Kindergarten - Gateway 1
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Focus & Coherence
Gateway 1 - Does Not Meet Expectations | 42% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 0 / 4 |
Criterion 1.3: Coherence | 4 / 8 |
The instructional materials reviewed for Kindergarten do not meet expectations for focus on major work and coherence. The materials do not devote the large majority of time to grade-level work with the inclusion of the pattern unit, but the materials can be utilized to appropriately assess grade-level content. In addition, there is no explicit connection made to the progressions of learning in the standards.
Criterion 1.1: Focus
The instructional materials reviewed for Kindergarten meet the expectations for assessing material at the grade level. Although there are multiple units and sessions noted that align to and assess standards that are beyond Kindergarten, the inclusion of these sessions and units is either Mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.
Indicator 1a
The instructional materials reviewed for Kindergarten meet expectations for assessment because above grade-level assessment items and their accompanying lessons, sessions, or units, could be modified or omitted without a significant impact on the underlying structure of the instructional materials. For this indicator, all of the assessment checklists and end-of-unit assessments for the seven units were reviewed. All assessments are student observation/interview in nature, and units and sessions accompanying above grade-level assessment items are noted in the following list.
- In unit 3, sessions 1.5 and 3.1 assess how to: construct, copy, and extend patterns; break a pattern into units; and construct a pattern from a known unit. These expectations for students align to 4.OA.C.5. The materials explain the inclusion of these expectations by saying they “raise student awareness of pattern and regularity which is what math is mostly about…relationships among mathematical objects” (page 13), but these topics are not clearly identified as beyond Kindergarten. Due to these topics aligning to a standard four grade levels above Kindergarten, the inclusion of these topics is not Mathematically reasonable within the materials, and the omission of these lessons and sessions would not significantly alter the underlying structure of the materials.
- In unit 4, session 1.1 assesses how to: measure the length of objects in non-standard units; line up units the length of the object; and accurately count the number of units used. These expectations align to 1.MD.A. These topics are not clearly identified as beyond Kindergarten, but their inclusion is Mathematically reasonable since the topics are only one grade level beyond Kindergarten and do not constitute a large number of lessons. Also, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials.
In unit 7, session 1.1 assesses how to: represent accurately the number of pieces of data; represent data so that others can produce representations from the data; and represent and organize data. In Unit 7, Session 3.5 assesses how to: identify and represent data needed to solve a problem; solve the problem accurately; represent the method used to solve the problem. These expectations align to 1.MD.D. These topics are not clearly identified as beyond Kindergarten, but their inclusion is Mathematically reasonable since the topics are only one grade level beyond Kindergarten and do not constitute a large number of lessons. Also, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials, especially since this would more than likely be the last unit of the school year.
*Evidence updated 10/27/15
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 do not meet expectations for time spent of the major clusters of the grade. This is largely due to one unit of the seven that is spent on additional work and one unit of the seven that is spent on work outside the grade level.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Kindergarten do not meet expectations for class time spent on the major clusters of the grade. According to the unit instructional plans, there are 163 days of lessons and assessments. Within that, there are areas where the work is aligned to supporting and additional clusters or is work outside of the grade level. For example:
- In unit 2, sessions 2.10-2.14, students in Kindergarten should be comparing two quantities, however these activities extend to comparing more than two quantities and ordering them.
- One major cluster, K.NBT is barely addressed; only three lessons in unit 6 are devoted to the composing and decomposing numbers 11-19 to gain a foundation for place value.
- Unit 3 focuses primarily on patterns. Patterns would be considered more of a mathematical practice and are not formally introduced until Grade 4.
- Unit 5 is aligned to geometry, which is additional work of Kindergarten. There are 18 lessons in the unit that do not focus on major clusters.
- There are 22 lessons in unit 3 aligned to patterns and 20 lessons in unit 5 aligned to geometry, additional clusters. This shows a percentage of possible alignment to the major clusters at 73%. That is not enough of a focus in Kindergarten on the major work of the grade, especially considering the near absence of K.NBT.A.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Kindergarten do not meet expectations for coherence. With the inclusion of Unit 3, the amount of appropriate content for the year and the extensive work on grade level materials diminishes.
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 partially meet expectations for enhancement of supporting content with major content at the grade. The review team found evidence where supporting content enhances focus, particularly in the area of counting and cardinality, but not for all major work of Kindergarten. For example:
- In units 3 and 5, the K.CC cluster is used in workshop activities within lessons dealing with additional content and also by including it in the Classroom Routines for the day.
- Specifically, in unit 5, lesson 2.2, "pattern block puzzles" asks the students to create a composite shape and to count the number of different shapes used and record the number of each shape.
- Unit 2 uses measurement standards as a support for K.CC. An example of this is name towers, where students build towers with snap cubes to represent the number of letters in their name. Each snap cube has a dot sticker placed on it that has a letter written on it. In this activity students gain a visual representation of the number that matches the number of letters in their names. Students also directly compare the length of their "name tower" to other students' name towers. This activity uses direct comparison of length, measurement vocabulary (longer than, shorter than) paralleled with counting and representing numbers 1-10 and comparison vocabulary (more than, less than).
On the contrary,
- In unit 4, measuring and counting, all lessons within investigation 1 focused on non-standard measurement which is not a Kindergarten standard. All lessons in investigation 2 simultaneously engage students in the major work of K.CC.A, K.CC.B and K.CC.C.
*Evidence updated 5/20/2015, score unchanged
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 partially meet expectations for viability of content for the scope of one year. The curriculum consists of 163 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, with the inclusion of unit 3 on patterns, the review team determined that the amount of content was not fully viable for one school year to foster coherence between Kindergarten and Grade 1. The depth of content needed to prepare students for Grade 1 needs to be further developed for K.NBT.A as well. Teachers would need to find supplemental resources in order to cover the content for Kindergarten.
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 partially meet expectations for consistency with the progressions. There is partial alignment to development of grade-by-grade progressions and to the amount of work with grade-level problems. Since there is no grade level prior to Kindergarten, there are no opportunities to explicitly relate the grade-level concepts to prior grade level standards. In the front of each unit, there are detailed explanations of the content addressed in a section called "Mathematics in this Unit." Within this section, the "Looking Back" and "Looking Forward" pieces explains content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. Some examples of alignment and misalignment with the indicator include:
- In unit 1, work in data analysis (surveys) is a future expectation, but its use is articulated as a means to count and compare quantities in a meaningful, real-world context.
- In unit 7, session 1.1, a math note provides a rationale for counting objects slightly beyond 20, acknowledging that this goes beyond Kindergarten expectations.
- Five of the lessons in unit 2 (sessions 2.10-2.14) extend comparing two quantities to ordering more than two is given no explanation or acknowledgement that this goes beyond Kindergarten expectations of comparing two quantities.
- Pattern work is not identified as future work in unit 3.
- In unit 4, non-standard length and weight with cubes and other non-standard units is not identified as future work, but is connected to Kindergarten counting work.
- Every lesson in unit 2 includes one or more of these differentiation suggestions.
- The one cluster lacking in extensive work is K.NBT.1 as only three lesson opportunities for students to work on gaining foundations for place value exist.
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 partially meet the expectations for fostering coherence through connections at a single grade. The materials include some instances where learning objectives are shaped by cluster headings and include some problems that connect clusters and domains. Examples for both arguments include:
- In unit 6, "Composing and decomposing the teen numbers into one ten and some number of ones" can be found as learning objectives. In sessions 5A.3-5A.5, students build teen numbers using ten frames and record using an addition of 10+ some number of ones in order to develop an understanding of place value.
- In unit 4, "modeling the action of combining and separating situations," "combining two amounts," and "adding or subtracting from a number" can be found in sessions 3.2-3.7; investigation 2 includes "finding the total after a small amount (1,2,3) is added to a set;" investigation 3, sessions 3.2-3.7 demonstrate "modeling the action of combining and separating situations," "combining two amounts," and "adding or subtracting from a number"; and investigation 4, sessions 4.2 and 4.5 include "recording decompositions and compositions of a number using addition and subtraction notation."
- In unit 6, investigation 1, six lessons involve "using numbers and addition notation to describe arrangements (combinations) of object;" investigation 2 includes "finding the total after a small amount (1,2,3) is added to or subtracted from a set;" and investigation 3 demonstrates "combining two single-digit numbers with totals to 10," "modeling action of combining and separating situations," "separating one amount from another," and "using numbers and addition notation to represent an addition situation." All support the K.OA.A cluster heading.
- In unit 2, session 1.4 connects number words, numerals, and quantities (shaped by K.CC.3).
- In unit 6, sessions 5A.3-5A.5 combine and connect K.NBT and K.CC.B.5 and K.CC.A.3.
- Unit 5 sessions 1.3-1.5 and most lessons in investigations 2 and 3 combine and connect work in K.G.A.2 and K.G.B.4 with counting in K.CC.A.3, K.CC.B.5 and comparing numbers in K.CC.C.6.
- Unit 1 investigation 3 lessons and Unit 7 investigations 2 and 3 lessons combine and connect work in sorting and classifying K.MD.B.3 with opportunities to rote count and write numbers K.CC.A.3 and comparing quantities K.CC.C.6.
- However, with the inclusion of Unit 3 on patterns, not addressing cluster headings in Kindergarten, or containing grade level problems, the review team saw that the math focus points and work students were engaged in were not shaped by Kindergarten clusters.