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Math 149S. Capstone Mathematics for Teachers. Spring 2024.

Pre/co-requisites: Math 151; Math 145 (may be taken concurrently); Math 161 (may be taken concurrently).

Units: 4 (3 hours per week in class, 24 hours total of service learning).

Catalog Description: Secondary school mathematics from an advanced viewpoint. This course builds on students' work in upper division mathematics to deepen their understanding of the mathematics taught in secondary schools. In collaboration with local in-service teachers and university faculty, students will actively explore topics in number theory, algebra, analysis, geometry, and apply their content knowledge in a service-learning context.

Informal Course Description: Research shows that amount of course work in mathematics taken by an undergraduate does not correlate to teaching effectiveness. One issue is that the undergraduate curriculum usually is not linked explicitly to high school mathematics. In this class, we will revisit high school mathematics with advanced mathematical tools and maturity. We will look at key questions that come up in high school classrooms and consider rigorous answers as well as explanations accessible to students.

Course goals
Upon completion of this course, students should know/understand:

Learning Outcomes
Upon completion of this course, students should be able to:

Grading policy: Your grade for the course will be based on your participation and your performance on quizzes, homework, tests, and field experience.

Homework 20%
Class participation 8%
Test 1 10%
Test 2 10%
Test 3 10%
Service Learning:
Observing and leading extracurricular activities
Presentation on Service Learning 3%
Final Project 15%
Points earnedGrade
90-100% A
80-89% B
70-79% C
60-69% D
0-59% F

Class attendance: It is important to attend every class because group/class discussions are an important part of the course. Attendance may be taken but will not be directly a part of your grade. Participation, however, will be a part of your grade. There are several ways to participate: present your solutions to homework problems, class problems, work on other activities done in class, and contribute to the class discussions. Some class discussions will be based on reading assignments and service learning, others on the material studied in class.

If you miss a class, you should contact one of your classmates or the instructor to find out what was done in class and whether important announcements were made or homework was assigned.

Homework: There will be weekly homework, consisting of reading summaries/reflections and problem sets. Homework is due at the beginning of the class period (2:00 pm). No late papers will be accepted except uless you have a serious and documented reason. Homework is to be done using overleaf (on-line collaborative LaTeX editor). To submit, share your overleaf file/project. Use the "share" feature and give me the "edit" permissions. You may either add me as a "collaborator" or share the link on Canvas. I will type my feedback in the file itself.

You are encouraged to (but you don't have to) do the homework in a group of 2-3 people. In this case, make and share only one file/project. Make sure that you write the names of all group members in the file. If desired, you may change your group composition from one homework to another, and you may do some homeworks as a group and some individually. Three of the homework assignmens are documents related to Service Learning: the Service Learning Plan and two progress reports. These documents must be completed (individually) and will count towards your homework grade.

Tests: There will be three 1-hour tests. If for any reason you are unable to take a test at the scheduled time, please let me know as soon as possible, and certainly before the test. In most cases, you will be expected to take the test before it is given in class. No late tests are given unless you have a serious and documented reason to miss class.

Service Learning: Service Learning is a key component of this course. It will involve at least 24 hours of observation, preparation for, and instruction of extra-curricular activities (for advanced and/or interested students).

For up to 6 hours, you may choose to observe extracurricular activities. You may also sometimes participate in sessions for high school students. For these two types of activities, you are expected to turn in your observation notes and reflections. Your observation notes and reflections will be graded by your instructor. For participation, your level of engagement will be evalueated as well.

For the majority of your hours, you will develop materials for and/or lead/assist with a math circle/club/team, competition practice, competition, or other extracurricular activities for interested advanced students. Your level of engagement, quality of preparation, and quality of instruction will be evaluated by your peers, the school teacher (if the activity is held at a school), and/or your instructor or another faculty in charge of the activity. You have to turn in your time log, any materials developed, reflections, and peer evaluations. In addition, if the teacher/faculty in charge is not your instructor, you have to request their evaluation of your work. It can be uploaded with the rest of your documents or sent by them to me directly.

All papers (time sheets, materials developed, notes, reflections, peer evaluations, teacher's evaluations) related to prep meetings and activities held during dates 1-15 should be turned in by the end of the same month. Papers related to meetings/activities held during dates 16-31 should be turned in by the 15th of the following month. Exception: all papers related to meetings/activities held in the month of May should be turned in by May 16.

Finally, you should prepare a short presentation (about 5 minutes long) about your service learning experience. You may choose the topic you want to present on: a class activity you liked (whether the class was taugh by you or the teacher you observed), your lesson plan, teaching strategies you learned, etc. Since you will be often working in groups, presentations may be prepared by groups as well. However, in this case, make sure that all of the group members are involved in preparing the presentation as well as presenting.

Note. As indicated above, you are expected to complete at least 24 hours total of service learning. If you complete less than the required hours of service learning, your grade for this component will be prorated. If you complete more than 24 hours, you may receive extra credit.

Work with your instructor on the details of your service learning placement. See the page on service learning for more detailed information.

Extra Help: It is essential not to fall behind, because many classes will use the material studied previously. If you have trouble with some material, seek help in the following ways:

If you are having any difficulties, seek help immediately - don't wait until it is too late to recover from falling behind!

Students with disabilities: Upon identifying themselves to the instructor and the university, students with disabilities will receive reasonable accommodation for learning and evaluation. For more information, contact Services to Students with Disabilities in the University Library, Room 1202 (278-2811).

University policies. The following University policies can be found on the web.

Fresno State is committed to fostering a safe, productive learning environment for all students. Title IX and CSU policy prohibit discrimination on the basis of sex, which includes sexual harassment, domestic and dating violence, sexual assault, sexual exploitation, and stalking. We understand that sexual violence can undermine students’ academic success and we encourage students who have experienced some form of sexual misconduct to access appropriate resources so they can get the support they need and deserve. As an instructor, I have a mandatory reporting responsibility as a part of my role. It is my goal that you feel comfortable sharing information related to your life experiences in classroom discussions, in your written work, and in our one-on-one meetings. I will seek to keep the information you share private to the greatest extent possible. However, I am required to report information I receive regarding sexual misconduct or information about a crime that may have occurred during your time at Fresno State. Students can report incidents of alleged sexual misconduct to either or both of the following resources:
Title IX and Clery Compliance Office, 559.278.5003
Fresno State Police Department, 559.278.8400
Students can access confidential support from two separate resources on campus:
Survivor Advocates, 559.278.6796
Counseling Services, 559.278.2734
If you have concerns and you are unsure who to contact, please visit the Concern & Action Guide.

Emergency Information: In the event of an emergency, everyone in the campus community becomes a partner in the response. To ensSupportNeture you are prepared and remain calm you must make yourself familiar with campus protocols. To contact the Fresno State Police Department call 559.278.8400 from your cell phone or 911 from a campus phone. Prior to an emergency, assess your environment for options depending on the emergency. Identify all possible exit routes, in an emergency always use the closest most safe exit. Once you exit the building go to the predetermined evacuation assembly point, if that is unavailable then go to an open safe space away from the emergency. Identify where and how you can secure yourself inside if you need to shelter in place or hide from a threat. Be prepared to help guide those around you and assist individuals who may be in need. Additional information can be found at

University Services: The following University services can be found on the web.

Dispute Resolution: If there are questions or concerns that you have about this course that you and I are not able to resolve, please feel free to contact the Chair of the department to discuss the matter: Dr. Carmen Caprau, Department of Mathematics,, 559.278.2992.

Intellectual Property: All course materials, including but not limited to the syllabus, readings, quiz questions, exam questions, and assignments prepared by the instructor are property of the instructor and University. Students are prohibited from posting course materials online (e.g., Course Hero) and from selling course materials to or being paid for providing materials to any person or commercial firm without the express written permission of the professor teaching this course. Doing so will constitute both an academic integrity violation and a copyright violation. Audio and video recordings of class lectures as well as images of chat or messages shared during course sessions are prohibited unless I give you explicit permission in advance. Students with an official letter from the Services for Students with Disabilities office may record the class if SSD has approved that service. Otherwise, recordings of lectures are included in the intellectual property notice described above. These provisions exist regardless of the modality of the course. That is they apply to in-person, hybrid and online courses.

COVID: The following sections regarding COVID are subject to change given changing circumstances on-campus and in the community. Please check the COVID website for the most up-to-date information Vaccination: The California State University system strongly recommends the COVID-19 vaccination and booster for all students, faculty, and staff. As a reminder, you are eligible for a booster five (5) months after receiving a final dose of the Pfizer or Moderna vaccine; or two (2) months after receiving a Johnson & Johnson vaccine. Face Coverings: Fresno State no longer requires masks to be worn indoors, but based on updated guidance from public health experts, the University highly recommends that all students, faculty, and staff, regardless of vaccination status, wear a surgical grade or KN95 mask indoors. Faculty will continue to have the discretion to require face coverings for their in-person classes as they evaluate the health and safety needs of their individual classroom environments. Testing: The campus was fortunate to receive the Higher Education Emergency Relief (HEERF) Funds during the pandemic and through June 2023 but funds are no longer available. Students will still be able to obtain free kits from the Student Health and Counseling Center. Additionally, free COVID-19 test options are offered by the Fresno County Department of Public Health.

Subject to Change: This syllabus and schedule are subject to change in the event of extenuating circumstances. If you are absent from class, it is your responsibility to check on announcements made while you were absent.

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This page was last revised on 17 January 2024.