This is the course homepage and syllabus for our independent study in, Calculus and its history for Teachers. Here you will find our course calendar, current assignments, basic course information, and links to additional content of interest. This syllabus may need to be updated as the course progresses, and you will always find the current version at http://www.nilesjohnson.net/teaching/SP18/1193.html.

The topics of middle-grade math bring adventure and excitement! Together, Math 2137 and 2138 will hone your skills of mathematical explanation and explore the profound relationships between algebra and geometry.

Course Objectives

This course serves to introduce students to the key ideas of calculus and to important historical developments in the subject. A thorough introduction to functions as mappings is given, and the trigonometric functions are used throughout the course as a key example of functions not given by algebraic expressions.

The essential concepts of limit, derivative, integral, and the fundamental theorem are emphasized, together with core applications. An introduction to Taylor series, especially the Taylor expansions for sine and cosine, completes the class.

Topics

• Functions
• The derivative as rate of change
• The derivative as slope of tangent line
• Higher order derivatives
• Sine and cosine
• Basic differentiation techniques
• Applications of the derivative
• Riemann sums and area
• Definite integrals as area
• Indefinite integrals as antiderivatives
• The fundamental theorem of calculus
• Applications of integration
• Taylor approximations
• Infinite series

Learning Goals

• Understand the concept of function as a mapping from domain to range.
• Understand derivative as instantaneous rate of change and integral as total accumulation.
• Understand the conceptual and computational significance of the fundamental theorem of calculus.
• Fluency in basic computation of derivatives and integrals, including basic applications.
• Familiarity with Taylor approximations and series.
• Identify major historical developments in calculus, including contributions of significant figures and diverse cultures.

Basic information

Instructor

Niles Johnson
Office: Hopewell 184

Textbook

Calculus by Frank Morgan. ISBN-13 978-1478356882.

(From the preface) Many students and faculty spend a lot of time wading through fat calculus books. This lean text covers single-variable calculus in 300 pages by

1. getting right to the point, and stopping there,
2. introducing some standard preliminary topics, such as trigonometry and limits, by using them in the calculus.

As an additional resource, check out mooculus.osu.edu for online text, video, and exercises!

Recommended Problems from Morgan

Resources related to mathematics education

Websites on math standards

• Ohio Department of Education Standards in Math and Model Curricula.
• National Common Core State Standards in English and Math: Adopted by 43 states (and counting), including Ohio.
• National Council of Teachers of Mathematics Standards and Focal Points.

Websites of elementary school texts from high performing countries

• Textbooks used in Singapore: singaporemath.com Primary Mathematics 1A, 1B (first grade) through 6A, 6B (sixth grade)
• Translations of textbooks used in Japan: http://www.globaledresources.com/ (Tokyo Shoseki’s Mathematics for Elementary School)

Other websites of interest

• Project INTERMATH, which focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology.
• Purplemath has lessons and practice problems for elementary mathematics.
• Khan Academy has math videos for children and resources for parents or teachers.
• Report by the National Council on Teacher Quality on mathematics in the U.S.: No Common Denominator. The report includes a great appendix on content that mathematics teachers must know, and ranks Beckmann’s textbook highest overall among elementary mathematics content textbooks.

GEC Information

This Mathematics course can be used, depending on your degree program, to satisfy the Quantitative and Logical Skills category of the General Education Requirement (GEC). The goals and learning objectives for this category are:

Goals:

Courses in quantitative and logical skills develop logical reasoning, including the ability to identify valid arguments, use mathematical models and draw conclusions based on quantitative data.

Learning objectives:

Students comprehend mathematical concepts and methods adequate to construct valid arguments and understand inductive and deductive reasoning, scientific inference and general problem solving.

Support Services

All students are encouraged to take advantage of campus support services. These include tutoring, academic advising, counseling, and the math learning center! A complete list is available at http://newark.osu.edu/students/support-services.html.

Accommodation Statement

If you need accommodations due to a disability, you must first register with the Office for Disability Services (ODS) at 226 Warner Center, ext. 441. After you receive your authorized accommodation from ODS, you should show me your access plan and discuss your needs with me. Ideally, we should meet within the first week of class.

http://newark.osu.edu/students/student-life/disability-services.html

http://slds.osu.edu/

Academic Misconduct Statement

It is the responsibility of the Committee on Academic Misconduct to investigate or establish procedures for the investigation of all reported cases of student academic misconduct. The term "academic misconduct" includes all forms of student academic misconduct wherever committed; illustrated by, but not limited to, cases of plagiarism and dishonest practices in connection with examinations. Instructors shall report all instances of alleged academic misconduct to the committee (Faculty Rule 3335-5-48.7). For additional information, see the Code of Student Conduct at http://studentlife.osu.edu/csc/