M4010-20: Mathematics for Elementary School Teachers I, II

*"What is best in mathematics deserves not merely to be
learned as a
task but to be assimilated as a part of daily
thought, and brought again and again before the mind with ever-renewed
encouragement. " *

Bertrand Russell, Mathematician and Philosopher

*"I touch the future, I teach." *

Christa McAuliffe, Mathematics Teacher

**Course Description: ** 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 M4010 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.