I. ASCRC General Education Form (revised 3/19/14)
Use to propose new general education courses (except writing courses), to change or
renew existing gen ed courses and to remove designations for existing gen ed courses.
Note: One-time-only general education designation may be requested for experimental courses
(X91-previously X95), granted only for the semester taught. A NEW request must be
submitted for the course to receive subsequent general education status.
Group
II. Mathematics
VII: Social Sciences
(submit
III. Language
VIII: Ethics & Human Values
separate forms X III Exception: Symbolic Systems * IX: American & European
if requesting
IV: Expressive Arts
X: Indigenous & Global
more than one
V: Literary & Artistic Studies
XI: Natural Sciences
general
w/ lab  w/out lab 
education
VI: Historical & Cultural Studies
group
* Require a Symbolic Systems Request Form.
designation)
Dept/Program Mathematical Sciences
Course #
M 171
Course Title
Prerequisite
Calculus I
M 122 or 151,
or ALEKS placement >= 5
Credits
II. Endorsement/Approvals
Complete the form and obtain signatures before submitting to Faculty Senate Office
Please type / print name Signature
4
Date
Instructor
Kelly McKinnie
Phone / Email x5694; kelly.mckinnie@mso.umt.edu
Program Chair Leonid Kalachev
Dean
III. Type of request
New
One-time Only
Renew X
Change
Remove
Reason for Gen Ed inclusion, change or deletion
N/A
Description of change
N/A
IV. Description and purpose of the general education course: General Education courses
must be introductory and foundational within the offering department or within the General
Education Group. They must emphasize breadth, context, and connectedness; and relate course
content to students’ future lives: See Preamble:
http://umt.edu/facultysenate/archives/minutes/gened/GE_preamble.aspx
Description:
M 171 - Calculus I (4 credits)
Offered autumn and spring. Prereq., M 122 or 151 or ALEKS placement >= 5.
Differential calculus, including limits, continuous functions, Intermediate Value
Theorem, tangents, linear approximation, inverse functions, implicit differentiation,
extreme values and the Mean Value Theorem. Integral Calculus including
antiderivatives, definite integrals, and the Fundamental Theorem of Calculus.
Purpose: To learn the basic subject matter of calculus and to prepare students for higher level
courses in mathematics.
V. Criteria: Briefly explain how this course meets the criteria for the group. See:
http://umt.edu/facultysenate/documents/forms/GE_Criteria5-1-08.aspx
1. rigorously present a mapping between a real- Calculus presents the tools for analyzing
world system and a human abstraction of the
mathematical models of real-world
system.
phenomena involving change.
2. applies analysis, reasoning and creative
This course utilizes tools within the language
thinking in the understanding and manipulation of mathematics (like differentiation and
of symbolic codes.
integration) to analyze models involving
change and to use them to make predictions.
3. utilizes alternative methods of
This course emphasizes the connection
communication, perception, and expression in
between graphical and analytical
order to encourage rigorous thinking.
representation of functions, derivatives and
integrals.
VI. Student Learning Goals: Briefly explain how this course will meet the applicable learning
goals. See: http://umt.edu/facultysenate/documents/forms/GE_Criteria5-1-08.aspx
1. demonstrate an understanding of the symbols One learning outcome in M171 is to ``Use
and the transformations of the system.
the derivative to solve challenging related
rate and optimization word problems’’. In
these problems students are required to
understand the meaning of the derivative
in real world situations.
2. relay and interpret information in terms of the
given symbolic system.
3. apply creative thinking using the symbolic
system in order to solve problems and
communicate ideas.
Also included in the learning outcomes is
the expectation that students will be able to
explain infinite limits, the limit definition of
continuity and the limit definition of the
derivative. These all involve interpreting
information in terms of a given symbolic
system (the language of mathematics).
The statement “Graphically analyze
functions including using continuity and
differentiation to determine local
and global extrema, concavity, and
inflection points” is included in the
learning outcomes. Creative thinking is
required to analyze graphs in this
manner.
VII. Assessment: How are the learning goals above measured? Please list at least one
assignment, activity or test question for each goal.
1. Learning outcomes are assessed by embedded questions on the final exam. Specific
questions are written to assess different learning outcomes and the assessment report is written
based on student performance on these questions. The final exam is common among all M171
students in a given semester.
2. See 1.
3. See 1.
VIII. Justification: Normally, general education courses will not carry pre-requisites, will
carry at least 3 credits, and will be numbered at the 100-200 level. If the course has more than
one pre-requisite, carries fewer than three credits, or is upper division (numbered above the 200
level), provide rationale for exception(s).
N/A
IX. Syllabus: Paste syllabus below or attach and send digital copy with form.  The syllabus
should clearly describe learning outcomes related to the above criteria and learning goals.
A sample syllabus is attached below.
Please note: Approved general education changes will take effect next fall.
General education instructors will be expected to provide sample assessment items and
corresponding responses to the Assessment Advisory Committee.
CALCULUS I MATHEMATICS 171 SECTION 3 CRN 70133
INSTRUCTOR Matt Roscoe
Office: Math 205A
Phone: (406) 243-6689 or (406) 203-2112
Email: matt.roscoe@umontana.edu
COURSE WEBPAGE http://www.math.umt.edu/roscoe/m171
Learning Outcomes: Upon successful completion of M171, a student will be able
to:
1. Understand the idea behind the definition of a limit. Use the rules
associated to limits to determine the limits of transcendental, rationaland
piecewise defined functions;
2. Understand the idea behind and the rules of infinite limits, limits at infinity,
asymptotes, indeterminate forms and how to use L'Hopitals Rule;
3. Explain the limit definition of continuity;
4. Explain the limit definition of the derivative of a function, how it relates to
the function itself, and how to use it to compute derivatives;
5. Use derivatives to find tangent lines to curves and velocity for particle
motion;
6. Apply the power, sum, product, quotient and chain rules of differentiation;
7. Use the derivatives of exponential, logarithmic, trigonometric and
hyperbolic functions;
8. Explain implicit and logarithmic differentiation;
9. Apply the Intermediate and Mean Value Theorems;
10. Graphically analyze functions including using continuity and differentiation to
determine local and global extrema, concavity, and inflection points;
11. Use the derivative to solve related rate and optimization word problems;
12. Explain Newton's Method for estimating zeros of a functions; and
13. Explain the Riemann integral, areas under graphs, anti-derivatives and the
Fundamental Theorem of Calculus.
TEXT Hughes-Hallet, D. et al. (2009).
Calculus: Single variable (6th ed.). Danvers, MA: John Wiley and Sons, Inc.
GRADING 10% Webwork Homework
10% Written Homework
10% Projects
45% Mid-Semester Exams
25% Final
HOMEWORK I will collect two forms of homework in the course: internetdelivered homework problems using the system Webworks and traditional pencil
and paper homework. Several Webworks problems will be assigned after the
conclusion of each book section. They will be due at midnight following the
next class meeting time. I will drop your 3 lowest Webworks homework scores in
the calculation of your Webworks homework grade at the end of the semester.
Written homework from the previous week's lecture is due at the start of class
every Wednesday. I will not accept late homework for any reason. Homework
must be done in pencil on loose leaf paper and be neat and stapled. I will drop
your one lowest written homework score in the calculation of your written
homework grade at the end of the semester.
EXAMS Exam 1 - September 26: Sections 1.1-1.8, 2.1-2.6
Differentiation Skills Test - October 17: Sections: 3.1-3.7
Exam 2 - October 24: Sections 3.1-3.10
Exam 3 - November 21: Sections 4.1-4.4, 4.6-4.8, 5.1-5.4
Final - December 10: Cumulative
PROJECTS Over the course of the semester I will assign three projects that will
provide an opportunity for you to apply the knowledge that you have acquired in
the course to investigate real and tangible phenomena. These projects will be
announced in class.
DST Each student must pass the Differentiation Skills Test (DST) in order pass
the course. A score of 80% is required in order to pass the test. The test will be
offered for the first time in class on October 17. Each student is allowed to take
the test as many times as they wish, however, the test must be passed by
December 1 in order to pass the course.
CALCULATORS Calculators are a useful tool for mathematics, making
computations less tedious and aiding in exploration and the development of
sound mathematical intuition. It is recommended that you own a graphing
calculator. You are encouraged to bring it to class and use it however you like on
homework assignments. I will use a TI-84+ in classroom demonstrations. On the
other hand, overreliance on calculators often hinders the development of
reasoning, estimation, and mental mathematics skills. Furthermore, at this point
in your mathematics education, it is essential that you develop an intuitive
understanding of calculus based in sound reasoning. For these reasons
calculators will not be allowed on exams.
HONESTY All students must practice academic honesty. Academic misconduct
is subject to an academic penalty by the course instructor and/or a disciplinary
sanction by the University. All students need to be familiar with the Student
Conduct Code. The Code is available for review online at
http://life.umt.edu/vpsa/student_conduct.php
ACCOMMODATION The University of Montana assures equal access to
instruction through collaboration between students with disabilities, instructors
and Disability Services for Students (DSS). If you think that you may have a
disability adversely affecting you academic performance, and you have not
already registered with DSS, please contact DSS in Lommassen 154. I will work
with you and DSS to provide an appropriate accommodation.