Kindergarten - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 77% |
|---|---|
Criterion 2.1: Rigor | 7 / 8 |
Criterion 2.2: Math Practices | 7 / 10 |
The instructional materials for My Math Florida Kindergarten partially meet the expectations for rigor and mathematical practices. The instructional materials meet the expectations for the criterion on rigor and balance and partially meet the expectations for the criterion on practice-content connections. Overall, the instructional materials attend to the language of mathematics but do not fully attending to the meaning of each practice standard.
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 My Math Florida Kindergarten meet the expectations for rigor and balance. The instructional materials 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 help 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.
The instructional materials for My Math Florida Kindergarten meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.
- The content in Chapters 1 and 4 through 6 address standards that are explicitly outlined as conceptual standards. (K.CC.2.4 and K.NBT.1.1)
- The majority of lessons have a section called “Investigate the Math” which targets conceptual understanding. This is contained in the online lesson presentation.
- All lessons in the series have a section called “Talk Math” which targets conceptual understanding. This is contained in the online lesson presentation.
- In the Student Edition, some of the lessons begin with an "Explore and Explain" section which targets conceptual understanding.
- There is limited time spent on conceptual understanding of numbers. For example, understanding 0 to 5 only has 15 days of instruction, and only two of those lessons, Lessons 1 and 3, actually deal with conceptual understanding.
Some Brain Builders enhance conceptual understanding. Examples include:
- Chapter 1, Lesson 2, Brain Builders, the picture on the page has a soup pot and the directions are to “Draw one tomato in the pot. Write the number two times. Draw one potato in the pot. Write the number two times. Draw two carrots in the pot. Write the number two times. Draw three onions in the pot. Write the number two times. Draw an X on three objects in the pot.” Students are developing conceptual understanding by representing objects and connecting those to numbers.
- Chapter 3, Lesson 4, Brain Builders, Item 7, the page contains two ten frames with five spaces filled, and students are directed to show sixteen.
- Chapter 5, Lesson 7A, Brain Builders, an empty basket is shown on the page, and below the basket is the beginning of an equation "10 = ______+______. Miles has strawberries and blueberries in his basket. He has 10 pieces of fruit in all. Draw strawberries and blueberries to show each group.” After finishing the problem, the students compare with a friend and discuss why there is more than one possible answer.
- Chapter 11, Lesson 2, Brain Builders, “Identify the circles and triangles on the fruit pizza by coloring the circles green and the triangles orange. Explain to a friend how you can tell the difference between a triangle and a circle.”
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 instructional materials for My Math Florida Kindergarten 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 has 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.1.5 (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 sequences is not provided in the materials.
- In the Student Edition, fluency practice to write numbers is present in many lessons.
- Math standard K.CC.1.1 (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.1 (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
The instructional materials for My Math Florida Kindergarten 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 a section called "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. 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.
Brain Builders and Performance Events sometimes provide additional opportunities for students to engage in the applications of mathematics. Examples Include:
- Chapter 3, Performance Event is divided into five parts, with each part related to visiting a sporting goods store. Part B: “Count the baseballs. Write the number.” There is a picture of baseballs on the page.
- Chapter 5, Lesson 1, Brain Builders, students have a page with two teeter totters. Teachers share the following problem with students, and students are told to use counters to model the story: “Two children are playing on the teeter-totters. Two more children join them. Write the numbers. How many are there in all? Three children are playing on the teeter-totters. One more child joins them. Write the numbers. How many are there in all? Tell a friend how many children are on both teeter-totters in all. Explain how you found the answer.”
- Chapter 6, Lesson 1, Brain Builders, the student page shows three dog bowls with food, and students listen to subtraction stories read by their teacher. Students use counters to model the stories and then write the answer on the page.
- Chapter 10, Performance Event is divided into four parts, with each part relating to different animals. Part A: “How many animals are above the bed? Circle them. Write the number.”
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 for My Math Florida Kindergarten 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 "Rigor" section exists to identify levels of complexity by problem or exercise number. For example, Chapter 3, Lesson 8 has two workbook pages for conceptual learning (understand concepts), one workbook page for fluency/procedural skill (apply concepts), and one workbook page 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 instructional materials for My Math Florida Kindergarten 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. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and engaging students in mathematical reasoning.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The instructional materials for My Math Florida Kindergarten meet the expectations for identifying the Standards for Mathematical Practices (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, lists the MPs and the corresponding pages.
- The practices are identified throughout all 89 lessons. Each lesson focuses on three to four practices.
- The Teacher Edition indicates which MP the student is working with in the lesson and in the homework.
- The Student Edition for Kindergarten does not indicate which MP is present.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials for My Math Florida Kindergarten 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. For example:
- 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 My Math Florida Kindergarten partially meet the criteria that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.
The materials offer some opportunities for students to share their thinking and analyze the thinking of others; however, there are frequent instances where something labeled as MP3 does not require the students to share thinking and/or analyze the thinking of others.
Examples where students are asked to justify their thinking or the reasoning of others:
- Chapter 2, Lesson 4, Problem of the Day, “Look at the bears. Use counters to show how many bears. Count how many bears. Write the number.” Construct Arguments, “Have students explain to a classmate how they decided how many bears were in the group. Instruct the classmate to tell if the student’s explanation is reasonable.”
- Chapter 5, Lesson 3, Problem of the Day asks students to "use color tiles to show a way to make 10 bears. Write the numbers." Check for Reasonableness, “Listen to a classmate as he or she explains how the color tiles were used to make 10. Discuss with your classmate how their answer does or does not make sense. Switch roles and discuss your way to make 10.”
- Chapter 11, Lesson 1, Problem of the Day states, “Sort the dogs one way. Then resort the dogs another way. Explain how you sorted the dogs, then how you sorted them another way.”
There are instances where problems and questions are labeled as MP3, but students do not construct arguments or analyze the arguments of others. For example:
- Chapter 1, Lesson 5, Talk Math: Collaborative Conversation, “In a game of soccer, if one team has zero points and the other team has five points, which team is losing the game?”
- Chapter 2, Lesson 3, Talk Math: Collaborative Conversation, “Count a column of seven blocks from top to bottom. Will there be more blocks if we count them from bottom to top? Explain.”
- Chapter 3, Lesson 1, Talk Math: Collaborative Conversation, “How is the number 12 different from the number 11?” This goes along with the guided practice page. Students are shown ten frames with 11 and 12 objects.
- Chapter 5, Lesson 6, Practice the Strategy, “Why is it important to check your work?”
- Chapter 6, Lesson 4, Talk Math: Collaborative Conversation, “Show students a subtraction number sentence and an addition number sentence. What symbol is in both an addition and a subtraction number sentence? How do you know whether to add or subtract? Explain.”
- Chapter 12, Lesson 1, Talk Math, “Show students a square paper cutout. If this shape was in the row of objects in Exercise 4 would it be circled? Explain.”
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 My Math Florida Kindergarten 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 Chapter 4, Lessons 1 and 8 and in Chapter 8, Lesson 2 provide opportunities for students to construct arguments.
- The content in Chapter 2, Lesson 6, pages 339A and 457 – 458 provide opportunities 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 instructional materials for My Math Florida Kindergarten 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 which 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.