Rhode Island College General Education Distribution Course Request

Use this form for any distribution course that is to be included in the General Education Program. If the course is new or revised, attach the appropriate Undergraduate Curriculum Committee forms. (Revised December 5, 2012) (Available at http://www.ric.edu/curriculum_committee/materials.php)

Date of Submission: April 26, 2013

Proposing Department or Program: Mathematics and Computer Science

Chair/contact: Raimundo Kovac

Department/Program Code (e.g., ENGL, PHYS, AFRI): MATH Course number: 324

Catalog title: (Remember the UCC 6-word limit.) College

Prerequisites: MATH 212 or 247 (as stated in the current catalog)

Credits: (General Education courses are four credits) 4 Learning Outcomes http://www.ric.edu/generaleducation/outcomes.php Category in General Education: Distribution Written Communication (WC) Critical and Creative Thinking (CCT) General Education outcomes that must be formally addressed and Research Fluency (RF) assessed are noted for each category. Oral Communication (OC)

Collaborative Work (CW) Mathematics (CCT, QL) Arts (A) Natural Science (lab required) (CCT, ER, QL, SL) Civic Knowledge (CK) X Advanced Quantitative/Scientific Reasoning (CCT, QL, SL) Ethical Reasoning (ER) History (CCT, RF, CK, ER, GU) Global Understanding (GU) Literature (CCT, WC) Quantitative Literacy (QL) Social and Behavioral Sciences (CCT, CK, ER, SL) Scientific Literacy (SL) Arts – Visual and Performing (CCT, A)

Courses in the distribution are content-based and students are expected to learn the material and demonstrate compe- tence in a manner appropriate to the discipline.

Append a syllabus or two-level topical outline. We are interested in the content and pedagogy of the course. Include the description, requirements, schedule, and topics but omit details on attendance policy, academic integrity, disabilities, etc. If UCC action is required, include the syllabus with the UCC form; an additional copy is not needed.

How often will this course be offered? Fall and Spring.

Number and frequency of sections to be offered (students/semester or /year)? Two sections per year (one Fall, one Spring), with 30 students per section.

In the table on the next page, explain briefly how this course will meet the General Education Outcomes for its category as indicated above. Describe the kinds of assignments in which the assigned outcomes will be assessed. The form on the next page is a Word table. The boxes will expand to include whatever text is needed. Rows that do not apply to the course being proposed may be deleted.

General Education Outcome: Assignments or Activities:

Quantitative Literacy Geometry and its applications are an integral part of understanding the relationships between mathematical proof, applications, and science. In this course students learn the development of classical , including lines, angles, triangles, polygons, and . Applications include finding areas of geometric figures using traditional formulas developed in class, or with alternative methods such as Pick’s Theorem. Traditional formulas for volume of 3-dimensional solids are also studied, and extended by using Cavalieri’s principle. Right-angle trigonometry is used to an- swer questions such as: How tall is that structure? or How wide is that lake? without a direct measurement, or, At what angle does your camera need to be at to photo- graph a hot air balloon? One of the topics studied in non-Euclidean geometry is Taxicab geometry. This ge- ometry uses a based on horizontal and vertical only, as a taxi would travel when traversing city blocks. Applications include minimizing distances, con- structing boundary lines for schools or voting districts, and finding optimal locations for regional service centers such as bus stops and fire stations.

These outcomes are assessed through homework assignments and in-class quizzes and exams, and also through the use of technology: students use the TI-nspire calcu- lator throughout the course, and several assignments that require the use of The Ge- ometer SketchPad.

Critical and Creative Thinking Critical and creative thinking is essential in geometry. Students need to prove theo- rems throughout the course, many of which can be done in more than one way. Stu- dents have to creatively use their mathematics knowledge in order to write logically accurate arguments. In transformational geometry, for example, students must determine how one figure can be transformed into another. The solution will involve a combination of transla- tions, rotations, and reflections. In Taxicab and Spherical geometry, students will identify precisely which well- known properties from Euclidean geometry no longer hold, such as the SSS congru- ence property and the parallel postulate.

These outcomes are assessed through homework assignments and in-class quizzes and exams, and also through the use of technology: students use the TI-nspire calcu- lator throughout the course, and several assignments that require the use of The Ge- ometer SketchPad.

Scientific Literacy When formulating theorems, students are required to investigate each hypothesis separately, so that the least number of assumptions is used to prove the desired re- sult. This is quintessential to scientific thinking, and is done repeatedly throughout the course. Students will understand how spherical geometry is used in air travel, where the shorter between two points is not intuitive. The same applies to Taxicab geometry, where distances are measured in yet another way.

These outcomes are assessed through homework assignments and in-class quizzes, and exams, and also through the use of technology: students use the TI-nspire calcu- lator throughout the course, and several assignments that require the use of The Ge- ometer SketchPad.

Course Outline Math 324 – College Geometry

TEXT(s) : Schaum’s Outline: Geometry, 4th edition, McGraw Hill Publishers Taxicab Geometry, Dover Publishers College Geometry using the Geometer’s Sketchpad, Key Curriculum Press Publishers

Optional Resources: Transformational Geometry, An Introduction to Symmetry by George E. Martin Springer, ISBN: 9780387906362. Geometry and Its Applications. Walter Meyer. (Use this text for transformational geometry, spherical and hyperbolic ge- ometries.)

Required Software TI-nspire and Geometer’s SketchPad

CHAPTER 2.& 14. Methods of Proof & Improvement of Reasoning This entire chapter is very important, but do not get bogged down in it; this is material which should be at least somewhat familiar to the students.

Introductory activities using geometry software package TI-nspire.

3. Congruent Triangles Develop both two-column and paragraph proof. Technology 4. Parallel Lines, Distances, and Angle Sum Using technology to develop inductive reasoning

5. Parallelograms, Trapezoids, Medians, and midpoints Relating the various quadrilaterals via paperfolding

6. Circles Do inscribed quadrilaterals Indirect proof

7. Similarity

9. Areas

10. Regular Polygons and the

12. Analytic Geometry Include proofs of parallel, perpendicular, , etc.

Advanced Euclidean Geometry Do the following proofs: o Ceva’s Theorem o Ptolemy’s Theorem o Menelaus’ Theorem o Stewart’s Theorem o Proofs of Pythagorean Theorem and its Converse o Brahmagupta’s and Heron’s Formulas o Golden Rectangle and Golden Triangle

Transformational Geometry Tessellations & technology

Non- Euclidean Geometry Model 1: Taxicab Geometry Use snap feature of GSP to make constructions

Chapter 17, Solid Geometry

Spherical Geometry: non-Euclidean Model 2 Hands-on activities and using technology Hyperbolic Geometry: non-Euclidean Model 3

Projects & Presentations Fractals, etc.