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Other Math Programs
Classroom Technologies for the Middle and High School Mathematics Teacher View Syllabus>>
Graduate Credit: MTH 3605
PDPs/CEUs: MTH 5905
Participants: Mathematics Teachers, grades 5–12
Dates/Times: July 7 - 11, 2008; 9:00 am – 4:00 pm
Location: Northeastern University, Boston Campus
Cost/Credit: 68 PDPs/6.8 CEUs, $500; 4 q.h. graduate credits, $820
Technology has become an integral part of the modern mathematics classroom, including the almost universal use of the graphing calculator. In addition, two computer programs, Excel and The Geometer’s Sketchpad have also been extensively used. All three of these technologies are meant to be tools that illuminate and enhance concepts and techniques in the math curriculum. The NCTM has emphasized multiple representations of problems and methods, and these programs and calculators are designed for that exact purpose.
Because there is little curriculum designed for the classroom use of the technologies, teachers must acquire and apply their own skills in adapting the technology into their teaching. This course is designed to improve the teacher’s skills in bringing together the curriculum and the technology to support student learning. Participants will have the opportunity to practice presenting lessons with particular emphasis on the graphing calculator.
Participants will explore:
- The many facets of the TI-83 or TI-84 graphing calculator: calculation, recursion, number patterns, graphing and operations with functions, statistics, matrices, programming and a brief look at calculus. All topics will be related.
- Excel: The spreadsheet as an algebra machine, formulas, constants vs. variables, “charts” or graphs.
- The Geometer’s Sketchpad: Dynamic graphical representation of theorems using visual and numeric evidence; constructions; exploration of locus problems.
Instructor: Michael Sherman is Chair of the Mathematics Department at Belmont Hill School. He has been teaching grades 7–12 for over thirty years and has taught courses at the Harvard Extension School and Simmons College.
Graduate Credit: MTH 3601
PDPs/CEUs: MTH 5901
Participants: Mathematics Teachers, grades 5–12
Dates/Times: July 14-18, 2008; 9:00 am – 4:00 pm
Location: St. Mark's School, Southborough, MA
Cost/Credit: 68 PDPs/6.8 CEUs, $500; 4 q.h. graduate credits, $820
This course will develop the principles of beginning and intermediate algebra. The goal is to help teachers develop a clear understanding of the mathematical concepts involved, and to translate personal mathematical accomplishments into effective teaching strategies.
At first, the course will take a non-traditional approach—exploring elements of arithmetic as a basis for understanding algebra. Many exciting “tricks” and “puzzles” will be explored that can also be used to enliven the classroom experience for students. The tools and techniques of arithmetic will then motivate an understanding of the general principles of algebra. Visual connections via graphing will be explored.
Topics covered include principles of arithmetic (algebraic rules, order of operations, exponents, logarithms), number theory (primes, Euclidean algorithm), elements of combinatorics (counting techniques, divided differences), number systems and bases, polynomial algebra, linear functions, manipulating quadratics, graphing and connections to area, rational functions, complex numbers, and more. This course will emphasize algebra and numbers, though integral parts of geometry will appear intertwined throughout discussions.
Instructor: James Tanton teaches at St. Mark’s School in Southborough, MA and is Director of the St. Mark’s Institute of Mathematics.
Graduate Credit: MTH 3603
PDPs/CEUs: MTH 5903
Participants: Mathematics Teachers, grades 5–12
Dates/Times: July 21-25, 2008; 9:00 am – 4:00 pm
Location Change: From Dedham Campus to St. Mark's School, Southborough, MA
Cost/Credit: 68 PDPs/6.8 CEUs, $500; 4 q.h. graduate credits, $820
This course serves as both a precursor to the course in calculus and as a stand-alone course in the methods of advanced algebraic thinking. The concept of a “function”, per se, is relatively new in the development of mathematics—Swiss mathematician Leonhard Euler (1707–83) was the first to formulate the notion—and as such plays a curious role in the development of mathematical thinking.
The course begins with an introduction to the study of functions—their definition, application, methods of manipulating them, generalized notions (so called “multi-valued functions” and “relations”), and their algebra. The act of graphing functions provides ties to geometry. Unlike most approaches to function theory, this course will utilize innovative geometric insights to provide a sound and comprehensive perspective to the topic.
The study of logarithms, the number “e”, complex numbers, trigonometry, growth and decay, and the conic sections will find a natural place in this very general setting. Ultimately, the goal of this course is to help teachers develop for themselves a clear understanding of mathematical concepts and a deep global perspective of algebraic thinking as a whole.
Instructor: James Tanton teaches at St. Mark’s School in Southborough, MA and is Director of the St. Mark’s Institute of Mathematics.
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