About MATH 3242
For Students in this Course
MATH 3242 is one of three
mathematics courses designed to prepare you to teach mathematics to students in
grades PreK-5. This course focuses on
geometry concepts whereas MATH 3241 focuses on number sense, and the focus of
MATH 4260 is data analysis, probability, and statistics.
Research conducted by
numerous groups and commissions indicate that the old ways of teaching and
learning mathematics are not preparing students to meet the demands of our
technological society. The National Council of Teachers of Mathematics (NCTM)
has extensively studied how to teach mathematics better in grades PreK-12 and
has produced the document Principles
and Standards for School Mathematics (PSSM) with recommendations for this
purpose. The Conference Board of the
Mathematical Sciences (CBMS) produced a report The Mathematical Education
of Teachers with recommendations for preservice
mathematics education. It is the advice
of these groups and others that for teachers to teach in ways recommended by
current research, they need a far deeper understanding of the mathematics they
will teach than has been common in the past. The new Georgia Performance Standards for
Mathematics were written to align with the recommendations
from NCTM.
Therefore, the goal of this
course is to help you as a future elementary school teacher to develop a deeper
understanding of the concepts of geometry. The emphasis will be on reasoning
and problem solving rather than on memorizing a rigid set of rules. In this way, it is hoped that you will gain a
sense of mathematics as a dynamic intellectual enterprise as opposed to a static
list of rules and formulas. Keep in mind
that the material taught in this course will go beyond that which is normally
taught in elementary school. This is by
design and supported by Judith Sowder and her colleagues
at the Center for Research in Mathematics and Science Education at
MATH 3242 will be taught in a
way to prepare you to teach geometry in grades K-5 as recommended by NCTM, CBMS,
and the Georgia Department of Education.
However, the purpose of this course is to provide you with mathematics
content, not the teaching methodologies that may or may not accompany the presentation
of such material to elementary students. While we will undoubtedly discuss such things
from time to time, the focus of the course is on developing your mathematical
understanding of geometry and not on pedagogy.
You will examine in depth geometry concepts that are taught in the
elementary school. Understanding and
explaining “why does it work this way?” or “why can’t it work this way?” will
be a common theme as these concepts are investigated. Certainly you already know some geometry
concepts at a certain level, but in order to be a knowledgeable teacher, you
must learn to think about and explain the concepts in a new and deeper
way. Please don’t underestimate the
importance of developing this new and deeper understanding. It is hard work to develop this understanding
so you are asked to be patient with yourself, with your classmates, and with
me. Please do not get discouraged but
instead continue your efforts to develop a deep understanding—it will pay off.
In order to achieve this
depth of understanding and to succeed in the course, you will need to engage
yourself in the material and take responsibility for your own learning. Don’t hesitate to ask questions, but don’t be
offended if you are asked to continue thinking with a hint or a question. Be willing to try out ideas and to modify
them if necessary. Learning for true
depth of understanding requires that you be very active in seeking this
understanding. Deep conceptual
understanding cannot be achieved by passive absorption of the material. Be willing to make mistakes but to learn from
your mistakes. Be willing to confront your
misconceptions. Be willing to learn from
others. Don’t give up when answers don’t
immediately come to you.
The course will challenge you
to think differently about what it means to teach and to learn
mathematics. You will probably be
uncomfortable at times. You will
probably be frustrated at times. You
will probably wonder why we “aren’t doing math like we’ve always done it.” However, please remember the goal of the
course is to allow you to develop a deep understanding so that you will be
prepared to teach mathematics as envisioned by NCTM and CBMS. I ask for you to be open to new ideas and to
keep your eyes on this goal.
But are you wondering why you are taking a course to
teach geometry in elementary school? If
so, read on……
Through the study of geometry, students will learn about geometric shapes and structures and how to analyze their characteristics and relationships. Spatial visualization—building and manipulating mental representations of two- and three-dimensional objects and perceiving an object from different perspectives—is an important aspect of geometric thinking…. Geometry is more than definitions; it is about describing relationships and reasoning.
Principles and Standards for School Mathematics (NCTM, 2000)
One important reason to study geometry is that it promotes the ability to visualize and mentally manipulate objects in space. This is a necessary skill for a number of professions. For example, a surgeon or dentist must be able to visualize the steps in and outcomes of an operation, a carpenter must be able to see different designs in his or her mind’s eye, an architect must be able to visualize many different possibilities for a building that satisfies certain design criteria, a clothes designer must be able to visualize how pieces of fabric will fit together to make a garment.
According to the report “What Work Requires of Schools” of the U.S. Department of Labor, being able to “see things in the mind’s eye” is a foundational skill for solid job performance. In order to be able to foster this in your students, you must first foster it in yourself.
Mathematics for Elementary Teachers (2005) by Dr. Sybilla Beckmann