MATH 381 A Mathematics Education Seminar Spring 2008
Professor: George Ashline
Office: Jeanmarie 261, Phone: 6542434
Class Meets: Tuesdays from 2:30 to 3:30 PM in Jeanmarie 281
Office Hours: M,W,F 9:4511:00 AM, Th 12:302:00 PM. Feel free to set up appointments at other times.
eCollege and Home Page: I will post lesson plans, course updates, materials, and email announcements on eCollege at http://www.smcvtonline.org/ Most of these will be in the “Doc Sharing” portion of the site, which you should visit regularly during the semester. You can access other information about the courses I teach at http://academics.smcvt.edu/gashline/. Our course homepage is http://academics.smcvt.edu/math_courses/seminar/, at which I have provided mathematics education information and some links to mathematics education sites.
Audience: students interested in mathematics education, either at the secondary, middle, or elementary level
Course Goals:
According to the Vermont Department of Education licensure requirements for secondary mathematics teachers, students should have “knowledge of key concepts, methods, and skills in mathematics with particular emphasis on:
a. properties of numbers and numeration, estimation, measurement, computation, descriptive geometry, applications in solving practical problems, and the use of calculators and computers appropriate for teaching elementary mathematics
b. algebra, geometry, probability and statistics, calculus, how the various branches of mathematics relate to each other and to other disciplines, the process of reasoning and analysis, mathematical proofs, axioms and theorems, computer science, logic and the foundations of mathematics appropriate for teaching secondary mathematics, as well as knowledge of a scientific area.”
In light of these requirements, goals for the course include:
· To enhance knowledge needed to teach mathematics at the secondary or other levels
· To assist students to effectively present mathematical concepts to an audience/class at various levels
· To address the use of technology in teaching mathematics
· To encourage the use of library and Internet resources
Course Breakdown:
· Throughout the semester, we will examine mathematical concepts and discuss ways to effectively teach them. Effective teaching requires a thorough knowledge of mathematics and “multiple representation” approaches, including the ability to appropriately use technology. Some specific fields that you may consider include calculus, trigonometry, geometry in two and three dimensions, algebra, arithmetic, probability and statistics, etc. Lesson material may come from the available mathematics texts and/or library and Internet resources. In your lessons, you may wish to use various presentation approaches (small group/discovery, minilecture or lecture, technology and/or no technology, examples then theorem and/or theorem then examples, etc.).
Some other seminar details:
· Several days before each class, each presenter should email me a lesson outline, intended grade level, lesson expectations, and mathematics standard(s) addressed to post in their eCollege “Doc Sharing” category folder. This will allow others beforehand to view lesson details and consider how to approach the topic(s).
· In the first part of the semester, you will give one shorter lesson/presentation of about 1520 minutes and another shorter lesson/presentation of about 2025 minutes. Toward the end of the semester, you will prepare a longer lesson/presentation (and resulting writeup) of about 4550 minutes.
· You will have an opportunity to provide each presenter with lesson feedback about what worked well and what may be improved. These comments are part of the pedagogical assessment of the presentation, and you are encouraged to be as detailed and helpful as possible. In addition to discussing weekly reading assignments, if time permits, we can also discuss advantages and disadvantages of various approaches for a given lesson.
Presentation Tips (see Joe Gallian’s Math Horizons article for other useful advice):
· Use legible and sufficiently large print on whiteboard, overheads, or PowerPoint slides.
· When presenting, be sure to face your audience as much as possible and try not to speak to the board.
· Organize your lesson/presentation beforehand and outline your plans at the beginning.
· Work out beforehand the mathematics in your lesson and effectively organize your presentation details.
· With overheads/slides, allow sufficient time so that each can be read and digested.
· To effectively create your overheads/slides, you may wish to first write on scrap paper exactly what to include each slide. Then, you can transcribe the final version. It can help to use multiple colors!
· Practice your lesson (in front of a friend?) before presenting it. This will increase your comfort with it and ensure it has the desired time length. Please see me ahead of time with any questions about this.
Semester Outline (tentative):
A. Jan. 15 Introductory class
B. Jan. 22, Jan. 29 First minilesson presentations (1520 mins. in length); Discussion
C. Feb. 5, Feb. 12 Second minilesson presentations (2025 mins. in length); Discussion
D. Mar. 4, Mar. 25, Apr. 8, Apr. 22 Major lesson presentations (4045 mins. in length); Discussion
Grading: Your grade will be based on your inclass lessons/presentations (including Internet outlines), and your participation in the class discussion. The approximate grade breakdown will be:
Minilesson presentation: 35 %
Full lesson/presentation: 50 %
Participation: 15 %
Learning Disabilities: Any student having a documented learning disability that may affect the learning of mathematics is invited to consult privately with me during the first week of the semester so that appropriate arrangements can be made.
Academic Integrity: You are reminded of the academic integrity policy of St. Michael’s College. Simply stated, academic integrity requires that the work you complete for this class is your own. Some examples of offenses against academic integrity include plagiarism, unauthorized assistance, interference, and interference using information technology. Details about academic integrity offenses and the possible sanctions resulting from them have been distributed at the beginning of the academic year and also can be found in the Assistant Dean’s office.
Class Attendance: The following is taken from the Saint Michael’s College 200708 Online Catalogue under “Academic Regulations”:
“Students should understand that the main reason for attending college is to be guided in their learning activities by their professors. This guidance takes place primarily in the classroom and the laboratory.
The following policies have been established:
1. Members of the teaching faculty and students are expected to meet all scheduled classes unless prevented from doing so by illness or other emergencies.
2. The instructor of a course may allow absences equal to the number of class meetings per week. Additional absences will be considered excessive.
3. The instructor may report excessive absences to the Assistant Dean, who may warn the student.
4. If absences continue, the Assistant Dean may remove the student from class with a failing grade.”
Week 1
Ø Reference Bibliography, Reserved Materials, Sample Text List, Syllabus
Ø Sample Peer Assessment Sheets (distributed for each presenter each week)
Ø NCSU Math. Dept. “How Not to Teach Mathematics.” six minute videotape.
Ø Gallian, J. “How to Give a Good Talk.” Math Horizons. Apr. 1998, pp. 2930.
Ø NCTM Principles and Standards FAQs. (http://standards.nctm.org/)
Ø VT Framework of Standards and Subject Area Endorsements.
(http://www.state.vt.us/educ/new/pdfdoc/pubs/framework.pdf) and (http://www.state.vt.us/educ/new/pdfdoc/board/rules/5440_endorsements/subj_mathematics.pdf)
Week 2
Ø Rich, D. “7 Habits of Good Teachers Today.” Education Week. 8/6/97. (http://www.edweek.org/ew/1997/41rich.h16)
Ø Ball, D et al, “Reaching for Common Ground in K12 Mathematics Education.” MAA Online 6/05 report. (http://www.maa.org/commonground/cgreport2005.html)
Week 3
Ø Polya, G. “Ten Commandments for Teachers.” Journal of Education of the Faculty and College of Education of the University of British Columbia. Vancouver and Victoria, no. 3 (1959), pp. 6169.
Week 4
Ø “Tips for New Teachers.” NCTM News Bulletin. 35, no. 2 (9/98), pp. 1, 46.
Week 5
Ø Burrill, G. “Show Me the Math!” NCTM News Bulletin. 33, no. 8 (4/97), p.3.
Ø Cuoco, Al. “What I Wish I Had Known About Mathematics When I Started Teaching: Suggestions for Teacher Preparation Programs.” Mathematics Teacher. 91, no. 5. (5/98).(http://www.nctm.org/mt/1998/05/soundoff.html)
Week 6
Ø Hilton, P. “The Joy of Mathematics: A Mary P. Dolciani Lecture.” The College Mathematics Journal. 23, no. 4 (9/92), pp. 274281.
Week 7
Ø Reys, R. “A Highly Qualified Teacher in Every Classroom by 20052006: Blueprint or Fantasy.” Mathematics Teacher 97, no. 1 (1/04), pp. 45.
Week 8
Ø “Calculators – What is Their Place in Mathematics Classrooms?” NCTM Dialogues. May/Jun. 1999. (http://www.nctm.org/dialogues/)
Ø Education Trust. “What New ‘AYP’ Information Tells Us about Schools, States, and Public Education.” 2003. (http://www2.edtrust.org/edtrust/ESEA)
Week 9
Ø Askey, R. “Knowing and Teaching Elementary Mathematics.” American Educator (American Federation of Teachers). Fall 1999. (http://www.aft.org/publications/american_educator/)
Week 10
Ø Wu, H.H. “Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education.” American Educator (AFT). Fall 1999. (http://www.aft.org/publications/american_educator/)
Ø Taylor, J. “Absolutely the Best Dentists.” 2004. (http://www.lcsd.k12.sc.us/lancnty/pages/stalkdentist.html )
Ø Taylor, J. “Forget the Children—My Dentist Now Gets a Top Rating.” 2004. (http://www.lcsd.k12.sc.us/lancnty/pages/stalkforgetdent.html
Week 11
Ø “Integrate to Make Whole?” NCTM Dialogues. Jan./Feb. 2001.
(http://www.nctm.org/dialogues/)
Week 12
Ø Highlights from TIMMS. US DoE, NCES. 2003. (http://nces.ed.gov/timss/Results03.asp)
Ø Rogers, J. “Mathematics as Art: The Missing Standard.” Mathematics Teacher. 92, no. 4 (Apr. 1999), pp. 284285.
Week 13
Ø “How We Measure Up: Is American Math and Science Education in Decline?” The New ATLANTIS. Summer 2005.
Week 14
Ø Lott, J. “A Professional Oath for Mathematics Teachers.” NCTM News Bulletin. 40, no. 8 (Apr. 2004), p.3.
MA 381 Mathematics Education Seminar Schedule Spring 2008
Week 1 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 1/15 
Discussion of Syllabus and Semester Plan; 
Gallian’s “How to Give a Good Talk”; NCTM P&S FAQs; 


View Videotape “How Not to Teach 
VT Framework of Standards and Subject Area Endorsements 


Mathematics” 






Week 2 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 1/22 
First pair of 1^{st} minilesson presentations; 
Rich’s “7 Habits of Good Teachers Today”; 



Ball’s “Reaching for Common Ground in K12 Mathematics Education” 


Discussion of Weekly Readings 






Week 3 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 1/29 
Second pair of 1^{st} minilesson presentations; 
Polya’s “Ten Commandments for Teachers” 






Discussion of Weekly Readings 






Week 4 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 2/5 
First pair of 2^{nd} minilesson presentations; 
NCTM News Bulletin’s “Tips for New Teachers” 






Discussion of Weekly Readings 






Week 5 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 2/12 
Second pair of 2^{nd} minilesson presentations; 
Burrill’s “Show Me the Math!”




Cuoco’s “What I Wish I Had Known about Mathematics When I Started Teaching”



Discussion of Weekly Readings 
Hilton’s “The Joy of Mathematics” 

Week 6 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 2/19 


MIDSEMESTER BREAK 












Week 7 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 2/26 
Discussion of Pedagogy and Weekly Readings 
Reys’ “A Highly Qualified Teacher in Every Classroom by 20052005: 



Blueprint or Fantasy” 









Week 8 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 3/4 
First major lesson presentation; 
NCTM Dialogues’ “Calculators – What is Their Place in Mathematics Classrooms?” 






Discussion of Weekly Readings 
Education Trust’s “What New ‘AYP’ Information Tells Us about Schools, States, and Public Education” 





Week 9 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 3/11 
Discussion of Pedagogy and Weekly Readings 
Askey’s “Knowing and Teaching Elementary Mathematics” 













Week 10 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 3/25 
Second major lesson presentation; 
Wu’s “Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education” 






Discussion of Weekly Readings 
Taylor’s “Absolutely the Best Dentists” and “Forget the ChildrenMy Dentis Now Gets a Top Rating” 





Week 11 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 4/1 
Discussion of Pedagogy and Weekly Readings 
NCTM Dialogues’ “Integrate to Make Whole?” 













Week 12 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 4/8 
Third major lesson presentation; 
NCES’ “Highlights from TIMMS” 



Rogers’ “Mathematics as Art: The Missing Standard” 


Discussion of Weekly Readings 






Week 13 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 4/15 
Discussion of Pedagogy and Weekly Readings 
New ATLANTIS’ “How We Measure Up: Is American Math and Science Education 



in Decline?” 









Week 14 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 4/22 
Fourth major lesson presentation; 
Lott’s “A Professional Oath for Mathematics Teachers” 






Discussion of Weekly Readings 






Week 15 
Plan for the Class 
Readings Assigned (due next class) 
Presenters 
T 4/29 
Discussion of Weekly Readings; 

FINAL CLASS 





Course Evaluations 





