6th Grade - Gateway 3
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Usability
Gateway 3 - Partially Meets Expectations | 74% |
|---|---|
Criterion 3.1: Teacher Supports | 7 / 9 |
Criterion 3.2: Assessment | 9 / 10 |
Criterion 3.3: Student Supports | 4 / 8 |
Criterion 3.4: Intentional Design |
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for Usability. The materials partially meet expectations for Teacher Supports (Criterion 1), meet expectations for Assessment (Criterion 2), and do not meet expectations for Student Supports (Criterion 3).
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for Teacher Supports. The materials provide: teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; explanations of the instructional approaches of the program and identification of the research-based strategies; and a comprehensive list of supplies needed to support instructional activities. The materials contain adult-level explanations and examples of concepts beyond the current grade so that teachers can improve their own knowledge of the subject, but do not contain adult-level explanations and examples of the more complex grade-level concepts. The materials partially include standards and correlation information that explains the role of the standards in the context of the overall series.
Indicator 3a
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
Materials provide comprehensive guidance to assist teacher delivery of student materials. The Teacher Edition of the materials contains Teacher Notes throughout to assist the teacher in presenting the student lessons. Examples include:
Important information about student learning at the beginning of lessons. For example, in Lesson 6.9, Distributive Property, the Introductory Teacher Notes states, “Students will continue to work with expressions in this lesson, specifically using the distributive property. Students should remember what they have learned about finding the greatest common factor. While working it may help to remind them that the process will be similar; they want to find the greatest common factor between two values. To start, students will review factors and then move on to writing equivalent expressions within a context. It might be helpful to remind students of the definition of equivalent expressions and provide some examples. If students are having trouble writing expressions within the given contexts, give them some simple expressions to practice using the distributive property.” (6.EE.3; 6.NS.3; 6.NS.4)
Answers to all Inline Questions
Instructions for help with the Interactives. For example, in Lesson 9.10, Nets, Activity 1, the Teacher Notes state, “This Interactive helps students think about different ways nets can be arranged. To start, students are given a rectangular prism (the birdhouse) on a 2D rectangle (the wooden board). Students can use the red circles to rotate and move the rectangle. Use the sliders at the bottom to open the prism into a net and see different arrangements of the net. Students can click and drag anywhere on the plane to rotate the polyhedra. Zoom using a mouse wheel or two fingers on a trackpad. Students should see if they can find a net arrangement that can be cut from the given rectangle.” (6.G.1-4)
Possible answers, further questions, and discussion ideas for the Discussion Questions are in the following examples. In Lesson 10.5, Measure of Center and Variability, Activity 3, Discussion Question, the Teacher Notes say, “The students should notice that Helena falling over a hurdle is not an outlier. She falls down regularly, approximately 1 out of every 6 races. The data is becoming bimodal, meaning that there are two underlying scenarios, races where Helena falls down and races where she does not. The median gives us a clearer idea of what time Helena can expect if she completes the race cleanly. Her coach is likely interested in both: the mean because it gives an indication of how likely Helena is to complete the race cleanly while the median gives a clear idea of where Helena fits, in terms of her speed, relative to other members of the team.” (6.SP.3; 6.SP.5d)
Specific learning standards and objectives for each lesson
Lesson-specific Teacher Notes
A scope-and-sequence at the end of the Teacher Edition
Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. In the Teacher Edition at the beginning of each lesson, there is an overview of the lesson to assist the teacher in lesson-planning:
Common Core Standard—the focus and prerequisite standard(s) for each lesson is listed.
Standard for Mathematical Practice—the mathematical practice(s) for each lesson is listed as well as where in the lesson it is developed.
Previous Learning Objectives—a majority of the lessons list these objectives and the standard(s) or grade(s) the objective is connected with.
Learning Objectives—goals for each lesson.
Agenda—here is an agenda listed for each lesson with the allotted times for the Warm-Up, the Activities, Review Questions, Related Modalities and Adaptive Practice.
Introductory Teacher Notes—located at the beginning of the lesson after the agenda, these notes describe what the students will be doing in the lesson. Some have helpful hints.
Interactives—Teacher Notes for the Interactive activities give the teacher direction on how the students are to use the Interactive and helpful hints.
Discussion Questions—Teacher Notes for Discussion Questions provide possible answers and/or possible questions to ask to further the discussion.
Extension Activities—some of the lessons give Extension Activity ideas that can enhance the learning.
Indicator 3b
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for CK-12 Middle School Interactive Math 6 for CCSS partially meet expectations for containing adult-level explanations, examples of the more complex grade-level concepts, and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The Teacher Edition does not contain any adult-level explanations and examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject. In the Subjects Menu, Math Flexlets are available for 6th, 7th and 8th Grade Math Essentials. These are shortened versions of some key lessons intended for review. For example, Interactive 6th Grade Math Essentials states, “This Flexlet is a great resource to prepare for or review Middle School Math 6. It is a collection of only the 'key' lessons in CK-12 Interactive Middle School Math 6. Additional detailed support for concepts introduced here is available in the full CK-12 FlexBook 2.0.” This resource does not offer adult-level explanations and examples of the more complex grade-level concepts since it addresses only key lessons and not more complex concepts.
Additionally, Study Guides can be found under the Explore menu, and are intended as a “Quick review with key information for each concept.” The math content covered in the Study Guides is beyond the current course and offers math high school courses Algebra and Geometry. These Study Guides can be used so that teachers can improve their own knowledge of the subject. However, not all Study Guides are connected to High School standards or standards at all.
Indicator 3c
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for CK-12 Middle School Interactive Math 6 for CCSS partially meet expectations for including standards and correlation information that explains the role of the standards in the context of the overall series. Correlation information is present for the mathematics standards addressed throughout the grade level. However, there are few, if any, explanations of the role of the specific grade-level mathematics in the context of the series and no connection to future learning.
Previous learning objectives are listed on most of the lessons. There are limited instances of objectives connecting to previous grade levels, and the remaining previous learning objectives listed are related to grade-level standards. Examples include:
Lesson 3.1, Dividing a Fraction by a Whole Number, lists the following as Previous Learning Objectives: Write a fraction that represents a given diagram or picture (3rd); Recognize and write simple equivalent fractions (halves, thirds, sixths) (3.NF.3b); and Recognize and write equivalent fractions (4.NF.1).
Lesson 4.5, Dividing Decimals in Diagrams, lists the following as Previous Learning Objectives: Compare two decimals to the hundredths place (4.NF.7) and Use visual models to multiply multi-digit decimals (6.NS.2-4).
Lesson 6.4, Order of Operations, lists the following as Previous Learning Objectives: Identify parts of an expression using mathematical terms (sum, product, quotient) (6.EE.2b); View one or more parts of an expression with parentheses as a single entity (6.EE.2b); and Understand that exponents represent repeated multiplication (6th).
Future learning objectives are seldom present and are usually referred to later in the grade level and not to a concept in future grade levels or courses. For example, in Lesson 3.1, Dividing a Fraction by a Whole Number, the Adaptive Practice Teacher Notes state, “Students should be comfortable with representing fractions with diagrams, it will help them visualize the statements they are working with throughout the chapter.” (6.NS.1)
Mathematics standards, practices, and learning objectives are listed throughout the grade level at the beginning of each lesson. Examples include:
In Lesson 5.1, Positives and Negatives, 6.NS.5 and 6.NS.6c are listed as Focus Standards, 6.NS.6a is listed as an Additional Standard, and the standards for mathematical practice listed with the lesson are MP2, and MP4. The Learning Objectives are the following: Understand that positive and negative numbers are used together to describe quantities having opposite values, recognize that the opposite of the opposite of a number is the number itself, explain the meaning of 0 in situations with positive and negative numbers, position integers on a vertical number line diagram, and use positive and negative numbers to represent quantities in real-world contexts.
In Lesson 8.2, Comparing Absolute Values, 6.NS.7d is listed as a Focus Standard, 6.NS.7 is listed as an Additional Standard and the standards for mathematical practice listed with the lesson are MP1 and MP2. The Learning Objective is, “Distinguish comparisons of absolute value from statements about order.”
In Lesson 10.9, Using Box Plots, 6.SP.4 and 6.SP.5 are listed as Focus Standards, and the standards for mathematical practice listed with the lesson are MP2 and MP3. The Learning Objectives are the following: Identify the components of box plots, and answer questions about a data set using a box plot.
Indicator 3d
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
Indicator 3e
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.
Instructional approaches of the program and identification of the research-based strategies can be found on the homepage, the citations for this research can be found under the “Resources” tab on the homepage. The materials state the following, “The CK-12 Interactive Middle School Math series promotes exploratory learning (Stein 2010). Each lesson contains interactive applets which actively engage students in the learning process and allow them to explore concepts in an open-ended environment (Cocea & Magoulas, 2015; Hoyles, 2018; NCTM, 20115). Inline question sets Socratically guide students to discover connections present in the interactive applets, and a list of Works Cited includes:
Stein, R. G. (2010). Math for Teachers: An Exploratory Approach. Kendall Hunt
Publishing Company.
Cocea, M., & Magoulas, G. D. (2015). Participatory learner modeling design: a
methodology for iterative learner models development. Information Sciences, 321,
48-70.
Schunk, D. H. (2012). Learning Theories: An Educational Perspective. Pearson.
Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers
through digital technology. Research in Mathematics Education.
Hoyles, C., & Lagrange, J. B. (Eds.). (2010). Mathematics education and technology:
Rethinking the terrain. New York: Springer.
National Council of Teachers of Mathematics. (2014). Access and equity in mathematics
education: A position of the national council of teachers of mathematics. National
Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2015). Strategic use of technology in
teaching and learning mathematics: A position of the national council of teachers of
mathematics. National Council of Teachers of Mathematics.
Wolf, D., Lindeman, P., Wolf, T., & Dunnerstick, R. (2011). Integrate Technology with
Student Success. Mathematics Teaching in the Middle School, 16(9), 556-560.”
Indicator 3f
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
The Interactives in the lessons are designed to replace any extra materials. There is a comprehensive list of supplies needed for the optional activities included at the beginning of the Teacher Edition under the Resources tab. The materials listed are provided for the lessons that need extra supplies for optional activities (Note: the quantity listed is per student unless otherwise noted.) Examples include:
In Lesson 1.3, Equivalent Ratios & Tape Diagrams, Activity 2, How is a ruler sort of like a tape diagram?: Blank Paper (1 Sheet), Ruler, and Pencil.
In Lesson 4.8, Using Greatest Common Factor, Activity 1, What shapes can you make shapes on a clock?: 1 Blank Sheet of Paper, Pencil, and Ruler.
Indicator 3g
This is not an assessed indicator in Mathematics.
Indicator 3h
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for Assessment. The materials include an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up, and the materials provide assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices. The materials partially include assessment information in the materials to indicate which standards are assessed.
Indicator 3i
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.
Formative assessments, including Inline Questions, Review Questions/Quiz, and Adaptive Practice are located in each lesson, however the materials only identify the standards and practices assessed for some of the formal assessments. In the Teacher Edition, at the beginning of each lesson, standards and mathematical practices are clearly listed, but specific standards and practices are not listed for each question on the Inline Questions, Adaptive Practice and Review Questions/Quizzes. The end of chapter assessments identify the standards for each question, but do not identify the mathematical practices. Examples include, but are not limited to:
In Lesson 3.9, Dividing Fractions with Diagrams, Warm-up, Inline Question 2, “Create a diagram to represent 1\frac{3}{7}+\frac{5}{7}. How many sections will there be in a diagram?” and Review Question 6: “Divide the following fraction. Be sure to convert any improper fraction to a mixed number. \frac{3}{4}\div\frac{1}{2}”
Chapter 2, Rates and Percentages, Question 1: “(6.RP.A.2, 6.RP.A.2, 6.RP.A.3.b) Ken drove 80 miles in 2 hours. Assume he drove at a constant speed. a. Write a ratio between Ken’s distance and time.”
Chapter 6, Expressions, Question 2: “(6.EE.A.2.c, 6.EE.A.3) Use the expression 4x-2*3+5^2 to answer the following questions. a. Write an equivalent expression.”
Indicator 3j
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for including an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, and most of the assessments provide sufficient suggestions for following-up with students. Examples include:
Every lesson has Adaptive Practice Questions which generate a report with the number correct, difficulty of the questions, time spent and mastery level.
Answer keys are provided for all Inline Questions, Discussion Questions, and End of Chapter assessments.
Each of the End of Chapter Assessments contains a rubric to assist the teacher in scoring student work. Each problem is given a 1-5 score and is correlated with the CCSS. Rubrics are provided for End of Chapter Assessments only. Scoring rubrics provide information on student performance but do not include suggestions for the teacher to follow up.
Statistics are given through reports to the teacher on each assessment component students take. The Skill Meter gauges student understanding and skill based question-by-question and is color-coded so teachers can quickly ascertain student understanding:
Beginning - new to concept (red)
Exploring - starting to understand (orange)
Developing - demonstrating familiarity (yellow)
Proficient - understands core concept (light green)
Mastery - deep, demonstrated understanding (dark green)
The Class Insights function uses the Skill Meter to give information on individual students and the entire class, by placing students on a quadrant analysis graph based on their skill level and engagement. The Class Insights function also has the Teacher Assistant which, “uncovers your students’ learning gaps and misconceptions, giving you (the Teacher) personalized insights on where you (the Teacher) can intervene effectively.” The Teacher Assistant provides suggestions for following-up with students through the “Insights and Recommendations” section. Examples of suggestions include:
Recommending specific “PLIX” activities to help students with low skill levels improve their skill levels.
Noting which students are doing exceptionally well on the current concept, and suggesting new concepts to keep those students challenged.
Information about the top question(s) students answered incorrectly, with the recommendations for students to review the following question(s) and the related paragraphs.
Information on which students are not reaching the goal of 10 correct answers on the Adaptive Practices, and recommending to remind students to complete that goal.
Indicator 3k
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.
The assessments regularly provide opportunities for students to demonstrate the full intent of grade-level standards and practices through a wide variety of assessment types, such as multiple choice, drag and drop, matching, short answer, true/false, computational response, and discussion response. Students use different types of modalities to demonstrate their understanding in assessment, including short answer explanations and multi-layered questions. The Inline Questions and Review/Quiz Questions are connected to standards and practices. The End of Chapter Assessments have the content standards identified on the answer keys.
Indicator 3l
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS do not meet expectations for Student Supports. The materials provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics, and partially provide extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. The materials do not provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.
Indicator 3m
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics. The materials have some general strategies, but they do not explicitly provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations or support their regular and active participation in the learning of grade-level mathematics.
Indicator 3n
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.
The program provides occasional opportunities for students to engage with grade-level mathematics at higher levels of complexity through Adaptive Practice and Review Questions. However, these are additional to the lesson so not all advanced students would be provided access to them. The advanced students would be completing more assignments than their classmates. Examples include, but are not limited to:
In Lesson 5.4, Symmetry on the Number Line, Review Questions, the Teacher Notes state, “To customize the questions click here:” Under Assign to Class, Customize, Add question set, various “hard” questions may be assigned. For example, in “Set 1, Question 1, The distance between the points 4 and -6 is -2.“ (6.NS.6)
In Lesson 8.2, Comparing Absolute Values, Review Questions, the Teacher Notes state, “To customize the questions click here:” Under Assign to Class, Customize, Add question set, various “hard” questions may be assigned. For example, in “Set 1, Question 2, Identify the Absolute Value of \left|-144\right|.” (6.NS.7)
Indicator 3o
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Indicator 3p
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials provide a means to change the language of the main text to any of the supported languages, which includes the directions for the Interactives. However, the text within the Interactive will not change, and the video content will still be in English. Additionally, the Adaptive Practice, which is expected to be homework, is available in two languages: English and Spanish. The materials do not provide any other strategies or support for students who read, write, and/or speak in a language other than English beyond changing the language of the text.
Indicator 3r
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
Indicator 3s
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
Indicator 3t
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
Indicator 3u
Materials provide supports for different reading levels to ensure accessibility for students.
Indicator 3v
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for providing manipulatives, both virtual and physical. They are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials provide suggestions and/or links for virtual and physical manipulatives that support the understanding of grade-level concepts. Manipulatives are accurate representations of the mathematical objects they represent and are sometimes connected to written methods. Physical manipulatives, while not included with the series, are listed in the beginning of the Teacher Edition under the Resource tab. The use of physical manipulatives is minimal.
Each lesson contains several Interactives where students use virtual manipulatives to gain an understanding of the math standard they are learning. They include a variety of manipulatives such as: graphs, x-y tables, number lines, coordinate planes, GeoGebra Interactives, word matching problems, tape diagrams, dice and playing cards. Examples include:
In Lesson 1.4, Double Number Line & Equivalent Ratios, Warm-up Activity, students solve problems as they use ratio reasoning. It states, “With the following Interactive, practice labeling points by where they belong on the number line.” (6.RP.3)
In Lesson 8.5, Inequalities with a Variable, Activity 1, students are learning about inequalities that include a variable. It states, “For this Interactive, students will practice matching inequality symbols to their meaning. Students should read the directions and click ‘Start’ when they are ready. They will have 15 seconds to match as many inequalities as they can. If they get an answer incorrect, it will turn red and students can guess again.” Following this activity, there are three Inline Questions which are all multiple choice. (6.EE.8)
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3w
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
Indicator 3x
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
Indicator 3y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
Indicator 3z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.