1st Grade - Gateway 2
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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 Grade 1 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 for Grade 1 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 Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Clusters 1.NBT.B and 1.NBT.C focus on understanding place value and using place value and properties of operations to add and subtract.
- Teacher Resources Part 1 Unit 2 has students use charts, tens and ones blocks, and number cards to develop place value. In Lesson 9 students use a number chart (1-20) to compare two numbers in order to determine which is larger/greater than (1.NBT.3).
- In Teacher Resources Part 2 Unit 1, students focus on understanding place value. In Lesson 15 students work with base ten blocks to understand 1 ten block is the same as 10 ones blocks. In Lesson 16 students draw base ten blocks to represent tens and ones.
- Teacher Resources Part 2 Unit 2 focuses on addition and subtraction using place value. Students use base tens blocks, charts, fingers, regrouping strategies, and equations to use place value to add and subtract.
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 Grade 1 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-30. The strategies are not incorporated into the lesson plans for the teacher.
- There are games in the teacher's edition pages A44-A45 that help to build student fluency. These games focus on adding and subtracting within 10, but these games are not mentioned in the lessons.
Standard 1.OA.6 requires students to add and subtract within 20 and fluently within 10.
- Much of the work in Grade 1 is around adding and subtracting. Teacher Resources Part 1 Units 3, 4, and 6 and Part 2 Unit 3 focus on Operations and Algebraic Thinking standards. Adding and subtracting within 20 can also be frequently seen in Teacher Resources Part 2 Units 1 and 2.
- Teacher Resources Part 1 Unit 3 Lesson 12 has solving simple addition problems, using problems involving zero. Students continue adding in Lessons 13- 16. Students continue with working towards fluency in Lessons 19-26.
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 Grade 1 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 is little evidence of the opportunity to work with engaging applications of the mathematics. Word problems are present in the materials, but the context has no bearing on the mathematics. Students are asked to use real-world items frequently, but these are used in place of counters and are more of a tool.
- Few problems regarding 1.OA.A, "Represent and solve problems involving addition and subtraction," include meaningful context.
- In Teacher Resources Part 1 Unit 3 Lesson 30, teachers should "draw a vase with four flowers and a vase with three flowers. Write the words 'four flowers' and 'three more flowers' above the pictures. Have a volunteer write the numerals above the number words. Ask: How many flowers are there altogether? Say: 'Altogether' means 'in total' or 'in all'." Similar problems follow.
There are very few non-routine problems throughout the year. Most word problems are single step and routine.
- Teacher Resources Part 1 Chapter 4 Lesson 41: "5 children were at the park, 2 of them left. How many are left?" and "John has 7 crayons. 4 of them are red. How many are not red?"
- Teacher Resources Part 1 Chapter 3 Lesson 13: "4 red crayons + 3 blue crayons = ______crayons altogether"
- Teacher Resources Part 2 Chapter 3 Lesson 61: "The teacher draws six circles on the board to represent apples and shades 4 of them to represent red apples. ASK 'How many apples are green?'"
- In Teacher Resources Part 1 Chapter 3 Lesson 27, students learn about doubles. They write number sentences from pictures and solve. There are no word problems.
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, many of the lessons focus on procedural skills and fluency with few opportunities for students to 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 Grade 1 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 Grade 1 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-21 . 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 Grade 1 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 1 Unit 3 Lesson 17, in the Activity the teacher tells the students that they have 5 pencils in the case. The teacher then shows students 4 pencils outside the case and asks how many pencils altogether. The teacher has the students count on to add. It then tells the teacher to repeat with various examples. This problem is scripted to the point that children do not have to persevere in solving the missing addend problems. Another example is found in Teacher Resources Part 2 Unit 1 Lesson 14; the teacher demonstrates to students how to skip count by 5's and then talks about skip counting by 10's. Then the student skip counts by 5's. There is no persevering and problem solving occurring.
- MP5: In Teacher Resources Part 1 Unit 3 Lesson 18, the teacher prompts students to answer a variety of prompts regarding choosing which number to count on from. For example, "given 2+9=__ and 9+2=___ ASK: will these problems have the same number? (yes) How do you know? (they are adding the same numbers) Which problem is easier to solve?" Students are not choosing appropriate tools strategically.
- MP6: In Teacher Resources Part 2 Unit 3 Lesson 54 students review equal and not equal. The teacher places different numbers of stacked blocks on two desks in the front of the room, and students determine if they are equal. Then the teacher changes the number, and students answer that they are not equal. Precise language is being used, but the nature of direct instruction has the students repeating the correct vocabulary word rather than communicating with others.
- MP7: In Teacher Resources Part 1 Unit 2 Lesson 5 students are provided a structure to determine which number is greater. The teacher tells students to pull 2 numbers out of a cup and then start counting up from 1 to determine the larger number. Students are not determining the structure on their own.
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 Grade 1 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 discussion, though there are occasional suggestions for students to work in groups. 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. One example is found in Teacher Resources Part 1 Unit 5 Lesson 11. The teacher demonstrates how to use a ruler to measure. "SAY: Look, this way the line is 6 units long. Is this correct? (no) Have students explain your mistake." The only time that students are constructing an argument themselves is when they try to explain how the teacher came up with the incorrect answer. Another example is in Teacher Resources Part 2 Unit 1 Lesson 16. The teacher reminds students that every tens block has 10 ones. The teacher then draws a picture on the board. The teacher is prompted to "ASK: What number is shown? (12) Can I show this number a different way if I use a tens block? (yes, you can replace 10 of the ones with a tens block)." These questions lead to understanding but do not address MP3 by having students construct their own arguments and/or critiquing the reasoning of others.
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 Grade 1 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 10 page 32: Questions are all true or false or yes or no.
- Teacher Resources Part 1 Unit 2 Lesson 6 page 16: "Challenge students to explain, in more than one way, how they know that 13 is greater than 3." Several example responses are provided. The teacher is prompted to "help students articulate all of these explanations."
- Teacher Resources Part 1 Unit 6 Lesson 45 page 15: Students are given between 6 and 10 counters and asked to place them on their five-frame. "ASK: Do they all fit? (no) Do you have more than 5 or less than 5 counters? (more than 5) How do you know?" An example response is provided, but no additional guidance is provided for the teacher.
- Teacher Resources Part 2 Unit 2 Lesson 17: All the questions are yes or no answers.
- Teacher Resources Part 2 Unit 5 Lesson 1 page 7: The teacher draws a rectangle on the board, counts the sides and says there are 6 sides. Then the teacher asks "Am I correct? (no) What did I do wrong? (counted some sides twice)."
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 Grade 1 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 2 Unit 5 page N-1 , there is discussion about the appropriate clarity expected from students regarding squares, rectangles and prisms.
- 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 1 Unit 3 Lesson 12 vocabulary includes the terms add, addition sentence, altogether, count, equals (=), in total, and plus (+). 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.