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M. Dennis Dranchak

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 Modern Geometry

 

COURSE DESCRIPTION

 

Modern Geometry

Spring 2010

 

Geometry is the “oldest” of the mathematical sciences, both due to its use in any spatial layout, building, and construction, and to the properties, sometimes expressed as equations, sometimes as proportions, that mediate these applications. This was the first branch of mathematics opened to the insights and strictures of logical deduction and “proof.” Special applications of triangles gave rise to trigonometry. Trigonometry on a spherical surface allowed navigation by the stars. Descartes was able to marry geometry with algebra, allowing each to illuminate the other, and providing a set of modeling tools still used today. The realization that the geometry of a plane is not, strictly speaking, the geometry of the world (or universe) led directly (within two generations) to the work of Einstein and Planck. Around the turn of the last century, study of geometry fell into disfavor, since many researchers thought that everything of interest had been discovered…Then Benoit Mandelbrot, following clues investigated by several others during the early twentieth century, invented the marvelous concept of the fractal, published in 1985, and “chaos theory” had its visual counterpart. We study geometry for all of these reasons today

 

Text: Geometry: Seeing, Doing, and Understanding..  Harold R. Jacobs. New York: W. H. Freeman and Company. 2003

 

Materials

•     Text. Must be brought to class every day.

•     PC. Must be brought to class every day.

•     Pencils and erasers - lots. I will look at NO work done in ink (unless it is printed), nor will you receive credit for it. I sell pencils, $.25 each, before class.

 

Tests:

·        as appropriate.

·        Unit tests will be announced, but not quizzes. Quizzes may happen any day following homework review for a section

·        Make-ups on day of return, unless longer illness, absence, etc. During class in the classroom.

 

Grade:  Tests 35%; Quizzes 15%; POD 25%; Homework 25%.

 

Cheating: Caught cheating: grade of 0 for quiz/test/exam.

 

Grading Policy:.

·        Average grade - C.

·        Honor grade - B.

·        Superb grade - A.

·        Passing grade - D.

·        Unfortunately, there may be some who choose to go to summer school. You are responsible for 50% of your grade. There is no reason to fail the course.

·        I  DO NOT EXEMPT from Final exams. There is no Midterm exam in this course.

 

Next course in sequence

•     Honors Algebra 2 and Trig. Requires grade of 90..

·        Algebra 2 and Trig. Requires passing

·        Algebra 2. Requires passing with teacher recommendation

·        College Math. Requires not qualifying for any of above.

·        Computer Programming. Requires passing.

 

Help

•     Teacher is available flex period 3 and 4 in Room 223.  Every day.

•     Calculus students offer “peer tutoring” five days per week during flex periods 3 and 4 in Room 223.

·        Any student in the school is welcome, and only has to show up. Most days we’re lonely. Mr. Sgroi is also in Room 223 during these periods 7 of the 10 flex periods per week.

 

Classroom behavior

·        Students are to be in the classroom on time with text, and PC

·        The expectation is that when the teacher is speaking the students are silent. Pay attention and allow others to pay attention and participate in the lesson.

·        There is limited availability to “hook up” the tablet PCs. Expectation is that they do not need external power source.

·        Uniforms are worn correctly at all times.

·        No food or drink (except water) is allowed at any time

·        Bathroom use: Personal business is taken care of on personal time. You have 7 minutes between blocks; flex time is practically unlimited. After the class bell, permission is routinely refused. Holy Cross students do not wander the halls during class time.

·        Each of us is a child of God with all of eternity shining from our eyes. We will treat each other respectfully, even playfully, at all times. “Please,” “Thank you,” and “I’m sorry” smooth out many a wrinkle and prevent many hassles. We can learn to walk the proverbial mile in the other’s shoes. Name-calling, put-downs, and belittling “humor” are not behaviors of self-respecting, charitable people.

 

Problem Of the Day (POD)

·        One a day, on screen as come into class. Students are responsible for copying each down or downloading from website. These will be available online after class.

·        Have until next class meeting to solve; send to Dropbox. See Dropbox directions for naming conventions/requirements. Done on paper, place in tray on closet door.

·        Will be graded on a 0 - 1 - 2 points basis. 2 points: correct answer, compelling argument/demonstration/proof/”work.” 1 point: correct answer with no argument, incorrect answer with corresponding (misleading) argument. 0 point: none of the above (including incorrect answer with no argument).

If the problems are done using pencil and paper, the following rules apply:

  • Must be on one side of a full sheet of paper.
  • One problem per side of the paper.
  • In pencil, the only acceptable writing instrument in mathematics
  • The entire problem must be copied, includiong all charts, diagrams, and accompanying answer choices. Then you can present your solution.

·        Points are totaled in each quarter and used as a grade. Passing is 50% of possible points, i.e., 1 point per problem. Grade ranges will be proportional. Will be posted on ParentConnect (and included in average) only at interim and course end. There is no minimum grade for this work, i.e., no “floor” of 60.

·        Parents who want to monitor student progress can email me for (weekly?) updates.

 

Homework

·        Assigned regularly, if not daily. May be from text, from worksheet, or some question that suggests itself in class.

·        If traditional form (written), may be submitted in the Dropbox. See Dropbox directions for naming conventions/requirements.

·        Must be identified with student name, date completed, and statement of assignment. (online or not)

·        Is due when collected. May be made up/turned in late if absent, otherwise not.

·        All work must be shown including reproductions of all figures/diagrams referenced. Lists of answers will get 1 point. Lack of diagrams reduces grade to 3 points.

·        Will be collected, inspected, and returned, usually the next day and graded on  0 – 5 scale: 5 = complete; 4 = missing one or two problems, 3 = missing more problems, 2 = some work shown, much work not shown, 1 = answers only (no or little work shown), 0 = not submitted or copied.

·        Homework will count as a grade and be averaged in with other grades. Will only appear on ParentConnect at interim and end of course.

·        Parents who want to monitor student  progress can email me for (weekly?) updates.

·         Students should realize that copying homework carries a built-in penalty, to wit, student does not learn what he/she is expected to learn. STUDENTS SHOULD REALIZE THAT THIS SUBJECT CANNOT BE CRAMMED, AND ATTEMPTS TO DO SO WILL INEVITABLY FAIL.

 

Note for PC use

 

There is an incredible amount of note-taking involved in studying Geometry, since to students today it is virtually all new: backgrounds from elementary school tend to be very spotty. Nearly every discussion involves one or more figures/diagrams, virtually all of which have identifying marks and some information, about which one then writes notes to aid memory and recall of important points (no pun intended). No single software suite provides the range of computer behaviors required for the course. You will find yourself going back and forth between One-Note or OpenOffice Document and Geogebra, but you will probably construct the figures in Geogebra or, if you can afford it, Geometer’s Sketchpad, and cut and paste them into your note or document. Arguments without diagrams are unintelligible, diagrams without arguments are silent.

 

The opening topics of the course will give simple examples of the means to achieve these behaviors. Of course, Periods 3 and 4 flex provide opportunity for more in-depth help.

 

We haven’t even spoken about the Web yet.

 

There is little likelihood that a student will have time to be conscientious about the course notes and to allow himself/herself to be come distracted via the PC. If in individual cases it becomes obvious that the tool is a problem, this will be addressed.

 College Math

 

COURSE DESCRIPTION

 

COLLEGE MATHEMATICS

Spring 2010

 

BELIEVE IT OR NOT, mathematics does not begin and end with arithmetic, algebra, and geometry. While these are important, and form the basis of all “higher” mathematics, there is an incredible spectrum of other mathematics with corresponding uses in today’s world. Some of them are quite powerful…such as the laws of logic and the modeling of these laws in electronic circuits, which (only) form the intellectual basis of the computers we use so much. We’ll explore some of these: number theory, logic, different number systems, so-called consumer mathematics, counting methods and probability. All will be grounded in real-world applications and explored singly and in groups. When will we ever use this stuff? Never… or often, depending on how much we need what “practical” math has to offer.

 

Text:

  • Mathematical Ideas, Miller et. al. Addison Wesley Educational Publishers, Boston, MA. 10th ed., 2005.

 

Materials

•     Text. Must be brought to class every day.

•     Notebook. Spiral? Loose-leaf? PC? Must be brought to class every day.

•     Pencils and erasers - lots. Outside of the POW, I will look at NO work done in ink, nor will you receive credit for it. I sell pencils before class, price $.25

•     Calculator. Must be at least the “scientific” type. The graphing type is in some ways preferable. If you have access to a graphing one, fine. If not, a TI-30 or equivalent will be sufficient. If you wish to use a calculator, you must supply one. I have none for loan. Students are not allowed to borrow calculators for tests. Since Holy Cross does not allow cell phone use during school, calculators on cell phones are not allowed.

 

Tests:

·        as appropriate.

·        Most will be individual, some will be group.

·        Unit tests are announced.

·        Assessments are graded on a points earned / points available format; the “curve” will be announced every time one is returned. Translation will be made to HC format before upload to IGPro/Parent Connect.

 

Grade: Tests50%. Homework 25%. POW 25%

 

Cheating: Caught cheating: grade of 0 for quiz/test/exam.

 

Grading Policy

·        Average grade - C.

·        Honor grade - B.

·        Superb grade - A.

·        Passing grade - D.

·        Unfortunately, there may be some who choose to go to summer school. You have the primary responsibility for 50% of your grade. There is no reason to fail the course. The only place to make up a failure is at BCC…with its own sets of bureaucracy and hurdles to cross, legitimate or otherwise.

·        I  DO NOT EXEMPT from Final exams. There will be no Midterm exam.

 

Help

•     Teacher is available flex period 3 and period 4 in Room 223.

•     Calculus students offer “peer tutoring” five days per week during flex periods 3 and 4 in Room 223.

·        Any student in the school is welcome, and only has to show up. Most days we’re lonely. Mr. Sgroi is also in Room 223 during these periods every day.

 

Classroom behavior

·        Students are to be in the classroom on time with text, notebook/note pages, and, when appropriate, calculator.

·        Uniforms are worn correctly at all times. ID’s and agendas are checked.

·        The expectation for student behavior is that when the teacher is speaking the students are silent. Please pay attention to the lesson and allow those around you also to participate in the lesson.

·        No food or drink (excluding water) is allowed at any time.

·        Bathroom use: One takes care of personal business on personal time (7 minutes between blocks; unlimited time during flex). Ask after the class bell, permission routinely denied.

·        Each of us is a child of God with all of eternity shining from our eyes. We will treat each other respectfully, even playfully, at all times. “Please,’ “Thank you,” and “I’m sorry” smooth out many a wrinkle and prevent many hassles. We can learn to walk the proverbial mile in the other’s shoes. Name-calling, put-downs, and belittling “humor” are not behaviors of self-respecting, charitable people.

  

Problem Of the Week (POW)

·        On Monday, a problem will be on the board. as you come into class.  I will distribute one copy to each student.

·        The first 10 minutes of class will be devoted to working on this problem, during the time that class business is transacted, such as attendance, homework/problem return, uniform check, whatever.

·        Students may attempt to solve the problem by themselves or in groups of no more than four people. These can change week to week. You will register them at the end of the business time Monday. People not submitting forms will be deemed to be working singly.

·        Solutions must be submitted in regular math format: Names of all in the group, date submitted, problem stated, problem solved, including all work and supporting documentation. The idea is that the solution will be readable and understandable by someone with normal math background

·        Problems will be graded on a scale of 1 to 10, depending on success of solution and completeness of work supplied. An incorrect answer only will receive a “1”; if it is correct, it will be considered a “2.”  To earn more, more must be provided. Incorrect solutions will receive some credit, typically 7 points or fewer. Remember: This is 25% of your grade, and, with your homework, constitutes the only “extra credit” I consider, since its completeness is entirely under your control.

·        Problems not submitted when collected will be given a grade of “0.” I will excuse 1 problem not submitted due to absence (it will be accepted late), but only 1, and only from a student working singly. If someone from your group is present, the problem is due; I do not listen to, “Dave has it, and he’s not here.” Take responsibility for your work.

·        In the event of weeks with fewer than 5 days, the problem will be collected at the beginning of class on the first day the following week, as the new problem is assigned..

·        Solutions may be submitted in pencil, pen, or printed from a PC.

·        Grades will be posted on IGPro regularly. There is no “floor” for this grade.

 

Homework

·        Assigned regularly, if not daily. May be from worksheet, from text, or some questions that suggests itself in class.

·        Must be done in pencil, the only acceptable writing instrument in math class.

·        Must be identified with student name, date completed, and statement of assignment.

·        Is due when collected. May be made up/turned in late if absent, otherwise not.

·        All work must be shown. Lists of answers will get 1 point...

·        Will be collected, inspected, graded and returned, usually the next day. 5 points – complete. 4 points – missing few problems. 3 points – missing many problems. 2 points – some work shown, but rest listed answers. 1 point – no work shown (even if otherwise complete).

·        Homework will count as 25% of class grade. Will only be calculated for interims and quarters and posted accordingly. There is no floor for this grade.

·        If parents want to keep abreast of student work, they can email me for (weekly?) updates.

·        Students should realize that copying homework carries a built-in penalty, to wit, student does not learn what he/she is expected to learn. STUDENTS SHOULD REALIZE THAT THIS SUBJECT CANNOT BE CRAMMED, AND ATTEMPTS TO DO SO WILL INEVITABLY FAIL.