Kindergarten - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 72% |
|---|---|
Criterion 2.1: Rigor | 6 / 8 |
Criterion 2.2: Math Practices | 7 / 10 |
The Kindergarten My Math instructional materials partially meet the expectations for rigor and mathematical practices. The instructional materials partially meet the expectations for the criterion on rigor and balance and partially meet the expectations on the criterion for practice-content connections due to not fully attending to the meaning of each mathematical practice standard. Overall, the instructional materials are strong in regards to the language of mathematics.
Evidence updated 10/27/15
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 for Kindergarten My Math partially meet the expectations for rigor and balance. The instructional materials do not give appropriate attention to conceptual understanding and procedural skill and fluency. Application is appropriately addressed, and the materials address these three aspects with balance, not always treating them separately and not always together. Overall, the instructional materials do not always reflect the balances in the CCSSM, which helps students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.
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.
Kindergarten My Math materials partially meet the expectations for developing conceptual understanding of key mathematical concepts, where called for, in specific content standards or cluster headings.
- The majority of the homework contains problems that provide students the opportunity to practice procedural skill and fluency and not conceptual understanding.
- Procedures for addition/putting together and subtraction/taking apart are emphasized in Kindergarten. More attention is needed for the conceptual understanding of addition/subtraction
- The content in chapters 1 and 4 through 6 address standards that are explicitly outlined as conceptual standards. (K.CC.B.4 and K.NBT.A.1)
- Of the 88 lessons, 16 are focused specifically on the conceptual understanding standards.
- The majority of lessons in Kindergarten My Math have a section called “Investigate the Math” which targets conceptual understanding. This is contained in the online lesson presentation. For example, see page 705B in the teacher edition.
- All lessons in the series have a section called “Talk Math” which targets conceptual understanding. This is contained in the online lesson presentation. For example, see pages 495 – 496 in the teacher and student editions.
- In the student edition, some of the lessons in Kindergarten My Math have a section “Explore and Explain” to begin the lessons which targets conceptual understanding. For example, see page 705 in the teacher and student editions.
- Most Investigate the Math is conceptual understanding; however, there are a few instances where this is not true. For examples, see chapter 1, lesson 8, page 55B TE; chapter 2, lesson 10, page 151B TE; and chapter 2, lesson 11, page 157B.
- The time spent on conceptual understanding of numbers is limited. For example, understanding 0 – 5 only has 15 days of instruction, and only two of those lessons, lessons 1 and 3, actually deal with the conceptual understanding.
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.
Kindergarten My Math materials partially meet the expectations for giving attention throughout the year to individual standards to set an expectation of procedural skill and fluency. Lessons contain some examples of fluency practice pages.
- Lessons contain few examples with fluency practice pages.
- In the student edition, K.OA.5 is addressed in chapters 5 and 6. For example, see chapter 5, pages 339-344, and chapter 6, pages 415–420.
- Homework does not contain multiple opportunities for students to practice fluency.
- A “Fact Dash” game is available online with the student login to practice fluency. Students can select the operation and number facts.
- The online teacher edition does have fluency pages available for printing.
- “Sail through the Math” is an app game for fluency and is available for purchase ($1.99).
- Eight lessons out of 89 address K.OA.A.5 Fluently add and subtract within 5 and are in chapters 5 and 6, which does not provide enough time to become fluent.
- Procedural skills and fluency are present in the majority of the lessons in "Model the Math" (TE 43B).
- Daily practice of counting /counting sequence is not provided in Kindergarten My Math.
- In the student edition, fluency practice to write numbers is present in many lessons.
- Math standard K.CC.A.1 (count to 100 by ones and tens) is addressed in 11 lessons out of 88 in chapters 1, 2 and 3. With counting to 100 by ones and tens being a required fluency for Kindergarten, 11 lessons are insufficient.
- The cluster K.OA.A (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from) has 13 lessons out of 88 that address the standard and are all in chapters 2 and 3.
- Procedural skills such as writing numbers are present in most of the lessons.
- Within the Connect Ed website, there are more opportunities to give fluency, but they are difficult to find.
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
Kindergarten My Math materials meet the expectations for being designed so teachers and students spend sufficient time working with engaging applications of the mathematics without losing focus on the major work.
- The majority of lessons include "Explore and Explain” which uses real-world problems to introduce concepts. For example, see chapter 1, lesson 5, page 35 and chapter 8, lesson 1, page 489.
- The teacher edition states “Explore and Explain” and “Real-World Problem Solving Readers” address application.
- While “Real-World Problem-Solving Readers” are available to provide additional problems, they were not reviewed by EdReports.org as they are not included in the basic package with the student and teacher editions and were therefore considered supplementary.
- In the online portion, several chapters include “Project-Based Learning,” which has students’ applying mathematics to real-world situations.
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.
Kindergarten My Math instructional materials meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials, and there is a balance of the three aspects of rigor within the grade.
- At the beginning of each lesson a section on rigor exists to identify levels of complexity by problem or exercise number. For example, lesson 8 in chapter 3 has two workbook pages (pages 225 – 226) for conceptual learning (understand concepts), one workbook page (page 227) for fluency/procedural skill (apply concepts), and one workbook page (page 228) for application (extend concepts).
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The Kindergarten My Math instructional materials partially meet the expectations for practice-content connections. The materials meet expectations for identifying the practice standards and explicitly attending to the specialized language of mathematics. Attending to mathematical vocabulary is a strength of the materials. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and engaging students in mathematical reasoning. Overall, in order to meet the expectations for meaningfully connecting the CCSSM and the mathematical practices, the instructional materials should carefully attend to the full meaning of every practice standard, especially MP3 in regards to students critiquing the reasoning of other students.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
In Kindergarten My Math, the materials meet the expectations for identifying the MPs and using them to enrich mathematics content within and throughout Kindergarten. Overall, the instructional materials do not over-identify or under-identify the MPs, and they are used within and throughout the grade.
- The teacher edition, pages T22 – T24, states the MPs and the corresponding pages.
- The practices are identified throughout all 89 lessons. Each lesson addresses three to four practices as a focus.
- The teacher edition indicates which Mathematical practice the student is working with in the lesson and in the homework.
- The student edition for Kindergarten does not indicate which Mathematical practice is present.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
Kindergarten My Math instructional materials partially meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the instructional materials carefully attend to the full meaning of some of the practice standards but not for all of them. The full meaning of each practice standard is not consistently addressed. Some examples include:
MP2, reason abstractly and quantitatively, pages 35 – 40, 383 – 388 and 583 – 588. Overall, practices labeled as “reason quantitatively” addressed the full intent of the practice; however, those labeled as “reason abstractly” do not.
The following list includes examples of when MPs are not met:
MP1: chapter 1, lesson 3, page 23 – 24 TE; chapter 1, lesson 5, page 35B TE; and chapter 1, lesson 8, page 55B TE.
MP2: chapter 1, lesson 2, page 17 – 18 TE; chapter 1, lesson 4, page 29A TE; and chapter 1, lesson 5, page 35 – 36 TE.
MP4: chapter 1, lesson 1, page 11B TE; chapter 1, lesson 2, page 17 – 18 TE; and chapter 1, lesson 6, page 43A TE.
MP5: chapter 1, lesson 3, page 23 – 24 TE; chapter 1, lesson 10, page 69 – 70 TE; and chapter 3, lesson 1, page 179A TE.
MP6: chapter 1, lesson 5, page 35A TE; chapter 2, lesson 9, page 145B TE; and chapter 3, lesson 2, page 185 – 186 TE.
MP7: chapter 2, lesson 2, page 99 – 100 TE; chapter 2, lesson 6, page 125 – 126 TE; and chapter 3, lesson 6, page 211A TE.
MP8: chapter 2, lesson 4, page 111 – 112 TE; chapter 2, lesson 9, page 145-146 TE; and chapter 3, lesson 8, page 225B TE.
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 My Math partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the materials consistently allow students to construct viable arguments, but they do not consistently prompt students to analyze other students' arguments.
- Materials providing opportunities for students to construct viable arguments in teacher chapter: chapter 1 (pages 11 – 12), chapter 2 (pages 105 – 106), chapter 3 (pages 197 – 198), chapter 4 (pages 289 – 290), chapter 5 (pages 351 – 352), chapter 6 (pages 409 – 410), chapter 7 (pages 469 – 470), chapter 8 (pages 509 – 510), chapter 9 (pages 559 – 560), chapter 10 (pages 583 – 584), chapter 11 (pages 629 – 630) and Chapter 12 (pages 705 – 706).
- More time is given to constructing arguments than analyzing the arguments of others.
- Examples of only constructing arguments: chapter, 4, lesson 1, pages 257 – 258 TE; chapter 4, lesson 22, pages 263 – 264 TE; and chapter 4, lesson 9, pages 307 – 308 TE.
- Examples of only analyzing arguments: chapter 4, lesson 8, page 301 – 302 TE
- Examples of non-alignment: chapter 3, lesson 8, page 225 – 226 TE; chapter 4, lesson 4, page 275 – 276 TE; and chapter 5, lesson 4, page 345 – 346 TE.
- Examples of full alignment to MP 3: chapter 5, lesson 3, page 339B TE and chapter 8, lesson 3, page 501 – 502 TE.
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 instructional materials reviewed for Kindergarten My Math partially meet the expectations for 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. Overall, the materials do not consistently assist teachers in having students construct viable arguments or analyze other students' arguments.
- The content in lessons 1 and 8 in chapter 4 and lesson 2 in chapter 8 provide opportunities for students to construct arguments.
- The content in chapter 2, lesson 6, pages 339A and 457 – 458 provides an opportunity for students to construct an argument and analyze the arguments of others.
- The content in chapter 10, lesson 2, pages 623B, 629 – 630 and 693 – 694 does not provide opportunities for students to construct arguments or analyze the arguments of others as stated in the teacher edition.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The Kindergarten My Math instructional materials meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that is consistently present throughout the materials.
- The special language of mathematics is a strength of the series.
- Individual vocabulary cards are found at the beginning of each chapter in the student edition.
- Vocabulary checks are included in some homework assignments. For example, see chapter 3, page 172.
- Vocabulary assessments can be created online.
- Virtual word walls are available online.
- “Match the Pairs” is an interactive vocabulary component.
- “Check my Progress” assesses vocabulary.
- Each chapter begins with a foldable that supports vocabulary development.
- “My Math Words” is at the beginning of some chapters. For example, see chapter 5, lesson 1, page 325A TE.
- The teacher, student, and online editions contain extensive glossaries in English and Spanish.
Oral and listening assessments are available online.