4cs rubrics - edl · sample vertical articulation of 21st century skills – critical thinking...

| 14Cs Rubrics: Additional Resources ©2014 EdLeader21. All rights reserved.

Additional Resources4Cs RUBRICS:


Overview ......................................................................................... 3

Contextualizing 21st Century Skills Rubrics for Use in Specific Domains............................ 3

Critical Thinking: Crafting an Argument

in Elementary Math ..................................................................... 3

Critical Thinking: Scientific Investigations

in High School Science ................................................................ 4

EdLeader21 Promising Practices ................................... 5

Southwest Allen County Schools .......................................... 5

Infusion of 4Cs into Unit Plans ................................................... 5

Infusion of 4Cs into Unit Plans ................................................... 5

Key Strategies Incorporated to Cultivate 4Cs ....................... 5

Critical Thinking and Creativity and Innovation................. 6

Capacity Building ............................................................................ 6

Upper Arlington City Schools .................................................. 6

Infusing 4Cs into Unit Design ...................................................... 6

Capacity Building ............................................................................ 7

Aptakisic-Tripp School District 102 ..................................... 7

Student Self -Assessment ............................................................. 7

Douglas County School District .............................................. 8

Educator Performance Evaluation ............................................ 8

Ballston Spa Central School District .................................... 9

Educator Performance Evaluation ............................................ 9

Unit Sketch ...................................................................................10

Teaching and Learning Process: .......................................... 11

CCSS Learning Targets ...............................................................12

The 4Cs in Academic Content Areas ..........................12

Science ..............................................................................................12

Critical Thinking (PEBC, 2006) ..................................................12

Collaboration ..................................................................................13

Communication ..............................................................................13

Creativity and Innovation ..........................................................13

Social Science ................................................................................13


Collaboration ..................................................................................13

Communication ..............................................................................14


Mathematics ..................................................................................14


Collaboration ..................................................................................14

Communication ..............................................................................14


Sample Vertical Articulation of 21st Century Skills – Critical Thinking .....................15

contents


Reasoning

Constructing Arguments

Analyzing Arguments

CRITICAL THINKING CATEGORY

GENERAL RUBRIC LANGUAGE CONTEXTUALIZED LANGUAGE (Knuth, 2009)

Clearly describes inferences; finds meaning that is not explicitly (clearly) stated by sources; makes conclusions on the basis of available information.

Gathers an adequate (acceptable) amount of proof from sources to support opinion.

Clearly explains a mathematical claim. (Describes what they are going to prove.)Explains how they are going to show that the claim will always work.

Considers the audience when presenting the mathematical claim. (Asks, “Who needs to be convinced? What do they need to be convinced of? How does my mathematical argument need to be explained based on my audience?”)

Uses more than one representation (physical objects, pictures, diagrams, or story contexts) to clearly prove that the claim will always work.

Uses mathematical terms and correctly specifies the units of measure.

Provides clear feedback about the reasoning used in peers’ arguments. (Did my classmate offer a strong argument? Am I convinced? Why or why not? What else would I need to know to be convinced?)

OverviewThis “Additional Resources Document” is a companion to the “4Cs Rubrics: Suggestions for Use” document. Included here are more

detailed examples of how the 4Cs rubrics can be used to support 21st century education systems. This document will be updated

regularly to include more examples as they become available.

Contextualizing 21st Century Skills Rubrics for Use in Specific DomainsThis section provides two examples of contextualized rubric language for Critical Thinking: Crafting an Argument in Elementary Math and Conducting Scientific Investigations in High School Science. In both examples, teachers identified areas of critical thinking on which to focus, drew subject-specific language from their content standards that related to the targeted critical thinking skills, and refined the rubric language to align with the design of the inquiry experience.

C R ITI C AL TH I n k I n g : C R Af TI n g An AR g U M E nT I n E LE M E nTARy MATH

Inquiry Experience: Students are set up to discern and “prove” a pattern or structure embedded in a rich problem solving task related to the communicative, associative, or distributive laws to develop mathematical argumentation as a habit of mind.


C R ITI C AL TH I n k I n g : S C I E nTI fI C I n V E S TI g ATI O n S I n H I g H S C H O O L S C I E n C E

*Contextualized language drawn from Envision Schools College Success Portfolio Performance Assessment and Stanford Center for

Assessment, Learning and Equity (SCALE): SCIENTIFIC INQUIRY.

Information and Discovery


Reasoning

Interpretation and Analysis


CRITICAL THINKING CATEGORY

GENERAL RUBRIC LANGUAGE CONTEXTUALIZED LANGUAGE (Envision Schools and Stanford Center for Assessment. Learning, and Equity, 2012)

Identifies inquiry questions clearly and precisely; engages in an open-ended thinking process to develop an initial set of questions related to the problem, investigation, or challenge; refines the initial set of questions; identifies a key question or prioritized set of questions on which to focus. Questions provide a solid foundation for inquiry.

Provides a claim that clearly articulates an opinion; clearly explains the reasoning for claims.

With independence, presents logical conclusions regarding how to solve the problem, meet the challenge, answer the question, etc…with few errors.

Compares and classifies information accurately; almost always identifies characteristics that create meaningful comparisons.

Evaluates the accuracy and relevance of information and the strengths of arguments with no significant errors.

Provides a claim that clearly articulates an opinion; clearly explains the reasoning for claims. Cites a sufficient quantity of relevant evidence to support most claims. Presents a clear and sufficient treatment of most available evidence relating to the argument; clearly and convincingly addresses counter arguments.

Formulates a specific and empirically testable scientific question.

Articulates a hypothesis about the investigated question, with a basic and accurate description of the variables. (“if.. then…”)

Aligns experimental design with testable question.

Gathers data from several repetitions of the experiment that are not consistent within a reasonable range.

Uses spreadsheets, data tables, charts, or graphs to accurately summarize and display data to examine relationships between variables.

Accurately analyzes data in using appropriate and systematic methods to identify patterns.

Compares consistency of outcome with initial hypothesis and identifies possible sources of error.

Explains the strengths OR weaknesses of the inferences drawn from data using grade appropriate techniques.

Suggests relationships or interactions between variables worth further investigation.

Constructs a scientific argument, explaining how data and acceptable scientific theory support the claim.

Identifies a counterclaim (possible weaknesses in scientific arguments or in one’s own argument) using evidence.


EdLeader21 Promising PracticesTo ensure the 4Cs are systemically integrated throughout a school or district, many EdLeader21 districts are using the rubrics for

purposes beyond teacher-led student assessment. Some examples of these promising practices are included below. Some of the

promising practices demonstrate how backwards design approaches for curriculum design are fundamental to authentic student

assessment; other examples detail educator performance evaluation examples.

S O U TH w E S T ALLE n C O U nT y S C H O O L S

Southwest Allen County Schools is located in Northeast Indiana, near Ft. Wayne. While rolling out a 1:1 laptop initiative, the district

recently took strategic steps to more explicitly teach and assess 21st century skills. As a high-achieving district, SACS wanted to maintain

current success levels while cultivating 21st century skills and adopted Project Based Learning as a unit design model and instructional

methodology to carefully embed the 4Cs into curriculum and assessment.

Infusion of 4Cs into Unit PlansAs part of the PBL implementation planning process, a leadership team composed of teachers, school-level instructional leaders, and

central office staff developed the following vision statement for the PBL initiative:

“SACS is committed to ensuring that students are provided with authentic and rigorous learning experiences that include a strong

foundation of content knowledge and understanding, balanced with essential 21st century skills, thus creating globally competitive

learners.”

The team crafted the following goals for students related to the initiative:

• Students will take ownership and become engaged in PBL learning experiences.

• Students will create meaningful, innovative products which will regularly demonstrate the 4Cs.

• Students will exhibit deep understanding of specific content standards and apply their new knowledge in subsequent studies.

• Students will have the ability to adapt to changing technology and learning opportunities.

• Students will prepare for and participate effectively in a range of conversations and collaborations with diverse partners.

Infusion of 4Cs into Unit Plans During the PBL Implementation planning process, the team decided to formally adopt district-wide 4Cs rubrics for grade level spans.

SACS provided a series of 3-day PBL workshops for an initial cohort of 100 secondary teachers in which participants strengthened their

understanding of the 4Cs and designed inquiry-based units using a backwards design process that embeds content standards and

targeted 21st century skills and provides a framework for assessing the 4cs using the adopted rubrics.

Key Strategies Incorporated to Cultivate 4CsDuring the PBL workshop, participants learned:

Collaboration

• How to strategically form teams for sustained collaboration.

• How to teach teams how to use project management tools (contracts, work plans, goal sheets, etc.) effectively.

• How to scaffold the collaborative inquiry process.

• How to use a collaboration rubric to formatively and summatively assess collaboration skills.


Communication

• How to guide teams to establish norms that align to the 21st century skill of communication.

• How to incorporate “think pair share”, a communication structure that builds communication skills.

• How to incorporate Socratic Seminars to build communication skills and critical thinking strategies (analysis of text, synthesis of

ideas, evaluation of concepts, and inferential reasoning).

• How to create healthy conditions in which students can successfully give and receive feedback; how to use peer critique protocols

like Gallery Walks and Critical Friends.

• How to prepare students to deliver effective oral presentations.

• How to formatively and summatively assess communication skills using a rubric.

Critical Thinking and Creativity and InnovationAdvanced workshops will continue to be offered to the PBL cohort to teach participants how to design units that explicitly teach and

assess Critical Thinking or Creativity and Innovation skills, dependent upon the targeted area of focus in the unit. Participants in these

sessions learn how to use tools to scaffold the critical thinking or creativity and innovation process, how to formatively assess each phase,

and how to use rubrics to summatively assess critical thinking or creative innovation captured in culminating products and performances.

Capacity BuildingAs part of the PBL Implementation planning process, the SACS team established a goal that staff will model and promote the 4Cs. To

achieve this goal, they adopted protocols to guide the cohort of teachers trained in PBL to engage in an inquiry process around their

practice of teaching and assessing 21st century skills with academic content. The inquiry process includes:

• Critical friends, a peer critique protocol, to analyze project plans in relation to established design criteria, including plans to

explicitly teach and assess targeted 21st century skills.

• Looking at Student work, a collaborative protocol designed to enable teachers to think critically about the level of success of

an instructional practice, determine next steps for the classroom, and refine learning targets and rubrics used to assess content

standards and 21st century skills.

• Post-project reflection, a protocol designed to enable teachers to reflect upon the success of the unit, including the degree to which

students demonstrated the targeted content areas and 21st century skills, and identify “need to knows” on which instructional

leaders can base plans for sustained support.

U PPE R AR LI n g TO n C IT y S C H O O L S

Upper Arlington City Schools (UACS) is located in Upper Arlington, Ohio, a northwest suburb of Columbus, Ohio. To prepare students

for life in a globalized 21st century, Upper Arlington City Schools adopted the International Baccalaureate (IB) Diploma Program in

2002 and is in the process of training teachers, coordinators, and administration in the IB Middle Years Program. UACS formed an

IB 21st Century Teacher Leader Professional Development team and a 21st Century Skills Advisory Committee to determine how to

systematically integrate 21st century skills into the IB program. The district launched a Twenty-first Century Learning Cohort (TCLC)

program for teachers and hired Integration Coaches for 21st Century Skills as program facilitators.

Infusing 4Cs into Unit Design To integrate 21st century skills into IB units of inquiry, the 21st Century Teacher Leader Professional Development team and the 21st

Century Skills Advisory Committee:

• Identified and defined core 21st Century Skills for all Upper Arlington students.

• Created 21st Century Skill Checklists to aid teachers in the development of unit plans.


• Planned professional development.

• Infused 21st century skills into IB units, piloted 21st century skills rubrics, and reflected upon results.

Capacity BuildingUpper Arlington’s Integration Coaches for 21st Century Skills facilitate the Twenty-first Century Learning Cohort (TCLC) program. TCLC is

a two-year commitment for participating teachers that addresses the question “What do teachers need to be effective in the twenty-first

century?” Participants commit to over sixty hours of professional development in the first year and showcase their work at a community

celebration in May. During this time, they learn to incorporate 21st century skills and technologies into instructional units. In the second

year of the program, teachers share the knowledge and skills gained in the cohort with colleagues in their respective school buildings.

AP TAk I S I C -T R I PP S C H O O L D I S T R I C T 102

Student Self -AssessmentIn Aptakisic-Tripp School District 102 in Buffalo Grove, IL, the 4Cs are core components of the district’s expectations for student

outcomes. The 4Cs rubrics have been customized for student self-assessment. For each 4Cs rubric, a set of “I Can” statements have been

created based on the existing rubric indicators. Below is an example of the customized communication rubric:

Engaging in Conversations and Discussions

Using 21st Century Communication Tools

Listening

Communicating in Diverse Environments

Delivering Oral Presentations

Communication Rubric Performance Area

Performance Target Student Language

Asks questions to check understanding about information shared during the discussion; makes comments that contribute to the discussion and connect to the comments of others.

When appropriate, uses digital media and environments to enhance oral and written communication, support individual learning, and contribute to the learning of others.

Uses strategies to listen effectively: Connects the information shared by the speaker to own background knowledge and experience; identifies the key points the speaker is trying to convey; draws logical inferences that show adequate understanding.

Develops cultural understanding by communicating with learners of other cultures; understands that learners of other cultures can have different perspectives.

When delivering oral presentations, uses an appropriate amount of facts and details to support the main ideas; speaks clearly at an understandable pace; accurately and confidently fields grade-level appropriate questions to demonstrate conceptual understanding and knowledge.

I can ask questions to help me understand the topic better and share ideas about the topic.

I can use different kinds of media to share ideas.

I can listen and give others my full attention as they share ideas and information.

I can communicate with people from cultures or backgrounds who might not share my exact beliefs or understanding of the world.

I can share information with audiences by speaking accurately about my topic, using supporting details, and answering questions that are asked of me.


D O U g L A S C O U nT y S C H O O L D I S T R I C T

Educator Performance EvaluationIn Douglas County School District, Castle Rock, CO, educators are expected to demonstrate mastery of the 4Cs along with students. As

part of the district’s system-wide transformation around world class outcomes, the 4Cs rubrics have served as key building blocks in the

new teacher performance system. The district’s CITE tool specifies the professional standards by which all educators will be evaluated

and the 4Cs have been integrated throughout these standards. Below is an excerpt from the CITE instrument.


B ALL S TO n S PA C E nT R AL S C H O O L D I S T R I C T

Educator Performance EvaluationIn Ballston Spa Central School District, in upstate New York, the rubrics are being used as a pilot component of a new teacher evaluation

system. The rubrics have been customized for teachers in the district’s Clean Technologies and Sustainable Industries Early College

High School. Eventually, the goal is to have this component apply to all high school teachers. The teacher evaluation rubrics are cross-

walked to the district’s student graduation competencies, which integrate the 4Cs. Below is an example of the Creativity rubric that has

been customized for the teacher evaluation pilot.

Performance Area N/A

C R E ATI V IT y

Exceeds Proficient Meets Novice

Idea Origination

Idea Refinement

working with Others – Communicate and Advocate for Ideas

Responsive and Open to feedback

Perseverance and Adaptability

Pragmatic Implementation

Explores and implements multiple avenues of idea generation. Creates meaningful solutions through consideration of both the challenge and the needs of those impacted.

In response to self reflection, independently revises and refines ideas or solutions.

Demonstration a willingness to promote the ideas of others. Effectively works within a team to initiate the development and communication of new ideas in a clear, coherent, and professional manner that promotes an environment of creativity and trust.

Consistently revises and refines ideas of solutions in response to feedback from peers, stakeholders, and varied perspectives.

Demonstrates a high degree of adaptability in response to obstacles. Maintains a creative, flexible, and positive approach in facing adversity.

Executes a tangible and pragmatic innovation based on the creative process.

Explores a few avenues of idea generation. Suggests possible solutions through consideration of both the challenge and the needs of those impacted.

In response to self reflection, seeks assistance in revising and refining ideas or solutions.

Encourages idea generation from all members of a team. Work within a team to develop and communicate new ideas in a clear, coherent, and respectful manner that promotes an environment of creativity and trust.

Revises and refines ideas or solutions in response to feedback from peers, stakeholders, and varied perspectives.

Demonstrates adaptability in response to obstacles. Maintains a flexible and positive approach in facing adversity.

Executes a pragmatic innovation based on the creative process

Exploration in the methods used to generate ideas is limited in variety. Identifies the nuances of the challenge and the needs of those impacted by that challenge.

Demonstrates limited self reflection, rather revises and refines based primarily on external feedback.

Recognizes the ideas of others. Works within a team to develop and communicate new ideas in a respectful manner that promotes an environment of trust.

Revises and refines ideas or solutions without a full understanding of the feedback from peers, stakeholders and varied perspectives.

Demonstrates adaptability in response to obstacles. Accepts and seeks to manage adversity.

Extends the creative process to pragmatic proposal.

Exploration in methods used to generate ideas is limited in both variety and scope. The needs of those impacted by the challenge are not considered.

Demonstrates no self reflection. Does not revise or refine.

Struggles to work collaboratively within a team to develop and communicate new ideas.

Revisions and refinements of ideas of solutions are limited and/or do not consider feedback from peers, stakeholders, and varied perspectives.

Demonstrates an unwillingness to adapt in response to obstacles. Does not acknowledge or address adversity.

Offers impragmatic solutions with no tangible product or proposal.


Unit Sketch

S I M U LTAn E O U S O U TC O M E S : H E ALTH An D TH E H U MAn B O Dy, R E S E AR C H An D I n fO R MATI O n AL w R ITI n g , An D C R E ATI V IT y An D I n n OVATI O n

This sample unit provided by Expeditionary Learning Schools illustrates how a middle school team created a meaningful context in

which students could gain deep knowledge and understanding of Science standards, acquire Science process skills, and demonstrate

the competencies of Collaboration and Creativity and Innovation. In this kind of unit design, specific performance areas in the

Collaboration and Creativity rubrics could be used to create a custom rubric that helps teachers evaluate the student’s performance on

the content standards as well as the 4Cs.

Project Title:

Anchor Content:

Problem:

Innovation Challenge:

Product format:

4Cs Application in Industry:

Operation Kidfit

Science - Health and the human body (infectious diseases across history, anatomy, physiology and health and nutrition)

39% of children in Rochester and 32% of children in America are obese.

Collaborate to propose an engaging health exhibition for the Rochester Museum and Science Center to show 8-14 year olds how choices affect their bodies.

An informational book containing recommendations that the museum will use to inform exhibit design and fabrication

Science museums employ experienced museum professionals in all areas of exhibit development and design. How do museum exhibit designers draw upon 21st skills in their work? Exhibit developers and researchers engage in a collaborative process of creative innovation to design exhibits that draw visitors in the target audience, deliver target educational content, and add fun and excitement to the visitor experience.


TE AC H I n g An D LE AR n I n g P R O C E S S

I D E A g E n E R ATI O n

Learning Experiences: Researched childhood obesity to gain a deep understanding of the problem;

visited museum to investigate what makes an engaging, effective exhibit; identified the target audience,

generated the “big idea” and content areas for the exhibit and generated ideas about the exhibit.

Rubric Assessment: Problem definition statements, summary of the target audience, and list of ideas.

I D E A D E S I g n An D R E fI n E M E nT

Learning Experiences: Reviewed, categorized, and evaluated ideas in relation to the problem using peer

critique protocol; selected the best idea and provided a clear rationale for decision; reviewed feedback,

determined “next steps”, and made revisions to improve the quality of the idea.

Rubric Assessment: Evaluation of research notebooks (idea categorization and comments; notes about

idea selection and rationale, refinement of ideas based on feedback.)

C R E ATI V E P R O D U C TI O n An D I n n OVATI O n

Learning Experiences: Shaped ideas into an exhibit plan.

Rubric Assessment: Evaluation of final products.


C C S S LE AR n I n g TAR g E T S

Reading Informational Texts• RI.6.7 I can use a variety of media to develop and deepen my understanding of a topic or idea.

Writing• w.6.2 I can write informative/explanatory texts that convey ideas and concepts using relevant information that is carefully selected

and organized.

• w.6.4 I can produce clear and coherent writing that is appropriate to task, purpose, and audience.

• w.6.5 With support from peers and adults, I can use a writing process to produce clear and coherent writing.

• w.6.9 I can use evidence from a variety of grade appropriate texts to support analysis, reflection, and research.

Speaking and Listening• SL.6.2 I can interpret information presented in different media and formats. I can explain how new information connects to a topic,

text, or issue I am studying.

Language• L.6.1 I can use correct grammar and usage when writing or speaking.

• L.6.2 I can use correct capitalization, punctuation, and spelling to send a clear message to my reader.

• L.6.3 I can use a variety of sentence structures to make my writing and speaking more interesting. I can maintain consistency in

style and tone when writing and speaking.

• L.6.6 I can accurately use 6th grade academic vocabulary to express my ideas. I can use resources to build my vocabulary.

The 4Cs in Academic Content AreasIn a 21st century school or district, the 4Cs are fully integrated into academic content areas. It is important to carry out this integration in

contextually-appropriate ways, however. Critical thinking in mathematics has a different context when compared to critical thinking in

science, and these can lead to important differences in how the 4Cs rubrics are used.

This section provides food for thought about how the 4Cs can be articulated in the contexts of Science, Mathematics and Social Studies.

S C I E n C E

21st Century Skills play a strong role in the lives of scientists as they collaborate, problem solve, and share their findings with the greater

scientific community.

Critical Thinking (PEBC, 2006)• Scientists build their background knowledge and understanding by reading the publications of other scientists, attending scientific

meetings, and participating in peer reviews of their work.

• Scientists focus each investigation by posing specific, testable questions and designing experiments that can give definitive answers.

• Scientists form hypotheses and draw inferences based on their background knowledge and inferences.

• When designing investigations, scientists determine the sequence of steps to take in the process.


• Scientists analyze and interpret data using tables, charts, graphs, and diagrams.

• Scientists draw inferences to explain their observations.

• Scientists often pose new questions or modify their hypothesis after gathering new data.

• Scientists reflect on the validity of their hypotheses in light of new data and assess the possibility of errors in their experiments.

• Scientists repeat their investigations to ensure that their results are replicable.

• Scientists draw conclusions from their data by synthesizing what they learned with what they already knew before an investigation.

Collaboration• As the nature of the questions that researchers ask becomes more complex, Scientists bring their unique expertise to find the

answers.

• Collaborating scientists define goals, expectations and outcomes and determine who will take charge of the collaboration.

Communication• Scientists share their thinking and justify their answers orally and in writing.

• Scientists record their findings.

• Scientists carefully communicate findings to make an impact with their research.

Creativity and Innovation• Scientists harness the forces of creativity and innovation to yield breakthroughs that will improve the lives of people.

S O C IAL S C I E n C E

The various disciplines of Social Science use a range of approaches to study society, including surveys, questionnaires, interviews and

statistics. 21st Century Skills play a strong role in the lives of Social Scientists as they engage in collaborative research, analysis, and

inquiry to find answers to complex problems, discover hidden relationships, and communicate findings.

Critical Thinking (PEBC, 2006)• Social Scientists ask questions and launch investigations.

• Social Scientists use a variety of sources to validate information and to check for accuracy.

• Social Scientists use research to infer why and how historical choices were made, the implications of those choices, and how those

choices impact us today.

• Social Scientists use primary source documents and artifacts to infer themes and patterns.

• Social Scientists ask critical questions of text: Is there a bias? Whose voice is left out? From whose point of view is this being told?

• Social Scientists recognize misinformation and reconcile conflicting points of view.

• Social Scientists create valid and reliable claims.

Collaboration• Social Scientists come together, bringing their unique expertise to find the answers.

• Collaborating Social Scientists define goals, expectations and outcomes and determine who will take charge of the collaboration.

Communication• Social Scientists record their findings.


• Social Scientists explain their thinking and justify their answers orally and in writing.

• Social Scientists carefully communicate findings to make an impact with their research.

Creativity and Innovation• Social Scientists harness the forces of creativity and innovation to yield breakthroughs that will improve the lives of people.

MATH E MATI C S

Mathematicians explore and investigate an often uncertain world and attempt to explain what they see. Sometimes a single explanation

works; more often, patterns, and relationships emerge that lead to several different conclusions. Logic helps mathematicians justify

their methods and determine the validity of their solutions as they try to make sense of the unknown.

Critical Thinking (PEBC, 2006)• Mathematicians ask questions.

• Mathematicians decide what information is relevant and irrelevant to a problem.

• Mathematicians work through cycles of data-gathering, visualization, abstraction, conjecturing, and proof.

• Mathematicians use patterns and relationships to generalize and infer what comes next in the problem-solving process.

• Mathematicians analyze evidence and look for counter examples to claims.

• Mathematicians prove their claims.

• Mathematicians are metacognitive as they continually ask themselves, “Does this make sense?” and “Is my answer reasonable?”

Collaboration• Mathematicians share and build on each other’s questions, conjectures, and theorems.

Communication• Mathematicians explain their thinking and justify their answers orally and in writing.

• Mathematicians visually represent their thinking through drawings, pictures, graphs, models, and charts.

• Mathematicians use accurate math vocabulary and show their work in clear concise forms so others can follow their thinking without

asking questions.

Creativity and Innovation• Mathematicians harness the forces of creativity and innovation to yield breakthroughs that will improve the lives of people.


Sample Vertical Articulation of 21st Century Skills — Critical ThinkingThis sample vertical articulation of critical thinking is based on the critical thinking rubrics and offered as a planning guide. District and

school leaders may wish to adapt this kind of documentation to help plan a systemic approach to the 4Cs.

grade 3-4

grade 7-8

grade 11-12

Grade Span

Anchor Skill: Identifies and defines the problem or challenge, creates questions, and collects information.

I n fO R MATI O n An D D I S C OV E Ry

Grade Span-Specific Proficiency

Clearly explains the problem, investigation, or challenge in his/her own words; creates an acceptable number of questions; and questions are usually clear.

Clearly defines the problem, investigation, or challenge; continuously seeks clarity and understanding.

Creates additional questions related to the problem, investigation, or challenge. Effectively refines and improves questions and identifies a key question or set of questions to investigate.

Conducts efficient research and gathers relevant information from multiple sources; effectively assesses the credibility and accuracy of each source.

Clearly defines the problem, investigation, or challenge; continuously seeks clarity and understanding.

Identifies inquiry questions clearly and precisely; engages in an open-ended thinking process to develop an initial set of questions related to the problem, investigation, or challenge; refines the initial set of questions; and identifies a key question or prioritized set of questions on which to focus. Questions provide a solid foundation for inquiry.

Selects information that is sufficient in terms of its quantity, diversity, and relevance to inquiry questions.


grade 3-4

grade 7-8

grade 11-12

grade 3-4

grade 7-8

grade 11-12

Grade Span

Grade Span

Anchor Skill: Assesses and analyzes relevant information.

Anchor Skill: Reasons effectively.

I nTE R P R E TATI O n An D An ALy S I S

R E A S O n I n g



Clearly and accurately describes points of view from a variety of sources.

Integrates information from multiple sources on the inquiry topic to build background knowledge, with independence.

Accurately determines sources’ points of view and analyzes how the sources address conflicting viewpoints.

Clearly explains the difference between his/her point of view and that of sources.

Is laying the foundation to thoroughly and accurately assess and describe arguments and claims provided by sources. Assesses whether the reasoning is sound, if the evidence is helpful to the argument, and if a sufficient amount of evidence is provided.

Consistently recognizes when irrelevant (i.e., unrelated; unimportant) evidence is introduced.

Compares and classifies information accurately; almost always identifies characteristics that create meaningful comparisons.

Evaluates the accuracy and relevance of information and the strengths of arguments, with no significant errors.

Clearly describes inferences, finds meaning that is not explicitly (clearly) stated by sources, and makes conclusions on the basis of available information.

Clearly explains and justifies assumptions (what student believes, but has not proven) about the problem, investigation, or challenge.

Consistently makes clear inferences from the inquiry experience.

Offers generalizations that relate in a significant way to the problem, investigation, or challenge.

Presents logical conclusions regarding how to solve the problem, meet the challenge, answer the question, etc., that illustrate substantial understanding.

Provides explanations that are generally clear, citing sufficient evidence for conclusions drawn.

Demonstrates ethical reasoning and judgment by clearly sharing perspectives on why the proposed course of action is morally the best decision.


grade 3-4

grade 7-8

grade 11-12

Grade Span

Anchor Skill: Solves authentic problems.

P R O B LE M S O LV I n g / S O LU TI O n fI n D I n g


Explains ideas about how to best solve the problem, meet the challenge, or answer the inquiry question. Clearly describes why their ideas make sense.

Uses systems thinking in problem solving. Describes the function of the whole system, names all of the parts, describes the function of each part, and predicts what would happen if a part is missing.

Clearly explains ideas about how to best solve the problem, meet the challenge, or answer the inquiry question; clearly describes why their ideas make sense.

Uses systems thinking in problem solving. Describes the function of the whole system, describes the subsystems, and describes how a change in the subsystems influences the entire system.

Tests ideas. With little assistance, assesses and clearly describes the outcome and decides if a new solution is necessary.

Accurately and clearly analyzes and describes how parts of a whole interact with each other to produce overall outcomes in complex systems, and how systems effectively interact with each other.

Identifies a sufficient number of plausible solutions to the problem, answers to the question, or approaches to meet the challenge.

Analyzes, with precision and accuracy, the relative effectiveness of proposed solutions or approaches. Uses relevant criteria to eliminate ineffective solutions or approaches and select those that are plausible.

grade 3-4

grade 7-8

Grade Span

Anchor Skill: Makes accurate judgments and decisions.

C O n S T R U C TI n g AR g U M E nT S


Gathers an adequate, acceptable amount of proof from sources to support opinion.

Clearly states opinion about inquiry question.

With little assistance, gathers proof (evidence) from sources to support opinion; uses accurate, correct, credible, and trustworthy sources to support opinion.

Clearly compares and contrasts personal opinion from differing opinions.

With minimal support, clearly organizes reasons and evidence and recognizes opposing claims.


grade 11-12 Provides a claim that clearly articulates an opinion; clearly explains the reasoning for claims. Cites a sufficient quantity of relevant evidence to support most claims.

Presents a clear and sufficient treatment of most available evidence relating to the argument; clearly and convincingly addresses counter arguments.

grade 3-4

grade 7-8

grade 11-12

Grade Span

Anchor Skill: Reflects critically on learning experiences, processes, and solutions.

S E Lf - R E g U L ATI O n An D R E fLE C TI O n


Clearly explains the critical thinking skills he/she used in the unit, in his/her own words.

Often assesses one’s own critical thinking dispositions with accuracy. (Does the student always try hard to understand? Allow enough time and effort for thinking? Reflect on the amount of support that he/she needs during the critical thinking process?)

Clearly explains the critical thinking skills assessed in the unit in his/her own words.

Monitors his/her thought process and articulates or describes strengths and weaknesses in thinking during parts of the inquiry experience. Describes how assumptions impacted the ability to think critically in the investigation.

Describes how inferences were helpful in the investigation.

Describes how his/her points of view compare and contrast with other points of view explored during the inquiry experience.

Shows awareness of how the ability to recognize and analyze points of view impacted the critical thinking process.

Often assesses one’s own critical thinking dispositions with accuracy. (Does the student continuously seek clarity and understanding? Use accuracy and detail? Dedicate enough time and effort to thinking? Reflect on the amount of support needed during the critical thinking process?)

Frequently identifies and corrects errors in the process.

Often analyzes and questions one’s own thinking, reasoning, and critical thinking dispositions with accuracy. (Does the student openly explore alternative points of view? Show open-mindedness and flexibility? Continuously seek clarity and understanding? Use precision and thoroughness? Dedicate enough time and effort to thinking? Assess whether the quality of his/her thinking is improving over time? Reflect about the amount of support that he/she needs during the critical thinking process?)

Often identifies factors that affect one’s objectivity or rationality.

Rarely makes significant errors in reviewing one’s own performance.

4cs rubrics - edl · sample vertical articulation of 21st century skills – critical thinking...

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