4th Grade - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
Gateway 1 - Does Not Meet Expectations | 7% |
Criterion 1.1: Focus | 0 / 2 |
Criterion 1.2: Coherence | 0 / 4 |
Criterion 1.3: Coherence | 1 / 8 |
The materials for Grade 4 do not meet expectations for focus and coherence. They do not meet the criteria for indicators 1a and 1b. Connecting Math Concepts assesses future grade level content (adding and subtracting decimals, adding and subtracting fractions with unlike denominators, multiplying and dividing fractions, ratios, graphing ordered pairs, and solving equations with multiple variables). Additionally, the instructional materials only devote 60 percent of class time to major work of the grade. The instructional materials reviewed for Grade 4 do not meet the expectations for being coherent and consistent with the standards. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days; however there are many major modifications that need to be made in order to teach at the depth required for students to master all grade-level standards. The instructional materials do not do the following: identify or connect prior or future grade-level work to Grade 4 work, provide students with extensive work with Grade 4 work, or relate Grade 4 concepts explicitly to prior knowledge from earlier grades. The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings. Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate. Overall, the Grade 4 materials do not support coherence and are not consistent with the progressions in the Standards.
Criterion 1.1: Focus
The materials for Grade 4 did not meet the criteria for focus. A positive of the assessment program is the formative assessments (mastery tests), which are aligned with a specific remedy section for repeated practice of concepts students have not mastered. Unfortunately, the following above grade-level topics are assessed: adding and subtracting decimals, adding and subtracting fractions with unlike denominators, multiplying and dividing fractions, ratios, graphing ordered pairs, and solving equations with multiple variables. Overall, the instructional materials assess numerous topics before they should be introduced. The materials only devote 60 percent of class time to major work of the grade. A larger percentage of major work is presented in Book 2, which is toward the end of the instructional year, and may not allow enough time for students to develop mastery. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4.
Indicator 1a
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) do not meet the expectations for focus within assessment. For this indicator, the review team examined all Mastery Tests and both Cumulative Tests. Overall, the instructional materials assess content from future grades within the majority of the summative assessments. The assessments would not be viable if the material that is above grade level was omitted, as there are too many assessment questions within the series that are above grade level.
Review Team note: The Level E (Grade 4) Teacher Guide identifies the cumulative tests as “optional” in two places (pages 3-4); however, the Publisher Orientation session identified these assessments as a required component of the grade level program. Therefore, the cumulative tests are included in this review.
Mastery Test 1:
- Items in part 8 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 2:
- Items in parts 5 and 6 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 3:
- Items in part 4 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 4:
- Items in part 5 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
- Items in parts 7e and 7f assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.
- Items in part 6 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 5:
- Items in part 7 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 6:
- Items in parts 7b and 7c assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
- Items in part 8 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in parts 7 and 9 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 7:
- Items in part 4 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in part 6 assess interpreting a fraction as division of numerator by denominator which aligns to standards within 5.NF.B.
- Items in part 3 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Mastery Test 8:
- Items in part 4 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
- Items in parts 3 and 7 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B
- Items in part 9 assess solving problems involving percents which aligns to standards within 6.RP.A.
- Items in part 10 assess determining complementary and adjacent angle measures which aligns to standards within 7.G.B.
Mastery Test 9:
- Items in part 7 assess identifying and graphing ordered pairs on a coordinate grid which aligns to standards within 5.G.A..
- Items in part 4 assess solving problems involving percents which aligns to standards within 6.RP.A.
- Items in part 2 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Mastery Test 10:
- Items in part 2 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in part 3 assess identifying and graphing ordered pairs on a coordinate grid which aligns to standards within 5.G.A.
- Items in part 2 assess solving problems involving percents which aligns to standards within 6.RP.A.
- Items in part 4 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Mastery Test 11:
- Items in part 6 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in part 2 assess identifying and graphing ordered pairs on a coordinate grid which aligns to standards within 5.G.A.
- Items in part 1 assess solving problems involving percents which aligns to standards within 6.RP.A.
- Items in part 6 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Mastery Test 12:
- Items in part 6 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
- Items in part 5 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Mastery Test 13:
- Items in part 8 assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.
- Items in part 1 assess solving problems involving percents which aligns to standards within 6.RP.A.
- Items in part 2 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Cumulative Test 1:
- Items in parts 10, 20b and 20c assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
- Items in part 11 assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.
- Items in part 21 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in parts 16 and 23 assess interpreting a fraction as division of numerator by denominator which aligns to standards within 5.NF.B.
- Items in parts 5b, 7, 20 and 22 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
Cumulative Test 2:
- Items in parts 10d, 10e and 10f assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
- Items in part 11 assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.
- Items in parts 11, 14 and 24 assess multiplying a fraction by a fraction which aligns to standards within 5.NF.B.
- Items in part 12 assess interpreting a fraction as division of numerator by denominator which aligns to standards within 5.NF.B.
- Items in part 19 assess writing and solving equations with variables which aligns to standards within 6.EE.B.
- Items in part 18 assess identifying and graphing ordered pairs on a coordinate grid which aligns to standards within 5.G.A.
- Items in parts 13, 25 and 33 assess solving problems involving percents which aligns to standards from 6.RP.A.
- Items in parts 27 and 36 assess solving problems which involve ratios which aligns to standards within 6.RP.A.
Criterion 1.2: Coherence
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.
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) do not meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4.
To determine this, two perspectives were evaluated: 1) the number of lessons aligned to major work by cluster and/or standard. and 2) the number of exercises aligned to major work (based on reviewer analysis). The review team found the second perspective to be the most accurate, as it indicates an amount of class time devoted to major work each day. A third perspective was not evaluated because the materials spiral and are not organized into units or chapters.
The percent of lessons aligned to major work clusters according to “Level E Correlation to Grade 4 Common Core State Standards for Mathematics” document in Presentation Book 1, pages 700-706, and Presentation Book 2, pages 617-708:
- The percentage of lessons aligned to 4.OA.A is 51 percent.
- The percentage of lessons aligned to 4.NBT.A is 77 percent.
- The percentage of lessons aligned to 4.NBT.B is 99 percent.
- The percentage of lessons aligned to 4.NF.A is 60 percent.
- The percentage of lessons aligned to 4.NF.B is 80 percent.
- The percentage of lessons aligned to 4.NF.C is 37 percent.
In book one, there are 363 out of 644 exercises, about 56 percent, that focus on major work. In book two, there are 310 out of 483 exercises, about 64 percent, that focus on major work. This is 673 out of 1127 total exercises, about 60 percent.
- Book one has less work focusing on major work of grade. This leaves the majority of major work toward the end of year, which may not be enough time to develop mastery of a concept.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 4 do not meet the expectations for being coherent and consistent with the standards. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, however there are many major modifications that need to be made in order to teach at the depth required for students to master all grade-level standards. The instructional materials do not do the following: identify or connect prior or future grade-level work to Grade 4 work, provide students with extensive work with Grade 4 work or relate Grade 4 concepts explicitly to prior knowledge from earlier grades. The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings. Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate. Overall, the Grade 4 materials do not support coherence and are not consistent with the progressions in the standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work.
Connections between CCSS Supporting Work and Major Work Math Standards are never identified in the Teacher Presentation Books or the Teacher Guide. Connecting Math Concepts is a “direct instruction” program, where teachers are encouraged to use instructional materials as written, with little to no deviation from the prescribed presentation script. The Teacher’s Guide states: “The script indicates the wording you use in presenting the material and correcting student errors. Once you are familiar with the program, you may deviate some of the exact wording; however, until you know why things are phrased as they are, you should follow the exact wording." (p. 10). This structured presentation discourages teachers from making missed connections explicit for students.
Connections between Supporting and Major Work:
- Lessons 129 and 130 have students working with line plot data (4.MD.B). A connection to adding and subtracting fractions (4.NF.B) is made.
- Lessons 32-33, 36-40 and 100-130 contain exercises where students are working with factors and multiples (4.OA.B). Connections to multiplication, division and remainders (4.NBT.B) are made.
- Lessons 56-67 and 71-130 contain exercises addressing measurement conversion (4.MD.A). Connections are made to identifying factors (4.OA.2), finding products and quotients (4.NBT.B) and using the language of multiplicative comparison (4.OA.A).
- Lessons 71-129 have students using area and perimeter formulas (4.MD.A). Connections are made to multiplication and division (4.NBT.B) and multiplicative comparison (4.OA.A).
Missed Connections between Supporting and Major Work:
- Lessons 32-33, 36-40 and 100-130 each contain 1-2 exercises where students are working with factors and multiples (4.OA.B). In this supporting cluster, students are mostly working with divisibility rules and it is not connected to multi-digit arithmetic (4.NBT.B) or equivalent fractions (4.NF.A).
- Lessons 122-130 introduces factors (4.OA.B). Students are asked to find prime factorization (Grade 5 standard), not factor pairs and this is not linked to fraction equivalence (4.NF.A).
- Beginning in Lesson 81, students work on coordinate systems (4.MD.B). Students are asked to graph functions, not line plots therefore missing the connection to adding/subtracting fractions (4.NF.A and B).
- Lessons 129 and 130 have students working with line plots (4.MD.B). A connection to partitioning whole shapes into appropriate factional increments is missed (4.NF.B).
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) do not meet the expectations for having an amount of content designated for one grade level as viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, however, due to the large amount of content that is not aligned to the grade level, there is not enough instruction at the depth required to prepare students for learning in future grades.
- The curriculum supplies 130 lessons, 13 mastery tests, and 2 cumulative tests. Although remedial worksheets are provided to support students struggling on concepts after each mastery test, these do not comprise the same amount of material as is contained in each lesson. These materials, if each mastery test is conducted in one lesson period (45-60 minutes) would be completed over 145 instructional days.
- A substantial number of unaligned exercises focus on skills and understandings not included in CCSSM and/or mastery of above level standards from Grade 5 and beyond (see report for Indicator 1b); this focus on above grade-level objectives takes time and focus away from foundational grade level understandings. Teachers using this program would need to make significant modifications to the daily lessons and/or omissions that would affect the integrity of the grade level program.
- Solving multi-step word problems using the four operations, 4.OA.3, which is part of a major cluster, appears in only three exercises (lessons 113.6, 127.3 and 130.7).
- Expressing a fraction with denominator 10 as an equivalent fraction with denominator 100, and using this technique to add fractions, 4.NF.5, which is part of a major cluster, appears in only five exercises (lessons 78.3, 121.3, 122.7, 123.2 and 124.7).
- Comparing two decimals to hundredths by reasoning about their size, 4.NF.7, which is part of a major cluster, appears in only four exercises (lessons 110.2, 111.1, 112.1 and 113.1).
- Representing and interpreting data, 4.MD.4 appears in only two exercises (lessons 129.3 and 130.5).
- Recognizing lines of symmetry, 4.G.3, does not appear anywhere in the core materials.
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.
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) do not meet the expectations for materials being consistent with the progressions in the standards. Overall, the instructional materials do not: identify or connect prior or future grade-level work to Grade 4 work, provide students with extensive work with grade-level problems, or relate Grade 4 level concepts explicitly to prior knowledge from earlier grades.
i. Materials do not develop according to the grade-by-grade progressions. Prior or future content is not clearly identified.
- Prior grade level topics taught and not identified include:3.NF.A, representing fractions on a number line (lessons 1-130), 3.NBT.A, multiplying one-digit whole numbers by multiples of 10 (beginning lesson 42), 3.NF.A, recognizing and generating simple equivalent fractions (beginning lesson 68), 2.OA.B, addition number families (lessons 1-130), 3.OA.C, multiplication number families (lessons 9-130), 3.OA.C multiplication and division facts (lessons 1-85).
- Future grade level topics taught and not identified include: 6.RP.A, converting decimals and percents (lessons 27-130), 5.NF.A, adding and subtracting fractions with unlike denominators (lessons 31-130), 5.NF.B, multiplying and dividing fractions (beginning lesson 54), 5.NBT.B, adding and subtracting decimals (beginning lesson 27), 6.RP.A, ratios (lessons 76-130), 5.G.A, graphing ordered pairs (lessons 81-130), 6.EE.C, graphing functions on a coordinate grid (lessons 81-130) and 6.EE.B, coefficients and inverse operations (lessons 85-130).
ii. Materials do not give students extensive work with grade-level problems.
- No lessons address lines of symmetry (4.G.A.3). This standard is only addressed when using three activities in the student practice software. There are no instructional notes within the teacher guide explaining how to incorporate this technology into daily instruction. In addition, the Planning Pages for each series of five lessons lists the student practice software activities as “Additional Practice.”
- Only lessons 129 and 130 address measuring and creating line plots (4.MD.4).
- Only lessons 113, 127 and 130 address the major work of multistep word problems, also an area for high Depth of Knowledge.
- Lessons 32-40 and 100-130 address work with factors and multiples (4.OA.B). While this work has a strong connection to division, the teaching of this standard never uses the word “multiple” nor are students asked to find factor pairs. Instead, a number is presented with the prime factorization already completed and students must compose prime factors to create additional factors for a given number.
- The major work of 4.OA.3 is addressed in three exercises, or about 30 minutes, for the entire school year. This is not enough time for students to master solving multistep word problems.
- The major work of 4.NF.7 is only addressed in four exercises of 10 minutes each. This is not enough time for students to master comparing two decimals to hundredths by reasoning about their size.
- The major work of 4.NF.5 is only addressed in five exercises. This is not enough time for students to master expressing a fraction with denominator 10 as an equivalent fraction with denominator 100 and then applying this technique to addition of fractions.
- Students who fail parts of the mastery test can be assigned Remedies aligned to standards below the current grade level to complete during independent practice, so these students would not be working with grade-level problems. Opportunities for enrichment of grade-level work do not exist in the program.
iii. Most materials do not explicitly relate grade-level concepts explicitly to prior knowledge from earlier grades.
- 4.NF.B, coherence in connecting prior work in multiplication, repeated addition, or equal groups of a fraction is not made. Instead, when converting whole numbers to fractions with a denominator of 1, students are asked to multiply fractions as two separate problems: problem for the top numbers and problem for the denominators (lesson 67, exercise 2).
- When exercises do occur over subsequent lessons, little of the teacher script connects back to a previous day’s learning/understanding.
- Opportunities to extend previous understanding are not made because lessons provide isolated practice of the standards.
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.
The instructional materials reviewed for Connecting Math Concepts Level E (Grade 4) do not meet the expectations for fostering coherence through connections at a single grade level.
The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings.
- Lessons are composed of exercises that are unrelated. In cases where there could be connections made, they are still treated as separate exercises.
- Lessons and exercises are not marked with CCSSM.
- Page 14-15 provides a chart with the Lessons and the CCSSM for Level E.
- Teacher Guide, page 169-194, shows how the CCSSM are presented in sample lessons.
- A comprehensive listing of the CCSSM and the correlating exercises are found in the back of Presentation Books 1 and 2.
- CCSSM aligned exercises do not meet the true intent of the standard:
- 4.OA.B - Familiarity with factors and multiples teaches prime factorization and divisibility rules.
- 4.OA.C - Not addressed in any tracks, but can be learned using practice software block 5, activity 2
- 4.NBT.A - Used to teach the relationship between numbers that are multiplied and the number of zeros when using the traditional multiplication algorithm.
- 4.MD.B - Students are taught functions, not line plots.
- 4.MD.C - Students are asked to find missing angles and supplementary and vertical angles.
Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate.
- There are no connections made between solving problems involving measurement and conversion of measurements (4.MD.A) and multiplying fractions by whole numbers (4.NF.B).
- There are no connections made between angle measurements (4.MD.C.5 and 4.MD.C.7) and adding fractions (4.NF.B). An attempt seems to have been made to do this, but it relates angle measures to a fraction of a number (for example, 1/2 of 360 degrees)