CRN 12700

• Time and Place. TR 13:30-14:50 in LART 206

• Instructor. Helmut Knaust, Bell Hall 219, hknaust@utep.edu, 747-7002

• Office Hours. M 17:30-18:20, R 11:00-12:00, or by appointment.

• 
  Textbook. Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto, and Dick Stanley. Mathematics for High School Teachers- An Advanced Perspective. Prentice Hall. Amazon sells the paperback edition for $59.40 (8/23/10). The textbook is required at all class meetings, and the parts covered in class are intended to be read in full.

• Course Requirements.
  • Quizzes (15%): I will give regular, but unannounced quizzes. Quiz problems will be identical to prior homework assignments. Your worst two quizzes will be dropped.
  • Exams (25%): You will have two in-class exams on the following days: Thursday, October 7 and Tuesday, November 23.
  • Class Presentations (25%): Small groups of students will design and conduct all classroom activities for part of one class session and will be responsible for the content covered in those sessions. Each group will also create homework assignments.
    • The groups will meet with me two weeks before their presentation for a ``trial run so that I will know that you are prepared. This is not optional. If you do not meet with me, you will lose half of your possible points.
  • Final Project (25%): There are mathematics problems that require more attention than just one day. Some of these problems are found at the end of the chapters in the textbook. Small student groups will complete one of these problems and present the results in class and in a written report at the end of the semester.
  • Class Participation (10%): Mathematics is not a spectator sport. During class I expect you to participate. This is an active class where students often present solutions to their peers. The participation grade will be based both on the quality and frequency of your contributions.

• Grades. Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.

• UTEP Qualifying Exam for Teacher Certification. All students must have taken the UTEP Qualifying Exam for certification as a secondary Mathematics teacher at least once by the end of the semester. Failure to do so will result in a temporary grade of "I" until you have taken the exam. In this case you must take the exam within one year after the end of class; otherwise the grade will irrevocably change to a grade of "F".

• Make-up Exams. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date. There will be no make-up quizzes.

• Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

• Attendance. You are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with five or more absences (excused or unexcused) will be dropped from the course with a grade of "F".

• Drop Policy. The class schedule lists Friday, October 29, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F". Beginning with the fall 2007 semester, all freshmen enrolled for the first time at any Texas public college or university will be limited to six course withdrawals (drops) during their academic career. Drops include those initiated by students or faculty and withdrawals from courses at other institutions! This policy does not apply to courses dropped prior to census day or to complete withdrawals from the university.

• Students with Disabilities. If you have a disability and need special accommodation, please contact the Disabled Student Services Office (DSSO) in Union East 106, 747-5148, dss@utep.edu.

• Academic Integrity. All students must abide by UTEP's academic integrity policies, see http://studentaffairs.utep.edu/Default.aspx?tabid=4386 for details.

Homework

Open Problems: 3.1.1: 6

• 11/16: Read 4.3.1-4.3.2. Prepare: 4.3.1: 2bc,3,5,6a. 4.3.2: 1acd,2,3
• 11/2: Read 4.2.2. Prepare: 4.2.2: 1ab,5e,7
• 10/28: Read 4.1.2-4.2.1. Prepare: 4.1.2: 1,2,3,9,11,16. 4.2.1: 3a-d,4abce
• 10/26: Read 4.1.1-4.1.2. Prepare: 4.1.1: 3, 5, and: "Are the following sets equal? \(A=\{x\in\mathbb{Z} \ |\ x^2<2\}\) and \(B=\{-1,0,1\}\)."
• 10/19: Read 3.1.1-3.1.2. Prepare: 3.1.1: 2ab,5a,6,7,8
• 10/5: Read 2.2.2, 3.1.1. Prepare: 2.2.2: 3,4,6,12,13,15
• 9/23: Read 2.2.1-2.2.2. Problems 2.2.1: #1bdef,2b,4,6d
• 9/16: Read 2.2.1-2.2.2.
• 9/14: Read 2.1.4, 2.2.1. Problems: 2.1.4: #1ac,5c,11
• 9/9: Read 2.1.4.
• 9/7: Read 2.1.3-2.1.4. Problems: 2.1.3 #1,4,6,8
• 9/2: Read 2.1.3-2.1.4. Problems: 2.1.2 #1,5a,6. 2.1.3 #1,4,6,8
• 8/31: Read 2.1.1-2.1.3. Problems: 2.1.1: 3,8,9b,12

Materials

• Final Projects: Assignments
• Student Presentations: Assignments | Grading Rubric | Random Choice
• Complex.nb | Roots.nb | Riemann.nb | FactoringIntegers.nb | DecimalRepresentation.nb | Remote access to Mathematica
• Worksheet 3 | Worksheet 2 | Worksheet 1
• TExES Content Review | Greater El Paso Council of Teachers of Mathematics
• ACT and College Readiness in Math | 55% by 2025 | Mathematical Practices
• Common Core State Standards for Mathematics, Common Core State Standards Initiative, 2010.
• Curriculum Frameworks developed by the El Paso Collaborative for Academic Excellence: Algebra I | Geometry | Algebra II | Precalculus
• Advanced Mathematics for Secondary Teachers: Course Portfolio by Curtis Bennett (Michigan State University)

References

• Amir D. Aczel, The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind". Basic Books, 2000.

"Aczel's compact and fascinating work of mathematical popularization uses the life and work of the German mathematician Georg Cantor (1845-1918) to describe the history of infinity of human thought about boundlessly large numbers, sequences and sets."

• Jo Boaler, Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and Their Impact on Student Learning. Routledge 2002.

"Through her comprehensive, penetrating study of the mathematics departments in two English schools, Jo Boaler shows how mathematics teaching and learning are shaped by teachers and by the settings in which they work." (Jeremy Kilpatrick)

• Edward B. Burger & Robert Tubbs, Making Transcendence Transparent: An intuitive approach to classical transcendental number theory. Springer-Verlag, 2004.

An introduction to transcendental number theory, at the advanced undergraduate/beginning graduate level.

Edward Burger Wins Cherry Award for Great Teaching

• Heinz-Dieter Ebbinghaus et al., Numbers. Springer-Verlag, 1996.

Real numbers, complex numbers, quaternions - what's next? The first part of the book is quite accessible, but the going gets tougher in the later chapters.

• Liang-shin Hahn, Complex Numbers and Geometry. Mathematical Association of America, 1994.

"Provides a self-contained introduction to complex numbers and college geometry written in an informal style with an emphasis on the motivation behind the ideas ... The author engages the reader with a casual style, motivational questions, interesting problems and historical notes." (Mathematical Reviews)

• David W. Johnson, Roger T. Johnson, Karl A. Smith, Active Learning: Cooperation in the College Classroom. Interaction Book Co., 1991.
• Edmund Landau, Grundlagen der Analysis. (Also available in English as Foundations of Analysis.) AMS Chelsea Publishing.

A classic written in the 1920s. An axiomatic construction of numbers and concise derivation of their fundamental properties, from the natural numbers to the complex numbers.

• Liping Ma, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Lawrence Erlbaum Associates, 1999.

...Ma has done a masterful job of showing how the conceptual approach of Chinese elementary school teachers succeeds where the procedural approach of their American counterparts flounders....I highly recommend this brief volume to elementary school teachers who wish to improve their teaching of mathematics... (Mathematics Teaching in the Middle Schools)

• Gary Martin, Focus in High School Mathematics: Reasoning and Sense Making. National Council of Teachers of Mathematics, 2009.

Executive summary.

• Tristan Needham, Visual Complex Analysis. Oxford University Press, 1999.

A unique book developing complex analysis from a geometric angle.

• Ivan Niven, A simple proof that π is irrational. Bull AMS 53 (1947), 509.

Only about half a page...