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Licensure
in Mathematics
"…to
be possessed of a vigorous mind is not enough; the prime requisite
is rightly to apply it. The greatest minds, as they are capable
of the highest excellences, are open likewise to the greatest aberrations;
and those who travel very slowly may yet make far greater progress,
provided they keep always to the straight road, than those who,
while they run, forsake it."
Rene Descartes
(1596-1650)
Discourse
on the Method of Rightly Conducting the Reason, and Seeking Truth
in the Sciences
OVERVIEW
The Teacher Education
Program at Davidson College offers licensure in secondary mathematics.
All students seeking licensure are required to complete a mathematics
major. All of the specialty area competencies, outside the area of
professional studies, are satisfied by courses offered by the Department
of Mathematics. Thus, the department is integrally involved in the
preparation of teachers.
REQUIREMENTS
FOR LICENSURE IN MATHEMATICS
- Completion
of the College requirements for graduation including the core curriculum
requirements.
- Completion
of the requirements for a mathematics major.
- Completion
of the requirements for the Teacher Education Program as follows:
Courses:
-
PSY
101 (General Psychology)
-
EDU
121 (History of Educational Theory and Practice)
-
EDU
242 (Educational Psychology and Teaching Exceptionalities)
-
EDU
240 (Reading, 'Riting, and Race), 250 (Multicultural Education), or 260
(Social Diversity and
Inequality in Education)
-
EDU
400 (Organization for Teaching)
-
EDU
410-411 (Internship in Teaching)
-
EDU
420 (Seminar in Secondary Education)
Other
Requirements:
-
Tutoring
(if not completed in Education 121)
-
Minimum
scores on the Praxis Series
-
Students
will need to meet the requirements for admission to the Program
and admission to student teaching.
GOALS
AND OBJECTIVES
The
Teacher Education Committee, including its representative from the
Department of Mathematics, has adopted the new standards for mathematics
set forth by the North Carolina Department of Public Instruction.
In addition to the general teaching competencies
and technology competencies addressed
in their portfolios, licensure students in English education will
demonstrate the following competencies in their electronic portfolios.
I.
Knowledge Standards for Teachers of Mathematics.
Teachers
know the essential mathematical knowledge and concepts and are able
to communicate their understanding and appreciation of mathematics
integrating content through the use of problem solving, communication,
connections, reasoning/proof and representation.
Standard
1: Number
sense, numeration, and numerical operation. Teachers have an in depth
understanding of concrete algebraic systems and applications.
- demonstrate
an understanding of the properties of, and operations on real and
complex numbers, polynomials, vectors, matrices, and other concrete
algebraic systems;
- demonstrate
an understanding of algebra and algebraic systems, including linear
and abstract algebra;
- demonstrate
an understanding of elementary number theory;
- demonstrate
an understanding of set theory;
use computational tools and strategies and estimate appropriately.
Standard
2:
Spatial sense, measurement, and geometry. Teachers understand measurement,
spatial sense, and the properties of relationships of two- and three-dimensional
space.
- demonstrate
an understanding of Euclidean and non-Euclidean geometry;
- recognize
geometry as an example of a deductive system, built from undefined
terms, axioms, definitions, and theorems;
- use deduction
to establish the validity of geometric conjectures and to prove
theorems;
- demonstrate
an ability to connect geometry to other strands of mathematics and
use it to solve problems;
- demonstrate
an understanding of the properties of two- and three-dimensional
geometric objects;
- demonstrate
an ability to solve geometric problems using vectors in two- and
three-dimensions;
- demonstrate
an understanding of other coordinate systems and representational
models and their uses;
- demonstrate
an ability to use trigonometric relationships to solve problems;
- use appropriate
technology to explore geometric concepts.
Standard
3.
Patterns, relationships, and functions. Teachers understand patterns,
relationships, functions, symbols and models.
- demonstrate
an ability to model and analyze situations and number patterns with
numerical, graphical, and symbolic representations; and explore
their connections;
- demonstrate
an ability to use methods of proof to prove theorems and verify
conjectures;
- demonstrate
an ability to analyze tables and graphs to identify properties and
relationships;
- demonstrate
an understanding of differential and integral calculus;
- demonstrate
the ability to use mathematics and technological tools to solve
"real world" problems that arise in social sciences, biological
sciences, physical sciences, and other mathematical sciences;
- demonstrate
an understanding of different classes of functions and relations
and the use of technology to investigate their properties.
Standard
4.
Data, probability, and statistics. Teachers understand the major concepts
of probability and statistics including collecting, displaying, analyzing,
and drawing conclusions from data.
- demonstrate
the ability to use a variety of standard techniques for organizing
and displaying data in order to detect patterns and departures from
patterns;
- demonstrate
the ability to use surveys to estimate population characteristics
and experiments to test conjectured cause-and-effect relationships;
- demonstrate
the ability to use theory and simulations to produce, analyze, and
apply probability distribution models;
- demonstrate
the ability to use probability models to draw conclusions from data
and measure the uncertainty of those conclusions;
- demonstrate
an understanding of topics in discrete mathematics such as finite
difference equations, graph and network theory, combinatorics, and
models for social decision-making;
- use appropriate
technology to collect, display, organize, and interpret data;
- develop
computer programs in a structured language.
II.
Pedagogy Standards for Teachers of Mathematics.
Teachers
use varied processes in the teaching of mathematics and make decisions
regarding appropriate instruction and assessment.
Standard
5.
Process Skills . Teachers understand and use the processes of problem
solving, reasoning and proof, communication, connection, and representation
as the foundation for the teaching and learning of mathematics.
Problem
Solving: Teachers develop instructional programs that enable
all students to
· build new mathematical knowledge through problem solving;
· solve problems that arise in mathematics and in other contexts;
· apply and adapt a variety of appropriate strategies to
solve problems;
· monitor and reflect on the process of mathematical problem
solving.
Reasoning
and Proof: Teachers of develop instructional programs that enable
all students to
§ recognize reasoning and proof as fundamental aspects of mathematics;
· make and investigate mathematical conjectures;
· develop and evaluate mathematical arguments and proofs;
· select and use various types of reasoning and methods of
proof.
Communication:
Teachers of develop instructional programs that enable all students
to
· organize and consolidate their mathematical thinking through
communication;
· communicate their mathematical thinking coherently and
clearly to peers, teachers, and others;
· analyze and evaluate the mathematical thinking and strategies
of others;
· use the language of mathematics to express mathematical
ideas precisely.
Connections:
Teachers develop instructional programs that enable all students
to
· recognize and use connections among mathematical ideas;
· understand how mathematical ideas interconnect and build
on one another to produce a coherent whole;
· recognize and apply mathematics in contexts outside of
mathematics.
Representation:
Teachers develop instructional programs that enable all students
to
· create and use representations to organize, record, and
communicate mathematical ideas;
· select, apply, and translate among mathematical representations
to solve problems;
· use representations to model and interpret physical, social,
and mathematical phenomena.
Standard
6.
Curriculum pacing and alignment. Teachers are aware of the importance
of and implement effective instructional pacing and alignment. Teachers
are:
- knowledgeable
of the NC Standard Course of Study, LEA (district) standards and
pacing guides, and the NCTM standards;
- able to
locate and use various resources that support daily classroom practices
(e.g. NCDPI, LEARNNC, NCTM Publications, etc.).
Standard
7. Instructional
strategies. Teachers use a variety of instructional strategies to
promote student understanding of mathematics. They recognize students'
level of mathematical understanding in order to implement the appropriate
instructional practice. Teachers:
- use varied
strategies, including problem-based learning, inquiry, investigations,
direct instruction, exposition;
- are knowledgeable
of current research on best practices;
- match the
appropriate strategy with the appropriate tools;
- are knowledgeable
about and sensitive toward various teaching/learning styles;
- are aware
that it will take a variety of teaching methods to lead all students
to excel in mathematics.
Standard
8. Instructional
tools. Teachers understand and use effectively the hierarchy of the
use of instructional tools. Teachers are able to identify, prescribe,
and use appropriate
- hands-on
tools (e.g. cubes, counters, rods, etc.);
- representational
tools (e.g. base-ten blocks, calculators, computer applications,
algebra tiles/blocks, fraction bars, decimal squares, geometric
blocks, etc.);
- transitional
tools (e.g. expanded notation, paper and pencil, calculator and
computer methods, metaphors, analogies, etc.) that enable students
to make connections between representational and symbolic levels
of understanding;
- symbolic
tools (e.g. standard and alternative algorithms, calculator and
computer applications, etc.).
Standard
9.
Assessment practices. Teachers understand a variety of formative and
summative assessment tools, strategies, and practices and their appropriate
use. Teachers are able to
- use assessment
to inform instructional practice;
- recognize
and use formative and summative assessment;
- match assessment
strategies to instructional strategies;
- use assessment
to enhance student learning.
III.
Diversity Standards for Teachers of Mathematics.
Teachers
believe that all students can learn mathematics. They exhibit an enthusiasm
for teaching mathematics and view diversity as a strength in the classroom.
Standard 10.
Ethnicity, gender, race, and socioeconomic status. Teachers recognize
that all students, regardless of their personal characteristics, backgrounds,
or physical challenges, must have opportunities to study and learn
mathematics. Teachers:
- are sensitive
to the needs and strengths of the mathematical backgrounds and abilities
of individual students and have high expectations for all students;
- treat students
equitably, not necessarily equally, by accommodating individual
student needs;
- understand
the need to encourage parental involvement in all students' education
and frequently communicate with parents or guardians of their students;
- strive to
dispel the myths regarding the learning of mathematics, challenging
derogatory and/or stereotypical beliefs based on ethnicity, gender,
race, or socioeconomic status;
- understand
and confront their own beliefs and biases to effectively and sensitively
accommodate differences among students.
Standard
11. Accommodating
individual needs. To promote diversity as a strength, teachers are
knowledgeable about and sensitive toward various teaching/learning
styles. Teachers keep abreast of current research which indicates
the optimal teaching methods to address students' diverse learning
styles, non-native speakers of English, students with disabilities,
and gifted students. Teachers are aware that it will take a variety
of teaching methods to lead all students to excel in mathematics.
Standard
12. Historical
perspective. Teachers understand that historically based pedagogy
can give all students, regardless of their learning preferences, the
opportunity to learn mathematics. It provides an opportunity to focus
on special interests, and it provides the teacher with insights into
the diversity in the development of mathematics. Teachers:
- are able
to plan instructional topics of particular interest through the
use of the historical development of mathematics;
- understand
that the investigation of historical topics in mathematics requires
the use of substantial mathematics;
- understand
and incorporate the mathematical contributions of all cultures into
their lessons.
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