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 1135, Number and Operations 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/AU18/1135.html.

[children writing numbers]

These students are using place value and the meaning of addition to understand multi-digit arithmetic.

Excellent math teachers have been far too scarce in American education. This course and its sequel, Math 1136, give you the keys to how and why elementary mathematics works. We will develop a thorough understanding of the ideas, how they are related to eachother, and how they are related to more advanced ideas. This is the basic knowledge which underpins truly great teaching!

Course Objectives

This course covers the concepts of whole numbers (positive and negative), place value (base-ten and alternate bases), decimals, and fractions. Some content on irrational numbers appears at the end, and this is extended in Algebra and coordinate geometry for teachers (2137). The four arithmetic operations are covered both conceptually and algorithmically. Attention is given to ensuring that students can perform the algorithms correctly and explain why they give accurate answers. Lastly, the course covers the concepts of proportions and how they are related both to multiplication/division and to fractions. Factors, divisibility, and some elementary number theory complete the course.


  • Counting numbers, decimals
  • Meaning of fractions
  • Meaning of addition and subtraction
  • Meaning of multiplication
  • Multiplying fractions, decimals, integers
  • Meaning of division
  • Dividing fractions, decimals, integers
  • Meaning of ratios, rates, proportions
  • Greatest common divisor, least common multiple
  • Rational and irrational numbers

Learning Goals

  • Conceptual understanding of positive and negative whole numbers and the meaning of fractions.
  • Fluency in multi-digit arithmetic for whole numbers using both elementary reasoning and standard algorithms.
  • Fluency in arithmetic with fractions and decimals using both elementary reasoning and standard algorithms.
  • Understand and solve proportion problems using both elementary reasoning and fraction arithmetic.
  • Familiarity with the concepts of divisibility, multiples, and their applications.
  • Identify major historical developments in number and operation, including contributions of significant figures and diverse cultures.

Section Information

During Autumn 2018 we have two sections of Math 1135; these are numbered 14921 and 14922. The syllabus and content for the sections will be the same but the class meeting times and locations are different (see below). Classes meet following the OSU Registrar's academic calendar.

Section 14921

LeFevre 164
Mondays, Wednesdays 12:45 – 2:05
and Fridays 12:45 – 2:50.

Section 14922

Hopewell 114
Mondays, Wednesdays 3:55—5:15
and Fridays 3:05 – 5:10.

Course Calendars

An approximate outline, updated regularly, is available on our course calendar.

Homework Assignments

Assignment information will be posted here as the semester unfolds. A number such as 1.3.6 refers to problem or practice exercise 6 at the end of section 1.3.

You only need to turn in the Problems; the Practice Exercises are suggestions for your study, and may be discussed in class. Remember to type your homework and upload it to Carmen!

Our homework is listed below or available on a separate homework page.

[number elves 1-5]

Basic information


Niles Johnson


LeFevre 288

Office Hours

  • Mondays and Wednesdays 2:15 – 3:45
  • Other days/times by appointment


Mathematics for Elementary Teachers with Activities, 5th Edition by Sybilla Beckmann. ISBN-13 9780134392790 (bound) or 9780134800196 (loose leaf, recommended). The 5th edition (peacock on the cover) and 4th edition (monkeys on the cover) are reasonably similar, so either one will be sufficient for this class.

We will use the activities every day in class. Most students prefer the loose-leaf format so that they can bring only the part they need with them; I recommend it. Note that this class and its sequel, Math 1136, will both use this text, so it is worthwhile to purchase instead of rent.


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.

Calculators and Mathematical Software

There are a variety of modern tools which support mathematics learning and application. We'll use several of them in this course, but no technology will be used on the quizzes or exams. In particular, calculators and cell phones will not be permitted. The only materials you'll need are writing instruments and your mind.

Exam Schedule

We will have six in-class exams and a final exam; exam dates are given below. Please notify Niles immediately if you cannot be present for one of the exams.

Midterm Exams

  • Wednesday, September 05
  • Wednesday, September 19
  • Wednesday, October 03
  • Wednesday, October 17
  • Wednesday, October 31
  • Wednesday, November 14

Final Exam

Scheduled by the registrar. See the 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: 13%
  • Homework: 10%
  • Quizzes: 15%
  • Midterm exams: 42%
  • Final exam: 20%


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.


The homework in this class is intended to give you time to develop your explanations and understanding of the content. You are encouraged to work with your classmates on this, but you must write your own explanations. Homework is designed to help you learn, and not as an assessment tool. Therefore grades for homework will be recorded on a complete/incomplete basis.

Homework should be typed, with explanations using complete sentences, as you would an essay. Homework is turned in by uploading it to Carmen -- please let Niles know if you have any trouble with this. If necessary, you may draw diagrams by hand on separate pages and upload a picture or scan.


We will have short in-class quizzes each Friday. These will usually be just one or two questions, and they give you a chance to evaluate your current grasp of the material. The quiz questions are based on previous homework problems or class activities. Quizzes are scored on a 10-point scale.

It is generally not possible to make up quizzes if you miss one. Instead, the lowest two quiz scores will be dropped at the end of the term. For students with extended illness or other recurring conflicts, exceptions may be made on a case by case basis -- contact Niles to discuss your situation.

[number elves 6-0]

Resources related to mathematics education

Websites on math standards

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

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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