Kindergarten - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
Gateway 1 - Partially Meets Expectations | 78% |
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 5 / 8 |
The Stepping Stones instructional materials for Kindergarten partially meet expectations for Gateway 1: Focus on Major Work and Coherence. The program focuses appropriately on grade-level content in a variety of assessments, with only minor exceptions. Analysis revealed that approximately 72 percent of lessons are aligned to the major work of Kindergarten; this focus on major concepts would allow students learning with this program to develop solid grade-level skills and understandings. The Kindergarten program partially attends to the coherent design of the CCSSM; modules and lessons support students in making connections between standards to deepen mathematical understanding, although some connections could be explored more fully. Learning targets for each lesson are explored in multiple formats, including whole-class and differentiated, small-group activities, giving teachers a sufficient amount of grade-level content for one school year. These materials are consistent with the progressions of learning outlined in the CCSSM. The instructional materials identify work that builds to future understandings, and all levels of learners have opportunities to engage with grade-level work, although some major Kindergarten standards are under-represented in the program materials. While there is only minimal attention paid to CCSSM cluster headings, lessons and activities capitalize on many natural connections to deepen students’ understanding of Kindergarten concepts. Overall, the Stepping Stones instructional materials for Kindergarten partially meet expectations for Gateway 1, so evidence will be collected for rigor and the mathematical practices in Gateway 2.
Criterion 1.1: Focus
The Stepping Stones instructional materials for Kindergarten meet expectations for assessing material at grade level. Overall, the majority of summative assessments include items that directly relate to grade-level standards. A small number of assessment items align to above grade-level CCSSM standards and could be easily modified or omitted without affecting the structure of the grade-level program. In addition, a small number of assessment items do not align with Kindergarten standards but are tagged by the program as Developmental Activities; these items are mathematically reasonable for students at this level.
Indicator 1a
The Stepping Stones instructional materials for Kindergarten meet expectations for assessing material at grade level. Overall, the majority of summative assessments include items that directly relate to grade-level standards. A small number of assessment items align to above grade-level CCSSM standards and could be easily modified or omitted without affecting the structure of the grade-level program. A small number of assessment items do not align with Kindergarten standards but are mathematically reasonable for students at this level.
For this indicator, the team reviewed all materials indicated as summative assessments: Check-Ups and Interviews for each of the twelve modules and the four Quarterly Tests included in Modules 3, 6, 9 and 12.
Module 1:
- All Check-Up and Interview items appropriately assess Kindergarten skills and understandings, including: match a given quantity to a numeral (K.CC.A.3); draw a quantity to represent a given numeral (K.CC.B.4); sort objects into like groups, and sort according to a given rule (K.MD.B.3).
Module 2:
- All Check-Up and Interview items appropriately assess Kindergarten skills and understandings, including: count to answer “how many?” (K.CC.B.5); match quantities to numerals and number words (K.CC.A.3—number words are outside the scope of this standard); count out a given quantity and then identify the matching numeral (K.CC.A.3, K.CC.B.4); and sort objects into groups (K.MD.B.3).
Module 3:
- The five items on Check-Up 1 give students a number path and ask them to identify the number before or after a given number; these items are tagged as K.CC.B.4 and K.CC.B.4.C. While the team felt these items are mathematically reasonable for Kindergarten, they seem to assess an understanding of position words (K.G.A.1) more than a relationship between numbers and quantities.
- Check-Up 2, Interview 1, and Interview 3 appropriately assess Kindergarten skills and understandings, including: position words (K.G.A.1); rote counting (K.CC.A.1).
- Interview 2 assesses students’ ability to subitize the quantities 1-6; this activity is tagged as a “Developmental Activity” (DA), rather than a Kindergarten standard. The ability to subitize is an important skill that will serve students well in the future, as explained in the Kindergarten Counting and Cardinality Progressions document: “Students come to quickly recognize the cardinalities of small groups without having to count the objects; this is called perceptual subitizing. Perceptual subitizing develops into conceptual subitizing…. Use of conceptual subitizing in adding and subtracting small numbers progresses to supporting steps of more advanced methods for adding, subtracting, multiplying, and dividing single-digit numbers” (page 4).
- Quarterly Tests: The majority of items on Tests 1-4 align with Kindergarten standards, including: match numeral to quantity and represent number of objects with a numeral (K.CC.A.3); sort objects according to a given rule (K.MD.B.3); use position words to describe an object (K.G.A.1). Two misaligned items are similar to the ones in Check-Up 1 (see Module 3 Check-Up 1 evidence above).
Module 4:
- All Check-Up and Interview items appropriately assess Kindergarten skills and understandings, including: identify the group with the greatest number of items (K.CC.C.6); identify the numeral that is less (K.CC.C.7); compare measurable attributes (K.MD.A.2).
Module 5:
- Check-Up 1 and Interviews 1-2 appropriately assess Kindergarten skills and understandings, including: count and represent numbers (K.CC.A.3); find the partner of 10 (K.OA.A.4); rote counting (K.CC.A.1); understand that the number of objects doesn’t change if counted differently (K.CC.B.4.B).
- Check-Up 2 assesses students’ ability to identify and continue patterns; this is tagged as “working toward content in” 4.OA.C.5 as in Module 5, Mathematics, Learning Targets, which states "Generate a number or shape pattern that follows a given rule. Creating and building shape patterns are not part of Kindergarten CCSSM; however, exploring patterns is developmentally appropriate at this level and gives students more exposure to different shapes.
Module 6:
- All items on Check-Ups 1-2 and Interviews 1-3 assess Kindergarten skills and understandings, including: represent addition with pictures and equations (K.OA.A); identify greater/less amount or numeral (K.CC.C); direct comparison of weight (K.MD.A.2); count and identify total number of items (K.CC.B.4).
- Quarterly Tests: The majority of items on Tests 1-4 align with Kindergarten standards, including: identify greater amount or numeral (K.CC.C); represent addition with pictures and equations (K.OA.A); match numeral to quantity and count and represent numbers (K.CC.A.3); find the partner of 10 (K.OA.A.4); compare measurable attributes (K.MD.A.2). Four items call for students to identify and continue a pattern (see Module 5 Check-Up 2 evidence above).
Module 7:
- All items on Check-Ups 1-2 and Interviews 1-3 assess Kindergarten skills and understandings, including: identify partners of numbers less than 10 (K.OA.A.3); count by tens (K.CC.A.1); identify flat and 3-D attributes and shapes (K.G.A).
Module 8:
- All items on Check-Ups 1-2 and Interviews 1-2 assess Kindergarten skills and understandings, including: find partners of 10 (K.OA.A.4); identify objects as 2-D or 3-D shapes (K.G.A.3); write an equation to match given objects (K.OA.A.1).
Module 9:
- All items on Check-Ups 1-2 and Interviews 1-2 assess Kindergarten skills and understandings, including: represent subtraction with pictures and equations (K.OA.A.1); identify and describe shapes and their attributes (K.G.A.2, K.G.B.4); addition fluency within 5 (K.OA.A.5); solve subtraction situation with concrete objects (K.OA.A.2).
- Quarterly Tests: The majority of items on Quarterly Tests 1-4 assess grade-level skills and understandings, including: match a picture to a given equation, and write an equation to represent a given picture (K.OA.A.1-2); find a partner of 10 and write a matching equation (K.OA.A.4, K.OA.A.1); identify and describe 2-D or 3-D shapes and their attributes (K.G.A). Two misaligned items call for students to circle numbers used when counting by tens (1.NBT.A.1).
Module 10:
- All items on Check-Ups 1-2 and Interviews 1-2 assess Kindergarten skills and understandings, including: represent subtraction pictures with equations (K.OA.A.1); count to tell “how many?” and draw a given number of objects (K.CC.B.5); count objects in organized and scattered arrangements, and count out a given quantity (K.CC.B.5); copy a picture using composed shapes, and decompose shapes (K.G.B).
Module 11:
- All items on Check-Ups 1-2 and Interviews 1-2 assess Kindergarten skills and understandings, including: count and represent objects as a group of ten and __ more (K.NBT.A.1, K.CC.A.3); rote counting from a given number to 100 (K.CC.A.1).
Module 12:
- All items on Check-Up 1 and Interviews 1-2 assess Kindergarten skills and understandings, including: represent addition and subtraction pictures with equations, and solve addition and subtraction equations (K.OA.A.1); count forward from a given number (K.CC.A.1); addition fluency within 5 (K.OA.A.5).
- Check-Up 2 calls for students to identify “one more” and “one less” than a given quantity and given numbers. These items are tagged as K.CC.B.4/K.CC.B.4.C; “one more” questions are within the scope of this standard as it states: "each successive number name refers to a quantity that is one larger". Although the standard does not explicitly address finding "one less," it is mathematically reasonable for Kindergarten students to engage in this process, even though 1.OA.C.5 specifically relates counting to subtraction.
- Quarterly Tests: The majority of items on Tests 1-4 assess grade-level skills and understandings, including: represent pictures with equations and equations with pictures, and solve equations with objects and pictures (K.OA.A.1); count and represent objects as a group of ten and __ more (K.NBT.A.1, K.CC.A.3); copy a picture using composed shapes, and decompose shapes (K.G.B). Misaligned items: Test 2 item 1 and Test 4 item 2 call for students to identify whether given activities take a short time or long time (seems more like a precursor to 3.MD.A.1 elapsed time); Test 2 item 3 and Test 4 item 4 call for students to identify “one more” and “one less” than a given number on the number path (“one less” is 1.OA.C.5), as indicated in the previous bullet, this is mathematically reasonable; Test 2 item 6 and Test 4 item 5 assess days of the week, which is not part of CCSSM and is tagged as a “Developmental Activity” (DA).
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 Stepping Stones instructional materials for Kindergarten meet expectations for spending the majority of class time on the major work of the grade. The program materials allocate an appropriate amount of instructional time (approximately 72 percent of lessons) to standards identified as major work in Kindergarten. In addition, each lesson in the program includes Ongoing Practice activities, which review lesson content from previous modules or provide opportunities for ongoing practice in counting and subitizing, numeral writing, and fact fluency. Overall, these materials devote an appropriate amount of instructional time to grade-level standards.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The Stepping Stones instructional materials for Kindergarten meet expectations for spending the majority of class time on the major work of the grade. The program materials allocate approximately 72 percent of lessons to standards identified as major work in Kindergarten. Although some standards that are part of the major work of the grade have a limited focus in these materials, overall the Kindergarten program devotes an appropriate amount of instructional time to the major work of the grade level.
To review materials for this indicator, the team considered two perspectives: 1) the number of MODULES aligned to major work by cluster and standard; and 2) the number of LESSONS aligned to major work by cluster and standard. The review team found the second perspective to most accurately reflect the intent of this indicator. A third perspective (MINUTES) was not considered, as the publisher gives multiple options for implementation that would vary across classrooms.
- 100 percent of the program’s MODULES are aligned to major work of the grade (at or above the prescribed 65-85 percent). In Modules 1, 3, 4, 5, 6, 7, 8, 10 and 12, four of the six lessons (67 percent) are aligned to major work of Kindergarten; in Modules 2 and 9, five of the six lessons (83 percent) are aligned to major work of Kindergarten; all six of the lessons (100 percent) in Module 11 are aligned to major work of Kindergarten.
- Approximately 72 percent of the program’s LESSONS are aligned to major work of the grade. The Stepping Stones Kindergarten materials include twelve modules, each comprised of a series of six lessons; every lesson includes Whole Class, Small Group, and Ongoing Practice activities. Only the Whole Class and Small Group components of lessons were considered to determine alignment to major work.
- Approximately 40 of the 72 lessons (56 percent) in the Kindergarten program focus on K.CC standards. Users of this program should note that K.CC.B.5 is only targeted in four lessons, although the Ongoing Practice activities also allow students opportunities to practice counting objects in different arrangements; only four lessons focus on K.CC.C.6-7 (comparing groups and/or numerals), although students do spend time comparing groups as they practice sorting skills (K.MD.B.3).
- Approximately 21 of the 72 lessons (29 percent) in the Kindergarten program focus on K.OA standards. 17 of these lessons focus on K.OA.A.1; lessons provide limited practice with decomposing numbers less than ten (K.OA.A.3-4). None of the lessons in the program specifically target K.OA.A.5; however, fact fluency is targeted in Ongoing Practice pages.
- Approximately 6 of the 72 lessons (8 percent) in the Kindergarten program focus on K.NBT.A.1. Lessons provide limited practice with numbers 11-19.
- All lessons in the program include Ongoing Practice pages. In Lessons 1, 3 and 5 of each module, these pages develop important skills and understandings from major clusters, including: counting and subitizing (K.CC.A-B), writing numerals (K.CC.A.3), and addition and subtraction fact fluency (K.OA.A.5); Lessons 2, 4 and 6 are designed to review lesson content from previous modules.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The Stepping Stones instructional materials for Kindergarten partially meet expectations for coherence and consistency with the standards. Supporting work for Kindergarten is connected to major work as appropriate, but many of these connections are not fully explored. The Stepping Stones program has designated a viable amount of grade-level content for one school year. The Kindergarten program materials generally follow the learning progressions outlined in the CCSSM; however, some important mathematical content is not fully explored and may not allow students to reach the depth of understanding necessary to be successful in future grades. The program includes a minimal amount of content that is not directly related to grade-level learning, but users could make adjustments without compromising the structure of the program. Additionally, the lessons and modules as designed allow students to make connections between concepts to develop a depth of understanding; however, many standards are taught as stand-alone skills and ideas, rather than as parts of a larger conceptual whole. Overall, the Kindergarten instructional materials support students in making mathematical connections, though not always to the full depth of the standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The Stepping Stones instructional materials for Kindergarten partially meet expectations for enhancing focus and coherence by engaging students in the major work of the grade. In most cases, supporting work is connected to major content at the grade level; however, in some of these cases, connections are not fully explored. Reviewers also noted some instances where natural connections are missed or only minimally explored.
- A natural connection between supporting and major work exists when students sort and classify objects into categories (K.MD.B) and then count the groups of objects (K.CC). In Lessons 1.5 and 1.6, students sort objects in different ways and describe sorting rules. The whole-class activities within these lessons do not involve students in counting the number of objects in each category, which would be a natural connection. The small group activities continue sorting practice, and call for students to compare group sizes and identify which groups have the most/least (K.CC.C). Lesson 2.6 has students graphing responses to a yes/no question, and then counting the total for each category (K.CC.A-B). The small group activities provide an opportunity for students to compare the groups of responses.
- Counting sides, corners, and faces (K.CC.B), while identifying, analyzing, drawing, and comparing 2D and 3D shapes (K.G.A-B), provides a natural opportunity to connect supporting content with major work in Kindergarten. Lessons 7.5, 7.6, 9.5, 9.6, and 10.5 call for students to identify and describe characteristics of curved and flat surfaces, sort objects based on attributes, draw various shapes, and compose pictures by joining shapes. The activities within these lessons seem to lend themselves to opportunities for students to practice counting the number of sides, corners, or faces; however, there is a minimal emphasis on counting in these activities.
- The “Grade K CCSS by lesson” document (start > stepping stones overview > resource tab) lists the targeted standards for each lesson. For the lessons that focus on supporting work, only the supporting standards are listed, even in lessons where the content supports and enhances major standards.
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 Stepping Stones instructional materials for Kindergarten meet expectations for designating a viable amount of grade-level content for one school year. The program materials include an appropriate amount of content to explore grade-level standards as written and would not require significant modifications.
- The Kindergarten program is organized into 12 modules, with a series of 6 lessons in each module. The authors of the program recommend two instructional days for each lesson, each spanning 45-60 minutes (support - slate tutorials - “Teaching a module in Stepping Stones (K)”). 12 modules x 6 lessons x 2 days = 144 days, which is a viable number of instructional days for one school year.
- The program authors suggest two different options for structuring lessons—alternating whole class and small group instruction each day; or teaching whole class lessons two days each week and small group lessons three days each week (support - slate tutorials - “Teaching a module in Stepping Stones (K)”). Both options advise spending 15 instructional days on each module, which includes time for formative and summative assessment opportunities. 15 days x 12 modules = 180 days, which is a viable amount of instructional time for one school year.
- Each lesson includes a whole class experience, two small group lessons, differentiation options, and ongoing practice; these lesson components support teachers in exploring content in multiple formats to foster deep learning of mathematical concepts within a reasonable timeframe.
- The Kindergarten program includes a minimal amount of instructional and assessment content that is not part of the Kindergarten CCSSM (see evidence for indicators 1a and 1b). Removing this content and/or modifying lessons would not significantly affect the timeline of the grade-level program.
- The team noted a lack of clarity regarding how to structure the material within each module (how to structure activities during small group instruction, how and when to administer assessments, how to integrate cross-curricular activities). There is also a concern that some individual lessons may not fill 45-60 minutes as written. Use of this program will require some teacher expertise in structuring class time effectively and encouraging student discourse to fully explore content.
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 Stepping Stones instructional materials for Kindergarten partially meet expectations for following the learning progressions outlined in the Standards. In many cases, non-CCSSM content and work from future grades is clearly identified. Materials give all students extensive work with targeted content; however, some grade-level content is not fully explored and may not allow students to learn at the depth required to be successful in future grades.
- Some content from future grades is clearly identified. For example, Lessons 5.5 and 5.6 focus on continuing growing and repeating patterns; on the “Grade K and the CCSS” documents, these lessons are tagged with >4.OA.5—building toward content in 4.OA.5. The publisher states: “Research has shown that providing children experiences with repeating and growing patterns in the early years of school lays the foundation for later work with number sequences and algebra." These lessons have some connection to using numbers and shapes for patterning, but the connections to grade-level content aren’t made explicit.
- Some of the fact fluency practice in modules 9, 10, and 12 (start - grade K - module __ - lessons - lesson __ - ongoing practice) extends beyond the limit of 5 set forth in K.OA.5, instead focusing on addition and subtraction within 10, which is the expectation for 1.OA.6. The Grade 1 standard is not identified in program materials.
- In Lessons 7.1 through 7.4 (tagged as K.OA.1 and K.OA.3), students are introduced to the idea of equality as a balance between two quantities. This work more closely ties to 1.OA.7, where students understand the meaning of the equal sign.
- Some lessons in the Stepping Stones program include content identified as a Developmental Activity (DA), “which has content that does not match any CCSSM but is considered essential for the development of certain Standards” (start - grade K - module 3 - mathematics - learning targets). In the Kindergarten program, this content includes subitizing and learning about the days of the week. Regarding subitizing, the authors explain the importance of subitizing as a precursor to addition and subtraction (start - grade K - module 3 - mathematics - focus); this view is supported by the Counting and Cardinality Progressions document. Learning about days of the week, however, does not support grade-level CCSSM expectations.
- The instructional materials provide resources for differentiated learning that include opportunities for students at all levels to engage with lesson objectives and grade-level content. Every lesson includes a differentiation tab (start - grade K - module __ - lessons - lesson __ - differentiation) that includes differentiation ideas for extra help, extra practice, and extra challenge, all explicitly tied to the lesson’s learning target.
- Suggestions for English language learners are provided for each module. This tab (start - grade K - module __ - mathematics - english language learners) explains specific skills to work on throughout the module for ELL students.
- Ongoing practice pages in each module provide opportunities for students to practice skills that have been previously taught, as well as to develop important grade level fluency.
- Some major grade-level content is under-represented in lessons. Work with comparing numbers and quantities (K.CC.C) only occurs in 4 lessons. Work with decomposing numbers less than or equal to 10 (K.OA.A.3-4) only occurs in 3 lessons. Developing fluency with addition and subtraction within 5 (K.OA.A.5) is not explicitly taught in any lessons in this program and only occurs within ongoing practice activities. This under-representation may not be enough to cover the true depth of these standards.
- An expectation to relate grade-level concepts explicitly to content from previous grades does not apply for Kindergarten instructional materials.
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 Stepping Stones instructional materials for Kindergarten partially meet expectations for fostering coherence through connections at a single grade. The materials include some attention to CCSSM cluster headings, although this could be stronger. Lessons and problems generally connect across domains and clusters in natural ways and when mathematically important.
- Each module includes a list of learning targets (start - grade K - module __ - mathematics - learning targets) that are tied to Kindergarten standards and organized beneath the related cluster statements. Many of the learning targets seem to be derived from individual standards, rather than cluster statements.
- The program materials don’t reference cluster headings in individual lessons or on assessments. Cluster notation is not used on either of the “Grade K and the CCSS” documents.
- Only 13 of the 72 lessons in the program explicitly connect related standards within clusters (“Grade K and the CCSS By Lesson” document). These connections only occur around: K.CC.A Know number names and the count sequence (Lessons 1.2, 5.2, 5.3, 10.4, 11.4, 12.2 and 12.4); K.CC.B Count to tell the number of objects (Lessons 2.3 and 2.4); K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from (Lessons 7.3 and 9.1); and K.MD.A Describe and compare measurable attributes (Lessons 4.5 and 4.6).
- The instructional materials connect students’ understanding of counting (K.CC.A) to cardinality (K.CC.B) as they create groups of objects to match given situations, match number to quantity, write numerals, work with relative positions of numbers, and understand benchmarks of 0 and 10 (Lessons 1.1-1.4, 2.1-2.4, 3.2-3.4, 5.1, 5.4, 12.4). An example of this natural connection occurs in Lesson 2.1 when students work with the five-frame to represent quantities of 1-9.
- The instructional materials connect students’ understanding of counting (K.CC.A) to comparing numbers and quantities (K.CC.C) as they compare and identify quantities that are greater/less (Lessons 4.1-4.4). An example of this natural connection occurs in Lesson 4.3, where students use counting skills to compare pictorial quantities of numbers to 10 in order to identify the quantity that is less.
- The instructional materials connect students’ understanding of counting and cardinality (K.CC) to addition and subtraction concepts (K.OA) as they develop an understanding of these operations, explore the commutative property, and decompose 10 (Lessons 5.4, 6.1-6.4, 7.2-7.4, 8.2, 8.4, 9.2, 9.4, 10.2, 12.2). An example of this natural connection occurs in Lesson 6.4 when students use a number track as a tool to explore addition concepts.
- The instructional materials connect students’ understanding of counting and cardinality (K.CC) to numbers greater than 10 (K.NBT) as they represent teen numbers as a group of ten ones and some more ones (Lessons 10.3-10.4, 11.2, 11.5-11.6). An example of this natural connection occurs in Lesson 10.3 when students count to match a given representation to a teen number, and represent a given teen number with a picture.