# Mathematics Education Courses

## Lower Division Courses

**MTHED 212. Children’s Mathematical Thinking (1-2)** **Prerequisite:** Credit or concurrent registration in Mathematics 210.

Children’s mathematical thinking and in-depth analyses of children’s understanding
of operations (addition, subtraction, multiplication, and division) and place value.
Students will observe individual children solving mathematics problems. Real, compact
disc, and/or web-based experience included.

## Upper Division Courses

Mathematics Courses for Mathematics Education

**MATH 501A. Reasoning: Place Value and Arithmetic Operations (1)** **Prerequisites:** Teaching credential and consent of instructor.

Place value and its role in development and understanding of arithmetic operations,
to include numeration systems, student methods, standard algorithms, and mental computation.

**MATH 501B. Reasoning: Rational Numbers and Real Number Systems (1)** **Prerequisites:** Teaching credential and consent of instructor.

Rational numbers and structure of real number system, to include meanings and models
for fractions with attention to operations on rational numbers.

**MATH 504A. Reasoning: Quantities and Mathematical Relationships (1)** **Prerequisites:** Teaching credential and consent of instructor.

Reasoning about measurable characteristics in problem context. and relationships among
these measurements. Additive, multiplicative reasoning, and proportional reasoning
in middle grades.

## Graduate Courses

Mathematics and Science Education (MTHED)

**MTHED 600. Teaching and Learning Mathematics in the Early Grades (Pre-K to 4) (3)** **Prerequisites:** Mathematics Education 603 or 604 and K-12 teaching experience.

Research in teaching and learning mathematics in preschool through grade four. Innovative
early childhood mathematics curricula, promising instructional practices. Assessment
techniques to guide instruction.

**MTHED 601. Teaching and Learning Mathematics in the Middle Grades (3)** **Prerequisites:** Mathematics Education 604 and K-12 teaching experience.

Research on teaching and learning mathematics in grades five through eight. Innovative
middle grades mathematics curricula, promising instructional practices. Assessment
techniques to guide instructions.

**MTHED 603. Seminar on Learning Theories in Mathematics Education (3)** (Syllabus)**Prerequisite:** Consent of instructor or graduate adviser.

Application of several major learning theories (e.g. behaviorism, structuralism, radical
constructivism, information processing, and sociocultural perspectives) to research
on the learning and teaching of mathematics.

**MTHED 604. Seminar on Teaching Issues in Mathematics (3)** (Syllabus)**Prerequisite:** Consent of instructor or graduate adviser.

Mathematics education research pertaining to teaching of mathematics. Readings chosen
to bridge theory and practice divide.

**MTHED 605. Algebra in the 7-14 Curriculum (3)** (Syllabus)**Prerequisite:** Consent of instructor or graduate adviser.

Curricular change in algebra, with attention to experimental curricula, to research
on learning of algebra, and to influences of technology. Implications for instruction.

**MTHED 606. Selected Topics in 7-14 Mathematics Curriculum (3)** (Syllabus)**Prerequisite:** Consent of instructor or graduate adviser.

Curricular change in school mathematics, to include geometry, probability, and statistics,
with attention to contemporary curricula, to research on learning and teaching in
those areas, and to the influences of technology. Implications for instruction.

**MTHED 607. Seminar on Research in Undergraduate Mathematics Education (3)** (Syllabus)**Prerequisite:** Consent of instructor or graduate adviser.

Research in undergraduate mathematics education and its implications for teaching.
Topics include research on student thinking on concepts from calculus through abstract
algebra and the teaching and learning of proof.

## Graduate Courses

Mathematics Courses for Mathematics Education

**MATH 600. Chaos and Fractals (3)** **Prerequisites:** Mathematics 320 and 510.

Non-linear dynamics to include Cantor sets, fixed and periodic points, fractal dimensions,
fractals, iterative processes, orbit diagrams, orbits, period doubling, and self-similarity.

**MATH 601. Topics in Algebra (3)** **Prerequisites:** Mathematics 320 and 330.

Unique factorization domains, rings and ideals, groups, algebraic field extensions.
A course designed for secondary school teachers.

**MATH 602. Topics in Analysis (3)** **Prerequisites:** Mathematics 320 and 330.

Topics in analysis, including the real number system, convergence, continuity, differentiation,
the Riemann-Stieltjes integral, complex analysis, designed to give the secondary teacher
a broad understanding of the fundamental concepts.

## Doctoral Courses

Mathematics and Science Education (MSE)

**MSE 801. Faculty Research (1) Cr/NC** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

Issues of learning with reference to how they are addressed by doctoral faculty. Students
will interview and write a one-page statement of research interests for each of eight
doctoral faculty members.

**MSE 802. Orientation Practicum (1-3) Cr/NC** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

Experience with research programs will introduce students to a variety of research
questions and approaches. One research program per unit; minimum three units required
in program. May be repeated with new content. See Class Schedule for specific content.
Maximum credit four units applicable to an advanced degree.

**MSE 805. Supervised Teaching of Teacher Preparation Courses (3) Cr/NC/RP** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

Students will plan and teach, under supervision, a course that prepares prospective
teachers to teach mathematics or science at either the elementary or secondary level.

**MSE 806. Supervised School Practicum (3) Cr/NC/RP** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

School-based project focusing on inservice of teachers or on curriculum development,
or work with a school district administrator or mathematics or science.

**MSE 807. Specially Designed Practicum (3) Cr/NC/RP** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

Practical experience to assist students in gaining experience in career they have
selected.

**MSE 810. Seminar in Research Design (3)** **Prerequisites:** Admission to doctoral program in Mathematics and Science Education; Psychology 670A,
and consent of instructor.

Issues such as analysis of protocols, problems of measurement in evaluation of learning,
development, and assessment of cognitive models in learning in mathematics and science.

**MSE 820. Research Project (3-6) Cr/NC/RP** **Prerequisite:** Admission to doctoral program in Mathematics and Science Education.

Participation in an ongoing research project and development of a related study.

**MSE 830. Research Seminar (3)** **Prerequisite:** Successful completion of qualifying examination.

Students and faculty present ongoing research for discussion and critique.

**MSE 897. Doctoral Research (1-15) Cr/NC/RP** **Prerequisite:** Mathematics and Science Education 820.

Independent investigation in general field of the dissertation.

**MSE 898. Doctoral Special Study (1-8) Cr/NC/RP** **Prerequisites:** An officially constituted doctoral committee and advancement to candidacy.

Individual study in the field of specialization.

**MSE 899. Doctoral Dissertation (1-15) Cr/NC/RP** **Prerequisites:** An officially constituted dissertation committee and advancement to candidacy.

Preparation of the dissertation for the doctoral degree. Enrollment is required during
the term in which the dissertation is approved.