Committee-This is a draft of the licensure document -  a rough first draft.
This is the only copy you will receive, so download and bring to our next
meeting. Please, feel free to edit, change, delete, spit on it, or
whatever.  It's a place for us to start.
 
Math Ed Committee-This is a rough draft of our statement concerning the
licensure issues.  We will discuss this at our next meeting, Wednesday,
April 2 at 4 pm.
 
 
This document contain two parts.  In the first, the rationale for our
recommendations is outlined and is based on the professional opinions of
the Mathematics Education Committee and two documents from the learned
mathematical societies:  The National Council of Teachers of Mathematics
(NCTM) Professional Standards for Teaching Mathematics (1991) and the
Mathematical Association of America's (MAA) A Call For Change:
Recommendations for the Mathematical Preparation of Teachers of Mathematics
(1991). The second part of this report outlines the specific course and
content requirements.
 
Part I - Rationale
 
A. 3-8 Age Group Both the MAA and NCTM recommend that teachers develop
competencies in the nature and use of number, patterns and functions,
geometry and measurement, and probability and statistics.  Both recommend
three years of college preparatory high school mathematics and at least
nine credits of college level mathematics in the listed areas.
 
Specific competencies for the courses listed in our recommendations were
drawn from those spelled out by the MAA and NCTM.  Major themes include:
exploration of mathematical properties as they relate to operations on
subsets of the real numbers;  the development of the notion of function;
utilization of problem solving strategies to discover mathematical ideas;
developing the understanding of geometric concepts and relationships to
describe the world in which we live; and developing methods to collect,
analyze, interpret and display data from theoretical and experimental
perspectives.
 
B. 8-14 Group: Math Concentration Both groups recommend that teachers
develop competencies in number concepts and relationships, geometry and
measurement, algebra and algebraic structures, probability and statistics,
and concepts of calculus.  Both recommend four years of college preparatory
high school mathematics and at least 15 credits of college level
mathematics.
 
These groups also point out that teachers at this level need a breadth and
depth of experiences which go considerably beyond the preparation of
elementary teachers, but which are quite different from that expected at
the secondary level.  Major themes include: exploration of fundamental
properties of number systems; conjectures and intuitive proofs of number
theory; functions; infinity and limits; differentiation and integration;
exploration of algebraic structures such as groups, rings, and fields;
formulating convincing arguments based on data analyses; inferential
decision making; and analyzing incorrect use of statistics.  The courses in
our recommendations include all of these competencies.
 
C. 8-14 Group:  NON Concentration  The Mathematics Education Committee is
recommending that for those 8-14 teachers who are not concentrating in
mathematics, that a basic 9 hour sequence of courses in mathematics be
required (same mathematics courses as 3-8 group, but no methods
requirement).  Our reasons for this are threefold.  First, while it appears
that the State's intended long term goal is to have teachers teach only in
their concentration area, it is currently not clear that this will actually
happen, at least in the near term.  Since it seems there is a fairly high
probability that non-concentration teachers may teach mathematics at this
level, we feel it is important that they have mastered at least the
competency levels in mathematics required of teachers at the 3-8 age group
level. Without such a requirement, it is possible to have teachers teaching
at this age level with NO mathematics beyond the two years required of high
school graduation in Ohio.  Second, the recommendations of the learned
societies for mathematics requirements of teachers at this level are
specified for ALL teachers, not just those concentrating in mathematics.
Finally, there is much discussion in the state and in the nation about
teaching subject matter from an integrated approach (NCTM also recommends
this.)  In order to do this, even non mathematics concentration teachers
must have a basic and fundamental understanding of the key competencies in
mathematics.
 
 
 
 
Part II - Course and Content Recommendations
 
AGE 3-8
Basic instructional methodology:  Courses generally taught utilizing a
variety of "hands-on" inquiry/discovery-based explorations that students
complete in a group setting.
 
Prerequisite:  Three years of high school mathematics.
 
        MTH 115 (4 credits) - Mathematics for Elementary Teachers:
Structure of                 Arithmetic
number systems and number sense, including mental mathematics,
estimation, and reasonableness of results;
use of number concepts, operations, and properties;
basic number theory;
place value;
underlying structure of arithmetic (properties) and their application to
subsets of the real number system;
utilization of a variety of problem solving strategies in making sense out
of   mathematics;
use of technology in mathematics;
properties of algebra;
idea of function.
 
        MTH 116 (3 credits) - Mathematics for Elementary Teachers: Geometry
informal, intuitive and formal ideas of size and shape;
analysis of two and three dimensional figures, including the study of
tessellations, symmetry, polygons, polyhedra, and curved shapes;
synthetic, coordinate, and transformational geometry as a basis for solving
geometric problems;
spatial visualization;
 
attributes of measurement: length, area, volume, capacity, time, angles,
weight and associated units;
standard and non-standard units to estimate areas, lengths, volume, etc.
development of formulas for perimeter, area, and volume of common two   and
three dimensional shapes;
indirect measurement;
use of technology in teaching and learning geometry.
 
        STAT xyz (2 credits) - Probability and Statistics for Elementary
School Teachers
collection, organization, representation, analysis and interpretation of
data;
measurement of central tendency, variation (range, standard deviation,
interquartile range, outliers) and general distributions;
probability of simple and compound events, both simulated and theoretical;
probability trees.
 
EDT pqr (3 credits) - Methods for Teaching Elementary School Mathematics
 
NOTE: We need to discuss what to list here.
Comment:  Course includes field experience.
 
AGES 8-14 (for students NOT selecting mathematics as a concentration)
 
same requirements as AGES 3-8 without the EDT pqr methods requirement.
 
AGES 8-14:  Mathematics Concentration
 
        prerequisite:  Four years of high school mathematics.
 
        MTH 117 (3 credits) - Mathematics for Elementary Teachers:
Structure of        Arithmetic
course content and methodology same as MTH 115
 
        MTH 218 (3 credits) - Geometry for Middle School Teachers
includes topics from MTH 116, but developed from inductive and deductive
approaches;
emphasis on topological properties;
introduction of non-Euclidean concepts.
 
        MTH 141 (4 credits) - Calculus for Elementary School Teachers
NOTE:  Course approaches the development of the fundamental ideas of
calculus from algebraic, numeric, and graphic perspectives.
 
review of basic categories of functions;
development of the idea of a derivative as rate of change;
idea of limit;
development of the integral as total change, average value, and "area";
computational formulas of derivative and integral;
Fundamental Theorem of Calculus.
 
        MTH 231 (3 credits) - Elements of Discrete Mathematics
systems of linear equations;
matrix algebra, determinants;
digraphs, networks, Boolean expressions;
propositional calculus.
 
        MTH 407 (3 credits) - Patterns and Structures in Mathematics
NOTE: Course is designed to model inquiry/discovery teaching and learning
for students and to examine a variety of areas of mathematical content.
 
structural properties of a variety of systems, including non-numerical
sets; development of ideas of groups and rings; proof of basic  results;
exploration of decimal representation of rationals and categorization of
types of repeating decimals;
exploration of patterns and relationships in integral and differential
calculus;
exploration of patterns in geometric-based problems.
 
        STAT 368 (4 credits) - Introduction to Statistics
probability, random variables;
binomial and normal probability distributions;
sampling distributions;
statistical inference;
linear regression;
data analysis methods, including analysis of variance.
 
        EDT pqr (4 credits; including field experience) - Methods for
Teaching Middle   School Mathematics