Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Kindergarten partially meet the expectation for alignment to the CCSSM. The materials partially meet expectations in the areas of focus and coherence and partially meet the expectations in the areas of rigor and the MPs. In the area of focus within the grade, there is a small number of above, grade-level topics included in the assessments, but it does not impact the structure of the materials. The materials spend an appropriate amount of class time on major work. In the area of coherence, the materials include content that is viable for one school year, but they only partially meet the expectations for the remainder of the indicators within coherence. The three aspects of rigor are well balanced, but each individual aspect of rigor is only partially met. In the area of practice-content connections, the materials typically identify the MPs, but they do not consistently enrich the content and do not attend to their full meaning. Students also do not consistently construct viable arguments or analyze the arguments of others, but the materials do explicitly teach the specialized language of mathematics.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
11
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
11
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Partially Meets Expectations

+
-
Gateway One Details

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 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
-
Criterion Rating Details

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 instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

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 1b

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.
4/4
+
-
Criterion Rating Details

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.
4/4
+
-
Indicator Rating Details

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 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
5/8
+
-
Criterion Rating Details

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.
1/2
+
-
Indicator Rating Details

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.
2/2
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-
Indicator Rating Details

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.
1/2
+
-
Indicator Rating Details

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.
1/2
+
-
Indicator Rating Details

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.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for Gateway 2: Rigor and MPs. All three aspects of rigor are present and attended to in the materials, though with varying degrees of emphasis. The program does a solid job of exploring and building understanding of counting and cardinality, as well as addition and subtraction concepts. Understanding teen numbers as a foundation for place value concepts is underdeveloped in this program, and there are few opportunities for students to engage in solving word problems. All eight MPs are included in ways that allows students to engage purposefully with grade-level concepts; however, some practice standards are under-represented, most notably MP1, Make sense of problems and persevere in solving them. The program materials set up opportunities for students to engage in mathematical reasoning as they discuss concepts and construct arguments; however, many of these opportunities are structured as whole-class activities, with little focus on student discourse or critiquing the reasoning of others. The Stepping Stones program does a solid job of emphasizing the importance of mathematical language. Overall, the Stepping Stones instructional materials for Kindergarten partially meet expectations for Gateway 2 and therefore will not proceed to Gateway 3.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
5/8
+
-
Criterion Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for Rigor and Balance. The Kindergarten program emphasizes the use of concrete materials and visual representations to support students’ conceptual understanding of counting and cardinality and addition and subtraction; however, there is an under-emphasis on developing an understanding of place value with teen numbers. The program includes opportunities for students to practice grade-level fluencies in every lesson; however, the materials don’t explicitly support the development of addition and subtraction fact fluency within five. The program includes opportunities for students to explore addition and subtraction in real-world contexts; however, there are few opportunities for students to independently explore and solve word problems. Overall, the Kindergarten materials include a balance of the three aspects of rigor as appropriate.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
1/2
+
-
Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for developing conceptual understanding of key mathematical concepts. The program consistently devotes instructional time to the use of manipulatives and multiple representations to introduce and develop students’ understanding of numbers and counting, as well as addition and subtraction. There are missed opportunities to develop a deep understanding of teen numbers as a foundation for place value.

K.CC.A-B

  • The publisher identifies three aspects that help students develop a full understanding of numbers (start - grade K - module 1 - mathematics - focus): a concrete or pictorial representation (visual), a sound or number name being said (auditory), and a written numeral or number word (written). At least two of these three aspects are included in lessons that focus on understanding numbers and counting. An example occurs in Lesson 1.4, where students are given cards with numerals, number words, or pictorial representations of the numbers 1 to 5 (visual/written). The teacher calls out a number (auditory), and any student with a matching card stands up; those students then clap as many times as the number called.
  • The Kindergarten program includes opportunities for students to engage in subitizing, where students practice recognizing numbers as groups rather than as individual objects. This emphasis on subitizing allows students to build number sense and prepares them to explore addition and subtraction concepts.
  • Visual representations are used to help students visualize numbers and quantities (five-frame and ten-frame), as well as to understand the relative position of numbers (number track) and explore concepts of one more and one less.

K.OA.A

  • The Kindergarten program has a strong focus on building a conceptual understanding of addition and subtraction, by structuring lessons purposefully using a concrete-pictorial-abstract approach (start - grade K - module 1 - mathematics - mathematical practices - resource tab - KMP2 video). For example, students begin to explore addition in module 6 by acting out situations (Lesson 6.1) and using manipulatives (Lesson 6.2). As students continue exploring, they add by making jumps on a number track (Lesson 6.4), and also drawing and analyzing pictures that represent addition stories. As students progress, they write addition sentences using numbers and words (Lesson 7.4: "2 add 5 is 7"), and then finally students write equations with symbols (Lesson 8.1: "2 + 5 = 7").
  • “Concrete materials and/or pictures are always used to assist children” in developing an understanding of addition and subtraction concepts (start - grade K - module 6 - mathematics - focus). “[Students] use stories and concrete/pictorial materials to identify the special feature of [addition] – the number in each of the parts that form the total.” For example, in Lesson 8.4, students use linking cubes to model situations in a story, as they explore pairs of numbers that equal 10.
  • As students transition to pictorial representations of subtraction, lessons are built around the idea of active subtraction: “When [children] work with pictures and it is not possible to move the objects, new words need to be introduced. The lessons suggest ‘cross out’ and ‘cover’ [as alternatives to ‘take away’]” (start > grade K > module 9 > mathematics > focus), which supports students understanding of the meaning of subtraction.
  • Whole class lessons conclude with reflection time, where students are encouraged to verbalize their developing understanding of addition and subtraction concepts. Some examples of conceptual reflection questions include: Lesson 6.3 “The example shows that 8 add 2 makes 10. What are some other ways that you could make 10 with two groups?” Lesson 8.1: “What is happening in each picture? What numbers do you know for each story? What numbers do you need to find out for each?” Lesson 12.2: “What is the difference between adding and subtracting?”

K.NBT.A

  • In discussion of the mathematics of module 11 (start - grade K - module 11 - mathematics - research into practice), the publisher states: “Because the number[s] 11 through 20 are so important to future counting, basic facts, and mental computation, it is sensible to devote special attention to them.” However, only 6 of the 72 lessons in the Kindergarten program focus on exploring the numbers 11-19; 2 of the 6 lessons focus on using pennies and dimes to represent teen numbers.
  • Students begin their exploration of teen numbers in Lessons 10.3 with the numbers 14, 16, and 17 because these number names are considered “easy.” Students begin by examining the letters in the number names, and writing the numerals, and then recall real world contexts where they have seen these numbers used. The student journal page calls for students to write the number words and then draw a matching quantity. Lesson 10.4 follows a similar structure using 19, 18, and 15. Each of these lessons ends with a brief activity with the teacher saying: “I’m thinking of a number that has one group of ten and (nine) more,” and then expects students to respond with the correct number, even though the structure of “ten ones and some more ones” wasn’t explored.
  • Lessons 11.2 and 11.3 develop the understanding of teen numbers as a group of ten ones and some more ones, with pictorial representations and the use of ten-frames. These lessons explore K.NBT.1 in a way that strongly supports students’ beginning understanding of the place value system. Teachers using this program should supplement with more lessons like these to develop this concept more fully.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for attention to procedural skill and fluency. Overall, the program materials appropriately develop procedural skill and fluency with rote counting, number writing and recognition, and fact fluency throughout the year. Students have daily opportunities to practice and develop these skills; however, a significant portion of the exercises for developing fact fluency extend beyond addition and subtraction within 5 (K.OA.5).

  • Rote counting practice, number writing, and number recognition are targeted routinely over the course of the year. Many lessons launch with counting practice before addressing the day’s learning target. Counting to 100 (K.CC.1) is explicitly targeted within lessons in modules 1, 3, 4, 5, 6, 7, 8, 10 and 12. Counting forward from a given number (K.CC.2) is explicitly targeted within lessons in modules 4, 6, 9, 11 and 12. Writing numbers (K.CC.3) is explicitly targeted within lessons in modules 1, 2, 5, 10 and 11.
  • Lessons 1, 3, and 5 in each of the first eight modules include supplemental whole-class “fluency practice” activities with a focus on developing counting and subitizing skills (K.CC.A-B). Lessons 2, 4 and 6 in each of the first eight modules include “ongoing practice” student pages for the development of counting skills, number writing, and number recognition (K.CC.A).
  • Progress toward fluency and procedural skill is interwoven with students’ developing conceptual understanding of the properties of operations. Students’ practice with fact fluency doesn’t begin until module 9, after students have had ample time to explore addition and subtraction concepts.
  • Although K.OA.5 is included in the learning targets for modules 9 and 12, the program does not have any whole-class or small-group lessons in these modules that specifically focus on developing addition and subtraction fact fluency within 5. All of students’ practice around fact fluency occurs in supplemental activities.
  • Lessons 1, 3 and 5 in each of the last four modules include supplemental whole-class “fluency practice” activities with a focus on developing fact fluency (K.OA.5). Lessons 2, 4 and 6 in each of the last four modules include “ongoing practice” student pages for developing fact fluency (K.OA.5). It should be noted that a significant amount of this practice (approximately one-third of all exercises) extends beyond addition and subtraction within 5, and practice doesn’t strategically emphasize mastering facts within 5 (K.OA.5) before directing students to explore facts within 10 (1.OA.7).

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for attention to engaging applications of grade-level mathematics. Overall, the program devotes adequate time to exploring addition and subtraction concepts using actions, manipulatives, pictures, and equations; however, there needs to be more problems presented in real-world contexts.

  • K.OA.2 specifically calls for students to apply their mathematical understanding as they “solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.” Only 4 of the 72 lessons in the Kindergarten program explicitly address this standard, according to the “Grade K and the CCSS” document. These 4 lessons include opportunities for students to apply counting skills as they act out addition and subtraction situations, using objects, pictures, and/or interactive software to write and solve equations.
  • The K.OA.A cluster heading calls for students to understand putting together, adding to, taking apart, and taking from situations (see Table 1, CCSSM page 88). The K-2, Operations and Algebraic Thinking Progressions document further identifies four specific problem subtypes that Kindergarten students should explore. Much of the work in this program is limited to adding to and taking from situations with the result unknown.
  • There is a missed opportunity for students to work with put-together/take-apart situations where both addends are unknown in application settings. Exploration of these types of situations in application settings would support students with the CCSSM required fluency of adding and subtracting within 5 (K.OA.5).
  • Much of the work with word problems in the Kindergarten program happens in whole-class lessons. The teacher poses addition and subtraction situations orally, or students interpret pictorial representations of addition and subtraction situations. There are minimal opportunities for students to generate their own representations of a given situation.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten meet expectations for balancing the three aspects of rigor. Each of the three aspects of rigor are represented in the program materials; there is a balance of separate and combined treatment of conceptual understanding, procedural skill and fluency, and application.

  • Each of the three aspects of rigor are evident in students’ exploration of addition and subtraction concepts. Students use concrete materials and visual representations such as 5- and 10-frames and the number track to support their conceptual understanding of these operations. As students continue to explore addition and subtraction, lessons begin to develop skill and fluency with the introduction of the “think big, count small” strategy (counting on) and begin fact fluency practice. Throughout the Kindergarten program, addition and subtraction is put into context to engage students in application of their understandings.
  • There is some emphasis on fluency practice in each of the six lessons in every module. Students engage in whole-class (counting and subitizing practice) and individual activities (student practice pages) that promote the development of procedural skills.
  • Concrete materials, visual representations, and literature are used to develop conceptual understanding of key grade-level concepts. For example, Lesson 5.2 introduces a book to support students as they practice representing the numbers 1 to 9 using fingers, and matching pictorial representations to numerals and number words.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/10
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Criterion Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the MPs. The eight MPs are clearly identified within the instructional materials, although it should be noted that MP1 and MP5 are under-represented. The Kindergarten materials attend to the full meaning of some, but not all, of the eight MPs. The program materials emphasize mathematical reasoning by including opportunities for engaging students and supporting teachers in constructing mathematical arguments, although this is done inconsistently. The Stepping Stones Kindergarten program devotes more time and attention to constructing arguments, and significantly less time critiquing the arguments of others. There is a strong emphasis on developing an understanding of the specialized language of mathematics in order to support Kindergarten students in communicating their mathematical thinking clearly.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for identifying and using the MPs to enrich grade-level mathematics content. Overall, the MPs are clearly identified in the program materials at both the module and lesson levels, and the practice standards are connected to mathematical content. However, two of the eight practices are significantly underrepresented, and the team noted misidentification of MPs in some lesson materials.

  • The MPs are clearly identified in the instructional materials in multiple places. Within each module, there is a chart that identifies the MPs targeted in each of the module’s six lessons (start - grade k - module # - mathematics - mathematical practices). Users can also click on the Resources Tab to access a “Mathematical Practice Overview” document, which identifies the MPs targeted in each of the 72 lessons in the Kindergarten program. Within each lesson, the targeted MPs are listed in the learning objective for each lesson, as well as on a lesson contents chart (start - grade k - module # - lessons - contents).
  • There were some inaccuracies/inconsistencies in the materials when identifying targeted MPs. For example, the Overview chart indicates that MP3 and MP5 are taught in Lesson 10.6; however, the lesson contents chart and whole class lesson reference MP3 and MP6. Another inconsistency occurs in Lesson 12.2, where the Overview chart indicates that MP4 and MP8 are targeted; the lesson contents chart and whole class lesson identify MP3 and MP8.
  • The MPs are interwoven within the curriculum to enrich the grade-level content and are not taught as separate entities. Each lesson contains a pop-up text box that describes how the MP enriches the lesson. For example, in Lesson 6.4, students use the number track (MP5) to add numbers in a concrete way (K.OA.1); the text box reads: “SMP5 Students are making the connection between the number track and finding sums of two quantities.” A second example occurs in Lesson 5.2, where students use their fingers to represent quantities from one to ten and identify how many more fingers would be needed to make the quantity of 10 (K.OA.4, MP7); the text box reads: “MP7 As students figure out the number necessary to make 10, they are beginning to make use of structure. Making ten is a foundational concept.”
  • The Kindergarten program focuses more heavily on some of the MPs than others. MP1 and MP5 are significantly under-represented. MP1 is only targeted in 2 of the 72 lessons; this limited experience is not enough for students to explore and develop the skills and understandings needed to develop perseverance in problem solving. MP5 is only targeted in 7 of the 72 lessons; Kindergarten students need extensive experience working in the concrete stage with a variety of manipulatives. The program’s limited focus on this practice would not allow students to develop an understanding of how to select and use tools strategically.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for attending to the full meaning of each practice standard. The materials attend to the full meaning of some, but not all, of the eight MPs.

  • Most of the lessons in the Kindergarten program (68 out of 72) identify only one or two targeted MPs. This pointed focus allows teachers and students to build a solid understanding of the targeted practices as they relate to grade-level content.
  • Each module of the program includes this relevant commentary about the MPs (start - grade k - module # - mathematics - mathematical practices): “The Standards for Mathematical Practice describe the actions and ‘habits of mind’ that mathematically proficient student develop over time.” The Resources Tab includes links to professional learning videos which specifically focus on individual MPs and Habits of Mind in order to assist teachers in understanding the full meaning of these practice standards.
  • MP1 Make sense of problems and persevere in solving them is not fully attended to in the Kindergarten program. This MP is listed as a target in 2 of the 72 lessons within the program, which is not enough to reach the full depth of this standard. In Lesson 6.1, students act out stories to model addition, “looking to see if their stories make sense” (whole class, pop-up text box); as a first introduction to MP1, it is appropriate to focus only on sense-making in this lesson. In Lesson 7.3, the whole-class lesson focuses largely on reading and writing the equal sign, while students find the total number of two groups of objects. MP1 is listed as a target in this lesson, with the note that during Step 4 of the lesson, teachers should “look for those students that persist in finding more than one way of making 10” (pop-up text box). It is appropriate to focus only on perseverance here; however, there are no instructional moves included to help students understand the importance of building perseverance and how to do that.
  • MP5 Use appropriate tools strategically is not fully attended to in the Kindergarten program. This MP is listed as a target in 7 of the 72 lessons within the program (“Mathematical Practice Overview”), which is not enough to reach the full depth of this standard. In addition, while students are given opportunities to work with tools in many lessons, students are told which tool to use and are not provided opportunities to select tools to use in order to solve problems. In Lesson 2.6, students are introduced to the use of a 2-column “graph” as a tool to analyze data. In Lessons 3.2 and 3.3, students are introduced to the number track as way to identify numbers that come before and after a given number. In Lesson 6.4, students are given a number track to represent and complete addition equations. In Lesson 6.5, students explore the ideas of heavy and light; Step 4 calls for teachers to question students about how they might check to see if objects are heavier or lighter. In Lesson 6.6, students are introduced to the pan balance as a tool to compare the weight of two objects. In Lesson 12.4, students are again given a number track to identify one more/one less than a given number. [Lesson 10.6 is incorrectly identified.]
  • Each whole class lesson includes an opportunity for students to reflect on the day’s learning (step 4: reflecting on the work). During this component of each lesson, the teacher poses questions to students about the work they completed in their journals and how that work ties to the day’s objective. This part of the lessons offers opportunities for students to engage in mathematical reasoning (MP2), construct arguments (MP3), explain how they used a particular tool or strategy (MP5), and/or explain an understanding of repeated reasoning (MP8).

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for prompting students to construct viable arguments and critique the arguments of others, concerning key grade-level mathematics detailed in the content standards. Many of the lessons include opportunities for students to construct viable arguments; however, these opportunities are often posed as whole-group questions. The program materials include few instances that prompt students to analyze the arguments of others.

  • A majority of the opportunities for children to engage in constructing and analyzing mathematical arguments are posed as whole-group questions during whole-class lessons. Students are only able and held accountable to share their thinking if called on by the teacher, which does not ensure that all students practice this important mathematical reasoning.
  • A significant number of the lessons tagged with MP3 focus on constructing viable arguments; there are very few opportunities available for students to critique the reasoning of others in this program. In Lesson 4.2, for example, students analyze pictorial quantities and are asked: “Which number is greater? How do you know?” The lesson doesn’t prompt students to consider the rationale of their peers. In Lesson 11.3, the class generates a list of equations to represent teen numbers: 10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13; students are asked to predict the next number sentence, and work with a partner to prove that the number sentences are true using a strategy of their choice. Pairs are invited to show and explain their work, but there is no mention of critiquing peers’ thinking or strategy choice.
  • MP3, "Construct viable arguments and critique the reasoning of others", is specifically tagged in 15 of the 72 Kindergarten lessons, according to the “Mathematical Practice Overview” document. This means that students are prompted to construct arguments about mathematical content in 1 of every 5 lessons. In addition, MP3 is not targeted in any lessons in Modules 2, 8 and 9. This translates to approximately 45 days of instruction where instruction doesn’t intentionally focus on constructing and analyzing mathematical arguments. Teachers using this program will want to embed additional opportunities for students to engage in constructing and analyzing arguments.
  • Each whole-class lesson includes an opportunity for students to reflect on the day’s learning (step 4: reflecting on the work). During this component of each lesson, the teacher poses questions to students about the work completed in Student Journals and how that work ties to the day’s objective. For example, in Lesson 4.3, students compare pictorial quantities of 1-9 to determine which amount is less; the teacher asks: “How do you know the number is less than 4?” Another example occurs in Lesson 12.2, where students are working with the concept of subtraction; the teacher asks: “What is the difference between adding and subtracting?” These questions allow students to construct arguments about their mathematical thinking, even in lessons that aren’t specifically tagged with MP3.
  • The Kindergarten program includes missed opportunities to engage students in constructing and analyzing mathematical arguments. For example, Lessons 1, 3 and 5 in Modules 1-8 include ongoing “fluency practice” that focuses on developing students’ counting and subitizing skills; however, the teacher materials only state: “As you advance each slide, have the students count the objects or subitize the quantities.” Another example of a missed opportunity occurs in Lesson 1.3, where students are connecting number to quantity. Students are prompted to compare their work with a partner, and “raise your hand if you and your partner have the same answer. If we move our fingerprint faces around, will we still have four faces. How do you know?” This could be an opportunity for students to engage in partner talk, but the materials do not explicitly call for this.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten partially meet expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Materials assist teachers in engaging students in constructing and analyzing arguments, although this assistance is inconsistent and focuses largely on constructing arguments more than analyzing arguments.

  • Teacher notes in some lessons are lacking in explicit instruction in how to engage students in sharing their mathematical thinking. Simply posing the question “How do you know?” is not explicit enough to develop Kindergarten students’ abilities to construct and analyze arguments. Simply hoping that students say certain things is also not enough to support teachers in developing this math practice. An example of this occurs in Lesson 11.3, where students represent and name teen numbers; the MP3 pop-up text box states: “Students demonstrate [MP3] with responses such as, ‘The sums are one bigger each time’ or ‘This is just like counting except now there is a ten there’.” There is no guidance for teachers in how to support students in crafting such responses.
  • This program gives more time and attention to constructing arguments, and significantly less time critiquing the arguments of others. Teachers are rarely prompted to promote partner talk or plan opportunities for students to consider incorrect mathematical reasoning.
  • Throughout each lesson, suggested questions for teachers to pose to students are highlighted in pink.
  • The Kindergarten materials for each module include a “research into practice” and “focus” page that gives teachers a summary of the mathematics being taught, why the content is important, and how students are exploring the content in a developmentally appropriate way. This information is helpful as it also draws attention to questioning that could play into reasoning and constructing a mathematical argument. For example, in Module 5 (start - grade k - module 5 - mathematics - focus), the publisher states: “For numbers 5 and 10, students should be encouraged to make 2 statements, for example, ‘Seven is 2 more than 5, and seven is 3 less than 10.’
  • Each module of the program includes relevant commentary about the MPs (start - grade k - module # - mathematics - mathematical practices). The Resources Tab includes links to professional learning videos, which specifically focus on MP3 and Habits of Mind, in order to assist teachers in understanding the full meaning of this practice standard. The KMP3 video discusses the importance of student discourse in the mathematics classroom. The DHM2 video discusses justifying claims, proving conjectures, and distinguishing between agreement and logical necessity when constructing and analyzing arguments.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The Stepping Stones instructional materials for Kindergarten meet expectations for attending to the specialized language of mathematics. The program materials include instructional notes and varied opportunities for students to use and understand grade-level appropriate mathematical vocabulary, numbers, and symbols.

  • Each module of the program includes relevant commentary about the MPs (start - grade k - module # - mathematics - mathematical practices). The Resources Tab includes links to professional learning videos, which specifically focus on MP6 and Habits of Mind, in order to assist teachers in understanding the full meaning of this practice standard. The KMP2 video discusses using appropriate vocabulary and making sure student answers have enough specificity. The DHM1 video discusses using precise definitions with students; developing both mathematical and everyday language; having discussions with children (“debating, defining, and redefining”); and the need to use mathematical definitions to communicate clearly with others.
  • Each module includes a list of terms that will be used and developed to communicate mathematical thinking (start - grade k - module # - mathematics - language development), organized by domain. This language is grade-level appropriate, without being “watered down” (examples: Counting and Cardinality: compare, fewer, greater/less than, quantity; Operations and Algebraic Thinking: sum of two parts, addition symbol, total; Number and Operations in Base Ten: group of 10, teen, place value; Measurement and Data: compare, length, wide, wider, widest; Geometry: 2D, 3D, orientation, rectangular-based prism, square rectangle).
  • Within each lesson, teacher notes include explicit comments and questions (highlighted in pink) that teachers should use to model appropriate mathematical language for students. In addition, bold type indicates words, symbols, and/or number sentences exactly as they should be written and displayed for students.
  • Individual lessons within this program specifically focus on developing mathematical communication with words and symbols: Lesson 3.5, Using Spatial Language; Lesson 7.2, Reinforcing the Language of Equality; Lesson 7.3, Introducing the Equality Symbol; 8.1, Introducing the Addition Symbol; 10.1, Introducing the Subtraction Symbol; and 10.2, Using the Subtraction Symbol.
  • The program attends to the importance of connecting language to help build understanding. For example, in Module 1 (module 1 - mathematics - focus), program materials identify “three aspects that help students develop a full understanding of numbers”: concrete or pictorial representations, sound or number names that are said, and the written symbol (numeral or number word). Each lesson in Module 1 involves two of these three aspects to promote student understanding. In Module 4, lessons and activities pair “less than” (more difficult concept) with “greater than” (easier concept) to support student understanding. Students also make direct comparisons of objects in Module 4 to develop comparative and superlative language (tall, taller, tallest; heavy, heavier, heaviest).
  • The program materials include a Glossary, where users can search for a specific term.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Fri Apr 08 00:00:00 UTC 2016

Report Edition: 0

Title ISBN Edition Publisher Year
null 978-1-921959-79-0 null null null

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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