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Department of Mathematical Sciences August 15, 2006 1/20 Math 1319 “Mathematics in the Modern World”

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Department of Mathematical Sciences August 15, 2006 2/20 Agenda –8:30-9:40 Introduction (Helmut) –9:40-10:00 Break –10:00-11:00 Pedagogy, Assignments (Art) –11:00-12:00 Lesson Study (Tuesday and Art) –12:00-13:00 Lunch –13:00-14:00? Syllabus Preparation

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Department of Mathematical Sciences August 15, 2006 3/20 Roundrobin: Introducing Ourselves…

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Department of Mathematical Sciences August 15, 2006 4/20 Core Curriculum –Introduced by the State of Texas in the early 90s. –Idea: Every student at every institution of higher education takes about 40-45 hours of general liberal arts courses during the first two years of college. –Idea: Courses transfer easily from one institution to the next.

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Department of Mathematical Sciences August 15, 2006 5/20 Core Curriculum at UTEP – 42 hours –English and Communications (9) –Mathematics (3) –Natural Sciences (6) –Visual and Performing Arts (3) –Humanities (3) –US History (6) –Political Science (6) –Social and Behavioral Sciences (3) –UNIV 1301 “Seminar in Critical Inquiry” (3)

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Department of Mathematical Sciences August 15, 2006 6/20 Core Curriculum in Mathematics Three hours = one course Originally two options: –Math 1320 “Math for Social Sciences” –Math 1508 “Pre-Calculus” (or higher) Problem: All non-science and non-engineering students are “stuck” in a Business Math course. Note: UTEP does not have a “College Algebra” course.

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Department of Mathematical Sciences August 15, 2006 7/20 The State also prescribed “Exemplary Objectives” for the Core Mathematics Course: 1.To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations. 2.To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically. 3.To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.

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Department of Mathematical Sciences August 15, 2006 8/20 Objectives (cont’d): 4.To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results. 5.To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them. 6.To recognize the limitations of mathematical and statistical models. 7.To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

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Department of Mathematical Sciences August 15, 2006 9/20 About three years ago the department started to think about (re)creating a “terminal” mathematics course for – liberal arts majors, –and elementary education majors.

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Department of Mathematical Sciences August 15, 2006 10/20 Two competing(?) philosophies for such a math course: –Critical Thinking –Quantitative Literacy

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Department of Mathematical Sciences August 15, 2006 11/20 The Department opted for the Critical Thinking approach…

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Department of Mathematical Sciences August 15, 2006 12/20 Course Description: Math 1319 - Mathematics in the Modern World An introduction to some of the great ideas of mathematics, including current applications of logic, algebra, geometry, statistics, and other topics. Intended for students whose majors do not require MATH 2301, MATH 1508 or MATH 1411. Prerequisite: An adequate score on a placement examination or MATH 0311.

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Department of Mathematical Sciences August 15, 2006 13/20 Five Main Objectives: –“Great Ideas” as an overarching theme –Logic –Algebra –Geometry –Statistics

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Department of Mathematical Sciences August 15, 2006 14/20 1.To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations. 2.To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically. 3.To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments. 4.To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results. 5.To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them. 6.To recognize the limitations of mathematical and statistical models. 7.To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines. State Objectives again…

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Department of Mathematical Sciences August 15, 2006 15/20 Courses offered in Fall 2006: 8 sections of Math 1319 (about 250 students) 19 sections of Math 1320 (about 900 students) 17 sections of Math 1508 (about 750 students)

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Department of Mathematical Sciences August 15, 2006 16/20 Students in Math 1319: College of Liberal Arts: –All majors except for Psychology and Social Work College of Education: –All majors except for 4-8 Math and Math/Science specialists

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Department of Mathematical Sciences August 15, 2006 17/20 Students in Math 1319: Preparation –Students have at least the skills taught in a “Beginning Algebra” course. –A substantial portion of the students has taken “Intermediate Algebra”.

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Department of Mathematical Sciences August 15, 2006 18/20 The textbook:

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Department of Mathematical Sciences August 15, 2006 19/20 The authors: –Edward Burger, Williams College –Michael Starbird, University of Texas at Austin

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Department of Mathematical Sciences August 15, 2006 20/20 Guiding questions for discussion: Do you believe… –… that every college student needs to know how to solve a quadratic equation? –… that the life of every student can be touched in a single math class? –… that learning mathematics improves the ability to think effectively? – … all students in such a course can/should gain a deep appreciation of the Cantor diagonalization procedure? What should students gain from taking Math 1319?

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