Kindergarten - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
Gateway 1 - Meets Expectations | 92% |
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The materials reviewed for Kindergarten meet the expectations for Gateway 1. These materials do not assess above-grade level content, and they spend the majority of the time on the major clusters of each grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are partially consistent with the mathematical progression in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the Kindergarten materials are focused and follow a coherent plan.
Criterion 1.1: Focus
The instructional materials reviewed for Kindergarten 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 summative assessments provided. Summative assessments considered during the review for this indicator include unit post-assessments and Number Corner assessments that require mastery of a skill.
Indicator 1a
The assessment materials reviewed for Kindergarten meet expectations 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.
For this indicator, the Kindergarten Assessment Map found on pages 12 – 14 in the Assessment Overview section was used to identify “summative” assessments. The Assessment Map indicates when mastery of each standard is expected and where the mastery standard is assessed. Based on the Assessment Map, the following were considered to be the summative assessments and were reviewed for Indicator 1a:
- Number Corner Checkups 1 – 4
- the Comprehensive Growth Assessment
- Select Unit Checkpoints
- Unit 2 Module 1, Session 5, Count and Compare Checkpoint
- Unit 3 M1, Session 4, Beat You to Ten Checkpoint
- Unit 4 M3, Session 3, Counting and Writing Numbers Checkpoint
- Unit 5 M1, Session 4, Sort and Count Checkpoint
- Unit 5 M3, Session 4, 2-D Shapes and Their Attributes Checkpoint
- Unit 6 M1, Session 4, Cylinder Tens and Ones Checkpoint
- Unit 6 M2, Session 4, 3-D Shapes and Their Attributes Checkpoint
Assessments are student observation/interview or written in nature. The Comprehensive Growth Assessment (CGA) and all of the Number Corner Quarterly Checkups are fully aligned to the Kindergarten CCSSM. In the Number Corner Quarterly Checkups, several skills/concepts in the K.CC cluster are benchmarked and assessed throughout the year. For example, K.CC.1 (Count to 100 by 1s) is assessed to 20 on NCCU1, to 60 on NCCU3, and to 100 on NCCU4.
The Unit Assessment Checkpoints that contain above grade-level or content not specifically required by the standards are noted in the following list:
- In the Unit 4 Module 3 Session 3 Counting and Writing Numbers Checkpoint, Prompt 4, students are asked to count backward from a number (4 – 9) until they reach zero. Counting backwards is not an explicit K CCSSM expectation; however, it makes mathematical sense to address it as a precursor to subtraction where counting backward is a necessary skill. This skill is identified in the assessment scoring guide as “Supports K.CC.”
- In the Unit 5 Module 3 Session 4 Two-Dimensional Shapes & Their Attributes Checkpoint, students are expected to identify a rhombus and a trapezoid. Those shapes are not specifically identified in K.G.2; however, it makes sense to include them since they are shapes in the pattern block set students use throughout the unit.
- In the Unit 6 Module 1 Session 4 Cylinder Tens & Ones Checkpoint, students are asked to create a cylinder using a strip of paper. Question 2 asks students to estimate how many unifix cubes they think it will hold and then to fill the cylinder with unifix cubes without counting them. After dumping out the cubes and arranging them into tens and ones, they are asked to count them (Question 5) and then compare the actual number of cubes to their estimate to determine if their estimate was more or less than the actual number of cubes (Question 6). Since teachers are instructed to provide each student with 40 cubes, it is reasonable to believe that the number of cubes students will be expected to count will exceed the limit of 20 designated in K.CC.5 and subsequently, students may be comparing numbers greater than 20. Additionally, the estimation of quantities is not a Kindergarten expectation. Adjusting the size of the cylinder to ensure the counting of smaller quantities and eliminating the estimation portion of the assessment would be an easy fix and would not affect the integrity of the unit.
- In the Unit 6 Module 2 Session 4 3-Dimensional Shapes and Their Attributes Checkpoint, the majority of the student observations are aligned to the K Geometry Standards: K.G.1, K.G.2, K.G.3, and K.G.4. However, in the observational task in which students use polydrons to build 3-D shapes, the teacher is to document if a student has successfully built rectangular prisms, triangular prisms and pyramids. This expectation is more appropriately aligned to 1.G.2 and not to K.G.5 (model shapes in the world by building shapes from components, e.g., sticks and clay balls, and drawing shapes) because the 3-D shapes identified in the K Geometry standards are limited to cube, cone, sphere and cylinder. However, as long as the focus is on building shapes and not naming them, this would be acceptable as most of these shapes are introduced within the K-2 grade band.
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 Kindergarten 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.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Kindergarten meet the expectations for focus by spending the majority of class time on the major clusters of the grade. All sessions (lessons), except summative and pre-assessment sessions, were counted as 60 minutes of time. Number Corner activities were counted and assigned 20 minutes of time. When sessions or Number Corner activities focused on supporting clusters and clearly supported major clusters of the grade, they were counted. Reviewers looked individually at each session and Number Corner in order to determine alignment with major clusters and supporting clusters. Optional Daily Practice pages and Home Connection pages were not considered for this indicator because they did not appear to be a required component of the sessions.
When looking at the modules (chapters) and instructional time, when considering both sessions and Number Corners together, approximately 90 percent of the time is spent on major work of the grade.
- Units – 8 out of 8 units spend the majority of the unit on major clusters of the grade, which equals 100 percent. Each unit devotes most of the instructional time to major clusters of the grade.
- Modules (chapters) – 28 out of 32 modules spend the majority of the time on major clusters of the grade, which equals approximately 88 percent. Units 2, 5, 7 and 8 had three Modules that focused on major work of the grade, and all other units had all four Modules focused on major work of the grade.
- Bridges Sessions (lessons) – 143 out of 160 sessions focus on major clusters of the grade, which equals approximately 89 percent. Major work is not the focus of the following sessions:
- Unit 1, Module 4, Sessions 1, 2, 3 and 4
- Unit 2, Module 4, Sessions 1, 2, 3 and 4
- Unit 4, Module 3, Session 2
- Unit 5, Module 1, Session 1
- Unit 5, Module 2, Session 5
- Unit 5, Module 4, Sessions 2, 3 and 4
- Unit 6, Module 2, Session 4
- Unit 8, Module 4, Sessions 4 and 5
- Bridges sessions require 60 minutes. A total of 143 sessions are focused on major work of the grade. Bridges sessions devote 8,580 minutes of 9,600 minutes to major work of the grade. A total of 155 days of Number Corner activities address major work of the grade. Number Corner activities are 20 minutes each adding another 3,100 minutes to this total. In all 11,680 of 13,000 minutes, approximately 90 percent, is devoted to 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 Kindergarten meet the expectations for coherence. The materials use supporting content as a way to continue working with the major work of the grade. For example, students count shapes in categories and then compare the quantities. The materials include a full program of study that is viable content for a school year, including 160 days of lessons and assessment. All students are given extensive work on grade-level problems, even students who are struggling, and this work progresses mathematically. However, future grade-level content is not consistently identified. These instructional materials are visibly shaped by the cluster headings in the standards; for example, one session is called "Classify Objects Into Categories." Connections are made between domains and clusters within the grade level. For instance, materials make connections between counting and cardinality and measurement and data. Overall, the Kindergarten materials support coherence and are consistent with the progressions in the standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Kindergarten meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade.
Supporting standard K.MD.1 is connected to K.CC and K.OA — major work of the grade — throughout the instructional materials. For example, in Unit 4, Module 3, Session 1, standard K.MD.1 supports major work of K.CC.6 by measuring and comparing lengths and then correlating the measurement into a number unit and comparing the quantities.
Supporting standard K.MD.2 is connected to the major work of K.CC.6 throughout the instructional materials. For example, in Unit 4, Module 3, Session 1 standard K.MD.2 supports major work of K.CC.6 by measuring and comparing lengths and then correlating the measurement into a number unit and comparing the quantities.
Supporting standard K.G.2 is connected to K.CC and K.OA, major work of the grade, throughout the instructional materials. For example, in Unit 5, Module 2, Sessions 1-3, after sorting, students are asked to count the number of shape cards in each category and then compare the quantities to find which group has the most or least, and combining amounts. This supports K.CC and cluster K.OA. Another example is found in Unit 6, Module 1, Session 2. In this session work in three-dimensional geometry is used as a vehicle to represent and solve addition situations. This supports K.OA. Also, in Unit 6, Module 2, Session 5, students use three-dimensional shapes as a vehicle to practice decomposing numbers and fluently adding within 5 (K.OA).
Supporting standard K.MD.3 is connected to K.CC and K.OA, major work of the grade, throughout the instructional materials. For example, in Unit 5, Module 2, Sessions 1-3, while sorting shape cards in various ways, students are asked to count the number in each category and then compare the quantities to find which group has the most or least, and in some sessions combining amounts. This supports standards in K.CC and K.OA. Also, in the March and May Calendar Collector, students examine data and connect it to clusters K.CC and K.OA through questions about counting, comparing and combining.
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 instructional materials reviewed for Kindergarten meet the expectations for this indicator by providing a viable level of content for one school year. Overall, the materials have expectations for teachers and students that are reasonable.
- Materials provide for 160 days of instruction. Each Unit has 20 sessions = 20 days. There are 8 Units. (20x8=160)
- The prescribed daily instruction includes both unit session instruction and a Number Corners session. (170 days). There are no additional days built in for re-teaching.
- Assessments are incorporated into sessions and do not require an additional amount of time. Instead, they are embedded into module sessions one-on-one as a formative assessment.
- The Number Corner Assessments/Checkups (a total of 10 assessments, 1 interview and 1 written, in each of the following months: September, October, January, March and May) would require additional time to conduct a 7-10 minute interview with each student.
- A Comprehensive Growth Assessment is completed at the end of the year and will require additional number of days to administer.
- There are no additional time/days built in for additional Support, Intervention or Enrichment in the pacing guide. The Publisher recommends re-teaching of strategies, facts and skills take place in small groups while the rest of the class is at Work Places (math stations) or doing some other independent task. There is a concern that if a particular session’s activities take up most of the 60 minutes allotted, there will be no time for the remediation and enrichment to take place.
- Based on the Bridges Publisher Orientation Video and Guide provided to the reviewers, unit sessions are approximately 60 minutes of each instructional day.
- Each unit session contains: Problems & Investigations (whole group), Work Places (math stations), Assessments (not found in each session), and Home Connections (homework assignments not found in each session).
- Based on the introduction section in the Number Corners Teacher Guide, as well as the Bridges Publisher Orientation Video, Number Corners sessions are approximately 20 to 25 minutes of each instructional day.
- Approximately 80-85 minutes is spent on the Bridges and Number Corner activities daily.
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 Kindergarten are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made, future grade level content is not always clearly identified to the teacher or student.
At times, the session materials do not concentrate on the mathematics of the grade. Some of the sessions within each module focus on above grade-level concepts. Examples of this include addition and subtraction beyond 10, counting quantities beyond 20, the use of greater than and less than symbols, patterns, volume, and identifying and counting money amounts using coins. The inclusion of off-grade level concepts takes away from the number of sessions that could be spent more fully developing the work on the mathematics of the grade.
In some cases, the above-grade level content is identified as such by the publishers, and in other cases it is not. On the first page of every session, the Skills & Concepts are listed along with the standard to which it has been aligned by the publisher. In some cases, this alerts the user to the inclusion of off-grade level concepts. Examples include:
- Unit 5, Module 1, Exploring Shapes Overview, page 1, the publisher describes the work in Module 1 as “extending the range of their counting and comparing skills” which somewhat signifies that students will be moving beyond the expected range of Kindergarten standards.
- Unit 5, Module 1, Session 3 warm-ups include counting backward from 20 which is not a Kindergarten standard, but the publisher alerts teachers to this by aligning it to “supports K.CC.”
- Unit 5, Module 4, Session 5- students make a quilt following an AB pattern which publisher identifies as “create and extend simple repetitive patterns with up to 3 elements. The publisher alerts teachers by aligning it to “supports K.OA.”
- In the Unit 6 Introduction, page ii, the publishers state that “a mastery of the forward and backward counting sequences, one-to-one correspondence, and cardinality helps students correctly determine sums and differences as they begin to solve addition and subtraction tasks,” thereby explaining an inclusion of counting backwards throughout the unit even though it is not a Kindergarten expectation.
In other cases, the above-grade level concepts are not identified as such within the sessions in the "Skills and Concepts" listing or at the beginning of the Units in the "Skills Across the Grade Levels" sections. Examples of unidentified above-grade level content include:
- Unit 3, Module 1, Session 2 and Session : Counting by 2’s is a skip counting strategy/skill that is not introduced until Grade 2 (2.NBT.2).
- Unit 4, Module 3 Sessions 2 -5: These focus on above-grade level content using standard units of measurement. The lessons are worded with the language of the standard for measurement in first grade (1.MD.1).
- Unit 4, Module 4, Session 2 and Session 5: Both sessions involve counting by 5’s, which is a skip counting strategy/skill that is not introduced until Grade 2 (2.NBT.2).
- Unit 5, Module 1, Session 5: This focuses on addition to 20, number combinations, and comparing numbers. This goes beyond K.OA expectations of adding to 10 as it continues on to 20, asking questions such as “how many more to 20?”
- Unit 6, Module 1, Sessions 3 and 4: The comparison of the cylinders as to which one holds more is a volume activity which is more appropriate for Grade 4.
- Unit 6, Module 2: Activities involve three-dimensional shapes that go beyond the shape expectations as outlined in the K.G cluster. The activities in this module include drawing and identifying rectangular prisms, triangular prisms and pyramids.
- Unit 6, Module 3, Session 4: Money is a Grade 2 standard, but is not specifically identified as such by the publisher. In this session, students are determining the total value of a collection of coins.
- Unit, 8, Module 4, Sessions 4 and 5: Students use repetitive patterns while completing a double Irish chain frog quilt. This moves beyond the grade-level work.
Materials provide students opportunities to work with grade-level problems. The majority of differentiation/support provided is on grade-level. Extension activities are embedded within sessions and allow students to engage more deeply with grade-level work. Additional extension activities are also provided online.
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 Kindergarten meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. The standards are referred to throughout the materials. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and include problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.
Instructional materials shaped by cluster headings include the following examples:
- Unit 5, Module 2, Session 3, "Sorting Shapes by Sides, and Corners," is shaped by K.G.B.
- Unit 6, Module 3, "Exploring the Teen Numbers," is shaped by the K.NBT cluster heading.
- Unit 7, Module 1, Session 1, “Compare Weights,” is shaped by the K.MD.A cluster heading.
- Unit 8, Module 1, “Catching, Counting, and Comparing,” is shaped by the K.OA.A cluster heading.
- The Unit 5, Module 1, Session 1 learning objectives include "Classify objects into categories," which is visibly shaped by K.MD.B.
- The Unit 5, Module 3, Session 1 learning objectives include "Classify objects into given categories" and "Count the number of objects in each category," which are visibly shaped by K.MD.B cluster heading.
Units, modules, and sessions that connect two or more clusters in a domain or two or more domains include the following examples:
- Unit 1 Module 1, Session 1: "One Shoe" connects cluster K.CC.A to K.CC.B as students are counting the number of shoes up to 10, saying the number in the standard form and pairing each shoe with only one number name.
- Unit 1 Module 1, Session 2: "Two Shoes" connects clusters K.CC.A and K.CC.B to K.CC.C as students count the number of shoes to by ones, say the number in the standard form, pair each shoe with only one number name, and finally compare which group is greater than, less than, or equal.
- Unit 1 Module 1, Session 3: "Five Shoes" connects clusters K.CC.A and K.CC.B to K.CC.C as students count the number of shoes, saying the numbers in standard order and pairing each shoe with only one number name, and identifying whether the number of shoes in one group is greater than, less than, or equal to the number of shoes in the other group.
- Unit 1 Module 2, Session 1: "Shoes to Toes" connects cluster K.CC.B with K.OA.A as students are counting dots on five-frame cards, and then decomposing the sums in more than one way.
- Unit 1 Module 2, Session 2: "Fabulous Fives" connects cluster K.CC.B with K.OA.A as students are counting dots on five-frame cards, and then decomposing the sums in more than one way with Unifix cubes and five-frame cards.
- Unit 1 Module 2, Session 3: "Fives with Fingers" connects cluster K.CC.B with K.OA.A as students are counting dots on five-frame cards, and then decomposing the sums in more than one way with fingers.
- Unit 1 Module 2, Session 4: "Numerals 1 to 5" connects K.CC.A and K.CC.B with K.OA.A and K.MD.3 as students shake two-colored beans, count each color, find the sum and record numeral on sheet.
- Unit 1 Module 2, Session 5: "Filling Five-Frames" connects K.CC.B with K.OA.A as students are flashed five-frames they show the number of dots on one hand and the number of blank spaces on the other.
- Unit 1 Module 3, Session 4: "Beat You to Five" connects K.CC.A and K.CC.B with K.OA.A as students play the game of spinning a number and working in teams to see if they can cover five cubes on their frames before the teacher's side is covered. Students determine which group is greater than, less than, or equal to the number on the other side of the five-frame card.
- Unit 2 Module 1, Session 1: "Two Red, Three Blue" connects clusters K.CC.B to K.OA.A as students count, compare and answer how many more as they are looking at 5-frame cards.
- Unit 2 Module 1, Session 2: "Funny Five-Frame Flash" connects clusters K.CC.B to K.OA.A as students compare irregular 5-frame cards with regular 5-frame cards.
- Activities in Unit 5, Modules 1 and 2 connect K.G.4 with K.MD.3 when sorting pattern blocks, shapes and shape cards and then counting and recording the number of each.
- Activities in Unit 5, Module 3 connect K.G to K.CC.6 and K.MD.3 when sorting and recording the number in each category and then compare the quantities to find which is greater.
- Activities in Unit 6, Module 1 connect K.G to K.MD.3, K.CC.3, and K.CC.6 and K.CC.7 when sorting three-dimensional shapes into categories and counting and recording the number in each category and then comparing the numbers and quantities.
- Activities in Unit 6 Module 2 connect K.G to K.CC and K.OA.3 by playing a game “Make it Five” and recording combinations of five shapes.
- In Unit 3, Module 3, Session 3, students are counting objects (K.CC.2), comparing amounts (K.CC.6), describing the attributes of the objects (K.MD.1), and comparing more and less of the objects (K.MD.2).
- In Unit 4, Module 3, Session1 students work on counting and cardinality domain and all three clusters while comparing measurable attributes from the measurement and data domain.
- Activities in Unit 8, Module 1 connect K.CC.A to K.OA.A when counting objects and writing equations based on information from story problems.