Math 406B: Methods of Teaching Mathematics in the Secondary School

Fall 2005


Course Description

This course is part of the secondary teaching option for a major in mathematics at The University of Arizona. It is designed to provide students with knowledge and experience to enable them to become effective secondary mathematics teachers. Emphasis will be on modes of instruction, problem solving, use of technology, assessment, and national standards. Special attention will be given to the teaching of geometry, algebra, statistics, and discrete mathematics.


Meeting Place and Time 

Math East, Room 143

Tuesdays and Thursdays, 9:30 a.m. – 10:45 a.m.

Practicum sites and times to be arranged


Virginia Horak, Assoc. Prof.                       Office Hours:    Monday, 1:00 – 1:50 p.m.

Office:  Math 522                                                               Tuesday, 11:00 – 11:50 a.m.   

Phone:  626-5987                                                              Wednesday, 10:00 – 10:50 a.m.          

E-mail:                            Or by appointment                               



Required Textbook

Wong, Harry K. and Rosemary T. Wong (2004). The First Days of School. Mountain View, CA: Harry K. Wong Publication, Inc., ISBN: 0-9629360-6-5.


Recommended Resources

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics (PSSM). Reston, VA: NCTM.  National Council of Teachers of Mathematics Website:

Arizona Department of Education, State Standards for Mathematics:

Tucson Unified School District:
, clink on link to Academic and Instructional Resources

Cooney, Brown, Dossey, Schrage and Wittmann (1996).  Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NM: Heinemann Press.


Course Objectives and Goals

1.      Students will be able to name, describe, identify, and use different modes of instruction and explain when each might be appropriate.

2.      Students will be able to develop lessons and lesson plans for the different modes of instruction and different content.

3.      Students will understand, appreciate, and be able to integrate the use of computers, calculators, and appropriate manipulatives into the teaching of the secondary mathematics curriculum.

4.      Students will appreciate the importance of problem solving in the mathematics curriculum, and will be able to integrate it into all content area topics.

5.      Students will be able to identify the characteristics of informal geometry instruction and develop informal geometry lessons appropriate for the middle or high school level.

6.      Students will be able to incorporate a variety of assessments of student learning into lessons they develop.

7.   Students will know and understand proportional reasoning and how it can be developed in middle school students.


Attendance:  Class participation is very important.  Thus, attendance and punctuality will affect your final grade.  More than one absence can cause your grade to be lowered or cause you to be dropped from the course.  Attendance will be taken at each class session.


Assignments:  Homework assignments will be collected at the beginning of class the day they are due.  In general, no late homework will be accepted for full credit.


Exams:  There will be a midterm exam and a final exam.  Everyone is expected to take the exams at the scheduled times.  There will be no exceptions.




 Tentative Class Schedule


Week                           Topic                                                                          


Aug. 22:           Course Overview, PSSM & Current Trends

                        Assignment on the Principles in PSSM


Aug. 29:           Conceptual/Procedural Knowledge               


Sept. 5:            Modes of Instruction                                                              

                        Student reports on journal articles to class


Sept. 12:          Promoting Discourse in the Classroom         


Sept. 19:          Planning for Instruction                                                                    


Sept. 26:          Teaching Middle School Mathematics                                               

                        Proportional Reasoning


Sept 20:           Teaching Algebra                                                                               


Oct. 3:              Teaching Algebra, continued                                                 

                        Student reports on “Issues” papers


Oct. 10:            Teaching Geometry                                                                           

                        MIDTERM EXAM tentatively set for October 11


Oct. 17:            Teaching Geometry, continued                                                          

                        Algebra lesson plan assignment due


Oct. 24:            Classroom Management 1                                                                 


Oct. 31:            Teaching Data Analysis                                                                     

                        Geometry lesson plan assignment due


Nov. 7:             Teaching with Technology                                                                 


Nov. 14:           CBR lesson taught to STCH 250 class, November 17

                        Teaching Probability and Topics of Discrete Mathematics


Nov. 21:           Teaching Probability and Topics of Discrete Mathematics (cont.)

                        (No class on 11/24)             


Nov. 28:           Classroom Management 2


Dec. 5:             Looking Back, Looking Ahead


The Final Exam will be Thursday, 15 December 2005, 8:00 – 10:00 a.m., Math East 143



Course Assignments/Grading Scale


Reviews of two articles in MT, MTMS, ON-Math                                  30 pts (15 pts ea)                  

Paper examining an issue in mathematics education                                  80 pts                        

Algebra Lesson Plan                                                                               80 pts                        

Geometry Lesson Plan                                                                80 pts            

Class assignments (3 of them)                                                     60 pts (20 pts ea)

Mid-term exam                                                                         100 pts                        

Final exam                                                                                            120 pts                       

Class participation                                                                                  30 pts

Practicum Reports/Reflections (5 points each)                             65 pts                        

Total                                                                                       645 pts                                              

580 points – A

516 points – B

451 points – C

387 points – D

386 or less – E


One-unit Practicum – A School-based Field Experience

  • Three hours per week in a middle school/high school classroom
  • Half of the semester will occur in a middle school and half the semester will occur in a high school.  Assignment to schools and classroom teachers will occur during the week of August 29.
  • Expectations

      A journal of each weekly classroom visit with reflection of the classroom activities, questions/issues that arise, etc.

      A report on your involvements in the classroom.  These involvements may include some, but not all of the following:

Tutor one or more students for several weeks

Collect and/or distribute homework assignments

Grade homework assignments

“Go over” homework assignments with class

Take attendance

Work with a small group of students

Present an activity to the class

Attend a faculty meeting (with permission)

Interview one or more (mathematics) teachers

Attend an IEP meeting on a student (with permission)

Attend other classes of a student

Interview a student

      Prepare and teach at least four lessons over the course of the semester



Things to remember for your practicum visits:

  1. Sign in at school according to school policy and procedures
  2. Introduce yourself to your practicum teacher; swap phone numbers and e-mail addresses
  3. Notify practicum teacher if you cannot make it to the classes on a day you are scheduled
  4. Reschedule to another day as soon as possible
  5. Ensure that you dress appropriately 
  6. Use appropriate language register
  7. If documents are needed from teacher, please request in writing at least one week in advance of the time they are needed.
  8. On your first visit to the school, get the bell schedule, a map of campus, the school calendar, and list of manipulatives/technology available in the classroom you will be visiting
  9. Wear your nametag on every visit