Math 135: Algebraic Reasoning for Teaching Mathematics
(Instructor: Steffen Lempp)


The Brookhill Foundation now supports Math 135 students as well as students taking the math/science minor for elementary and special education majors by a scholarship!


Handout stating class policies



Homework will be assigned on Wednesdays at the beginning of lecture and due the following Wednesday at the beginning of class.

There will be no credit for late homework except in case of illness or family emergency.


Each project requires a group of two students to compare how the topic is introduced in one of our Singapore math schoolbooks and one American math schoolbook of your choice. Each student should pick a partner and a joint topic. (Pick an American schoolbook of your choice from CIMC, e.g., the one you yourself used in your own school, or one that is currently used in a school you are familiar with. The more different that book is from our Singapore math schoolbooks, the more interesting the project will be.)

The comparison I am looking for is how the mathematical concepts are introduced. I'm not necessarily looking for a value judgment from you, which one you like better, but mainly for an investigation of how the presentation of the topic differs from a mathematical point of view. E.g., is the concept defined differently? Are the examples by which it is introduced very different? Etc.?

Your project will consist of a short (joint) paper (of 2-3 pages), with copies of the relevant "other" schoolbook pages attached, and a short presentation (10-15 minutes) in class about this comparison of topics. You can use an overhead projector or copied handouts if you prefer. (I'll help you get an overhead projector if you need one.) Presentations will start in mid-April. I suggest that each group meet with me briefly a few days before your presentation for feedback.

Here is a list of possible topics (with reference to treatment in my Lecture Notes):

  1. How are the properties of arithmetic (commutative law, etc.) first presented? (Cf. Proposition 1.2. Presentation by NC and KH on April 29.)
  2. How is the slope of a line defined? (How is it motivated that one can define the slope as one single number? (Cf. section 2.4. Presentation by CM and JR on May 2.)
  3. How is solving two linear equations in two unknowns presented? (Cf. section 2.5. Presnetation by SS and KVD on May 4.)


For copyright reasons, the links below are password protected. Please get your user name and password from me by">email if you have forgotten it. Use of these links will be monitored, and unauthorized use is prohibited.


Makeup exams will be scheduled only with the instructor's consent, and only in case of illness or family emergency or conflict with another required class. In the latter case, please let me know as soon as possible!
Calculators of any kind are discouraged for any part of this course and will not be allowed during exams.



This course is the first of three courses of the math component of the Mathematics-Science Dual Minor for all Elementary Education and Special Education majors wishing to enhance their content preparation in mathematics and science. This minor is particularly suitable for those Elementary Education majors seeking Middle Childhood-Early Adolescence certification and intending to teach mathematics and science in middle school.

The other two math courses for this minor, Math 136 and Math 138, will focus on precalculus and early calculus; and on probability, statistics and combinatorics, respectively.

Note that in spring semester 2011 only, Math 135 can also be taken in place of Math 132 by students already admitted into the Elementary Education or Special Education program.

Math 135 focuses on the mathematical content needed to teach pre-algebra and algebra in upper-level elementary and middle school.

The core instructional goals of Math 135 are:

The mathematical content topics of Math 135 include:
Prepared by Steffen Lempp (">