MATH 7495
I.
Course:
MATH 7495: Advanced Perspectives on School Mathematics
Department of Mathematics, College of Science and Mathematics
Kennesaw State University
II.
Instructor:
Mary Garner
Office: Science 522
Phone: 770-423-6664
e-mail: mgarner@kennesaw.edu
III.
Class Sessions:
IV.
Texts:
Problem Analysis for Middle Grades and Secondary Mathematics Teachers
by Drs. Mary Garner, Sarah Ledford, and Virginia Watson.
TI Nspire software will be used. [You can purchase the software online at a
variety of vendors or you can use Citrix.]
TI-83 or 84 or TI Nspire calculator is required.
Algebra texts are recommended.
V.
Catalog Description: 3-0-3
This course is for prospective 6-12 mathematics teachers who have a strong undergraduate training in
mathematics. This course is designed so that students can revisit key ideas in school
mathematics, bringing with them the skills and understandings of college course work in
mathematics and connecting more advanced ideas to the topics they will teach in middle
school and high school. The goal of the course is to deepen and broaden students’ understanding
of fundamental ideas involving algebra, functions, trigonometry, number theory, discrete
mathematics, probability, and mathematical modeling. The emphasis is on engaging the
students in reasoning and problem solving, communicating about mathematics, making connections
among different areas and concepts of mathematics, and exploring different ways of representing
mathematical principles.
VI.
Purpose/Rationale:
The purpose of this course is to advance the knowledge and skills of prospective 6-12 mathematics
teachers to enhance their effectiveness as facilitators in the teaching of school mathematics.
According to a publication by the Mathematical Association of America (MAA) “There is much
evidence of a vicious circle in which too many future teachers enter college with serious holes in
their understanding of school mathematics, have little college instruction focused on the
mathematics they will teach, and so enter their classrooms inadequately prepared to teach
mathematics.” Furthermore, “Future teachers should learn mathematics in a coherent fashion that
emphasizes the interconnections among theory, procedures, and applications.” This course is
designed so that students can revisit key ideas in school mathematics, bringing with them the skills
and understandings of college course work in mathematics, deepening and broadening their
understanding, and connecting more advanced ideas to the topics they will teach in middle school
and high school.
Collaborative Development Of Expertise In Teaching And Learning:
The Professional Teacher Education Unit (PTEU) at Kennesaw State University is committed to
developing expertise among candidates in initial and advanced programs as teachers and leaders
who possess the capability, intent and expertise to facilitate high levels of learning in all of their
students through effective, research-based practices in classroom instruction, and who enhance the
structures that support all learning. To that end, the PTEU fosters the development of candidates as
they progress through stages of growth from novice to proficient to expert and leader. Within the
PTEU conceptual framework, expertise is viewed as a process of continued development, not an
end-state. To be effective, teachers and educational leaders must embrace the notion that teaching
and learning are entwined and that only through the implementation of validated practices can all
students construct meaning and reach high levels of learning. In that way, candidates are facilitators
of the teaching and learning process. Finally, the PTEU recognizes, values and demonstrates
collaborative practices across the college and university and extends collaboration to the
community-at-large. Through this collaboration with professionals in the university, the public and
private schools, parents and other professional partners, the PTEU meets the ultimate goal of
assisting Georgia schools in bringing all students to high levels of learning.
Knowledge Base:
Teacher development is generally recognized as a continuum that includes four phases: preservice,
induction, in-service, renewal (Odell, Huling, and Sweeny, 2000). Just as Sternberg (1996) believes
that the concept of expertise is central to analyzing the teaching-learning process, the teacher
education faculty at KSU believes that the concept of expertise is central to preparing effective
classroom teachers and teacher leaders. Researchers describe how during the continuum phases
teachers progress from being Novices learning to survive in classrooms toward becoming Experts
who have achieved elegance in their teaching. We, like Sternberg (1998), believe that expertise is
not an end-state but a process of continued development.
Use of Technology:
The use of calculators and computers is an encouraged and accepted practice to enable students to
discover mathematical relationships and approach real world applications. Familiarizing teachers with a
variety of technological tools is an integral part of the math sequence for teachers.
Diversity Statement:
A variety of materials and instructional strategies will be employed to meet the needs of the
different learning styles of diverse learners in class. Candidates will gain knowledge as well as an
understanding of differentiated strategies and curricula for providing effective instruction and
assessment within multicultural classrooms. One element of course work is raising candidate
awareness of critical multicultural issues. A second element is to cause candidates to explore how
multiple attributes of multicultural populations influence decisions in employing specific methods
and materials for every student. Among these attributes are age, disability, ethnicity, family
structure, gender, geographic region, giftedness, language, race, religion, sexual orientation,
and socioeconomic status. An emphasis on cognitive style differences provides a background for
the consideration of cultural context.
Kennesaw State University provides program accessibility and accommodations for persons defined
as disabled under Section 504 of the Rehabilitation Act of 1973 or the Americans with Disabilities
Act of 1990. A number of services are available to support students with disabilities within their
academic program. In order to make arrangements for special services, students must visit the
Office of Disabled Student Support Services (ext. 6443) and develop an individual assistance plan.
In some cases, certification of disability is required.
Please be aware there are other support/mentor groups on the campus of Kennesaw State University
that address each of the multicultural variables outlined above.
VII.
7495 Learning Outcomes
Students will be able to:
(Content)
1. Explain the ways that basic ideas of number theory and algebraic structures underlie rules for
operations on symbolic expressions, equations, and inequalities (e.g. group properties,
equivalence relations, axioms of equality). (NCATE 2.2, 2.3, 10.3)
2. Derive general formulas to solve different types of problems and justify the derivation (e.g.
quadratic formula, formula for the sum of the first n integers). (NCATE 2.2, 2.3, 10.3)
3. Write discrete linear, quadratic, and exponential functions in closed and recursive forms and
derive those forms in different ways (e.g. system of equations, method of finite differences).
Connect arithmetic sequences to discrete linear functions and geometric sequences to
exponential functions. (NCATE 10.1, 10.2, 10.4).
4. Analyze the characteristics of functions and relations in algebraic, tabular, and graphical form
and interpret those characteristics in specific problem contexts. (Characteristics include
symmetry, rate of change, domain, range, zeros, intercepts, intervals of increase and decrease,
maximum and minimum values, end behavior. Function types include polynomial, piecewise,
rational, radical, logarithmic, exponential, trigonometric, polar, and parametric). (NCATE 10.1,
10.4)
5. Analyze the characteristics of inverses, transformations, and compositions of functions (e.g.
polynomial, piecewise, rational, radical, logarithmic, exponential, trigonometric, polar, and
parametric).
6. Explain, derive, and use basic counting formulas to solve problems and determine discrete
probabilities (e.g. addition and multiplication principle of counting, combinations, and
permutations). (NCATE 13.1)
7. Determine coordinates and associated reference angles on the unit circle and use the unit circle
to define the trigonometric functions and the inverse trigonometric functions (NCATE 12.2).
(Process)
8. Apply a variety of strategies to solve problems from the secondary curriculum, including
appropriate technology, and monitor and reflect on the process of mathematical problem
solving. (NCATE 1.1, 1.4, 6.1)
9. Analyze mathematical concepts that appear in problems from the secondary curriculum
exploring definitions, applications, and history of those concepts as well as connections to other
concepts. (NCATE 4.1, 4.3)
10. Communicate mathematical thinking coherently and clearly using the language of mathematics
to express ideas precisely, and evaluate the mathematical thinking and strategies of others.
(NCATE 3.1, 3.3, 3.4)
11. Use a variety of representations to model, interpret, communicate, and solve problems,
including vertex-edge graphs. (NCATE 5.1, 5.2, 5.3)
VIII.
Course Requirements/Assignments:
Weekly assignments, readings, class work, and quizzes. Each student is expected to participate in
all classes and attend class ready to discuss readings and assignments, or make presentations to the
class. Please seek help with the assignments during office hours or through GeorgiaVIEW Vista.
DO NOT SEEK HELP WITH AN ASSIGNMENT AFTER THE ASSIGNMENT IS DUE! SEEK
HELP BEFORE THE ASSIGNMENT IS DUE! It is strongly recommended that you form a study
group with other students in the class and schedule regular meetings to discuss assignments. You can
also seek help from the instructor and other students through GeorgiaVIEW Vista. Finally, you can visit
the instructor during office hours or make an appointment with the instructor for some other time. Late
assignments WILL NOT BE ACCEPTED. Hard copies of assignments must be turned in during class
periods, on the due date, not in electronic form.
Examinations. There will be two in-class tests and a final examination. There will be no reviews for
the examinations. This is not a course in which students can simply review procedures before the
test and then regurgitate those procedures on the examination. Students can best prepare for the
exams by working on the assigned problems on a daily basis and participating in whole-class, small
group, and GEORGIAVIEW VISTA discussions. Dates for the exams will be announced in class
and posted on GEORGIAVIEW VISTA.
Problem analysis. Each student will choose a problem from the high school mathematics
curriculum and analyze that problem. The student will be provided with a list of problems from
which he/she can choose. The first half of the problem analysis will be due by mid-term. The
second half will be due by the end of the semester. Dates will be posted on GEORGIAVIEW
VISTA.
The students are required to do a great deal of writing in this class. The rationale:
“Cognitive psychologists discuss the intimate relationship between thinking and writing. Their
research tells us that language and writing not only reflect thinking but also help to shape and
influence thinking as well. The relationship between thinking and writing is circular in that, as our
writing becomes clearer, so does our thinking – and as our thinking becomes clearer, so does our
writing.” -- From Successful Beginnings for College Teaching (2001) by A.P. McGlynn, page 117.
IX.
Evaluation and Grading:





Weekly assignments and class work
Test #1
Test #2
Final exam
Problem Analysis
30%
15%
15%
10%
30%
Grading of assignments and exams will be based on both the correctness of the mathematical
content and the quality of the associated write-up which may include proofs, explanations,
justifications, and discussion of connections, history, generalizations, and extensions. All parts of the
problem analysis MUST BE TYPED. Other assignments may be required to be typed as announced.
Final grades will be assigned as follows:
A 90%
B 80-89%
C 70-79%
D 60-69%
F less than 60%
X.
Withdrawal from the university or from individual courses and academic integrity:
See “Withdrawal and Academic Integrity.”
XI.
Class Attendance Policy:
Regular attendance is assumed and will be monitored. Although it is impossible to reconstruct
classroom lectures, discussions, and activities, in the event of unavoidable absence, the student will
assume full responsibility for any material and/or announcement missed.
This syllabus is subject to change, with notice.
“If you don’t love and hate and play and joke with your objects of study, then you’re really not treating
them properly. I tell my students if you’re not angry and excited and enthralled by your topic, you should
choose a different one.” – Dr. Robert Proctor (Stanford University)
“Real knowledge is to know the extent of one's ignorance." -- Confucius
“Certainty stunts thought, in ourselves and others … Thought flourishes as questions are asked, not as
answers are found.”