"Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. ... The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus."
"Measurement explains how math should be done. With plain English and pictures, [Lockhart] makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living."
A college institutional researcher reveals some data concerning math placement tests and the pressures impacting students to opt for more difficult math courses without adequate preparation and unsatisfactory results. He writes: "In my mind, this disconnect exemplifies the degree to which incoming students and families don't grasp the difference between going to college to acquire content knowledge and going to college to develop skills and dispositions. ... [I]f students understand that college is about developing skills and dispositions, I think that they might be more likely to appreciate the chance to start at the beginning that is appropriate for them, savoring each experience like a slow cooked, seven course meal because they know that the culmination of college is made exponentially better by the particular ordering and integrating of the flavors that have come before."
This site features a math category, math concepts explained informed by the principle that "math is no about equations than poetry is about spelling .. .[but exist] to convey an idea."
" The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks designed to observe what students do as they construct meaning. APOS Theory was used as a framework for analysis of growth.
APOS Theory is a useful theoretical framework for studying and explaining conceptual development. Closely linked to Piaget's notions of reflective abstraction, it begins with the hypothesis that mathematical activity develops as students perform actions that become interiorized to form a process understanding of the concept, which eventually leads students to a heightened awareness or object understanding of the concept. Prior to any investigation, the researcher must provide an analysis of the concept development in terms of the essential components of this theory: actions, process, objects, and schemas. This is referred to as the genetic decomposition. The results of this study suggest a framework that a learner may use to construct meaning for logarithmic concepts. Using tasks aligned with the initial genetic decomposition, the researcher made revisions to the proposed genetic decomposition in the process of analyzing the data. The results indicated that historical accounts of the development of this concept might be useful to promote insightful learning. Based on this new set of data, iterations should continue to produce a better understanding of the student's constructions. " (from the abstract)
"This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves. "Visit the book's companion web site, gamemath.com, to download the example code and access other resources.
review of "THE CALCULUS OF FRIENDSHIP: What a Teacher and a Student Learned about Life While Corresponding about Math" published in 2010 and now in paperback. Transverses thirty years of correspondence between Strogatz and his teacher, insights into student-teacher relationship and lifelong learning
"Stacey Roshan is using an approach dubbed by her students as the "backwards classroom."... The students watch pre-recorded lectures the night before the class, when homework problems are traditionally done, then spend the time in class getting answers to questions, working on additional problems with partners, and getting one-on-one assistance from the teacher. No more lectures in class."
from The Backwards Class, by Dian Schaffhauser, THE Journal, 02/02/11