Famous Problems in the History of Mathematics
The web site, Famous Problems in the History of Mathematics, discusses seven math problems that have puzzled mathematicians throughout history. The problems discussed include: "The Bridges of Konigsburg," "The Value of Pi," "Puzzling Primes," Famous Paradoxes," "The Problem of Points," "A Proof of the Pythagorean Theorem" and "A Proof that e is irrational." From the home page, the student links to a detailed discussion of the problem and its historical origin. Additional links connect the student to the solution of each problem, biographies of the mathematicians and other math history sites.
The site was designed to "present a small portion of the history of mathematics through an investigation of some of the great problems that have inspired mathematicians throughout the ages." The problems are suitable for ABE students at NRS 4-6 to explore in class. The "Bridges of Konigsburg" problem would make an excellent problem solving exercise and introduction to topography for ABE students. The "Problem of Points" would provide excellent background information for the study of probability. Other problems that would be useful in ABE classes are the "Value of Pi' and "A Proof of the Pythagorean Theorem."
ABE teachers will find this site an excellent source of math history. The information and problems the site contains, if included in the appropriate ABE lesson, can transform an average lesson to one that is outstanding.
This resource is also valuable as an introduction to The Math Forum, which describes itself as a "leading online resource for improving math learning, teaching, and communication since 1992. The website produces Problems of the Week, Ask Dr. Math, and Teacher2Teacher, among other resources. The Math Forum is currently offering free online professional development workshops, underwritten by the National Science Foundation and by Microsoft. ("Tools for Building Math Concepts" "Using Technology and Problem-Solving to Build Algebraic Reasoning".)
This set of famous math problems was developed ten years ago, but it has withstood the test of time (and use in my classrom with adult learners). It is a product of the well-established Math Forum, which originated at Swarthmore College and now resides at Drexel University. The problems exemplify problem-solving, both specifically for each problem and generally as a process ("What steps did mathematicians go through to solve these problems?" "To what extent did they rely on prior knowledge?" "Were the problems solved immediately, or did the solution come after much trial and error?")
In my experience, these math problems are best used by small groups of adult learners with some direction by teacher, tutor, or other facilitator. The website is not as highly interactive as more recent products, but the information is valuable and the author's approach is refreshing. Through guided work on any one of these famous math problems in the history of mathematics, learners will develop confidence in their abilities to do tackle problems that initially may seem "too hard". The problems lead to further discussion and investigation. ("What else was going on at the time this math problem was being solved?" "Where is Konigsberg, with the famous bridges"? "How long ago did Zeno live-a problem in negative numbers!")
The National Council of Teachers of Mathematics states that it is important for students to make connections with mathematical concepts. This resource provides practitioners and their students with various historical perspectives on famous mathematical problems that could be used for students to make these valuable connections. However, I found some of the problems involving mathematical number theory that may be too complex for ABE/ASE teachers to understand. Despite this concern, there were many rich problems, especially the problems involving the history of pi and proof of the Pythagorean Theorem, that could be utilized by a GED class. Also many of the historical topics could be used by more advanced students as extensions to various mathematical topics.