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

1. Completion of the College requirements for graduation including the core curriculum requirements.
2. Completion of the requirements for a mathematics major.
3. 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.