Our twelve-course (48 quarter-hour) program is designed for teachers certified in grades K-8. The program will allow participants to meet the requirements for an endorsement in middle school mathematics. This is a cohort program with groups of teachers taking the same courses together in the same order. All courses are 4 credit hours and twelve courses are required.
Required Courses: 48 quarter hours, grade of C or better required
EXPERIMENTATION, CONJECTURE, AND REASONING WITH NUMBERS
This course will focus on furthering the participants' number sense together with providing them with opportunities to: 1) Use and discuss the roles of experimentation, conjecture, and logical reasoning in developing mathematical understanding; 2) Appreciate the value of algebraic notation in problem solving by comparing solutions done both with and without algebra; 3) Engage in mathematical speaking and writing with discussion of (a) how to evaluate accurate vs. inaccurate statements, (b) what level of detail is appropriate in an answer given the point of the problem, (c) what ways of presenting solutions are suitable for various audiences; 4) Discuss the distinction between "how" a mathematical strategy works and "why" it works, and articulate the pedagogical value of knowing the "why."
FOUNDATIONS OF MATHEMATICAL THINKING AND LEARNING IN THE MIDDLE SCHOOL
This course is designed to help participants construct meaningful connections between being a learner of mathematics (i.e., a person who can solve problems, reason mathematically, communicate findings and thinking, and make connections) and being a teacher of mathematics (i.e., a person who can help others understand, use, and apply mathematical ideas). The course will begin the process (which will be continued throughout the remainder of the Master of Arts in Middle School mathematics Education program) of having students explore the interplay between narratives describing their own classroom experiences as well as literature and research about others' experiences in order to analyze the impact of developmental and interpersonal experiences on the learning and teaching of mathematics.
GEOMETRY FOR MIDDLE SCHOOL TEACHERS
An introduction to geometry designed to engage students in the construction, description, and analysis of geometric objects, including three-dimensional objects. These activities will be used to generate questions and hypotheses that will lead to more abstract concepts and general arguments. Emphasis throughout will be on informal reasoning, experimental methods, inductive as well as deductive arguments, local organization, and the development of mathematical thinking. Appropriate technology will be used to explore hypotheses and support mathematical reasoning. Topics will include: polyhedra, and their nets, cross sections, and projections; triangles, quadrilaterals, and polygons; congruence and similarity; the Pythagorean theorem; perimeter, area, and volume; circles and spheres, symmetry and transformations; and tessellations. The course will also include discussion and reflection on learning mathematics.
ALGEBRA FOR MIDDLE SCHOOL TEACHERS I
This course is the first of a 3-quarter sequence designed in part to prepare elementary and middle grade teachers to teach an algebra class to qualified 8th grade students in their schools. It is based on a vision of mathematics instruction throughout the grades that continuously builds students' algebraic skills and thinking. This first course in the sequence emphasizes problem-solving as an entry point into algebra for mathematics learners. Students see algebra as an active process for solving problems and as arising naturally as a way to generalize the laws of arithmetic, analyze patterns, and describe relationships in tables, graphs, and equations. In addition, students review and examine foundational concepts in algebra (variables, equations, relations, graphs, slopes of lines, and equations of lines) and are introduced to research on the development of algebraic thinking in middle grade students.
ALGEBRA FOR MIDDLE SCHOOL TEACHERS II
The second course in the algebra sequence builds on the first and maintains emphases on problem-solving, deeper understanding of the central concepts of beginning algebra, and awareness of difficulties students have when encountering the subject for the first time. Topics include systems of linear equations, solving linear inequalities and systems of inequalities, absolute values equations and inequalities, and quadratic functions.
FUNCTIONS AND MODELING
Advanced concepts in beginning algebra provide a basis for a deeper treatment of the relationship between functions and data, and lay the groundwork for the development of polynomial, exponential, and logarithmic models. The course will integrate the use of technology such as graphing calculators and spreadsheets.
TEACHING, LEARNING, AND ASSESSMENT OF MIDDLE SCHOOL MATHEMATICS
This course will examine, in the context of classroom practice, the following themes: 1) How students can learn mathematics with conceptual understanding; 2) How to teach mathematics so that students learn with understanding; 3) How to assess students' mathematical knowledge to inform instruction and determine their growth; 4)The nature and content of innovative curriculum projects designed to teach mathematics for conceptual understanding.
THE DEVELOPMENT OF MIDDLE SCHOOL MATHEMATICS LEARNERS
Critical to the success of middle school mathematics learners, is their teachers' understanding of the multiple perspectives that research has taught us, as educators, about how people learn. In this course, participants will engage with the history and evolution of how the fields of educational psychology, cognitive science, applied developmental psychology, and mathematics education have contributed to a modern understanding of what constitutes effective practice for middle school mathematics teaching. Major theoretical positions and their seminal architects will be highlighted, examined and discussed. A particular emphasis will be put on each position's impact on curriculum development and classroom pedagogy for middle school mathematics.
DATA ANALYSIS AND PROBABILITY
This course covers the fundamental concepts of probability that are part of the middle school curriculum and recent research findings on student learning of probability and classroom implications of this research. In addition, it covers the principles of graphically displaying, collecting and analyzing data with and without the use of technology. Topics will include measures of central tendency and dispersion, graphical representations of data (histograms, boxplots, bar charts, pie charts, and line graphs), and the design of experiments and simulations.
IDEAS OF CALCULUS IN THE MIDDLE SCHOOL CURRICULUM
The course will introduce students to the "big ideas" of Calculus including limits, derivatives, and integrals. The course will emphasize how the mathematics in the middle school curriculum can lay a foundation for the study of continuous mathematics and to the role that Calculus plays in the sciences. In particular, direct connections to the topics of this course and the middle school curriculum will be made by studying activities from curriculum materials currently used in CPS that are relevant to the topics of Calculus. Trigonometry from the perspective of the middle school classroom will be used as the launching point for introducing the major ideas of the course. The course will also give the students the opportunity to understand the interplay between the concepts and tools they learned in the MMT 415-417 sequence and Calculus.
HISTORY AND CULTURAL FOUNDATIONS OF MATHEMATICS
This course is a cross-cultural survey of the history of mathematics, with emphasis placed on the development of concepts encountered by students in elementary and middle school. The course will also serve as a capstone for the program in that it will include references to content from all the earlier courses and will explicitly ask teachers to make connections across the middle school mathematics curriculum. The students will complete a small group research project in which they choose a mathematical concept from the program and use it as a focal point to study the development of mathematical ideas across time and across cultures.
APPLIED PROJECT IN MATHEMATICS EDUCATION
This course will span the three quarters of the second academic year of the program and will be partnered with the three content-focused courses offered during the second year. Participants will be introduced to the field of educational inquiry through a study of various designs and methods of doing educational research. In addition, this course will help participants consider current issues in mathematics education in relationship to their own teaching and learning of mathematics and what it means to transfer the mathematics learned in other courses into one's practice as a math teacher. They will identify concrete changes they want to implement in their teaching during the years following their completion of the program based on the new content and ideas to which they have been exposed. As part of the course, the teachers will design an action research project during the first quarter, implement the project during the second quarter, and analyze the data during the third quarter.