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# Mathematics and Statistics

## College of Natural Sciences and Mathematics

### Mathematics and Statistics - MTED Courses

Satisfying the Entry-Level Math (ELM) requirement (see “Undergraduate Programs” section of this Catalog) is a prerequisite for all mathematics education courses.

### LOWER DIVISION

#### 110. The Real Number System for Elementary and Middle School Teachers (3)

Prerequisite: ELM or ELM exemption or MAPB 11.
Introduction to problem solving processes and strategies. Development and analysis of structure, properties, and operations of real number system. Concept and process development using appropriate models, manipulative, and activities.
Not open for credit to Mathematics majors. (Lecture 2 hrs., activity 2 hrs.)

#### 205. Activity Based Probability and Statistics for Elementary and Middle School Teachers (3)

Prerequisites: ELM or ELM exemption or MAPB 11 and MTED 110.
Activity-based exploration of randomization, data representation, measures of central tendency and dispersion. Analysis of experiments requiring hypothesizing, experimental design and data gathering. Basic laws of probability and set theory, combinations, permutations, and simulations.
Letter grade only (A-F). (Lecture 2 hrs., activity 2 hrs.) Not open for credit to mathematics (all options) and statistics majors or for students with credit in MTED 105.

#### 211. Geometry and Measurement for Elementary Teachers (3)

Prerequisites: “C” or better in MTED 110 and one year of high school geometry.
Problem solving and hands-on modeling of real-world geometry situations focusing on patterning, informal geometry, congruence, similarity, constructions, transformations, tessellations, measurement in 1, 2, and 3 dimensions (English and Metric units). Computer applications are integrated into the course.
Not open for credit to Mathematics majors or any student with credit in MTED 312. (Lecture 2 hrs., activity 2 hrs.)

### UPPER DIVISION

#### 301. Computer Applications in Mathematics for Teachers (3)

Prerequisites: One year of high school geometry and one of MTED 110 or MATH 122.
Designed for pre-service or inservice teachers. Software evaluation; teacher tools (spreadsheets, databases, email, collaborative tools, and applications); mathematics using technology; programming; technology use issues in schools.
Satisfies California Level I teaching credential computer technology standard. Open for credit to pre-service or in-service teaching credential students only. (Lecture 2 hrs., activity 2 hrs.)

#### 311. Topics of Enrichment in Mathematics for the Elementary Teacher (3)

Prerequisites: MTED 110 and either MTED 211 or MATH 122 or consent of instructor. Formerly MATH 311.
Enrichment topics in mathematics for elementary teacher, such as theory of arithmetic, numeration systems, elementary logic, mensuration, metric system, topological equivalence, probability and statistics and network theory.
Not open for credit to mathematics majors or to students with credit in MATH 311. (Lecture 3 hrs.)

#### 312. Geometry and Measurement for Mathematics Specialists in Elementary and Middle Schools (4)

Prerequisites: MTED 110 and one year of high school geometry.
Exploration, conjecture, justification of geometric relationships, applications relevant to teaching geometry (K-10). Problem solving, informal geometry, proof, non-Euclidean geometry, congruency, similarity, constructions, transformations, tessellations, measurement (English and Metric) in 1, 2 , and 3 dimensions. Computer construction utility used.
Not open for credit to Mathematics majors. Letter grade only (A-F). (Lecture 2 hrs., activity 2 hrs.)

#### 402. Problem Solving Applications in Mathematics for Elementary and Middle School Teachers (3)

Prerequisites: “C” or better in both MTED 110, and either MTED 211 or 312 or the equivalent and a course in Critical Thinking.
Problem solving processes and strategies; interrelates and applies content from many mathematics areas (real number system, algebra, number theory, geometry, measurement, probability and statistics); develops questioning strategies, fostering understanding of algebra and geometry. Technology integrated throughout.
Not open for credit to Mathematics majors. (Lecture 2 hrs., activity 2 hrs.)

#### 411. Topics and Issues in Secondary School Mathematics (3)

Prerequisites: MATH 310, 341, 355, 380, 410, 444; EDSS 300M or consent of the instructor.
Analysis of topics and issues in secondary school mathematics curriculum. Problem solving, mathematical connections, communication, structures, conjecture, proof, manipulatives, technology, assessment. Observations/interview experiences and portfolio assemblage required. Intended for students preparing to enter Single Subject Credential Program in mathematics.
(Lecture 2 hrs., activity 3 hrs.)

#### 415. History of Mathematics for Elementary and Middle School Teachers (4)

Prerequisite: "C" or better MTED 312.
Mathematics ideas throughout history with orientation toward various civilizations and cross-cultural views. Covers origins and interrelationships of areas of K-9 mathematics curriculum, including arithmetic, algebra, geometry, statistics and probability, cryptography, and other mathematics topics.
Not open for credit to mathematics (all options) or statistics majors or for students with credit in MATH 310 or MTED 315. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

#### 420. Number Theory for Elementary and Middle School Teachers (4)

Prerequisite: "C" or better in MTED 312.
Concepts and justification involving basic properties of natural numbers, mathematics induction, Euclidean algorithm, and the Fundamental Theorem of Arithmetic. Topics include proofs and problem-solving with divisibility, primes and composites, and prime factorization; congruences and other examples.
Not open for credit to mathematics (all options) or statistics majors or for students with credit in MATH 341 or MTED 320. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

#### 424. Algebraic Structures for Elementary and Middle School Teachers (4)

Prerequisite: "C" or better MTED 312.
Properties of real and complex numbers, groups, rings, reals and complex fields; polynomial equations and inequalities; polynomial, rational, radical, absolute value, exponential, and logarithmic functions; matrices and vectors.
Not open for credit to mathematics (all options) or statistics majors or for students with credit in MATH 444 or MTED 324. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

#### 425. Functions, Models and Concepts of Calculus for Elementary and Middle School Teachers (4)

Prerequisite: "C" or better in MTED 312.
Numeric, symbolic, graphical, verbal representation of functions; sequences and sums. Intuitive development of concepts of limit, continuity, derivative, intergral. Applications, including differential equations. Algebraic methods and technology emphasized in context of learning calculus. Not open for credit to mathematics (all options) or statistics majors or for students with credit in MTED 325. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

#### 430. Connections, Integrations, and Reasoning in Mathematics for Teachers (4)

Prerequisites: "C" or better in MTED 205 or 300; MTED 312, 402, 415, 420, 424, and 425.
Examination, analysis, and integration of mathematics topics appropriate for elementary and middle school teachers. Topics will include problem solving, hypothesis and justification, and mathematics connections and communication.
Not open for credit to mathematics (all options) or statistics majors or for students with credit in MTED 403. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

#### 495. Special Topics in Mathematics Education (1-3)

Prerequisite: Consent of instructor.
Topics of interest in Mathematics Education.
May be repeated to a maximum of 9 units with different topics in different semesters. Letter grade only (A-F).

### GRADUATE LEVEL

#### 500. Advanced Perspectives of Concepts Foundational to Algebra for Teachers (3)

Prerequisite: Multiple Subjects Credential, or consent of instructor.
Analytic investigation of foundational algebra concepts using representations, reasoning and proof, and problem solving. Topics include: number theory, properties of real numbers, proportional reasoning, algebra, discrete mathematics, and functions. This course will not count toward any M.S. degree options in the Department of Mathematics and Statistics.
Letter grade only (A-F). (Lecture 3 hrs)

#### 511. Mathematics Teaching and Learning (3)

Prerequisite: Consent of instructor.
Theories of mathematics teaching and learning. Key issues in mathematics and mathematics education. Historical development and contemporary views of various theoretical perspectives for teaching and learning mathematics, including the roles of standards and various mathematics and education organizations.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 512. Curriculum and Assessment in Mathematics (3)

Prerequisite: MTED 511 or consent of instructor.
Theories of mathematics curriculum and forms of assessment. Introduces major philosophies, issues, resources and technologies pertaining to curricula and assessment of mathematics. Relevant histories and contemporary practices of design and implementation of curriculum and assessment of mathematics.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 540. Algebra in the School Curriculum (3)

Prerequisite: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.
Issues/topics concerning algebraic learning using curricular standards. Examining texts, curricula, algebraic thinking and teaching research. Common errors and possible remedies, algebra for mathematizing situations. Relationship of K-12 algebra curriculum to modern algebra and its structures. Fundamental theorem of algebra.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 550. Geometry and Measurement in the School Curriculum (3)

Prerequisite: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.
Content, curriculum, standards, and research in learning and teaching geometry, spatial sense and measurement in K-12. Justification and proof, applications and abstraction, tools and technology in geometry teaching and learning. Current issues in teaching and learning of geometry and measurement.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 560. Analysis in the Secondary Curriculum (3)

Prerequisites: MTED 511 and MATH 361A; prerequisite or corequisite: MTED 512 or consent of instructor.
Fundamental concepts of calculus, functions, mappings, related topics and proofs in real and complex analysis, relating mathematics analysis to secondary curriculum. Issues and techniques in teaching and learning of mathematical analysis. Examination of mathematics education research and mathematics frameworks.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 580. Probability and Statistics in the School Curriculum (3)

Prerequisite: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.
Content, curriculum, and research in learning and teaching probability and statistics in K-12 schools. Includes role of applications, abstraction, tools and technology in probability and statistics teaching and learning.
Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

#### 590. Special Topics in Mathematics Education (1-3)

Prerequisite: Consent of instructor.
Advanced study of special topics in the field of mathematics education.
May be repeated for a total of six units with different topics. Letter grade only (A-F). (Seminar 1-3 hrs.)

#### 695. Seminar in Mathematics Education (1-3)

Prerequisite: Consent of instructor.
Presentation of and discussion of advanced work in mathematics education.
May be repeated for a total of six units. Letter grade only (A-F). (Seminar 1-3 hrs.)

#### 697. Directed Studies in Mathematics Education (1-3)

Prerequisites: MTED 511, 512; EDP 520; Advancement to Candidacy; consent of instructor.
Research project in mathematics education.
Letter grade only (A-F).

#### 698. Thesis in Mathematics Education (1-4)

Prerequisites: MTED 511, 512; EDP 520; Advancement to Candidacy; consent of instructor.
Research in mathematics education culminating in a formal report.
Letter grade only (A-F).