Vector Unit Sources:
Annotated Bibliographies
Borisenko A. I. & Tarapov I. E. ( 1979 ). Vector and Tensor Analysis with Applications.
New York New York: Dover
The original was published in Moscow in 1966, and the translation was by a Richard A.
Silverman. The authors introduce vectors as a subset of a more general type of object,
the tensor. Although mathematical in nature, the text is a very good introduction to
vectors and tensors in the context of Physics and Engineering. Distinction between
different kinds of vectors provides an introductory taxonomy that forces the reader to
consider what we are modeling in a firm context.
Hoffman, Banesh. (1975). About Vectors. Mineola New York: Dover
About Vectors introduces vectors and tensors as descriptive mathematical objects, but
does not employ exotic operators. This text is an introduction to the mathematics of
higher dimensional objects and applications. Calculus is not used in this text, even
though vectors when subjected to the operators of calculus reveal the nature of many
physical phenomena. This book is about the character of vectors and some of their
applications.
Schultz, J. E., Hollowell, K. A., Ellis, W. & Kennedy P.A. (2004). Holt Geometry.
Austin: Holt, Rinehart and Winston
This comprehensive Geometry text provides the student with a rigorous introduction to
the various subjects it covers. Many exercises provide real world situations to illustrate
the applications that the subjects covered lend themselves to. Abstract mathematical
objects are also given as forms to be addressed in problems.
Larson, R. Boswell, L & Stiff, L. (2004). Geometry: Measuring, Reasoning and Applying.
Evanston Illinois: McDougal Littell
This is a high school text book that covers many subjects with a shallow degree depth.
The subjects covered are many and hints of sophisticated mathematics populate the
book. The level of coverage makes this text a good general survey for a majority of
students, but may not be sufficiently challenging for the gifted student. Considering
the subject of vectors, the level of depth presented to a high school student could be
deepened.
Moses, Robert P. (2001). Radical Equations: Civil Rights from Mississippi to the Algebra
Project. Boston: Beacon Press
Math is a means towards social justice, implies a course of action toward empowering
people who have been traditionally powerless due to nonparticipation. The Algebra
Project is a formalization of the need to educate minority people in the skill sets of
mathematics. The idea being, that involvement in the mainstream operations of the
world would be real empowerment. In an appendix the concept of a number line is
made tangible by comparison to stops at train stations.
Tomlinson, Carol Ann & McTighe, Jay. ( 2006). Integrating Differentiated Instruction +
Understanding by Design. Alexandria Virginia: ASCD
To make mathematics meaningful and relevant to the multitude of students of different
intelligences, UbD models a method of curriculum design that starts with the end in
mind. Starting with an essential question and learning goals for the student, the
practitioner lastly plans a system of instruction. Differentiated instruction and
meaningful projects are keys to deeper understanding according to this design
philosophy.
Van de Walle, John A. & Lovin LouAnn H. (2006). Teaching Student-Centered
Mathematics: Grades 5-8
This book advocates constructive mathematics education. In every subject covered,
activities are suggested where a student learns mathematics by doing some activity and
discovering relationships. Each content centered chapter suggests many activities that
can be employed used to make math more tangible.