Welcome to Math for Elementary Teachers!

[picture of Niles]

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 1125, Mathematics for Elementary Teachers I. 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/AU13/1125.html.

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Excellent math teachers have been far too scarce in American education. This course and its sequel, Math 1126, 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!

Section Information

Math 1125 focuses on concepts of number systems and operations, including some algebra and number theory. During Autumn 2013, we have two sections of Math 1125; these are numbered 2703 and 2704. The syllabus and content for the courses will be the same, but the class meeting times are slightly different. To distinguish them, each section also has a codename after one of the standard web colors.

Both sections meet in Hopewell 106, following the OSU Registrar's academic calendar.

Section 2703 (SeaGreen)

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

Section 2704 (OrangeRed)

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

Fun Topics

Click here for some short descriptions of fun topics related to our class.

Homework Assignments(+)

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

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 bring a printed copy to class!

Homework 21 due Monday, 11/25

Problems: 8.4.5, 8.6.13, 9.1.3, 9.1.5
Additional problem: Explain why the square-root of 6 must be irrational. (Note: this will require a new lemma, but the idea is similar to the one we used in class.)

Homework 20 due Wednesday, 11/20

Problems: 8.4.4, 8.5.8, 8.5.9, 8.5.17, 8.6.4, 8.6.5
Additional problem: Explain the relationship between the numbers in each row of the table in Activity 8N in terms of how the Spirograph flowers are constructed. Use this to complete the table. (Hint: the column named "petal connects every __th dot" could also be named "number of dots per petal".)

Homework 19 due Wednesday, 11/13

Problems: 7.2.10, 7.2.14, 7.3.4, 7.3.7, 8.1.2, 8.1.6, 8.3.9

Homework 18 due Wednesday, 11/6

Problems: 7.1.3, 7.1.8, 7.1.9, 7.2.2, 7.2.12
For 7.1.3, also graph the distances and times in a coordinate plane.

Homework 17 (do not turn in)

Write solutions for problems on the review sheet.

Homework 15 and 16 due Friday, 10/25

Problems: 6.1.8, 6.2.3, 6.2.7, 6.3.5, 6.3.9, 6.3.17

Writing assignment due Thursday, 10/17 and Saturday, 10/26

See the description of this assignment in our Carmen discussion board.

Homework 14 due Friday, 10/18

Problems: 5.1.1, 5.1.16, 5.2.6, 5.2.10, 5.3.1, 5.4.6, 5.4.7
Modify 5.4.7 to find (888 x 123456123456)

Homework 13 due Friday, 10/11

Turn in solutions to problems on the review sheet.

Homework 12 due Monday, 10/7

Read section 5.1 and write solutions to activity 5C.

Homework 12 due Monday, 10/7

Read section 5.1 and write solutions to activity 5C.

Homework 11 due Friday, 10/4

Problems (turn in): 4.6.4, 4.6.5, 4.6.12
Additional: Give a multiplication algorithm for base-four place value, and work a couple of two and three digit examples.

Homework 10 due Monday, 9/30

Problems (turn in): 4.3.17, 4.4.16, 4.4.18, 4.5.5

Homework 9 due Friday, 9/27

Problems (turn in): 4.3.6, 4.3.10, 4.3.14
Additional 1: Draw chip model diagrams to show 3 + (-8) and 3 - 8.
Additional 2: Represent the following numbers in base ten and base four: three; thirty; three hundred; twelve; fourty eight; one hundred ninety two.

Homework 8 due Monday, 9/23

Practice Exercises (do not turn in): 3.5.3, 4.2.1
Problems (turn in): 3.4.4, 3.5.4, 4.2.1, 4.2.2

Homework 7 due Friday, 9/20

Practice Exercises (do not turn in): 3.3.6, 3.4.10
Problems (turn in): 3.3.11, 3.3.12, 3.4.10, 3.4.26

Homework 6 due Monday, 9/16

Practice Exercises (do not turn in): 3.2.7, 3.2.11, 3.3.6
Problems (turn in): 3.2.8, 3.2.10, 3.3.5

Writing assignment due Monday, 9/16

Contribute to our Carmen discussion forum on the history of zero.

Homework 5 due Friday, 9/13

Practice Exercises: 3.2.8, 3.2.12, 3.3.6
Problems: 2.4.3, 3.1.5, 3.2.3, 3.2.11

Homework 4 due Monday, 9/9

Practice Exercises (do not turn in): 2.3.8, 2.3.9, 2.4.2
Problems (turn in): 2.4.11, 2.3.18, 2.5.13, 3.1.1

Homework 3 due Wednesday, 9/4

Practice Exercises (do not turn in): 1.4.1, 2.2.1, 2.2.6, 2.3.1
Problems (turn in): 2.2.10, 2.2.18, 2.3.1

Homework 2 due Wednesday 8/28

Problems 1.2.5, 1.2.7, 1.3.3, 1.3.11

Homework 1 due Monday 8/26

Practice Exercise 1.1.4
Problems 1.1.1, 1.1.2, 1.1.7, 1.2.1
Additional Problem: Alice was born August 1, 2000, and her cousin Bob is fifteen years older. Write Alice and Bob's ages using base 4 and the digits 0, A, B, C.

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Basic information


Niles Johnson
Office: Hopewell 189
Office Hours: Mondays and Wednesdays 10:00 – 11:30; Thursdays 3:00 – 4:30.


Mathematics for Elementary Teachers with Activities, 4th Edition by Sybilla Beckmann. ISBN 0-321-82572-1. The 4th edition (Monkeys on the cover) is substantially improved over earlier editions. Moreover, it is available in electronic or loose-leaf formats which are cheaper and more portable than the bound version.

Exam Schedule

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


Fridays in class; September 13, October 11, November 1.


To be determined. Check the campus schedule for exam times.


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. Homework is due at the beginning of each class, and late homework cannot be accepted unless prior arrangements have been made.

Math Learning Center

The Math Learning Center (Warner 214) is a great resource, and I encourage you make use of it. The staff there has experience with our course and would love to help you!

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.

Assessment (+)

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: 12%
  • Homework: 5%
  • Writing Assignments: 4%
  • Quizzes: 14%
  • Midterm exams: 15% each, for a total of 45%
  • Final exam: 20%

The two lowest quiz and homework grades will be dropped. If your final exam score is higher than one of your midterms, then that grade will replace the lowest midterm grade.


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.

Homework and Quizzes

Homework and Quizzes will be scored using the rubric below. Scores are based both on mathematical correctness and quality of explanations. Homework should be typed and presented as you would an essay. If necessary, you may draw diagrams by hand on separate pages. Quizzes will be hand-written during the first 10 or 15 minutes of class.

The homework 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 (scores of 3 and higher are complete). The numerical scores are given only for your information.

The weekly quizzes are opportunities to evaluate your current grasp of the material. They will be very short and based on previous homework problems or class activities. Quiz grades will be recored as scored.

Grading Rubric

The descriptions on the rubric below are meant as a guide to help answer the question What constitutes a good explanation of mathematics? This is a subtle and challenging question—one that is worthy of considerable time and energy. As you write your explanations, consider the distinction between Procedure and Conceptual Meaning. A complete explanation addresses both of these, but the conceptual meaning is essential. Explanations that address procedure only are a disservice to students and do not support their future learning. They are also much less interesting!

Quizzes and exams will follow this scale; Niles will use these for comments on homework too, although homework grades are recorded on a complete/incomplete basis. Homework will be considered complete if the average score is 3 or higher.

Excellent work that exceeds the assignment guidelines.
Very good
Correct procedure with an explanation that effectively addresses relevant definitions and concepts.
Correct procedure with nearly complete explanation.
Minor procedural errors with a well-developed but incomplete explanation.
Minor procedural errors with emerging explanation that shows understanding.
Minor procedural errors with explanation that mentions core definitions or conceptual meaning relevant to the question.
Work that has merit but also has significant shortcomings in the procedure and/or explanation.
Work that shows relevant effort but is seriously flawed.
No credit.
No work submitted, or no relevant effort shown.
[number elves 6-0]

Websites on math standards

Websites of elementary school texts from high performing countries

Other websites of interest

  • Project INTERMATH, which focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology.
  • Problems and tasks that Sybilla Beckmann wrote for her 6th graders during the 2004/2005 school year organized according to the grade 6 Georgia Performance Standards.
  • 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:


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.

Disability Statement

Students with disabilities that have been certified by the Office for Disability Services will be appropriately accommodated, and should inform the instructor as soon as possible of their needs. The Office for Disability Services is located in 150 Pomerene Hall, 1760 Neil Avenue; telephone (614) 292-3307 and VRS (614) 429-1334; webpage http://www.ods.ohio-state.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. For additional information, see the Code of Student Conduct:

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