Idea Transcript
Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 New Course
OR Existing Course
Instructor(s)/Author(s): J. Von Bergen Subject Area/Course No.: MATH-029 Course Name/Title: Accelerated Elementary & Intermediate Algebra Discipline(s): Mathematics
Units: 7.0
Pre-Requisite(s):
One year high school algebra or completion of Math 12 with a grade of "C" or better, or completion of coursework at another college that is comparable to Math 12 with a grade of "C" or better, or demonstration of equivalent prealgebra skills based on our LMC assessment process, or equivalent assessment recommendation from another college. Co-Requisite(s): None Advisories: None Catalog Description: Math 29 is an accelerated Elementary and Intermediate Algebra equivalent to both Math 25
and Math 30. This course focuses on proportional reasoning and linear, quadratic, exponential, and logarithmic functions. Students will investigate algebra concepts from multiple perspectives including tables, graphs, symbolic forms with variables, and written descriptions. Students will develop proficient skills in communication of mathematics, problem-solving, use of multiple representations, effective learning skills and learning to apply Algebra to analyze and solve real-life problems takes time and effort. A graphing calculator is required. Schedule Description: Want to complete the same content as Math 25 & 30 in one semester? Math 29 is an accelerated Elementary and Intermediate Algebra equivalent to taking both Math 25 and Math 30. In this course you will study proportional reasoning and linear, quadratic, exponential, and logarithmic functions. You will investigate algebra concepts from multiple perspectives including tables, graphs, symbolic forms with variables, and written descriptions. A graphing calculator is required. This course is recommended for students who are motivated to learn at an accelerated pace and willing to spend a minimum of 14 study hours outside of class each week. Hrs/Mode of Instruction: Lecture: _126 Scheduled Lab: ____ HBA Lab: _36_ Composition: ____ Activity: ____ Credit
Credit Degree Applicable (DA) Credit Non-Degree (NDA) (If Non-Credit desired, contact Dean.)
Grading
Pass/No Pass (P/NP) Letter (LR) Student Choice (SC)
Total Hours (Total for course)
Repeatability
Last date of Assessment: ______2012-2013_________ Cohort #: ___1__
0 1 2 3
Please apply for: LMC General Education Requirement(s): Mathematics (Please list the proposed area(s) this course meets, or indicate “none”)
Transfer to:
CSU
UC
Course is Baccalaureate Level:
Form Revised 082013
IGETC Area ____ Yes
CSU GE Area____
C-ID Number ______
No
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029
Signatures:
Department Chair
Date
Librarian
Date
Dean/Sr. Dean
Date
Curriculum Committee Chair
Date
President/Designee
Date
CCCCD Approval Date (Board or Chancellor's Office)
Date
For Curriculum Committee Use only: STAND ALONE COURSE:
YES
NO
FOR OFFICE OF INSTRUCTION ONLY. DO NOT WRITE IN THE SECTION BELOW. Begin in Semester ______________ Dept. Code/Name:_______________ ESL Class: ____Yes / No___________ Class Code A Liberal Arts & Sciences B Developmental Preparatory C Adult/Secondary Basic Education D Personal Development/Survival E For Substantially Handicapped F Parenting/Family Support G Community/Civic Development H General and Cultural I Career/Technical Education J Workforce Preparation Enhanced K Other non-credit enhanced Not eligible for enhanced
Catalog year 20____/20_____ T.O.P.s Code: _____________ DSPS Class: ____Yes / No_____ SAM Code A Apprenticeship B Advanced Occupational C Clearly Occupational D Possibly Occupational E* Non-Occupational F Transfer, Non-Occupational *Additional criteria needed 1 One level below transfer 2 Two levels below transfer 3 Three levels below transfer
Class Max: ________________ Crossover course 1/ 2: _____________ Coop Work Exp: ___Yes / No_____ Remediation Level B Basic Skills NBS Not Basic Skills
Course approved by Curriculum Committee as Baccalaureate Level: _Yes / No_ LMC GE or Competency Requirement Approved by the Curriculum Committee:
_________________
Distribution: Original: Office of Instruction Copies: Admissions Office, Department Chairperson Rev 09-17-2008 Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 Institutional Student Learning Outcomes Check the institutional student learning outcomes (or category of outcomes) below that are reflected in your course: General Education SLOs (Recommended by GE Committee) At the completion of the LMC general education program, a student will: 1. read critically and communicate effectively as a writer and speaker. 2. understand connections among disciplines and apply interdisciplinary approaches to problem solving. 3. think critically and creatively 4. consider the ethical implications inherent in knowledge, decision-making and action. 5. possess a worldview informed by diverse social, multicultural and global perspectives. (Each of the above student learning outcomes for the general education program has a written explanation with illustrations and examples of its application within courses, as well as specific assessment criteria. Consult the GE program information pages.)
Program-Level Student Learning Outcomes (PSLOs) Developmental Math 1. Problem-solving abilities: Students will use mathematical reasoning to solve problems and a generalized problem solving process to work word problems. a. The student can apply standard problem-solving methods and use relevant concepts to solve problems. b. The student uses a generalized problem-solving rubric if such a rubric is used in the class. c. The student’s written work demonstrates a conceptual understanding of course concepts. d. The student’s written work supports his/her solution. e. The student evaluates the reasonableness of his/her answer. 2. Mathematical versatility: Students will use verbal, graphical, numerical, and symbolic representations of mathematical ideas to solve problems. a. Students will use a variety of representations to demonstrate their understanding of mathematical concepts. b. Students will use a multi-prong approach to problem solving. c. Students will use appropriate technology to solve mathematical problems and judge the reasonableness of their results. 3. Communication skills: Students will read, write, listen to, and speak mathematics with understanding. a. Students will read and listen to mathematical presentations and arguments with understanding. b. Students will communicate both in speaking and in writing their understanding of mathematical ideas and procedures using appropriate mathematical vocabulary and notation. c. Students will coherently communicate their own mathematical thinking to others. 4. Preparation: Students will recognize and apply math concepts in a variety of relevant settings and demonstrate the math skills and knowledge necessary to succeed in subsequent courses. 5. Effective Learning Attributes: Students will demonstrate the characteristics of an effective learner. a. Student has the will to succeed and demonstrates the characteristics of a successful student: motivation, responsibility, focus, perseverance, the ability to cope with anxiety, a good attitude toward learning, and time management skills. b. Student has the skills to succeed. (S)he uses appropriate resources to improve learning and reach goals. c. Student self-monitors and self-regulates. (S)he assesses personal strengths and weaknesses in his/her learning process and then seeks and implements a strategy for improving learning.
Course-Level Student Learning Outcomes (CSLOs): Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 Students will be able to: CSLO1: Use mathematical reasoning and a generalized problem solving process (e.g., Polya’s problem solving process) to solve Elementary and Intermediate Algebra problems, including the explicit identification of extraneous information and necessary assumptions, as well as the interpretation of solutions within context. CSLO 2: Create and use tables, graphs, and equations to solve problems involving proportional reasoning, linear functions, linear systems, exponential, logarithmic and quadratic functions, using technology to evaluate expressions, create tables, graphs, and equations, model relationships, and verify solutions. CSLO 3: Synthesize critical information from a variety of sources, and communicate in writing problem solving processes, knowledge of the Elementary and Intermediate Algebra concepts underlying these processes, examples that illustrate concepts, and interpret concepts in context. CSLO 4: Recognize and apply Elementary and Intermediate Algebra concepts in a variety of relevant settings and demonstrate the skills and knowledge necessary to succeed in transfer math courses; students will demonstrate mastery of procedural skills without the use of calculators, and demonstrate proficiency of other skills in the context of problem solving. CSLO 5: Demonstrate characteristics of responsible students, use resources that support their learning and performance, assess their own learning process and performance, and articulate their educational goals.
CSLO Assessment Criteria: CSLO 1 (Problem Solving) The successful Math 029 student will: a. apply the steps in a general problem-solving process (e.g. Polya’s problem solving process). This process will include: (1) communicating an understanding of the problem; (2) identifying extraneous information and necessary assumptions; (3) making reasonable estimates when prompted; (4) choosing one or more appropriate representations; (5) applying standard problem-solving methods; (6) checking his/her answer; (7) interpreting answers in the context of the problem. b. apply standard algebra problem solving methods to solve problems that differ in context from those discussed in class and demonstrated in the text, including situations with extraneous information. These standard methods include: (1) solving linear equations and systems of linear equations by symbolic, graphical, and tabular means; (2) solving (2x2) linear systems by substitution, elimination, and graphs; (3) using proportional reasoning in contexts of linear applications; (4) solving quadratic equations using (a=1), using the quadratic formula, and by graphical means (5) solving exponential equations using logarithms and by graphical means; (6) solving logarithmic equations using equivalent exponential forms and by graphical means; (7) unit analysis; c. demonstrate problem-solving strategies in a clear, organized, and logical manner Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 d. explain the reasonableness of her/his answer by using relevant previous knowledge and check answers using standard methods (e.g. use of technology, use of inverse operations, substituting answers back into equations). CSLO 2 (Multiple Representations) The successful Math 029 student will: 2) 2.a.) produce and use different representations to explain course concepts (e.g. use tables, graphs, equations, and verbal descriptions to explain the difference between exponential and linear growth); 2.b.) use information that is given in a tabular, graphical, symbolic and verbal form to solve problems involving linear, quadratic, exponential, and logarithmic functions; 2.c.)without prompts, create and use appropriate models (tables, graphs, and symbolic representations) to solve problems involving linear, quadratic, exponential, and logarithmic functions; 2.d.) use technology to make estimates, solve problems, and check answers derived by symbolic means. 2.e.) demonstrate effective use of technology by generating tables with increments appropriate to a given problem setting and generating graphs with windows appropriate to a given problem setting. 2.f.) use technology to model data using linear and non-linear regression, to find intersection points for two equations, to solve non-linear equations, and to solve problems involving scientific notation. 2.g.) use technology to evaluate numeric expressions involving rational exponents, roots, fractions, decimals, and logarithms. CSLO 3 (Communication) The successful Math 029 student will: a. identify, extract, and meaningfully organize critical information from a variety of sources, such as the lecture, the text, or computer tutorials; b. accurately paraphrase and give relevant examples to illustrate mathematical concepts; c. correctly use common mathematical terminology and notation; d. write solutions that are clear, organized, and logical with correct use of mathematical notation; e. clearly label graphs, tables, and diagrams and accurately define variables used in applications; f. interpret the meaning of intercepts, slopes, and solutions in a context CSLO 4 (Skills and Applications) Part I: Mastery: The mastery-based skills are not required to be in the context of application problems. The successful Math 029 student will demonstrate mastery in the following procedural skills without the use of technology or other resources: a) Evaluate expressions that contain square roots, absolute values, and/or integer exponents; b) Symbolically solve linear equations in one variable, including equations with parenthesis and x on both sides; c) Solve linear 22 systems using algebra and graphs; d) Solve proportions. e) Find the equation of a line given two points; f) Symbolically solve quadratic equations using factoring (a=1) or the quadratic formula, including complex solutions; g) Symbolically solve exponential equations using logarithms; h) Symbolically solve logarithmic equations of the form logb f (x) n by changing to an equivalent exponential form Simplify algebraic expressions and polynomials using properties of exponents, arithmetic operations, and the distributive law. Part II: Proficiency The successful Math 029 student will be able to demonstrate a proficient ability in the following skills. Opportunities will be provided for the student to meet the previously described objectives
i)
Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 in communication, problem-solving, and use of a multi-pronged approach in the context of applying the following math skills. (Calculators or other technology allowed; note that use of technology is a course objective under Outcome 3.) j) Use unit analysis in unit conversions; k) Solve real-life problems involving perimeter, area, and volume l) Solve literal equations for a specified variable, as part of solving problems that involve real formulas, such as perimeter and area. m) Use scientific notation to represent and compare numbers n) Construct linear equations from tables and solve linear equations using tables. o) Construct linear equations from graphs and solve linear equations using graphs. p) Set up and solve one variable linear inequalities in applications; q) Set up and solve linear systems of equations in applications. r) Use the Pythagorean theorem to find lengths or distances; s) Solve quadratic equations (with lead coefficient 1) using tables, graphs, factoring, and the quadratic formula; t) Apply proportional reasoning to problems in a real-life context u) Modeling: Construct linear and exponential functions from tables, graphs and verbal descriptions; v) Using models: use linear, quadratic, exponential, and logarithmic functions in an applied context to make predictions or decisions; w) Use, evaluate, and interpret function notation; identify functions in tables, graphs, and symbolic form; x) In the context of real-life applications: • solve non-linear literal equations for a specified variable; • solve rational equations; • apply proportional reasoning to linear modeling problems and to the estimation component of a general problem solving process. CSLO 5: Effective Learning The successful Math 029 student will: a) have a clear educational goal and articulate how math is connected to personal and academic goals; b) follow instructions, complete required tasks, attend class regularly and complete assignments in a timely manner; c) identify and utilize support services as needed (e.g. Math Lab, instructor’s office hours, counseling services, and tutoring services) d) effectively utilize the textbook or computer as a resource; e) devise and implement appropriate strategies for improving her/his performance (e.g. study strategies and test-preparation strategies that fit her/his learning style); f) articulate knowledge of her/his own learning process and factors that help her/him learn; g) monitor her/his thinking, self-correct, and learn from errors; h) use specific public criteria from a rubric or other criteria-based list to assess her/his own performance.
Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 Assessments: The table below shows the types of assignments that will be used to evaluate student achievement of the five course student learning outcomes. Instructors may use these types of assessments in additional ways (e.g., using writing to assess CSLO3), or may use other assessment tools in addition to those outlined in the table, such as projects, presentations, or verbal communication during class activities.
CSLO 1 Communication 2 Problem Solving 3 Multiple Representations 4 Skills and Application 5 Effective Learning
A. Homework x x x
Assessment Instruments B. Lab C. Journals/ Assignments Writing x x x x x
x
x
x
x
D. Quizzes, tests, exams x x x x
x
A. Homework: On a regular basis throughout the semester, homework assignments should provide students with opportunities to demonstrate their abilities to use mathematical terminology, write solutions that are clear, organized and reflect the use of a general problem solving process, and create and use tables, graphs and equations to solve problems involving linear, quadratic, exponential and logarithmic relationships and systems of linear equations. Students will demonstrate developing skills as effective learners by completing homework assignments in a thorough and timely fashion, and by seeking assistance when needed. Students should have frequent opportunities to develop procedural skills through homework assignments, such as computer-based learning or skills-oriented exercises. Mastery-oriented assignments should be given in addition to, and not in place of assignments that help students develop skills in problem solving, communication, and multiple representations. B. Lab assignments: Lab assignments are meant to be more in-depth than homework and require students to collaborate with classmates and seek support in the Math Lab. Students will appropriately utilize the tutoring services in the Math Lab. Throughout the semester, these assignments should provide students with opportunities to demonstrate their abilities to use mathematical terminology, write solutions that are clear, organized and reflect the use of a general problem solving process, and create and use tables, graphs, and algebra concepts to solve problems. Students will demonstrate developing skills as effective learners by completing lab assignments in a thorough and timely fashion, and by seeking assistance when needed. C. Journals and writing assignments Journals and writing provide students opportunities to communicate understanding of mathematical concepts and problem solutions in an open-ended format. Writing assignments will also allow students to reflect on and assess their skills as effective learners. Students will reflect on implementation of appropriate study and test-preparation strategies, use of support services including the Math Lab, improvement of performance, learning from errors and self-correction. Students will articulate knowledge of the mathematical learning process.
Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 D. Mastery quizzes Mastery quizzes provide students opportunities to demonstrate mastery of procedural skills. Mastery is defined as at least 85% of a skill-based quiz or test taken without the use of calculator, notes or other resources. Students will be given multiple testing opportunities to achieve mastery. The design and weight of mastery-based assignments is the prerogative of the individual instructor (i.e. while the student must achieve mastery level of at least 85% at least once, the mean grade of the student may be above or below 85%). E. Exams Exams will be used to assess student development on CSLOs 1, 2, 3, and 4. Exams will cover all four of these SLOs and each exam should give equal attention to each SLO. A comprehensive final exam that counts as at least 20% of the course grade is required. Sample exercise: According to the Real Estate Report Web site, the average price for single-family, re-sale homes jumped 11.5% from July’s average value of $654,793. a. Write the function. b. Determine when the average home value in CC County would reach $1 million.
Method of Evaluation/Grading: Instructors will assign homework, lab work, writing assignments, or computer work on a regular basis, give at least two exams in addition to a final, and have students complete mastery quizzes. Instructors have the option to give quizzes and/ or short homework based quizzes. Students should receive regular feedback on their progress toward course SLOs prior to quizzes or exams. Feedback may include instructor’s written feedback, self- or peer-assessment, or computer-aided assessment. Mastery is defined as at least 85% of a skill-based quiz or test taken without the use of calculator, notes or other resources. Students will be given frequent homework practice and multiple testing opportunities to achieve mastery. The design and weight of mastery-based assignments is the prerogative of the individual instructor (i.e. while the student must achieve mastery level of at least 85% at least once, the mean grade of the student may be above or below 85%). Department policy requires that a final exam be weighted at least 20% of the course grade. Here are suggested guidelines for weighting the other assessments: Homework, Lab and Writing Assignments Mastery and other quizzes Exams Final Exam
30-50% 10-30% 20-40% at least 20%
A-level student work shows use of a general problem solving method, including efficient problem solving, clear communication of problem solutions, estimation and relevant assumptions; accurately creates, models with and interprets graphs and tables, and uses tables, graphs, or equations to solve problems; checks work for accuracy and reasonableness; shows mastery of procedural intermediate algebra skills; uses procedural skills in service of solving problems; shows strong effective learning skills, including following directions, meeting deadlines, completing assignments, and using resources as necessary. C-level student work shows consistent use of a general problem solving methods, but makes minor mistakes, is inefficient in solving the problem, communicates but not clearly problem solutions, estimates Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 and assumptions; can use tables and graphs to solve problems 70% of the time, but with some mistakes in creating and interpreting graphs and tables; shows mastery of procedural intermediate algebra skills; uses procedural skills in servicing of solving problems with minor errors; shows a moderate level of effective learning skills, including following directions, meeting deadlines and completing assignments.
Course Content: Evaluating and simplifying algebraic expressions Solving linear equations (and inequalities) Solving linear systems (2x2 systems) Solving proportions Unit conversions and proportions: applications Perimeter, area, and volume: applications Linear systems and Pythagorean Theorem: applications Linear, quadratic, exponential, and logarithmic equations: tables, graphs, verbal descriptions, applications Algebraic expressions and polynomials: simplifying and evaluating Constructing mathematical models: linear and exponential functions (tables, graphs, verbal descriptions, applications) Using mathematical models: linear, quadratic, exponential, logarithmic Working with the concept of a function: identification, interpretation, evaluation and use Solving non-linear equations and using unit analysis in applications: non-linear literal equations, rational equations, proportions, unit analysis Study skills: for example, reading and note-taking techniques, organization and time management, test preparation and test-taking skills Self-assessment: for example, using performance criteria to judge and improve one’s own work, analyzing and correcting errors on one’s test Use of resources: for example, strategies for identifying, utilizing, and evaluating the effectiveness of resources in improving one’s own learning, e.g. computer resources, lab services
LAB BY ARRANGEMENT ACTIVITY: Lecture hours will consist of the introduction of new concepts by the instructor, practice in group work of new concepts and reinforcement of existing material, student presentation of selected questions to show mastery, and (optional) discussion of in-class activities from the LMC curriculum module. During lecture, the instructor’s role is to communicate the new topics through lecture, interaction with groups, and class discussion in a manner that reinforces and supports students’ existing knowledge of algebra concepts. Additionally, the instructor’s role is to support and encourage students in developing independent problem solving and critical thinking skills, and drawing appropriate conclusions regarding creation, use, and interpretation of tables, equations, and graphs. Form Revised 082013
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Course Outline of Record Los Medanos College
2700 East Leland Road
Pittsburg CA 94565
(925) 439-2181
Course Title: Accelerated Elementary & Intermediate Algebra Subject Area/Course Number: MATH-029 Lab hours by arrangement will consist of lab assignments more in-depth and conceptual than homework assignments, completion of which requires instruction in the Math Lab. Lab assignments typically include continued topics from those discussed in class, and often involve realistic applicable scenarios. During lab hours by arrangement, the instructor’s role is to use the Socratic method to question students to stimulate mathematical thinking and support students in drawing the correct conclusions. When needed, the instructor should provide one to one instruction in conceptual areas the student is misunderstanding. By the end of the semester, the student should have an increased independence in problem solving and improved mathematical communication skills.
Instructional Methods: Lecture Lab Activity Problem-based Learning/Case Studies Collaborative Learning/Peer Review Demonstration/Modeling Role-Playing Discussion Computer Assisted Instruction Other (explain) ________________________________________
Suggested Textbooks: Los Medanos College Math 25 & Math 30 modules, published 2015 and additional Algebra Skills support module or online text skills support (e.g. Carnegie Learning software)
George Woodbury, Elementary and Intermediate Algebra, 978‐321‐08778‐5 by Pearson, published 2015
Form Revised 082013
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