Kindergarten - Gateway 2
Back to Kindergarten Overview
Note on review tool versions
See the series overview page to confirm the review tool version used to create this report.
- Our current review tool version is 2.0. Learn more
- Reports conducted using earlier review tools (v1.0 and v1.5) contain valuable insights but may not fully align with our current instructional priorities. Read our guide to using earlier reports and review tools
Loading navigation...
Rigor & Mathematical Practices
Gateway 2 - Does Not Meet Expectations | 55% |
|---|---|
Criterion 2.1: Rigor | 5 / 8 |
Criterion 2.2: Math Practices | 5 / 10 |
The instructional materials reviewed for Kindergarten do not meet the expectations for rigor and mathematical practices. The instructional materials partially meet the expectations for rigor and do not meet the expectations for mathematical practices.
Criterion 2.1: Rigor
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.
The instructional materials reviewed forKindergarten partially meet expectations for rigor and balance. The materials include specific attention to both conceptual understanding and procedural skill and fluency; however, there are limited opportunities for students to work with engaging applications. As a result, the materials do not exhibit a balance of the three aspects of rigor.
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.
The instructional materials for Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Cluster K.NBT.A focuses on working with numbers 11-19 to gain foundations for place value.
- Students work with K.NBT.A in Teacher Resources Part 2 Unit 10. Lesson 2 has students counting 11, 12, and 13 with and without ten frames, and Lesson 3 uses ten frames and number bonds to develop an understanding that teen numbers consist of ten ones and some more ones. Lessons 4-12 continue this development through all teen numbers.
K.OA.A focuses on understanding putting together and adding to, and understanding subtraction as taking apart and taking from.
- In Teacher Resources Part 1 Unit 7, students begin their understanding of addition within 5 by counting on (Lesson 2), acting out (Lesson 3), adding with objects and pictures (Lessons 4 and 5), Putting together with objects and pictures (Lessons 6-8), decomposing (Lessons 9 and 10), adding 1 and 0 (Lesson 12).
- Students continue their understanding in Teacher Resources Part 2 Unit 8 by continuing to use adding on strategies, acting out, objects, pictures, and decomposing.
- Teacher Resources Part 2 Units 11 and 12 extend student understanding from addition to subtraction. Again, students use counting strategies, objects and pictures, composing, and subtraction.
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.
The materials for Jump Math Kindergarten meet the expectations for procedural skill and fluency by giving attention throughout the year to individual standards which set an expectation of procedural skill and fluency.
- The teacher's edition gives strategies for mental math in the teacher's edition page A-29. The strategies are not incorporated into the lesson plans for the teacher.
- There are games in the teacher's edition pages A34-A35 that help to build student fluency. These games focus on learning pairs to 5 and 10, but these games are not mentioned in the lessons.
Standard K.OA.5 requires students to fluently add and subtract within 5.
- Much of the work in Kindergarten is around adding and subtracting. Teacher Resources Part 2 Units 7, 8, 11, and 12 focus on Operations and Algebraic Thinking standards.
- Teacher Resources Part 2 Unit 7 Lesson 2 has students counting on to 5. Subsequent lessons in the unit include Acting Out with Addition, Adding with Objects, Adding with Pictures, Putting Together with Objects/Pictures, and Decomposing 5.
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
The materials for Kindergarten Jump Math do not meet the expectation for being 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.
There are 25 lessons in the series that identify a focus on K.OA.2. This cluster calls on students to understand putting together, adding to, taking apart, and taking from situations with unknowns in all positions. Work in this series is limited to adding to, taking from, and putting together with the result unknown as well as put together with both addends unknown. This represents 4 of the 12 possible application situations for this cluster as identified in Table 1 of the Common Core Glossary. There were no problems that addressed add to change unknown, add to start unknown, take from change unknown, take from start unknown, put together addend unknown, take apart total unknown, take apart addend unknown, and take apart both addends unknown. In addition, Teacher Resources Part 2 Unit 8 Lessons 21 and 22 and Teacher Resources Part 2 Unit 11 Lesson 31 list K.OA.2 as one of the standards addressed in the lesson, but the lessons do not contain word problems. Therefore, this series does not provide the depth called for in the cluster.
Word problems included in the instructional materials are often routine.
- Teacher Resources Part 2 Unit 7 Lesson 6: "I like apples and pears, so I buy one apple and two pears. How can I find out how much fruit I bought in all?"
- Teacher Resources Part 2 Unit 8 Lesson 18: "Friendly Farm has seven cows. Welcome Farm has three cows. How many cows in all?"
- Teacher Resources Part Unit 11 Lesson 28: "I have five apples. Kate eats two apples. How many apples are left?"
- AP book K.2, pg. 191: "3 ants climb a wall, 2 fall down. How many ants are on the wall now?"
- AP book K.2, pg. 185: "3 cats chase a ball, 2 dogs chase a ball. How many pets in total?"
- AP book K.2, pg. 165: "Draw circles to show bunnies. Cross out circles to show bunnies that hop away. How many bunnies stay?"
Lessons focus on a whole class approach; therefore, most word problems are performed as a whole class, not independently.
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.
The instructional materials partially meet the expectation that the materials balance all three aspects of rigor with the three aspects almost always treated separately within the curriculum including within and during lessons and practice. Overall, the majority of the lessons focus on procedural skills and fluency with very few opportunities for students to discover and apply procedures for themselves. There is a not a balance of the three aspects of rigor within the grade.
- The three aspects of rigor are not pursued with equal intensity in this program.
- Conceptual knowledge and procedural skill and fluency are evident in the instructional materials. There are multiple lessons where conceptual development is the clear focus.
- The instructional materials lack opportunities for students to engage in application and deep problem solving in real world situations.
- There are very few lessons that treat all three aspects together due to the relative weakness in application. However, there are several lessons that include conceptual development leading to procedural practice and fluency.
- There are minimal opportunities for students to engage in cognitively demanding tasks and applications that would call for them to use the math they know to solve problems and integrate their understanding into real-world applications.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The instructional materials reviewed for Jump Math Kindergarten do not meet the expectations for practice-content connections. Although the materials meet expectations for identifying and using the MPs to enrich mathematics content, they do not attend to the full meaning of each practice standard. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of each MP, especially MP3 in regards to students critiquing the reasoning of other students and teachers engaging students in constructing viable arguments and analyzing the arguments of others.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The instructional materials reviewed for Kindergarten meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
In Teacher Resources Part 1, a discussion of MPs is given starting on page A-22 . According to a statement in the materials, “We guide students to develop Mathematical Practice Standards by explicitly teaching the skills required.” The MPs are not listed in the beginning with the lesson goals but in parentheses in bold within the lesson at the part where they occur. As stated on page A-22 in Teacher Resources Part 1, "While the development of these practices occur in virtually every lesson, only some lessons have grade-level application to the standards. These grade-level applications are identified in the margin"
Overall, the materials clearly identify the MPs and incorporate them into the lessons. The MPs are incorporated into almost every lesson; they are not taught as separate lessons. All of the MPs are represented and attended to multiple times throughout the year, though not equally. In particular, MP5 receives the least attention.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials reviewed for Kindergarten do not meet the expectations for carefully attending to the full meaning of each practice standard. The publisher rarely addresses the Mathematical Practice Standards in a meaningful way.
The materials only identify examples of the Standards for Mathematical Practice, so the teacher does not always know when a MP is being carefully attended to. MPs are marked throughout the curriculum, but sometimes the problems are routine problems that do not cover the depth of the Math Practices. Many times the MPs are marked where teachers are doing the work.
Examples where the material does not meet the expectation for the full meaning of the identified MP:
- MP1: In Teacher Resources Part 2 Unit 12 Lesson 35, Activity 1 is marked as MP1. Students create subtraction stories. Students are given magazines and told to cut out pictures to create a subtraction story with an associated number sentence. Students share these with classmates, but they are not looking for entry points to solve a problem. It is a missed opportunity to have students trade stories and create the subtraction number sentence for another student’s story which would allow them to make sense of math problems and persevere in problem solving. Another example is found in Teacher Resources Part 1 Unit 2 Lesson 10; in the lesson, students practice writing the digit 4 as a whole class. Students who finish the whole class lesson early can go to the Assessment and Practice Book Part 1 Unit 1 Lesson 10 and trace the number 4. While writing the digit 4 is a Kindergarten standard, there is no mathematical thinking occurring while students are tracing digits. Students do not have to make sense of mathematical situations or persevere while tracing digits.
- MP4: In Teacher Resources Part 1 Unit 3 Lesson 21, students are using a blackline master to match houses with doors. This is a matching activity, and there is no modeling.
- MP5: In Teacher Resources Part 2 Unit 7 Lesson 9, students are directed to use five frames for counting which does not allow the opportunity to choose an appropriate tool for the math. Typically students do not select tools when MP5 is indicated in a lesson.
- MP6: In Teacher Resources Part 2 Unit 14 Lesson 6, students fill containers to determine which has a larger capacity. Students work in groups filling containers with sand and rice to determine which holds more and which holds less. While students are talking and working in groups they are not required to use the precise vocabulary of the lesson during their group work (i.e. bigger, less, more, same amount, and smaller).
- MP7: While the publisher attaches MP7 to many lessons, sometimes the structure is found in the standard itself and not the indicated exercise. For example, in Teacher Resources Part 1 Unit 2 Lesson 12, in the activity “Associating written numbers 1, 2, 3, 4, 5, with spoken numbers” the teacher makes a small deck of card numbered 1-5. The teacher holds up a number card for each number and says: “We learned that this is the number 5 .” The teacher repeats as needed and then changes the question to “What is this number?” In this activity students are not discerning anything about the structure of this series of numbers; they are simply matching the digit with its matching word form. Another example is Teacher Resources Part 1 Unit 5 Lesson 30, Activity 2. In this activity students have cards numbered 5-7. The teacher clearly says a number from 5 to 7, and students hold up the number card for the number read. These problems do not require students to look closely to discern a pattern or structure.
Indicator 2g
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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.
The instructional materials reviewed for Kindergarten partially meet expectations that the materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Materials occasionally prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards; however, there are very few opportunities for students to both construct arguments and analyze the arguments of others together.
In the lessons provided in the Teacher Resources Part 1 and 2, examples identified as MP3 are often in a whole group or small group discussion. Students rarely have the opportunity to either construct viable arguments or to critique the reasoning of others in a meaningful way because of the heavy scaffolding of the program. For example, in Teacher Resources Part 2 Unit 10 Lesson 2, students are asked if 11 or 12 is greater and then asked to explain why. Students are not given an opportunity to analyze the arguments of others.
There are several instances where MP3 is incorrectly identified in the materials:
- Teacher Resources Part 1 Unit 1 Lesson 4, the Counting Correctly activity, is labeled MP3. In this activity students are taught three elements of counting objects correctly- touching each object once, saying one number for every object touched, and saying the counting numbers in the correct order. Students show a thumbs up or down to indicate if the teacher is counting correctly, but students are not constructing viable arguments or analyzing the arguments of others.
- In Teacher Resources Part 1 Unit 4 Lesson 33 the teacher is holding up fingers to represent the numbers 9 and 10. The teacher shows either 9 or 10 and has the class say the number together. Then the teacher is then prompted to ask, “Is there another way to show 10 using my fingers? (no)." Students are not constructing viable arguments or analyzing the arguments of others.
- In Teacher Resources Part 2 Unit 9 Lesson 16 students are shown a 3-D shape such as a sphere. The teacher asks “Is this a sphere,” and students respond with a thumbs up or down. Students provide no justification about why it is a sphere.
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.
The materials reviewed for Kindergarten partially meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
Within lessons, the teacher materials are not always clear about how teachers will engage and support students in constructing viable arguments or critiquing the reasoning of others. Materials identified with the MP3 standard often direct teachers to "chose a student to answer" or "have a volunteer fill in the blank." Questions are provided but often do not encourage students to deeply engage in MP3. In addition, although answers are provided, there are no follow up questions to help re-direct students who didn’t understand.
- Teacher Resources Part 1 Unit 1 Lesson 14 page 57: The teacher is told to alternate between counting correctly and incorrectly and have students signal if the teacher has counted correctly or incorrectly. "Have students identify mistakes and discuss them as a class."
- Teacher Resources Part 1 Unit 3 Lesson 2 page 9: "Does this look like a wheel? (no) Is this a circle? (no)."
- Teacher Resources Part 1 Unit 4 Lesson 33 page 30: The teacher holds up either 9 or 10 fingers and has the class say the number together. Then asks "Is there another way to show 10 using your fingers? (no)." The teacher calls out 9 or 10 and has students show the number of their fingers.
- Teacher Resources Part 2 Unit 9 Lesson 17: The teacher holds up various shapes, and students do thumbs up or thumbs down if the shape is a cylinder. It also states "you can prompt students by asking whether the object looks like a can."
Overall, some questions are provided for teachers to assist their students in engaging students in constructing viable arguments and analyzing the arguments of others; however, additional follow-up questions and direct support for teachers is needed.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Jump Math Kindergarten partially meet the expectation for attending to the specialized language of mathematics. Overall, there are several examples of the mathematical language being introduced and appropriately reinforced throughout the unit, but there are times the materials do not attend to the specialized language of mathematics.
Although no glossary is provided in the materials, each unit introduction includes a list of important vocabulary, and each lesson includes a list of vocabulary that will be used in that lesson. The teacher is provided with explanations of the meanings of some words.
- In Teacher Resources part 1, page A-21 states that “words being introduced and defined for the first time are presented in bold font in the list and in italics in the lesson plans.”
- Unit introductions sometimes include vocabulary. For example, in Teacher Resources Part 1 Unit 3 page E-1 , there is discussion about the teacher using "quadrilaterals," "pentagons," "parallelograms," and so on but states "you do not need to use these words with your students."
- Vocabulary words are listed at the beginning of each lesson plan in the Teacher’s Guide, but definitions, if any, are within the lesson.
While the materials attend to the specialized language of mathematics most of the time, there are instances where this is not the case.
- Often students are not required to provide explanations and justifications, especially in writing, which would allow them to attend to the specialized language of mathematics. For example, in Teacher Resources Part 2 Unit 9 Lesson 15, vocabulary includes the terms count and number. Each time, however, that these words are used in the lesson, they are used by the teacher. The student is not required to provide an explanation or justification for their answers that would allow them to use the words in this lesson.
- Many of the discussion prompts provided are guided by the teacher so that the student is merely repeating the teacher's language. This limits student ability to actively use mathematical language.