Math 4010-20 is a two-semester sequence of required mathematics courses for elementary 
school teachers. The sequence is designed to help K-6 preservice teachers develop a conceptual 
framework for mathematics, especially for those aspects normally experienced in elementary school. 
Through their work in each course the students study the main themes of mathematics throughout the 
curriculum, considering both mathematical and pedagogical content issues in teaching mathematics. 
As the students develop their own understanding of the mathematics they will teach, they also 
increase their awareness of children's mathematical thinking and the various stages of growth in 
learning mathematical concepts. In each course, the students do a six-hour practicum in a local school 
relating their course work to the classroom situation. The first course, Math 4010, looks at the real 
number system from a mature perspective, focusing on the concepts of number and operation. The second
course, Math 4020, focuses on elementary geometry (two-thirds of the semester) and data analysis. The 
texts used in the courses are listed below. A more detailed description of the topics covered and the 
course emphasis is available here.
 
Note: This course sequence is designed for preservice elementary school teachers and requires time 
spent in the elementary school classroom. Students must complete the practicum (described below) in 
order to pass each of the courses in the sequence.

Texts: Mathematics for Elementary School Teachers: A Contemporary Approach, by Musser, Burger, 
and Peterson (7th edition); The Graph Paper Fractions Book and the Graph Paper Geometry Book, by 
Herb Clemens. 

Prerequisite: Math 1050 with a grade of C or better is the prerequisite for Math 4010; 
Math 4010 is a prerequisite for Math 4020.

Course Work and Grading: The Math 4010 and 4020 courses are each four semester credits and 
involve demanding work on the part of students both in class and in related field experiences. There's 
a lot of truth in the statement, "Knowing math for oneself isn't the same as  knowing math in order to teach". 
This difference can be illustrated with a simple example. College students generally know when a practical 
problem can be solved by finding a product and for them, calculating 48 x 23 is a simple task. But, 
teaching others when multiplication will provide an appropriate answer and how to find a product raises 
questions about what multiplication means and  why certain procedures for finding a product work. In a 
larger sense, a teacher needs to know how multiplication of whole numbers is related to that of fractions,
decimals, and algebraic expressions such as (a+b)(x+y) as well as the common misunderstandings that 
children may develop of these concepts. A teacher equipped with such a background can build on a child's
previous knowledge and experience, to guide the child's growth in mathematically appropriate directions.

In Math4010 and Math 4020 it is assumed that students can perform calculations through college algebra 
and have had basic school geometry. However, they  may not know why certain algorithms, or rules, work, 
why a geometric statement is true, or how to evaluate statistical information. As teachers, this type of
knowledge, conceptual understanding, is very important. Elementary school pupils begin their learning by
wanting to make sense of the world around them and of the ideas they encounter. To help students develop
mathematical understanding, teachers need to develop their own ability to make sense of mathematical 
concepts. "Making sense" of ideas lies at the heart of mathematics and this goal will be a primary focus
of class work in the Math 4010-20 sequence.

Prospective elementary school teachers need opportunities to relate their own course work to what 
happens in the elementary school. For this reason, in each course in the sequence, students spend a 
six-hour practicum in a local elementary school classroom. The first three hours of the practicum
are spent observing in the elementary school classroom and are the subject of homework assignments and 
class discussions. The second three hours are spent working on a topic in mathematics with a small group
of children from the classroom visited. A typewritten report analyzing this experience is due towards 
the end of the semester.

Grading in the course will be based on a combination of extensive homework assignments, in-class 
midterms, the practicum report, a portfolio of course work, and a comprehensive final exam.