Kindergarten - Gateway 1

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).

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.

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.