Welcome to Math for Teachers!

NOTE: This is the syllabus for a PREVIOUS VERSION of the course. See nilesjohnson.net/teaching.html for current courses.

This is the course homepage and syllabus for Math 2137, Algebra and Coordinate Geometry 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 https://www.nilesjohnson.net/teaching/SP19/2137.html.

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This boy is using geometry to understand algebra and algebra to understand geometry.

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 integrates the various types of numbers introduced in the previous course to present them as members of a single (real) number system. The notion that new numbers are discovered as solutions to equations is promoted, and motivated by connecting various equations with mathematical models.

Matrices are introduced and used as linear transformations, mainly in the plane. The complex numbers are introduced as general solutions to quadratic equations and the relationship between complex arithmetic and transformations in the plane is explored.

The course finishes with several weeks of geometry content for middle grade teachers, including more material on proofs, triangle congruence, and non-Euclidean geometry. The main example is "Taxicab geometry", based on the ell_1 norm.


  • Polynomial arithmetic as “base-x” and binomial theorem
  • Real number system
  • Polynomial equations and their roots
  • Exponential and logarithm functions
  • Complex numbers
  • Matrices
  • Complex arithmetic and linear transformations in the plane
  • Geometry proofs
  • Taxicab geometry

Learning Goals

  • Understand polynomial arithmetic from the perspective of place value.
  • Unified perspective on the real number system, including situations modeled by different numbers, and numbers as solutions to equations.
  • Familiarity with complex numbers and matrices from algebraic and geometric points of view.
  • Awareness of non-Eulidean geometries and the importance of the parallel postulate.
  • Ability to create and evaluate geometric proofs.
  • Identify major historical developments in algebra and number systems including contributions of significant figures and diverse cultures.

Section Information

Class meets at the following place and times following the OSU Registrar's academic calendar:

Adena 130
Mondays, Wednesdays 2:20—3:40

Course Calendar

Our class will generally follow this calendar of topics; this may be adjusted as the course goes on.

Course Notes

Here is a page listing the course notes!

Homework Assignments

Our homework is available on the homework page.

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Basic information


Niles Johnson
Office: LeFevre 288
Office Hours: Mondays and Wednesdays 10:30 – 12:00; other days/times by appointment


Basic Mathematics by Serge Lang. ISBN-13 978-0387967875.

The style of this book is different from typical math textbooks, and is much closer to the way mathematicians communicate with eachother. Lang invites the student to experience and learn mathematics at a level which is deep, but not complex. Our focus will be Parts III and IV, but it is illuminating to compare the first two parts with Beckmann's text.

Additional Texts:

Bart Snapp has developed free texts for middle grade teachers, and they can be a helpful supplement to Lang.

Exam Schedule

We will have two in-class midterms and a final exam. All students must take the exams at the scheduled times indicated here.

Midterms (2):

  • Monday, February 11
  • Monday, April 01


Scheduled by the registrar. See campus schedule for exam times.


Your final grade will be based on written homework, written and oral in-class participation, quizzes, midterms, and a final exam. The precise breakdown is as follows:

  • In-class participation: 20%
  • Homework: 20%
  • Midterm exams: 20% each, for a total of 40%
  • Final exam: 20%


Active participation in class is an essential part of this course, and so attendance every day is required. Please let Niles know as soon as possible if an illness or other commitment will prevent you from attending. We will answer questions about homework at the beginning of class, and you can upload your homework after class on the day it's due.


Thoughout this semester we will be focused on the how and why of elementary mathematics. This means that you will be responsible both for knowing the content and for knowing how to explain the content. We will practice this in a variety of ways, and much of this practice will take place in class.

Teaching mathematics requires listening carefully to students, assessing their ideas, and responding in ways that make sense. Our class participation is designed to practice these essential skills. You will have opportunities on a daily basis to listen to your fellow classmates explain ideas and ask questions. You will be asked to respond with your ideas and with additional questions. Together we will see how and why mathematics works! Participating in this course includes all of the following:

  • Show interest in mathematical ideas.
  • Show interest in different ways of approaching mathematical ideas.
  • Listen carefully to different ways of solving a problem.
  • Carefully evaluate a proposed method of solution.
  • State whether you agree or (respectfully) disagree with a statement.
  • Show interest in learning with and from others.

Late Work Policy

If you must miss class on the date of a quiz or exam, please do the following:

  • Contact me before the time of the assessment to let me know you will be away.
  • Provide a reason and objective documentation (e.g., a note from your health care provider).
  • Make up the assessment within two days of your return to campus, and before the next class if possible.
  • Miss no more than two assessments this way.

If you do each of the items above, you will have no penalty. For each item that you do not complete there will be a 10% reduction in your final score.

Exceptions may be made in the case of an emergency; please contact me as soon as you are able.

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Resources related to mathematics education

Websites on math standards

Websites of elementary school texts from high performing countries

Other websites of interest

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:


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 https://newark.osu.edu/students/support-services.html.

Accommodation Statement

The University strives to make all learning experiences as accessible as possible. If you anticipate or experience academic barriers based on your disability (including mental health, chronic or temporary medical conditions), please let me know immediately so that we can privately discuss options.

Any student who needs accommodations due to any type of disability must first register with Student Life Disability Services (SL-DS). Please call Student Life at 740-364-9578 or stop by Warner Center 226 to discuss procedures for getting accommodations. After accommodations are authorized, you will receive an Access Letter to share with your professors to help with the conversation about your needs. You do not need to disclose your disability to faculty.

Although accommodations may be authorized any time in a term, it is in your best interest to disclose your needs during the first week of class.



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 https://studentlife.osu.edu/csc/

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