Course Description
Exploration of various secondary mathematics topics with an explicit focus on ways of reasoning that connect critical concepts of secondary mathematics. A problem solving approach will be used to foster and explore topics including similarity, transformations, conics, linear systems, and sequences and series.
Additional Requirements for Graduate Students:
Graduate students will be expected to complete additional
assignments that familiarize them with mathematics education
research and practice. Additional assignments will include
readings suitable for graduate students (e.g., articles from
high-impact research journals), and the students will be
expected to connect the advanced readings to their experiences
in the courses (e.g., conducting article syntheses of all
course readings; designing tasks that incorporate ideas from
their advanced readings).
Athena Title
Connections Secondary Math III
Undergraduate Prerequisite
EMAT 4860/6860
Graduate Prerequisite
EMAT 4860/6860
Undergraduate Corequisite
EMAT 4900/6900 and EMAT 4900L/6900L
Graduate Corequisite
EMAT 4900/6900 and EMAT 4900L/6900L
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
In this course students will do the following, focusing on geometry, advanced algebra, and sequences and series: •Engage in mathematical, epistemological, curricular, and pedagogical investigations •Address and investigate basic concepts in the secondary mathematics curriculum •Reflect on the content knowledge necessary for a mathematics teacher and the role content knowledge plays in teaching •Communicate and reason mathematically, engage in problem solving, investigate different representations, and make mathematical connections •Design and analyze instructional tasks focusing on connecting concepts and ways of reasoning •Become familiar with and operational with using technological tools in doing mathematics •Use general tools such as word processing, spreadsheets, and the Internet to facilitate mathematical investigations and to communicate about mathematical investigations •Use application software to solve mathematical problems, create mathematical demonstrations, and construct new ideas of mathematics •Explore mathematics using a variety of technologies, including graphing calculators, computer software, and textbooks; communicate mathematical ideas using various technological tools
Topical Outline
•Congruence/similarity, including Connect to Transformations, More than triangles – what are the minimal conditions necessary to construct a quadrilateral congruent to another one • Properties of figures and relationships among figures, including Construction/Loci, Triangle and Quad Centers, Classification, Midpoint Quad & Cyclic Quad, Symmetry, Spherical geometry •Transformations, including Reflections, rotations, translations, dilations, sheer, Compositions, Connections to matrices, Tesselations, Fractals • Linear systems, including matrices, transformations • Conics, including Loci, Connections • Equations of line in space, plane, including vector equations • Sequences and Series, including Square-root spiral, Golden Spiral, shell structures, Connect to Fractals, Geometric, Arithmetic, Taylor series