UTCH/MATH315 Functions and ModelingSample Syllabus
Morehead State University
Colleges of Education and Science
Department of Mathematics, Computer Science, and Physics
MSUTeach
Functions and Modeling
UTCH/MATH 315 (3 credit hours) Spring 2017
TTh9:10–10:10 (face-to-face) LA 113
Mike Dobranski, Ph.D.
Lappin Hall 202D
Office phone: (606) 783-5171
Office hours: M-F 8:15 – 9:00, 11:30 – 12:20 and by appointment
Course Description:Functions and Modeling (3-0-3) Students will engage in lab-based activities designed to strengthen and expand knowledge of the topics in secondary mathematics, focusing especially on topics from precalculus and the transition to calculus. Students will explore a variety of contexts that can be modeled using families of functions, including linear, exponential, polynomial and trigonometric functions. Topics involving conic sections, parametric equations and polar equations will be included. Explorations will involve the use of multiple representations, transformations, data analysis techniques(such as curve fitting) and interconnections among geometry, probability and algebra. Most labs will include significant use of various technologies, including computers, calculators and multimedia materials. The use of quantitative approaches (for example to rate of change, limits and accumulation) and building relationships between discrete and continuous reasoning will be recurrent themes.Equated with UTCH 315.
Major Topics:
Functions and Relations
Qualitative Graphing
Sequences/Patterns – Function Patterns
Mathematical Modeling - Data, & Regression, Matrices
Polar & Parametric Relations
Complex Numbers and Properties
Exponential growth and Decay Models
Student Learning Outcomes (SLOs):After completing the required readings and participating in class activities, the prospective mathematics or science educator will be able to do the following. The InTASC Standards addressed by these Objectives and SLOs are InTASC Standard 4: Content Knowledge and InTASC Standard 5: Application of Content. The IRA Standard addressed is IRA Standard 6: Professional Learning and Leadership.
Students will be able to:
- Deepen and broaden function-related mathematical content knowledge from Algebrathrough Calculus by exploring relevant topics in an inquiry based learning situation.
- Build new mathematical knowledge through problem solving.
- Select and use various types of reasoning and methods of proofand to develop an inquisitive and exploratory approach to mathematics.
- Communicate mathematical thinking coherently and clearly to peers, professors, and others.
- Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
- Use of multiple representations to model and interpret physical, social, and mathematical phenomena.
- Demonstrate skills, explain concepts, and justify generalizations in the content area of the three fundamental concepts of calculus: Closeness, Differentiation, and Integration.
Required Text:
Armendariz, E. P. & Daniels, M. (2011). Functions in Mathematics: Introductory Explorations for Secondary School Teachers. San Diego, CA: Cognella.
Technology Requirements: TI-83/84 Plus Graphing Calculator and a spreadsheet application.
Required Field Experience: Still being considered.
Conceptual Framework Outcomes (CFO)
The Unit and the faculty within individual programs assess the degree to which its graduates:
1)Master the content knowledge, professional and the twenty – first century skills need to make an optimal contribution to “whole” student learning in education settings.
2)Are competent in the collection and use of data to inform decision – making and to demonstrate accountability for student learning.
3)Demonstrate professional dispositions.
4)Are culturally competent and understand the regions from which they have come utilizing knowledge and experiences to effectively “bridge the gaps” (economic, achievement, and geographic) ensuring optimal learning for all students.
5)Engage in authentic field experiences in collaboration with committed school – based partners and are empowered to improve the quality of education throughout this region and beyond.
Course Evaluation: Since a majority of this work hinges on group work done during the class time, attendance is of utmost importance. Students are expected to prepare for and participate in class discussions and activities. Throughout the semester you will be asked to work individually and in groups on homework, projects or laboratory activities and present your ideas to the rest of the class. In addition, students will be assessed on homework, written work, labs, presentations, projects and exams.
Exams: If an exam is missed and the absence is excused with proper documentation an immediate make-up will be given if the student notifies the instructor within 48 hours of the exam, otherwise the final exam score will count as the make-up exam score. If the absence is not excused, “0” points will be recorded for that exam.
Projects/Labs: During the semester you will participate in laboratory and/or project activities. These will be done in a cooperative group environment. Each group of up to three students will be expected to turn in a report neatly typed, double spaced, using margins. In addition, each group may be asked to present its findings to the rest of the class. These presentations will allow you to express yourself mathematically and encourage you to organize your thoughts before coming to class.
Homework: Assignments must be ready to turn in at the beginning of class on the specified due date and must be written carefully and neatly. Late assignments may not receive full credit.
Attendance and Class Participation: You are expected to attend every class on time and to be prepared. Attendance and participation are necessary for success in this class.
EvaluationPercentGrading policy
Projects/Labs/HW/Quizzes40%A90%-100%
Exam 120%B80%-89%
Exam 220%C 70%-79%
Exam 320%D 60%-69%
E0% - 59%
HelpRemember, if you get stuck, seek help. Do not wait until it is too late!
- I will be glad to help. Come to see me anytime during my office hours or schedule an appointment.
- Free tutoring is available from the Academic Services Center, in 208 Allie Young. Please call 783-5200 to make an appointment.
- Free tutoring is available in the Math Department Tutoring Lab Lappin 108.
- Form a study group with other students in the class.
The last day to drop a class with a grade of “W” is Friday, April 7, 2017.
Tentative Daily Schedule
DAY / TOPIC OR ACTIVITY1 / 1st Day Handouts. Prob solving - Conundrum. Connections 1.
UNIT 1 Functions and Patterns
2 / Definition of Function. Function Sorting Activity.
Writing - Def. Of Function.
3 / Definitions of Function. Parabola Roots Exploration.
4 / A qualitative look at ‘rate of change’ of f . Finding Roots Prob. Continued.
5 / Conic Sections. Homework 1
6 / Conic Sections continued
7 / Spring Mass Lab
8 / Sequences. Triangular Differences Activity Homework 1 Due
9 / Triangular Differences continued. Homework 2
10 / Functions as Sequences (i.e. Function Patterns)
11 / Functions Patterns Exploration Homework 2 Due
12 / Exponential Growth and decay_Rate of Change
13 / TEST 1
UNIT 2 Modeling Using Regression and Matrices
14 / Modeling Functions from data: Thunder Storms, Charles Law, and LinearRegression
15 / Modeling Functions from data. More regression. Residuals.
Midterm Assignment
16 / Terminal Velocity Lab Homework 3
17 / Modeling Functions from Data: Data with Matrices
18 / Modeling Functions from Data: Standard Forms Homework 3 Due
19 / Roller Coaster Exploration
20 / TEST 2
UNIT 3 Exploring Functions in Other Systems
21 / Parametric models Midterm Assignment Due
22 / Parametric Exploration Problems
23 / The Golf Shot – An Exploration
24 / Vector Lab Homework 4
25 / Polar Coordinate System
26 / Geometry of Complex Numbers
27 / Geometry of Complex Numbers continued Homework 4 Due
28 / Polar Complex - Euler Number
Final Exam
Academic Honesty
Cheating, fabrication, plagiarism or helping others to commit these acts will not be tolerated. Academic dishonesty will result in severe disciplinary action including, but not limited to, failure of the student assessment item or course, and/ or dismissal from MSU. If you are not sure what constitutes academic dishonesty, read the Eagle: Student Handbook or ask your instructor. An example of plagiarism is copying information from the internet when appropriate credit is not given. The policy is located at
Americans with Disabilities Act (ADA)
Students withdisabilities are entitled to academicaccommodations and services to support their accessand safety. The Office for Disability Servicesin 109-J Enrollment Services Center coordinates reasonable accommodations for students with documented disabilities. Although a requestmay be made at any time, services are best applied when they are requested at or before the start of the semester. Please contact Disability Services at 606-783-5188 or or visit their website at
Campus Safety Statement
Emergency response information will be discussed in class. Students should familiarize themselves with the nearest exit routes in the event evacuation becomes necessary. You should notify your instructor at the beginning of the semester if you have special needs or will require assistance during an emergency evacuation. Students should familiarize themselves with emergency response protocols at
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January 2017