Core Curriculum Course Proposal

Course MATH 2413 Prefix/Number** Calculus I Course Name Mathematics Academic Department

In which Foundational Component Area is the course (refer to the “Core Matrix”)?

Mathematics 020 and Component Area Options - Area B 090 Foundational Area

Check all Core Objectives that apply (refer to the “Core Matrix”)

_x__ Critical Thinking _x__ Communication Skills _x__ Empirical & Quantitative Skills ___ Teamwork ___ Social Responsibility ___ Personal Responsibility Mathematics 2413 Calculus I (4-0)

Course Description: Calculus of functions of one variable including a study of limits, continuity, differentiation of different classes of functions, applications of the derivative, introduction to the integral, the relationship between the derivative and integral, and the Fundamental Theorem of Calculus.

Prerequisite: Mathematics 1316 and 2312; or a suitable score on a placement exam.

Mathematics 2413 Calculus I (4-0)

Mathematics Student Learning Outcomes

1. The students will demonstrate factual knowledge including the mathematical notation and terminology used in this course. Students will read, interpret, and use the vocabulary, symbolism, and basic definitions used in Calculus I as they pertain to functions, limits, derivatives, and integrals.

2. The students will describe the fundamental principles including the laws and theorems arising from the concepts covered in this course. Students will identify and apply the laws and formulas that result directly from the definitions; for example, domain and range of a function, operations on functions, the limit laws, the differentiation formulas, and application of the Fundamental Theorem of Integral Calculus.

3. The students will apply course material along with techniques and procedures covered in this course to solve problems. Students will use the facts, formulas, and techniques learned in this course to sketch graphs of functions, to study position-velocity-acceleration problems, to solve related rate and optimization (“max-min”) problems, and to compute areas bounded by curves.

4. The students will develop specific skills, competencies, and thought processes sufficient to support further study or work in this field or related fields. Students will acquire a level of proficiency in the fundamental concepts and applications necessary for further study in academic areas requiring Calculus I as a prerequisite, or for work in occupational fields requiring a background in Calculus I. These fields might include computer science, engineering, the physical and natural sciences as well as mathematics.

Course Content

1. Preparing for Calculus. Brief summary of functions, operations on functions, different classes of functions and their properties. 2. Limits and Continuity. Evaluating limits using numerical and graphing techniques, evaluating limits using properties of limits, continuity, limits of transcendental functions, infinite limits. 3. The Derivative. Rates of change, limit definition of the derivative, the derivative of polynomials, the natural exponential function, and the trigonometric functions, product rule, quotient rule, higher derivatives. 4. Differentiation Rules. The chain rule, implicit differentiation, derivatives of the inverse trigonometric functions and logarithmic functions, differentials, linear approximations. 5. Applications of Differentiation. Related rates, maximum and minimum values, the Mean Value Theorem, concavity, sketching graphs, L’Hopital’s Rule, optimization, antiderivatives. 6. The Integral. Areas and distances, the definite integral, evaluating definite integrals, the Fundamental Theorem of Calculus, integration by substitution. MATHEMATICS STUDENT LEARNING OUTCOME ALIGNMENT FORM

Course Prefix/Number: MATH 2413 Course Title: Calculus I Brief Course Description:

Calculus of functions of one variable including a study of limits, continuity, differentiation of different classes of functions, applications of the derivative, introduction to the integral, the relationship between the derivative and integral, and the Fundamental Theorem of Calculus. Prerequisite: Mathematics 1316, 2312, or a suitable score on a placement exam.

Foundational Component Area: Mathematics. Courses in this category focus on quantitative literacy in logic, patterns, and relationships. Courses involve the understanding of key mathematical concepts and the application of appropriate quantitative tools to everyday experience.

Core Curriculum Student Learning Outcomes and Assessments

THECB Core University SLO Course SLO Assessment Method Objective Area Critical CT1: Gather, Thinking analyze, evaluate, and synthesize information relevant to a question or issue. CT2: Develop and Students will use mathematical Assessment will be based on demonstrate a theorems and formulas to the AACU Critical Thinking logical position calculate limits, identify critical VALUE Rubric * (i.e. perspective, points and extrema of a function, thesis, hypothesis) and find areas bounded by that acknowledges curves. ambiguities or contradictions. Communication CS1: Develop, interpret, and express ideas through effective written communication. CS2: Develop, interpret, and express ideas through effective oral communication. CS3: Develop, Students will understand the Assessment will be based on interpret, and geometrical relationship the AACU Communication express ideas between a function, its VALUE Rubric * through effective derivative, and its antiderivative. visual communication. Empirical & EQS1: Manipulate Quantitative and analyze Skills numerical data and arrive at an informed conclusion. EQS2: Manipulate Students will interpret functions Assessment will be based on and analyze and their limits, derivatives, and the AACU Problem Solving observable facts antiderivatives physically. VALUE Rubric * and arrive at an informed conclusion. * Association of American Colleges & Universities, Valid Assessment of Learning in Undergraduate Education (VALUE), information & rubrics available at: http://aacu.org/value-rubrics Visual Communication Rubric

Capstone Milestones Benchmark

4 3 2 1

Graphs Accurately drawn Minor discrepancies Graphs depict the Graphs included graphs with between the graphs; overall general show no real appropriate scale scale of the relationship; graphs relationship as showing relative derivative may not may indicate a expected. values of the accurately reflect misinterpretation of Carelessly drawn derivative function. actual values. the graph that was graphs. Graphs are well provided. Graphs drawn. reasonably well drawn.

Labeling All appropriate Most of the Very little labeling Little to no attempt points included and appropriate points but attributes of to clarify the properly labeled. included with graphs giving some important features possibly minor clarity as to of the graphs. labeling issues. important points.

Calculus Maxima, horizontal Majority of the Some of the maxima, No clear indication Interpretation asymptotes, and maxima, horizontal horizontal that the graph is points of asymptotes, and asymptotes, and interpreted

nondifferentiability points of points of correctly. are all listed and nondifferentiability nondifferentiability properly are listed and are listed and categorized. properly properly categorized. categorized. CRITICAL THINKING VALUE RUBRIC for more information, please contact [email protected]

Definition Critical thinking is a habit of mind characterized by the comprehensive exploration of issues, ideas, artifacts, and events before accepting or formulating an opinion or conclusion.

Evaluators are encouraged to assign a zero to any work sample or collection of work that does not meet benchmark (cell one) level performance.

Capstone Milestones Benchmark 4 3 2 1

Explanation of issues Issue/ problem to be considered critically is Issue/problem to be considered critically is Issue/problem to be considered critically is Issue/ problem to be considered critically is stated clearly and described stated, described, and clarified so that stated but description leaves some terms stated without clarification or description. comprehensively, delivering all relevant understanding is not seriously impeded by undefined, ambiguities unexplored, information necessary for full omissions. boundaries undetermined, and/ or understanding. backgrounds unknown. Evidence Information is taken from source(s) with Information is taken from source(s) with Information is taken from source(s) with Information is taken from source(s) without Selecting and using information to investigate a enough interpretation/ evaluation to develop enough interpretation/ evaluation to develop some interpretation/ evaluation, but not any interpretation/ evaluation. point of view or conclusion a comprehensive analysis or synthesis. a coherent analysis or synthesis. enough to develop a coherent analysis or Viewpoints of experts are taken as fact, Viewpoints of experts are questioned Viewpoints of experts are subject to synthesis. without question. thoroughly. questioning. Viewpoints of experts are taken as mostly fact, with little questioning. Influence of context and assumptions Thoroughly (systematically and Identifies own and others' assumptions and Questions some assumptions. Identifies Shows an emerging awareness of present methodically) analyzes own and others' several relevant contexts when presenting a several relevant contexts when presenting a assumptions (sometimes labels assertions as assumptions and carefully evaluates the position. position. May be more aware of others' assumptions). relevance of contexts when presenting a assumptions than one's own (or vice versa). Begins to identify some contexts when position. presenting a position. Student's position (perspective, Specific position (perspective, Specific position (perspective, Specific position (perspective, Specific position (perspective, thesis/hypothesis) thesis/ hypothesis) is imaginative, taking into thesis/hypothesis) takes into account the thesis/ hypothesis) acknowledges different thesis/ hypothesis) is stated, but is simplistic account the complexities of an issue. complexities of an issue. sides of an issue. and obvious. Limits of position (perspective, Others' points of view are acknowledged thesis/ hypothesis) are acknowledged. within position (perspective, Others' points of view are synthesized thesis/ hypothesis). within position (perspective, thesis/ hypothesis). Conclusions and related outcomes Conclusions and related outcomes Conclusion is logically tied to a range of Conclusion is logically tied to information Conclusion is inconsistently tied to some of (implications and consequences) (consequences and implications) are logical information, including opposing viewpoints; (because information is chosen to fit the the information discussed; related outcomes and reflect student’s informed evaluation related outcomes (consequences and desired conclusion); some related outcomes (consequences and implications) are and ability to place evidence and implications) are identified clearly. (consequences and implications) are oversimplified. perspectives discussed in priority order. identified clearly.

ORAL COMMUNICATION VALUE RUBRIC for more information, please contact [email protected]

Definition Oral communication is a prepared, purposeful presentation designed to increase knowledge, to foster understanding, or to promote change in the listeners' attitudes, values, beliefs, or behaviors.

Evaluators are encouraged to assign a zero to any work sample or collection of work that does not meet benchmark (cell one) level performance.

Capstone Milestones Benchmark 4 3 2 1 Organization Organizational pattern (specific Organizational pattern (specific Organizational pattern (specific Organizational pattern (specific introduction and conclusion, sequenced introduction and conclusion, sequenced introduction and conclusion, sequenced introduction and conclusion, sequenced material within the body, and transitions) material within the body, and transitions) material within the body, and transitions) material within the body, and transitions) is clearly and consistently observable and is clearly and consistently observable is intermittently observable within the is not observable within the presentation. is skillful and makes the content of the within the presentation. presentation. presentation cohesive. Language L anguage choices are imaginative, L anguage choices are thoughtful and L anguage choices are mundane and L anguage choices are unclear and memorable, and compelling, and enhance generally support the effectiveness of the commonplace and partially support the minimally support the effectiveness of the the effectiveness of the presentation. presentation. L anguage in presentation is effectiveness of the presentation. presentation. L anguage in presentation is L anguage in presentation is appropriate to appropriate to audience. L anguage in presentation is appropriate to not appropriate to audience. audience. audience. Delivery Delivery techniques (posture, gesture, eye Delivery techniques (posture, gesture, eye Delivery techniques (posture, gesture, eye Delivery techniques (posture, gesture, eye contact, and vocal expressiveness) make contact, and vocal expressiveness) make contact, and vocal expressiveness) make contact, and vocal expressiveness) detract the presentation compelling, and speaker the presentation interesting, and speaker the presentation understandable, and from the understandability of the appears polished and confident. appears comfortable. speaker appears tentative. presentation, and speaker appears uncomfortable. Supporting Material A variety of types of supporting materials Supporting materials (explanations, Supporting materials (explanations, Insufficient supporting materials (explanations, examples, illustrations, examples, illustrations, statistics, analogies, examples, illustrations, statistics, analogies, (explanations, examples, illustrations, statistics, analogies, quotations from quotations from relevant authorities) make quotations from relevant authorities) make statistics, analogies, quotations from relevant authorities) make appropriate appropriate reference to information or appropriate reference to information or relevant authorities) make reference to reference to information or analysis that analysis that generally supports the analysis that partially supports the information or analysis that minimally significantly supports the presentation or presentation or establishes the presenter's presentation or establishes the presenter's supports the presentation or establishes establishes the presenter's credibility/ authority on the topic. credibility/ authority on the topic. the presenter's credibility/ authority on the credibility/ authority on the topic. topic. Central Message Central message is compelling (precisely Central message is clear and consistent Central message is basically Central message can be deduced, but is stated, appropriately repeated, memorable, with the supporting material. understandable but is not often repeated not explicitly stated in the presentation. and strongly supported.) and is not memorable.

PROBLEM SOLVING VALUE RUBRIC for more information, please contact [email protected]

Definition Problem solving is the process of designing, evaluating, and implementing a strategy to answer an open-ended question or achieve a desired goal.

Evaluators are encouraged to assign a zero to any work sample or collection of work that does not meet benchmark (cell one) level performance.

Capstone Milestones Benchmark 4 3 2 1 Define Problem Demonstrates the ability to construct a clear Demonstrates the ability to construct a Begins to demonstrate the ability to Demonstrates a limited ability in identifying and insightful problem statement with problem statement with evidence of most construct a problem statement with a problem statement or related contextual evidence of all relevant contextual factors. relevant contextual factors, and problem evidence of most relevant contextual factors. statement is adequately detailed. factors, but problem statement is superficial. Identify Strategies Identifies multiple approaches for solving Identifies multiple approaches for solving Identifies only a single approach for solving Identifies one or more approaches for the problem that apply within a specific the problem, only some of which apply the problem that does apply within a solving the problem that do not apply context. within a specific context. specific context. within a specific context. Propose Solutions/Hypotheses Proposes one or more solutions/ hypotheses Proposes one or more solutions/ hypotheses Proposes one solution/ hypothesis that is Proposes a solution/ hypothesis that is that indicates a deep comprehension of the that indicates comprehension of the “off the shelf ” rather than individually difficult to evaluate because it is vague or problem. Solution/ hypotheses are sensitive problem. Solutions/ hypotheses are sensitive designed to address the specific contextual only indirectly addresses the problem to contextual factors as well as all of the to contextual factors as well as the one of factors of the problem. statement. following: ethical, logical, and cultural the following: ethical, logical, or cultural dimensions of the problem. dimensions of the problem. Evaluate Potential Solutions E valuation of solutions is deep and elegant E valuation of solutions is adequate (for E valuation of solutions is brief (for E valuation of solutions is superficial (for (for example, contains thorough and example, contains thorough explanation) example, explanation lacks depth) and example, contains cursory, surface level insightful explanation) and includes, deeply and includes the following: considers history includes the following: considers history of explanation) and includes the following: and thoroughly, all of the following: of problem, reviews logic/ reasoning, problem, reviews logic/ reasoning, examines considers history of problem, reviews considers history of problem, reviews examines feasibility of solution, and weighs feasibility of solution, and weighs impacts logic/ reasoning, examines feasibility of logic/ reasoning, examines feasibility of impacts of solution. of solution. solution, and weighs impacts of solution. solution, and weighs impacts of solution. Implement Solution Implements the solution in a manner that Implements the solution in a manner that Implements the solution in a manner that Implements the solution in a manner that addresses thoroughly and deeply multiple addresses multiple contextual factors of the addresses the problem statement but ignores does not directly address the problem contextual factors of the problem. problem in a surface manner. relevant contextual factors. statement. Evaluate Outcomes Reviews results relative to the problem Reviews results relative to the problem Reviews results in terms of the problem Reviews results superficially in terms of the defined with thorough, specific defined with some consideration of need defined with little, if any, consideration of problem defined with no consideration of considerations of need for further work. for further work. need for further work. need for further work

WRITTEN COMMUNICATION VALUE RUBRIC for more information, please contact [email protected]

Definition Written communication is the development and expression of ideas in writing. Written communication involves learning to work in many genres and styles. It can involve working with many different writing technologies, and mixing texts, data, and images. Written communication abilities develop through iterative experiences across the curriculum.

Evaluators are encouraged to assign a zero to any work sample or collection of work that does not meet benchmark (cell one) level performance.

Capstone Milestones Benchmark 4 3 2 1 Context of and Purpose for Writing Demonstrates a thorough understanding Demonstrates adequate consideration of Demonstrates awareness of context, Demonstrates minimal attention to Includes considerations of audience, of context, audience, and purpose that is context, audience, and purpose and a audience, purpose, and to the assigned context, audience, purpose, and to the purpose, and the circumstances responsive to the assigned task(s) and clear focus on the assigned task(s) (e.g., tasks(s) (e.g., begins to show awareness assigned tasks(s) (e.g., expectation of surrounding the writing task(s). focuses all elements of the work. the task aligns with audience, purpose, of audience's perceptions and instructor or self as audience). and context). assumptions). Content Development Uses appropriate, relevant, and Uses appropriate, relevant, and Uses appropriate and relevant content to Uses appropriate and relevant content to compelling content to illustrate mastery compelling content to explore ideas develop and explore ideas through most develop simple ideas in some parts of the of the subject, conveying the writer's within the context of the discipline and of the work. work. understanding, and shaping the whole shape the whole work. work. Genre and Disciplinary Conventions Demonstrates detailed attention to and Demonstrates consistent use of Follows expectations appropriate to a Attempts to use a consistent system for Formal and informal rules inherent in successful execution of a wide range of important conventions particular to a specific discipline and/or writing task(s) basic organization and presentation. the expectations for writing in particular conventions particular to a specific specific discipline and/or writing task(s), for basic organization, content, and forms and/or academic fields (please see discipline and/or writing task (s) including organization, content, presentation glossary). including organization, content, presentation, and stylistic choices presentation, formatting, and stylistic choices Sources and Evidence Demonstrates skillful use of high- Demonstrates consistent use of credible, Demonstrates an attempt to use credible Demonstrates an attempt to use sources quality, credible, relevant sources to relevant sources to support ideas that are and/or relevant sources to support ideas to support ideas in the writing. develop ideas that are appropriate for the situated within the discipline and genre that are appropriate for the discipline and discipline and genre of the writing of the writing. genre of the writing. Control of Syntax and Mechanics Uses graceful language that skillfully Uses straightforward language that Uses language that generally conveys Uses language that sometimes impedes communicates meaning to readers with generally conveys meaning to readers. meaning to readers with clarity, although meaning because of errors in usage. clarity and fluency, and is virtually error- The language in the portfolio has few writing may include some errors. free. errors.