By Joseph L. Bass

I have a question for teachers and parents who work with children, helping them learn their numbers. Is it possible that their learning might be enhanced if they had available a mathematics reference book? Such a book would include the complete scope of fundamental mathematical concepts in one handbook. Abraham Lincoln made me think about this and I just wondered.

Recently news articles were published dealing with ciphering sheets done by Abraham Lincoln. University professors reviewed the pages and determined that Abe knew his stuff. This resulted in speculation about how much formal education Lincoln had. Previously it was thought that he had attended school for only a few years.

All of this discussion about how Lincoln learned his numbers overlooks how he and others like him became educated prior to the development of our current public education system. People who saw the need for an education often got one through individual study.

In thinking about Lincoln’s education it is important to remember he eventually became a lawyer. How could a person with limited formal education become a lawyer? He was admitted to the bar through “reading for the law.”

Under this process, a person studies law under the supervision of a practicing attorney. This informal educational process continues until the student passes the bar exam. Even today it is possible to become a lawyer in Virginia through reading for the law.

During earlier centuries, people who wanted to be educated did so though individual study. Lincoln is known to have said he educated himself.

How would a person go about studying mathematics in those days without going to school? Lincoln would have purchased or borrowed a book that included in one volume the complete spectrum of mathematical concepts. I have a copy of such a book, published in 1848. The full title is “The National Arithmetic, on the Inductive System; combining the Analytical and Synthetic Methods, together with the cancelling system; forming a Complete Mercantile Arithmetic.” The book was written by Benjamin Greenleaf, A.M., Principal of Bradford Teachers’ Seminary.

In 360 small-print pages the author discusses in detail the complete scope of arithmetic concepts, starting with numeration and place. How would you say 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000? That’s one vigintillion.

The book ends with information few would have use for today with chapters on: Tonnage of Vessels, Mensuration of Lumber, Philosophical Problems, Mechanical Powers, Specific Gravity, Strength of Materials, and Astronomical Problems. It is highly likely that Lincoln studied mathematics using one or more books something like Greenleaf’s.

What might we learn from Lincoln’s process of learning through studying such a book? It is first important to know that mathematical concepts do not change much over time. Today’s student could use this very old book as a reference today.

One of the challenges in teaching children mathematics today is that concepts are presented in fragments without reference to the unifying whole of fundamental concepts. I suspect that making available a book something like Greenleaf’s to all students beginning in about the seventh grade would enhance the effectiveness of daily lessons and activities. Students would keep this one reference book and use it throughout their continuing schooling and later in life.

Joseph L. Bass, Ed.D., is the executive director of ABetterSociety.Info Inc., a nonprofit organization in Hobson. Email him at ABetterSociety1@aol.com.