General Education Assessment (GEA) Authentic Assignment Tool (AAT) Competency: Quantitative Reasoning STEP 1 STEP 2 STEP 3 Read the Quantitative Reasoning Rubric on pages 2-3 of this form. Identify an authentic assignment 1 required in your course which directs students to provide detailed/substantial demonstrations of all learning outcome dimensions identified in the Quantitative Reasoning Rubric 2. Direct questions to Jennifer Ferguson at jferguson@tcc.edu. Online resources such as sample assignments are available through the General Education Assessment Resource System (GEARS), created for faculty by the Tidewater Community College Instruction Committee at www.tcc.edu/gears. Provide the requested information on pages 4-8 of this form. STEP 4 By 02/09/2018, email the following to mdegaraff@tcc.edu 3 : a. Completed AAT form, and b. Separate document(s) containing the assignment instructions as provided to students for the assignment(s) identified on pages 4-8 of the AAT form. 1 Authentic Assignments require students to apply standard-driven knowledge and skills to real-world challenges by demonstrating understanding through active use of the material. For example, Authentic Assignments may direct students to construct, perform, analyze, synthesize, and/or apply concepts and/or skills. * Multiple choice, true/false, matching, fill in the blank, and group assignments may NOT be used in the GEA. 2 If you do not require an assignment which prompts students to demonstrate all dimensions of the rubric, you may revise an existing assignment, create a new assignment, or identify multiple assignments which in combination comprehensively support the rubric. 3 Hard copies may be sent via campus mail to Jennifer Ferguson, Suite 623, Green Building, District, Norfolk or faxed to Jennifer at 757.822.1060. 1
Association of American Colleges and Universities QUANTITATIVE REASONING RUBRIC DEFINITION Quantitative Reasoning (QR) is a habit of mind, competency, and comfort in working with numerical data. Individuals with strong QR skills possess the ability to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations. They understand and can create sophisticated arguments supported by quantitative evidence and they can clearly communicate those arguments in a variety of formats (using words, tables, graphs, mathematical equations, etc., as appropriate). A person who is competent in quantitative reasoning can use numerical, geometric, and measurement data and concepts, mathematical skills, and principles of mathematical reasoning to draw logical conclusions and to make wellreasoned decisions; the person demonstrates the ability to: use logical and mathematical reasoning within the context of various disciplines; interpret and use mathematical formulas; interpret mathematical models and draw inferences from them; use graphical, symbolic, and numerical methods to analyze, organize, and interpret data; and, estimate and consider answers to mathematical problems in order to determine reasonableness. FRAMING LANGUAGE This rubric has been designed for the evaluation of work that addresses quantitative reasoning in a substantive way. QR is not just computation, not just the citing of someone else s data. QR is a habit of mind, a way of thinking about the world that relies on data and on the mathematical analysis of data to make connections and draw conclusions. Teaching QR requires us to design assignments that address authentic, data-based problems. Such assignments may call for the traditional written paper, but we can imagine other alternatives: a video of a PowerPoint presentation, perhaps, or a welldesigned series of web pages. In any case, a successful demonstration of QR will place the mathematical work in the context of a full and robust discussion of the underlying issues addressed by the assignment. GLOSSARY The definitions that follow were developed to clarify terms and concepts used in this rubric only. Interpretation: Ability to explain information presented in mathematical forms (e.g., equations, graphs, diagrams, tables, and words). Representation: Ability to convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words). Application/Analysis: Ability to make judgments and draw appropriate conclusions based on the quantitative analysis of data, while recognizing the limits of this analysis. Assumptions: Ability to make and evaluate important assumptions in estimation, modeling, and data analysis. Communication: Expressing quantitative evidence in support of the argument or purpose of the work (in terms of what evidence is used and how it is formatted, presented, and contextualized). Excerpted with permission from Assessing Outcomes and Improving Achievement: Tips and Tools for Using Rubrics, edited by Terrel L. Rhodes. Copyright 2010 by the Association of American Colleges and Universities. 2
QUANTITATIVE REASONING VALUE RUBRIC for more information contact value@aacu.org Evaluators are encouraged to assign a zero to any work sample or collection of work that does not meet benchmark (cell one) level performance. 4 3 2 1 Interpretation Provides accurate explanations of information presented in mathematical forms. Makes appropriate inferences based on that information. For example, accurately explains the trend data shown in a graph and makes reasonable predictions regarding what the data suggest about future events. Provides accurate explanations of information presented in mathematical forms. For instance, accurately explains the trend data shown in a graph. Provides somewhat accurate explanations of information presented in mathematical forms, but occasionally makes minor errors related to computations or units. For instance, accurately explains trend data shown in a graph, but may miscalculate the slope of the trend line. Attempts to explain information presented in mathematical forms, but draws incorrect conclusions about what the information means. For example, attempts to explain the trend data shown in a graph, but will frequently misinterpret the nature of that trend, perhaps by confusing positive and negative trends. Representation Skillfully converts relevant information into an insightful mathematical portrayal in a way that contributes to a further or deeper understanding. Competently converts relevant information into an appropriate and desired mathematical portrayal. Completes conversion of information but resulting mathematical portrayal is only partially appropriate or accurate. Completes conversion of information but resulting mathematical portrayal is inappropriate or inaccurate. Calculation Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations are also presented elegantly (clearly, concisely, etc.) Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations attempted are either unsuccessful or represent only a portion of the calculations required to comprehensively solve the problem. Calculations are attempted but are both unsuccessful and are not comprehensive. Application / Analysis Uses the quantitative analysis of data as the basis for deep and thoughtful and logical judgments, drawing insightful, carefully qualified conclusions from this work. Uses the quantitative analysis of data as the basis for logical judgments, drawing reasonable and appropriately qualified conclusions from this work. Uses the quantitative analysis of data as the basis for workmanlike (without inspiration or nuance, ordinary) judgments, drawing plausible conclusions from this work. Uses the quantitative analysis of data as the basis for tentative, basic judgments, although hesitant or uncertain about drawing conclusions from this work. Assumptions Explicitly describes assumptions and provides compelling rationale for why each assumption is appropriate. Shows awareness that confidence in final conclusions is limited by the accuracy of the assumptions. Explicitly describes assumptions and provides compelling rationale for why assumptions are appropriate. Explicitly describes assumptions. Attempts to describe assumptions. Communication Uses quantitative information in connection with the argument or purpose of the work, presents it in an effective format, and explicates it with consistently high quality. Uses quantitative information in connection with the argument or purpose of the work, though data may be presented in a less than completely effective format or some parts of the explication may be uneven. Uses quantitative information, but does not effectively connect it to the argument or purpose of the work. Presents an argument for which quantitative evidence is pertinent, but does not provide adequate explicit numerical support. (May use quasi-quantitative words such as many, few, increasing, small, and the like in place of actual quantities.) 3
*To complete this form electronically, save as [Your Last Name] AAT, close, reopen, complete form, save, close. Faculty Name COURSE DATE Name of Assignment Due date for Students Learning Outcome Interpretation Ability to explain information presented in mathematical forms (e.g., equations, graphs, diagrams, tables, words) Provides accurate explanations of information presented in mathematical forms. Makes appropriate inferences based on that information. For example, accurately explains the trend data shown in a graph and makes reasonable predictions regarding what the data suggest about future events. Provides accurate explanations of information presented in mathematical forms. For instance, accurately explains the trend data shown in a graph. Provides somewhat accurate explanations of information presented in mathematical forms, but occasionally makes minor errors related to computations or units. For instance, accurately explains trend data shown in a graph, but may miscalculate the slope of the trend line. Attempts to explain information presented in mathematical forms, but draws incorrect conclusions about what the information means. For example, attempts to explain the trend data shown in a graph, but will frequently misinterpret the nature of that trend, perhaps by confusing positive and negative trends. NA (Assignment does not require dimension) 4 4 Support each dimension of the rubric through one or more assignments. Adapt existing or create new assignments as necessary. 4
Learning Outcome Representation Ability to convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words) Skillfully converts relevant information into an insightful mathematical portrayal in a way that contributes to a further or deeper understanding. Competently converts relevant information into an appropriate and desired mathematical portrayal. Completes conversion of information but resulting mathematical portrayal is only partially appropriate or accurate. Completes conversion of information but resulting mathematical portrayal is inappropriate or inaccurate. NA (Assignment does not require dimension) 5 Learning Outcome Calculation Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations are also presented elegantly (clearly, concisely, etc.) Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations attempted are either unsuccessful or represent only a portion of the calculations required to comprehensively solve the problem. Calculations are attempted but are both unsuccessful and are not comprehensive. NA (Assignment does not require dimension) 5 5 Support each dimension of the rubric through one or more assignments. Adapt existing or create new assignments as necessary. 5
Learning Outcome Application / Analysis Ability to make judgments and draw appropriate conclusions based on the quantitative analysis of data, while recognizing the limits of this analysis Uses the quantitative analysis of data as the basis for deep and thoughtful and logical judgments, drawing insightful, carefully qualified conclusions from this work. Uses the quantitative analysis of data as the basis for logical judgments, drawing reasonable and appropriately qualified conclusions from this work. Uses the quantitative analysis of data as the basis for workmanlike (without inspiration or nuance, ordinary) judgments, drawing plausible conclusions from this work. Uses the quantitative analysis of data as the basis for tentative, basic judgments, although is hesitant or uncertain about drawing conclusions from this work. NA (Assignment does not require dimension) 6 Learning Outcome Assumptions Ability to make and evaluate important assumptions in estimation, modeling, and data analysis Explicitly describes assumptions and provides compelling rationale for why each assumption is appropriate. Shows awareness that confidence in final conclusions is limited by the accuracy of the assumptions. Explicitly describes assumptions and provides compelling rationale for why assumptions are appropriate. Explicitly describes assumptions. Attempts to describe assumptions. NA (Assignment does not require dimension) 6 6 Support each dimension of the rubric through one or more assignments. Adapt existing or create new assignments as necessary. 6
Learning Outcome Communication Expressing quantitative evidence in support of the argument or purpose of the work (in terms of what evidence is used and how it is formatted, presented, and contextualized) Uses quantitative information in connection with the argument or purpose of the work, presents it in an effective format, and explicates it with consistently high quality. Uses quantitative information in connection with the argument or purpose of the work, though data may be presented in a less than completely effective format or some parts of the explication may be uneven. Uses quantitative information, but does not effectively connect it to the argument or purpose of the work. Presents an argument for which quantitative evidence is pertinent, but does not provide adequate explicit numerical support. (May use quasi-quantitative words such as many, few, increasing, small, and the like in place of actual quantities.) NA (Assignment does not require dimension) 7 7 Support each dimension of the rubric through one or more assignments. Adapt existing or create new assignments as necessary. 7
Instructor s Narrative: In a brief narrative, summarize how your course supports the [Competency] competency. Send completed AAT form and instructions to students for the chosen assignment(s) to: Electronic copies (preferred): Hard copies: email Melissa Degaraff at mdegaraff@tcc.edu via campus mail to Jennifer Ferguson, Suite 623, Green Building, District, Norfolk via fax to Jennifer Ferguson at 757.822.1060 Completed AAT forms and instructions to students are due by 02/09/2018. 8