M 315C/M375T- Foundations, Functions, and Regression Models
Unique#: 55530
Fall 2011 TTH 12:30-2 PM
PAI 4.08
Dr. Mark Daniels - Instructor
Email
[email protected]
Office: RLM 10.114
512-232-5767
FAX
512-232-1491
Office hours: Email/call for appt. or try dropping by, W or F 11-12 PM
Kelsey Payne: Teaching Assistant email: [email protected]
Course Prerequisite: Precalculus (Calculus concurrently or completed is a plus)
Course Text: Functions in Mathematics: Introductory Explorations for Secondary
School Teachers
Course Materials: a TI 83/84 calculator is optional (but if you have one bring it!), an
open mind, creativity, and enthusiasm for learning, there is no textbook for this course so
bring a large notebook
Attendance Policy:
Since a majority of this work hinges on group work done during the class time,
attendance is of utmost importance. Therefore, attendance is extremely important and
you are expected be in class each and every day. Two points will be deducted for each
absence. If you contact your instructor before the class begins, only one point will be
deducted. One point will be deducted for each tardy after the first. If you leave class
early or consistently choose not to participate, points will be deducted. *Regarding
consistent absences, I reserve the right to lower your grade by one letter or fail you for
excessive absences.
.
Grading Policy:
Tests
40 %
Written Assignments/Labs/Homework
25 %
Attendance /Engagement and Contribution
10 % *
Midterm Project
10 %
Final
15 % (on Dec.9, 9-12 PM )
Total: 100 %
Final Grades will be determined by:
The standard university +/- grading system
Late Work
In general, late work will not be accepted. One half of the assigned points will be
deducted for work that is submitted after the due date if there is a legitimate excuse.
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
Course Objectives
In revisiting secondary mathematics, prospective mathematics teachers are expected to:
- Deepen and broaden function-related mathematical content knowledge from Algebra
through Calculus by exploring relevant topics in an inquiry based learning situation.
- Make connections between college mathematics and secondary school mathematics;
- Build preliminary knowledge of professional and state mathematics curriculum
standards;
- Use reflective and collaborative learning, and develop a stronger sense of
professionalism and leadership;
- Create efficient seekers of content knowledge;
- Explore and learn appropriate use of technology in the mathematics classroom
Tests/Labs/Homework:
There will be frequent homework assignments, labs, and exams to test your knowledge of
the concepts we are currently discussing in class. Tests and labs will be in class;
homework needs to be finished outside of class time. You are expected to enhance
classroom discussion with extended research of topics outside of the classroom. YOU
ARE RESPONSIBLE FOR KNOWING ALL TECHNOLOGY TECHNIQUES
PRESENTED IN CLASS.
Midterm Project SP09
You will explore the beauty of mathematics. Details will be given later.
Final Project: ONLY FOR THOSE IN M375T:
This project is designed to give you an opportunity to make sense of all that we have
talked about. The grade for this project will be averaged with your final test grade.
Details will be given later._________________________________________________
Quick Grade Tracker:
1. Test Grades: _____, _____, _____ Total = _____
Average = _____ Average X 40% = _____
2. HmWk, Writing, Labs: _____, _____, _____, _____, _____, _____, _____, _____, _____, _____,
_____, _____, Total = _____ Average = _____ Av. X 25% = _____
3. Attendance/Participation – 10pts possible = _____
4. Midterm Project ____ X 10% = ______
5. Final : = _____ X 15% = _____
4. FINAL GRADE FOR THE COURSE: Total of Final Points from 1-5 above = ___
For Students with Disabilities:
The University of Texas at Austin provides upon request appropriate academic accommodations for
qualified students with disabilities. For more information, contact the office of the Dean of Students
at 471-6259, 471-4641.
Functions and Modeling Course Outline for Fall_2011
DAY
1
st
1 Day Handouts.
TOPIC OR ACTIVITY
Prob solving - Conundrum.
Connections 1.
UNIT 1 Functions and Patterns
2
Definition of Function. Function Sorting Activity.
Writing - Def. Of Function.
3
4
5
6
7
8
9
10
11
12
3 Definitions of Function. Parabola Roots Exploration.
A qualitative look at ‘rate of change’ of f . Finding Roots Prob. Continued.
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Conic Sections.
Homework 1
Conic Sections continued
Spring Mass Lab
Sequences. Triangular Differences Activity Homework 1 Due
Triangular Differences continued. Homework 2
Functions as Sequences (i.e. Function Patterns)
Functions Patterns Exploration Homework 2 Due
Exponential Growth and decay_Rate of Change
UNIT 2 Modeling Using Regression and Matrices
Modeling Functions from data: Thunder Storms, Charles Law, and Linear
Regression
TEST 1
Modeling Functions from data. More regression. Residuals.
Midterm Assignment
Terminal Velocity Lab Homework 3
Modeling Functions from Data: Data with Matrices
Modeling Functions from Data: Standard Forms Homework 3 Due
Roller Coaster Exploration
UNIT 3 Exploring Functions in Other Systems
Parametric models Midterm Assignment Due
TEST 2
Parametric Exploration Problems
The Golf Shot – An Exploration
Vector Lab Homework 4
Polar Coordinate System
Geometry of Complex Numbers
Geometry of Complex Numbers continued Homework 4 Due
Polar Complex - Euler Numb