Ph.D. in Science/Mathematics Education Description of Individual Courses

600, Foundations of Education Science/Mathematics Education (3 Credits). A graduate level survey of the history and basic foundations of educational paradigms in general and those of science and mathematics education in particular; the evolution of modern theories of teaching and learning; the various paradigms of research in science/mathematics education (i.e. quantitative vs. qualitative; cognitivism vs. behaviorism, and their connections); the relevance of information processing to teaching and learning.

601, Developmental Psychology and Science/Mathematics Education (3 Credits). An in-depth coverage of the fundamentals and recent developments in developmental psychology and their implications for science/ mathematics education.

602, Cognitive Psychology and Science/Mathematics Education (3 Credits). An in-depth coverage of the fundamentals of cognitive psychology and recent developments in cognitive psychology, implications for science/ mathematics education; the cognitive domain, memory and cognition, cognitive models of learning, applications to the design of computer/multimedia assisted delivery systems.

603, Behavioral Psychology and Science/Mathematics Education (3 Credits). An in-depth treatment of behavioral, its recent developments, and applications to science/mathematics education.

610, History and Structure of Science/Mathematics: Biology, Chemistry, Computer Science, Mathematics, or Physics (3 Credits). Basic history and philosophy of the applicable science/ mathematics discipline; structure, sub-branches and their recent developments; implications of current topics in a discipline on the curriculum (content, delivery, feedback) at various levels of the educational pipeline; introductory survey of related trends in research on teaching and learning in the discipline.

611, Advanced Problems in Science/Mathematics Education (3 Credits). Please see the attached detailed syllabus.

615, Science/Mathematics Curriculum (3 Credits). A macroscopic and microscopic examination of elementary science and mathematics curriculum. General structure, strands, and themes, analysis of sample classroom activities, delivery methods and media, and related assessment of learning outcomes; cognitive and behavioral bases for the curriculum; contemporary trends for the elementary science/mathematics curriculum; concept and process maps applied to the curriculum and to specific activities. The elementary level is covered as a part of a continuum.

616, Science/Mathematics Curriculum (3 Credits). A macroscopic and microscopic examination of secondary science and mathematics curriculum. General structure, strands, and themes, analysis of sample classroom activities, delivery methods and media, and related assessment of learning outcomes; cognitive and behavioral bases for the general curriculum; contemporary trends for the secondary science/mathematics curriculum; concept and process maps applied to the curriculum and to specific activities. The secondary level is covered as a part of a continuum.

617, Science/Mathematics Curriculum at the College Level: Biology, Chemistry, Computer Science, Mathematics, Physics, or General (3 Credits). A macroscopic and microscopic examination of college curriculum in the affected science/mathematics discipline(s); general structure, strands and themes, analysis of sample classroom activities, delivery methods and media, and related assessment of learning outcomes; cognitive and behavioral bases for the curriculum; contemporary trends for the college science/mathematics curriculum for the affected discipline(s); concept and process maps applied to the curriculum and to specific classroom activities.

618, Teaching for Conceptual Change (3 Credits). Please see the attached detailed syllabus.

620, Technology in Science/Mathematics Education (3 Credits). A survey of current educational technologies and their integration into teaching, learning, assessment, and instructional materials development; specific operation of selected technologies (computers, multimedia, telecourses, interactive systems); identification of cognitive and affective parameters involved in the integration of selected technologies; outcome assessments congruent with the technological integration into the content, delivery, feedback, and related research issues.

621, Design in Science/Mathematics Education: Instruction and Outcome Assessment (3 Credits). This course focuses on the design of instruction (subject and skill content, organization, delivery methods, and related assessment of outcomes and effectiveness), taking into account, explicitly, the relevant cognitive and affective parameters and objectives; applications of concept and process mapping, for various grade levels; the integration of new developments in the fields into the content and of applicable technologies into the delivery and assessment processes is an integral part of this course; implications for research are explicitly addressed. Prerequisite: Course No. 600.

622, Advanced Design in Science/Mathematics Education (3 Credits). Unlike its prerequisite, Course No. 621, which is a general course, this course deals with an intensive examination, development, and implementation of instruction and the design of the assessment instruments (qualitative and quantitative) needed to ascertain instructional effectiveness and to capture potential research data; computer-assisted instruction, multimedia instruction, expert systems, and curriculum condensation are among the areas of focus available to a student taking this course that entails extensive independent work under the guidance of the instructor(s). Students will select one or more of the above topical areas. Prerequisite: Course No. 621.

623, Special Topics in Physical Chemistry with Mathematical Preparation (Credits - 4 Semester Hours - 3 lectures/1 laboratory per week) This course, designed for teachers of chemistry and other sciences, has a twofold purpose: (1) to elucidate the principal concept(s) behind selected topics in physical chemistry and (2) to formulate approaches to teaching the elucidated concepts to high school students and college freshmen. The course provides instruction in the elementals of mathematics (mainly calculus and differential equations) needed to communicate the fundamentals of physical chemistry. Chemical and mathematical concepts covered in lectures are demonstrated in the laboratory through dry-lab computer simulations and calculations.

624, Inorganic Chemistry for Science Teachers (3 Credits - 3 lectures per week). This one-semester course, for teachers of chemistry and other sciences, is designed to present an overview of the principles of quantum theory, bonding, spectroscopy, periodicity of the elements, structure, stereochemistry, coordination chemistry, synthesis, acid-base theories, boron chemistry, and organometallics, with special emphasis on teaching the elementary concepts of these principles to high school students and college freshmen. Computer software is used to supplement instruction and present ideas on approaches to preparing computer-assisted instruction packages for communicating the basic concepts of inorganic chemistry to high school and undergraduate students.

630, Seminar in Science/Mathematics Education Research (1 Credit). This formalized weekly seminar serves to expose graduate students to contemporary issues in science and mathematics teaching, learning and particularly research in science/mathematics education. About one half of the presentations in a given term will be made by experts outside SUBR. Cognitive, behavioral, quantitative, and qualitative approaches in science/mathematics education research are each expected to be the subject of at least one seminar per term.

632, Topics in Number Theory (3 Credits). This course will briefly review fundamental concepts from Number Theory, with emphasis on intuition, proof, history, applications to modern algebra, discrete mathematics, coding, and the role of number theory in the school curriculum. Topics will include divisibility, the fundamental theorem of arithmetic, the Euclidean algorithm, congruence, number theoretic functions, Diophantine equations, systems of linear congruencies, topics in algebraic number theory, induction and well-ordering.

633, Special Topics in Organic Chemistry with Teaching Software Development (4 Credits - 3 lectures/1 Laboratory per week) This course, designed for teachers of chemistry and other sciences, has the twofold purpose of (1) elucidating the principal concepts associated with selected topics in organic chemistry and (2) formulating approaches to teaching the elucidated concepts to high school students and college freshmen. The course provides instruction on selecting and preparing tutorial software for communicating some basic concepts of organic chemistry to high school and undergraduate students.

635, Practicum in Mathematics Teaching at the Elementary, Secondary, or College Levels (3-6 Credits). This practicum is "taught," or more accurately guided and supervised, by a team of faculty members, at least one of whom is a graduate education faculty member and one of whom is a mathematics graduate faculty member. Prerequisite: Course Nos. 600, 615 or 616, and 621.

636, Practicum in Science Teaching at the Elementary or Secondary Levels (3-6 Credits). This practicum is "taught," or more accurately guided and supervised, by a team of faculty members at least one of whom is a graduate education faculty member and one of whom is a graduate faculty member in the affected science. Prerequisite: Course Nos. 600, 615 or 616, and 621.

637, Practicum in College Science Teaching in Biology, Chemistry, Computer Science, Mathematics, or Physics (3-6 Credits). This practicum is "taught," or more accurately guided and supervised, by a team of faculty members at least one of whom is a graduate education faculty member and one is a graduate faculty member in the affected science discipline. Prerequisite: Course Nos. 600 and 617 (for the affected science discipline), and 621.

640, Quantitative Methods in Science/Mathematics Education Research (3 Credits). This course surveys the quantitative methods in science/mathematics education research. Emphasis is placed on applications of basic statistical methods to the design and conduct of research. The validity of basic statistical inferences and related confidence levels are rigorously treated. Linear models and their implementation using the computer are operationally treated. Prerequisite: Statistics (basics, distributions, sampling, models, confidence levels).

641, Qualitative Methods in Science/Mathematics Education Research (3 Credits). This course is designed to expose every graduate student to the qualitative dimensions of research in science/mathematics education. Limitations of the quantitative approaches in research on conceptual understanding and on the interplay of the cognitive and affective domains are initially discussed. This is followed by the fundamentals of qualitative research in science/mathematics education and the different and complementary natures of quantitative and qualitative approaches. 643, Science/Mathematics Research Design (3 Credits). The first half of this course is devoted to fundamentals of research design for qualitative and quantitative research. The second half of the course entails actual practicum in designing specific research projects. Prerequisite: Course Nos. 640 and 641.

650, Advanced Quantitative Methods in Science/Mathematics Education Research (3 Credits). Theories, models, and methods for the analysis of quantitative data; advanced experimental design and statistical inference; correlation and regression methods; factor analysis; survey of multivariate methods. Explicit applications to research in science/mathematics education. Prerequisite: Course Nos. 640 and 641.

655, Advanced Qualitative Methods in Science/Mathematics Education Research (3 Credits). Intended mainly for students whose dissertation research entails significant qualitative research, this course explores in detail contemporary methods of qualitative research in science/mathematics education, with applications to realistic cases. Prerequisite: Course Nos. 640 and 641.

680, Research in Mathematics Education (3 Credits). This course includes a brief historical survey of educational research, with a focus on factors leading to the development of modern research in mathematics education. Topics include: the difficulties of educational research, factors affecting internal and external validity, the structure of research designs and methods considered appropriate for research in mathematics education, factors affecting curricular and research activities in mathematics education prior to 1975, selected studies prior to 1975, and a careful study of two of the documents from NCTM's Research Agenda:ÿEffective Mathematics Teaching and Setting a Research Agenda.

681, Transitional Mathematics and Algebra: Curricula and Research Topics (3 Credits). This course is designed for students already familiar with research methods and the curriculum standards in grades 5-12. Advanced issues involving curriculum and/or research in mathematics education will be studied, especially in the areas of transitional mathematics and algebra. Several curricular projects in the areas described will be studied in detail, as well as selected research studies involving the teaching of mathematics in the middle grades and algebra. A research and/or development mini-project will be required in the areas indicated.

682, Critical Thinking and Geometry: Curricula and Research Topics (3 Credits). This course is designed for students already familiar with research methods and the curriculum standards in Grades 5-12. Advanced issues involving curriculum and/or research in mathematics education will be studied, especially in the areas of critical thinking and geometry. Several approaches to the development of geometry will be reviewed in detail, as will selected research studies involving problem solving, critical thinking, and the teaching of geometry. A research and/or development mini-project will be required in the areas of critical thinking and/or geometry.

683, Calculus: Curricula and Research Topics (3 Credits). The following topics will be included: the nature of precalculus mathematics, the roots of calculus in early K-12 experiences, number sense experiences needed for intuitive understanding of limits, the effect of technology on the curriculum (e.g., graphing calculators), the conceptual development of calculus, and error patterns in calculus. Research on the development of new curricula (i.e., the Harvard Calculus Reform Materials) will be followed with the development of a mini-proposal on some aspect of curriculum development and/or research in the teaching of calculus.

687, The School Mathematics Curriculum I (3 Credits). This course seeks to understand the forces which shape the elementary and middle school curricula: mathematical, educational, societal, technological, psychological, political, and economic. Major curricular projects beginning in the 1950's and extending to the present time will be studied and contrasted. The impact of various psychological theories and curricular trends such as discovery teaching, the use of manipulatives, problem solving and the use of technology will be explored as well as attempts to project curricular trends into the future. The NCTM Standardsÿwill then be studied as a logical culmination of trends of the last four decades.

688, The School Mathematics Curriculum II (3 Credits). This course seeks to understand the forces which shape the elementary and middle school curricula: mathematical, educational, societal, technological, psychological, political, and economic. Major curricular projects beginning in the 1950's and extending to the present time will be studied and contrasted. The impact of various psychological theories and curricular trends such as discovery teaching, the use of manipulatives, problem solving and the use of technology will be explored as well as attempts to project curricular trends into the future. The NCTM Standardsÿwill then be studied as a logical culmination of trends of the last four decades.

699, Ph.D. Dissertation Research (3-9 Credits, may be repeated). A scholarly research report, whose scope and depth are commensurate with the number of credit hours, is required.