3. An example can be found on pages 389c-389d for Topic 7.
- Individual lessons also include coherence headings. An example is in lesson 5-6 on page 285A that includes the heading, "Coherence: In lesson 5-5, students broke apart a 1-digit subtrahend to make it easier to subtract mentally. In this lesson, students subtract a 2-digit number from a 2-digit number by breaking apart the lesser number..."
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The instructional materials reviewed for Grade 2 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.
The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.
- The focus of Topic 3 is 2.NBT.5 and 2.NBT.9: Add within 100 using strategies. Lesson objectives in Topic 3 include: L1 - Add tens and ones on a hundreds chart, L2 - Add tens and ones on an open number line, and L4 - Break apart numbers to add.
- A similar example for Topic 10 can be found on pages 583I - 583J.
The materials for Grade 2 enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the Grade 2 program focus within a single domain and cluster. Of 116 lessons, 85 lessons focus within a single cluster and domain.
- In Topic 1, lessons 1-9 and 1-10 are identified as addressing standards within two clusters 2.OA.1 and 2.OA.2.
- In Topic 2, all five lessons address standards in two clusters (2.OA.A, 2.OA.B, 2.OA.C), all within the same domain.
- Topic 3 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
- Topic 4 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
- Topic 5 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
- Topic 6 includes one of nine lessons that addresses more than one domain, all other lessons are within a single cluster.
- All lessons within Topic 7 are within a single cluster and domain.
- In Topic 8, all eight lessons address standards in two domains.
- Topic 9 includes two lessons that address two clusters.The remaining lessons focus on one cluster, all within the same domain.
- All lessons within Topic 10 are within a single cluster and domain.
- All lessons within Topic 11 are within a single cluster and domain.
- Topic 12 includes one lesson that addresses two clusters within a single domain.
- In Topic 13, three of five lessons (13-2, 13-3, and 13-5) address standards within two domains.
- In Topic 14, two of six lessons (14-1, 14-2) address standards within two clusters and the same domain, and two of six lessons (14-5, 14-6) address standards from two domains.
- In Topic 15, two of eight lessons (15-5, 15-8) address standards within two domains.
Further analysis of Topics 8 and 12, which address supporting work, provided the following examples:
- In Topic 8, as students work with time and money, they sometimes connect the use of operations to telling time and finding values. Lessons 8-1 through 8-3 do not connect counting coin and dollar values to operations or place value, missing opportunities to make connections across domains.
- In Topic 12, as students work with measuring lengths, the lessons focus on the procedure of measuring. There are missed opportunities for students to make connections to fluency (2.OA.1) by comparing lengths or comparing estimates and lengths.